NASA Astrophysics Data System (ADS)
Jackiewicz, Jason
2009-09-01
With the rapid advances in sophisticated solar modeling and the abundance of high-quality solar pulsation data, efficient and robust inversion techniques are crucial for seismic studies. We present some aspects of an efficient Fourier Optimally Localized Averaging (OLA) inversion method with an example applied to time-distance helioseismology.
Jackiewicz, Jason
2009-09-16
With the rapid advances in sophisticated solar modeling and the abundance of high-quality solar pulsation data, efficient and robust inversion techniques are crucial for seismic studies. We present some aspects of an efficient Fourier Optimally Localized Averaging (OLA) inversion method with an example applied to time-distance helioseismology.
Asteroid spin and shape modelling using two lightcurve inversion methods
NASA Astrophysics Data System (ADS)
Marciniak, Anna; Bartczak, Przemyslaw; Konstanciak, Izabella; Dudzinski, Grzegorz; Mueller, Thomas G.; Duffard, Rene
2016-10-01
We are conducting an observing campaign to counteract strong selection effects in photometric studies of asteroids. Our targets are long-period (P>12 hours) and low-amplitude (a_max<0.25 mag) asteroids, that although numerous, have poor lightcurve datasets (Marciniak et al. 2015, PSS 118, 256). As a result such asteroids are very poorly studied in terms of their spins and shapes. Our campaign targets a sample of around 100 bright (H<11 mag) main belt asteroids sharing both of these features, resulting in a few tens of new composite lightcurves each year. At present the data gathered so far allowed to construct detailed models for the shape and spin for about ten targets.In this study we perform spin and shape modelling using two lightcurve inversion methods: convex inversion (Kaasalainen et al. 2001, Icarus, 153, 37) and nonconvex SAGE modelling algorithm (Shaping Asteroids with Genetic Evolution, Bartczak et al. 2014, MNRAS, 443, 1802). These two methods are independent from each other, and are based on different assumptions for the shape.Thus, the results obtained on the same datasets provide a cross-check of both the methods and the resulting spin and shape models. The results for the spin solutions are highly consistent, and the shape models are similar, though the ones from SAGE algorithm provide more details of the surface features. Nonconvex shape produced by SAGE have been compared with direct images from spacecrafts and the first results for targets like Eros or Lutetia (Batczak et al. 2014, ACM conf. 29B) provide a high level of agreement.Another way of validation is the shape model comparison with the asteroid shape contours obtained using different techniques (like the stellar occultation timings or adaptive optics imaging) or against data in thermal infrared range gathered by ground and space-bound observatories. The thermal data could provide assignment of size and albedo, but also can help to resolve spin-pole ambiguities. In special cases, the
Wave-Propagation Modeling and Inversion Using Frequency-Domain Integral Equation Methods
NASA Astrophysics Data System (ADS)
Strickland, Christopher E.
Full waveform inverse methods describe the full physics of wave propagation and can potentially overcome the limitations of ray theoretic methods. This work explores the use of integral equation based methods for simulation and inversion and illustrates their potential for computationally demanding problems. A frequency-domain integral equation approach to simulate wave-propagation in heterogeneous media and solve the inverse wave-scattering problem will be presented for elastic, acoustic, and electromagnetic systems. The method will be illustrated for georadar (ground- or ice-penetrating radar) applications and compared to results obtained using ray theoretic methods. In order to tackle the non-linearity of the problem, the inversion incorporates a broad range of frequencies to stabilize the solution. As with most non-linear inversion methods, a starting model that reasonably approximates the true model is critical to convergence of the algorithm. To improve the starting model, a variable reference inversion technique is developed that allows the background reference medium to vary for each source-receiver data pair and is less restrictive than using a single reference medium for the entire dataset. The reference medium can be assumed homogeneous (although different for each data point) to provide a computationally efficient, single-step, frequency-domain inversion approach that incorporates finite frequency effects not captured by ray based methods. The inversion can then be iterated on to further refine the solution.
A surface misfit inversion method for brain deformation modeling
NASA Astrophysics Data System (ADS)
Liu, Fenghong; Paulsen, Keith D.; Hartov, Alexander; Roberts, David W.
2007-03-01
Biomechanical models of brain deformation are useful tools for estimating the shift that occurs during neurosurgical interventions. Incorporation of intra-operative data into the biomechanical model improves the accuracy of the registration between the patient and the image volume. The representer method to solve the adjoint equations (AEM) for data assimilation has been developed. In order to improve the computational efficiency and to process more intraoperative data, we modified the adjoint equation method by changing the way in which intraoperative data is applied. The current formulation is developed around a point-based data-model misfit. Surface based data-model misfit could be a more robust and computationally efficient technique. Our approach is to express the surface misfit as the volume between the measured surface and model predicted surface. An iterative method is used to solve the adjoint equations. The surface misfit criterion is tested in a cortical distension clinical case and compared to the results generated with the prior point-based methodology solved either iteratively or with the representer algorithm. The results show that solving the adjoint equations with an iterative method improves computational efficiency dramatically over the representer approach and that reformulating the minimization criterion in terms of a surface description is even more efficient. Applying intra-operative data in the form of a surface misfit is computationally very efficient and appears promising with respect to its accuracy in estimating brain deformation.
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
2001-01-01
For interpreting observational data, and in particular for use in inverse methods, accurate and realistic chemical transport models are essential. Toward this end we have, in recent years, helped develop and utilize a number of three-dimensional models including the Model for Atmospheric Transport and Chemistry (MATCH).
Dynamic inversion method based on the time-staggered stereo-modeling scheme and its acceleration
NASA Astrophysics Data System (ADS)
Jing, Hao; Yang, Dinghui; Wu, Hao
2016-09-01
A set of second-order differential equations describing the space-time behavior of derivatives of displacement with respect to model parameters (i.e. waveform sensitivities) is obtained via taking the derivative of the original wave equations. The dynamic inversion method obtains sensitivities of the seismic displacement field with respect to earth properties directly by solving differential equations for them instead of constructing sensitivities from the displacement field itself. In this study, we have taken a new perspective on the dynamic inversion method and used acceleration approaches to reduce the computational time and memory usage to improve its ability of performing high-resolution imaging. The dynamic inversion method, which can simultaneously use different waves and multi-component observation data, is appropriate for directly inverting elastic parameters, medium density or wave velocities. Full wave-field information is utilized as much as possible at the expense of a larger amount of calculations. To mitigate the computational burden, two ways are proposed to accelerate the method from a computer-implementation point of view. One is source encoding which uses a linear combination of all shots, and the other is to reduce the amount of calculations on forward modeling. We applied a new finite difference method to the dynamic inversion to improve the computational accuracy and speed up the performance. Numerical experiments indicated that the new finite difference method can effectively suppress the numerical dispersion caused by the discretization of wave equations, resulting in enhanced computational efficiency with less memory cost for seismic modeling and inversion based on the full wave equations. We present some inversion results to demonstrate the validity of this method through both checkerboard and Marmousi models. It shows that this method is also convergent even with big deviations for the initial model. Besides, parallel calculations can be
NASA Astrophysics Data System (ADS)
Grigorov, Igor V.
2009-12-01
In article the algorithm of numerical modelling of the nonlinear equation of Korteweg-de Vrieze which generates nonlinear algorithm of digital processing of signals is considered. For realisation of the specified algorithm it is offered to use a inverse scattering method (ISM). Algorithms of direct and return spectral problems, and also problems of evolution of the spectral data are in detail considered. Results of modelling are resulted.
Laboratory evaluation of a hydrodynamic inverse modeling method based on water content data
NASA Astrophysics Data System (ADS)
Lambot, S.; Hupet, F.; Javaux, M.; Vanclooster, M.
2004-03-01
The inverse modeling method of [2002] for estimating the hydraulic properties of partially saturated soils, which was numerically validated, is further tested on laboratory-scale transient flow experiments. The method uses the global multilevel coordinate search algorithm combined sequentially with the local Nelder-Mead simplex algorithm to obtain the inverse of the one-dimensional Richards equation using soil moisture time series measured at three different depths during natural infiltration. Flow experiments were conducted on a homogeneous artificial sand column and three undisturbed soil columns collected from agricultural fields. Three models describing the unsaturated soil hydraulic properties were used and compared: the model of Mualem and van Genuchten, the model of Assouline, and the decoupled van Genuchten-Brooks and Corey combination. The performances of all three models were similar, except for Assouline's model, which provided poorer results in two cases. The inversion method provided relatively good estimates for the water retention curves and also for the saturated conductivity when the moisture range explored was not too small. Water content time series were very well reproduced for the artificial soil and a sandy loam soil, but for two silt loam soils, larger errors were observed. The prediction of the water transfer behavior in the soil columns was poor when flow properties were estimated using directly determined hydraulic properties. The main limiting factor for applying the inversion method, particularly for nonsandy soils, was the characterization of the initial conditions in terms of the pressure head profile. Furthermore, the use of only soil moisture data is essential to enable the hydrogeophysical characterization of soils.
NASA Astrophysics Data System (ADS)
Michalak, Anna M.; Kitanidis, Peter K.
2004-08-01
As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical exposure to contamination. Such problems are typically strongly underdetermined, with a large number of points at which the distribution is to be estimated. To address this challenge, the computational efficiency of the new method is increased through the application of the adjoint state method. In addition, the adjoint problem is presented in a format that allows for the reuse of existing groundwater flow and transport codes as modules in the inverse modeling algorithm. As demonstrated in the presented applications, the geostatistical approach combined with the adjoint state method allow for a historical multidimensional contaminant distribution to be recovered even in heterogeneous media, where a numerical solution is required for the forward problem.
Interpretation of Trace Gas Data Using Inverse Methods and Global Chemical Transport Models
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
1997-01-01
This is a theoretical research project aimed at: (1) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for long lived gases important in ozone depletion and climate forcing, (2) utilization of inverse methods to determine these source/sink strengths which use the NCAR/Boulder CCM2-T42 3-D model and a global 3-D Model for Atmospheric Transport and Chemistry (MATCH) which is based on analyzed observed wind fields (developed in collaboration by MIT and NCAR/Boulder), (3) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple titrating gases, and, (4) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3-D models. Important goals include determination of regional source strengths of methane, nitrous oxide, and other climatically and chemically important biogenic trace gases and also of halocarbons restricted by the Montreal Protocol and its follow-on agreements and hydrohalocarbons used as alternatives to the restricted halocarbons.
Studies of Trace Gas Chemical Cycles Using Inverse Methods and Global Chemical Transport Models
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
2003-01-01
We report progress in the first year, and summarize proposed work for the second year of the three-year dynamical-chemical modeling project devoted to: (a) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for long lived gases important in ozone depletion and climate forcing, (b) utilization of inverse methods to determine these source/sink strengths using either MATCH (Model for Atmospheric Transport and Chemistry) which is based on analyzed observed wind fields or back-trajectories computed from these wind fields, (c) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple titrating gases, and (d) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3D models. Important goals include determination of regional source strengths of methane, nitrous oxide, methyl bromide, and other climatically and chemically important biogenic/anthropogenic trace gases and also of halocarbons restricted by the Montreal protocol and its follow-on agreements and hydrohalocarbons now used as alternatives to the restricted halocarbons.
Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H
2016-05-01
The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel. PMID:27250181
Lura, Derek; Wernke, Matthew; Alqasemi, Redwan; Carey, Stephanie; Dubey, Rajiv
2012-01-01
This paper presents the probability density based gradient projection (GP) of the null space of the Jacobian for a 25 degree of freedom bilateral robotic human body model (RHBM). This method was used to predict the inverse kinematics of the RHBM and maximize the similarity between predicted inverse kinematic poses and recorded data of 10 subjects performing activities of daily living. The density function was created for discrete increments of the workspace. The number of increments in each direction (x, y, and z) was varied from 1 to 20. Performance of the method was evaluated by finding the root mean squared (RMS) of the difference between the predicted joint angles relative to the joint angles recorded from motion capture. The amount of data included in the creation of the probability density function was varied from 1 to 10 subjects, creating sets of for subjects included and excluded from the density function. The performance of the GP method for subjects included and excluded from the density function was evaluated to test the robustness of the method. Accuracy of the GP method varied with amount of incremental division of the workspace, increasing the number of increments decreased the RMS error of the method, with the error of average RMS error of included subjects ranging from 7.7° to 3.7°. However increasing the number of increments also decreased the robustness of the method.
A Monte Carlo simulation based inverse propagation method for stochastic model updating
NASA Astrophysics Data System (ADS)
Bao, Nuo; Wang, Chunjie
2015-08-01
This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder-Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.
An efficient, advanced regularized inversion method for highly parameterized environmental models
NASA Astrophysics Data System (ADS)
Skahill, B. E.; Baggett, J. S.
2008-12-01
The Levenberg-Marquardt method of computer based parameter estimation can be readily modified in cases of high parameter insensitivity and correlation by the inclusion of various regularization devices to maintain numerical stability and robustness, including; for example, Tikhonov regularization and truncated singular value decomposition. With Tikhonov regularization, where parameters or combinations of parameters cannot be uniquely estimated, they are provided with values or assigned relationships with other parameters that are decreed to be realistic by the modeler. Tikhonov schemes provide a mechanism for assimilation of valuable "outside knowledge" into the inversion process, with the result that parameter estimates, thus informed by a modeler's expertise, are more suitable for use in the making of important predictions by that model than would otherwise be the case. However, by maintaining the high dimensionality of the adjustable parameter space, they can potentially be computational burdensome. Moreover, while Tikhonov schemes are very attractive and hence widely used, problems with numerical stability can sometimes arise because the strength with which regularization constraints are applied throughout the regularized inversion process cannot be guaranteed to exactly complement inadequacies in the information content of a given calibration dataset. We will present results associated with development efforts that include an accelerated Levenberg-Marquardt local search algorithm adapted for Tikhonov regularization, and a technique which allows relative regularization weights to be estimated as parameters through the calibration process itself (Doherty and Skahill, 2006). This new method, encapsulated in the MICUT software (Skahill et al., 2008) will be compared, in terms of efficiency and enforcement of regularization relationships, with the SVD Assist method (Tonkin and Doherty, 2005) contained in the popular PEST package by considering various watershed
A novel model for diffusion based release kinetics using an inverse numerical method.
Mohammadi, Hadi; Herzog, Walter
2011-10-01
We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important.
Validation of a 'displacement tomography' inversion method for modeling sheet intrusions
NASA Astrophysics Data System (ADS)
Menassian, Sarah
The study of volcano deformation data can provide information on magma processes and help assess the potential for future eruptions. In employing inverse deformation modeling on these data, we attempt to characterize the geometry, location and volume/pressure change of a deformation source. Techniques currently used to model sheet intrusions (e.g., dikes and sills) often require significant a priori assumptions about source geometry and can require testing a large number of parameters. Moreover, surface deformations are a non-linear function of the source geometry and location. This requires the use of Monte Carlo inversion techniques which leads to long computation times. Recently, 'displacement tomography' models have been used to characterize magma reservoirs by inverting source deformation data for volume changes using a grid of point sources in the subsurface. The computations involved in these models are less intensive as no assumptions are made on the source geometry and location, and the relationship between the point sources and the surface deformation is linear. In this project, seeking a less computationally intensive technique for fracture sources, we tested if this displacement tomography method for reservoirs could be used for sheet intrusions. We began by simulating the opening of three synthetic dikes of known geometry and location using an established deformation model for fracture sources. We then sought to reproduce the displacements and volume changes undergone by the fractures using the sources employed in the tomography methodology. Results of this validation indicate the volumetric point sources are not appropriate for locating fracture sources, however they may provide useful qualitative information on volume changes occurring in the surrounding rock, and therefore indirectly indicate the source location.
NASA Astrophysics Data System (ADS)
Kong, Changduk; Lim, Semyeong
2011-12-01
Recently, the health monitoring system of major gas path components of gas turbine uses mostly the model based method like the Gas Path Analysis (GPA). This method is to find quantity changes of component performance characteristic parameters such as isentropic efficiency and mass flow parameter by comparing between measured engine performance parameters such as temperatures, pressures, rotational speeds, fuel consumption, etc. and clean engine performance parameters without any engine faults which are calculated by the base engine performance model. Currently, the expert engine diagnostic systems using the artificial intelligent methods such as Neural Networks (NNs), Fuzzy Logic and Genetic Algorithms (GAs) have been studied to improve the model based method. Among them the NNs are mostly used to the engine fault diagnostic system due to its good learning performance, but it has a drawback due to low accuracy and long learning time to build learning data base if there are large amount of learning data. In addition, it has a very complex structure for finding effectively single type faults or multiple type faults of gas path components. This work builds inversely a base performance model of a turboprop engine to be used for a high altitude operation UAV using measured performance data, and proposes a fault diagnostic system using the base engine performance model and the artificial intelligent methods such as Fuzzy logic and Neural Network. The proposed diagnostic system isolates firstly the faulted components using Fuzzy Logic, then quantifies faults of the identified components using the NN leaned by fault learning data base, which are obtained from the developed base performance model. In leaning the NN, the Feed Forward Back Propagation (FFBP) method is used. Finally, it is verified through several test examples that the component faults implanted arbitrarily in the engine are well isolated and quantified by the proposed diagnostic system.
NASA Astrophysics Data System (ADS)
Olsen, Scott Charles
In this dissertation, new inverse scattering algorithms are derived for the Helmholtz equation using the Extended Born field model (eikonal rescattered field), and the angular spectrum (parabolic) layered field model. These two field models performed the 'best' of all the field models evaluated. Algorithms are solved with conjugate gradient methods. An advanced ultrasonic data acquisition system is also designed. Many different field models for use in a reconstruction algorithm are investigated. 'Layered' field models that mathematically partition the field calculation in layers in space possess the advantage that the field in layer n is calculated from the field in layer n - 1. Several of the 'layered' field models are investigated in terms of accuracy and computational complexity. Field model accuracy using field rescattering is also tested. The models investigated are the eikonal field model, the angular spectrum (AS) field model, and the parabolic field models known as the Split-Step Fast-Fourier Transform and the Crank-Nicolson algorithms. All of the 'layered' field models can be referred to as Extended Born field models since the 'layered' field models are more accurate than the Born approximated total field. The Rescattered Extended Born (eikonal rescattered field) Transmission Mode (REBTM) algorithm with the AS field model and the Nonrescattered AS Reconstruction (NASR) algorithm are tested with several types of objects: a single-layer cylinder, double-layer cylinders, two double-layer cylinders and the breast model. Both algorithms, REBTM and NASR work well; however, the NASR algorithm is faster and more accurate than the REBTM algorithm. The NASR algorithm is matched well with the requirements of breast model reconstructions. A major purpose of new scanner development is to collect both transmission and reflection data from multiple ultrasonic transducer arrays to test the next generation of reconstruction algorithms. The data acquisition system advanced
NASA Astrophysics Data System (ADS)
Pham, H. V.; Elshall, A. S.; Tsai, F. T.; Yan, L.
2012-12-01
The inverse problem in groundwater modeling deals with a rugged (i.e. ill-conditioned and multimodal), nonseparable and noisy function since it involves solving second order nonlinear partial deferential equations with forcing terms. Derivative-based optimization algorithms may fail to reach a near global solution due to their stagnation at a local minimum solution. To avoid entrapment in a local optimum and enhance search efficiency, this study introduces the covariance matrix adaptation-evolution strategy (CMA-ES) as a local derivative-free optimization method. In the first part of the study, we compare CMA-ES with five commonly used heuristic methods and the traditional derivative-based Gauss-Newton method on a hypothetical problem. This problem involves four different cases to allow a rigorous assessment against ten criterions: ruggedness in terms of nonsmooth and multimodal, ruggedness in terms of ill-conditioning and high nonlinearity, nonseparablity, high dimensionality, noise, algorithm adaptation, algorithm tuning, performance, consistency, parallelization (scaling with number of cores) and invariance (solution vector and function values). The CMA-ES adapts a covariance matrix representing the pair-wise dependency between decision variables, which approximates the inverse of the Hessian matrix up to a certain factor. The solution is updated with the covariance matrix and an adaptable step size, which are adapted through two conjugates that implement heuristic control terms. The covariance matrix adaptation uses information from the current population of solutions and from the previous search path. Since such an elaborate search mechanism is not common in the other heuristic methods, CMA-ES proves to be more robust than other population-based heuristic methods in terms of reaching a near-optimal solution for a rugged, nonseparable and noisy inverse problem. Other favorable properties that the CMA-ES exhibits are the consistency of the solution for repeated
NASA Astrophysics Data System (ADS)
Schmidt, L. S.; Karlsson, N. B.; Hvidberg, C. S.
2016-09-01
High-resolution images of the martian surface have revealed numerous deposits with complex patterns consistent with the flow of ice. Here we applied ice-flow models and inverse methods to estimate the ice thickness and volume of these deposits.
NASA Astrophysics Data System (ADS)
Groh, Andreas; Krebs, Jochen
2012-08-01
In this paper, a population balance equation, originating from applications in chemical engineering, is considered and novel solution techniques for a related inverse problem are presented. This problem consists in the determination of the breakage rate and the daughter drop distribution of an evolving drop size distribution from time-dependent measurements under the assumption of self-similarity. We analyze two established solution methods for this ill-posed problem and improve the two procedures by adapting suitable data fitting and inversion algorithms to the specific situation. In addition, we introduce a novel technique that, compared to the former, does not require certain a priori information. The improved stability properties of the resulting algorithms are substantiated with numerical examples.
On the feasibility of inversion methods based on models of urban sky glow
NASA Astrophysics Data System (ADS)
Kolláth, Z.; Kránicz, B.
2014-05-01
Multi-wavelength imaging luminance photometry of sky glow provides a huge amount of information on light pollution. However, the understanding of the measured data involves the combination of different processes and data of radiation transfer, atmospheric physics and atmospheric constitution. State-of-the-art numerical radiation transfer models provide the possibility to define an inverse problem to obtain information on the emission intensity distribution of a city and perhaps the physical properties of the atmosphere. We provide numerical tests on the solvability and feasibility of such procedures.
NASA Astrophysics Data System (ADS)
Xue, Haile; Shen, Xueshun; Chou, Jifan
2015-10-01
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
Best Basis Methods for the Modelling and Inversion of Potential Fields
NASA Astrophysics Data System (ADS)
Michel, Volker; Telschow, Roger
2016-04-01
There are many trial functions (e.g. on the sphere) available which can be used for the modelling of a potential field. Among them are orthogonal polynomials such as spherical harmonics and radial basis functions such as spline or wavelet basis functions. We present an algorithm, the Regularized Functional Matching Pursuit (RFMP), and an enhancement (the ROFMP), which construct a kind of a best basis out of trial functions of different kinds. This basis is tailored for the particular problem and the given data set. The objective of the optimization is the minimization of the Tikhonov-regularized data misfit. One main advantage is that the constructed approximation inherits the advantages of the different basis systems. By including spherical harmonics, coarse global structures can be represented in a sparse way. However, the additional use of spline basis functions allows a stable handling of scattered data grids. Furthermore, the inclusion of wavelets and scaling functions yields a multiscale analysis of the potential. In addition, ill-posed inverse problems (like a downward continuation or the inverse gravimetric problem) can be regularized with the algorithm. We show some numerical examples to demonstrate the possibilities which the algorithms provide.
NASA Astrophysics Data System (ADS)
Murphy, R. Kim; Sabbagh, Harold A.; Sabbagh, Elias H.; Zhou, Liming; Bernacchi, William; Aldrin, John C.; Forsyth, David; Lindgren, Eric
2016-02-01
The use of coupled integral equations and anomalous currents allows us to efficiently remove `background effects' in either forward or inverse modeling. This is especially true when computing the change in impedance due to a small flaw in the presence of a larger background anomaly. It is more accurate than simply computing the response with and without the flaw and then subtracting the two nearly equal values to obtain the small difference due to the flaw. The problem that we address in this paper involves a 'SplitD' probe that includes complex, noncircular coils, as well as ferrite cores, inserted within a bolt hole, and exciting both the bolt hole and an adjacent flaw. This introduces three coupled anomalies, each with its on 'scale.' The largest, of course, is the bolt hole, followed (generally) by the probe, and then the flaw. The overall system is represented mathematically by three coupled volume-integral equations. We describe the development of the model and its code, which is a part of the general eddy-current modeling code, VIC-3D®. We present initial validation results, as well as a number of model computations with flaws located at various places within the bolt hole.
Bledsoe, Keith C.
2015-04-01
The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric. This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hirahara, K.; Hori, T.; Hyodo, M.; Hori, M.
2013-12-01
Many studies have focused on geodetic inversion analysis method of coseismic slip distribution with combination of observation data of coseismic crustal deformation on the ground and simplified crustal models such like analytical solution in elastic half-space (Okada, 1985). On the other hand, displacements on the seafloor or near trench axes due to actual earthquakes has been observed by seafloor observatories (e.g. the 2011 Tohoku-oki Earthquake (Tohoku Earthquake) (Sato et. al. 2011) (Kido et. al. 2011)). Also, some studies on tsunamis due to the Tohoku Earthquake indicate that large fault slips near the trench axis may have occurred. Those facts suggest that crustal models considering complex geometry and heterogeneity of the material property near the trench axis should be used for geodetic inversion analysis. Therefore, our group has developed a mesh generation method for finite element models of the Japanese Islands of higher fidelity and a fast crustal deformation analysis method for the models. Degree-of-freedom of the models generated by this method is about 150 million. In this research, the method is extended for inversion analyses of coseismic slip distribution. Since inversion analyses need computation of hundreds of slip response functions due to a unit fault slip assigned for respective divided cells on the fault, parallel computing environment is used. Plural crustal deformation analyses are simultaneously run in a Message Passing Interface (MPI) job. In the job, dynamic load balancing is implemented so that a better parallel efficiency is obtained. Submitting the necessary number of serial job of our previous method is also possible, but the proposed method needs less computation time, places less stress on file systems, and allows simpler job management. A method for considering the fault slip right near the trench axis is also developed. As the displacement distribution of unit fault slip for computing response function, 3rd order B
NASA Astrophysics Data System (ADS)
Dadić, Martin
2013-06-01
The increased interest in vacuum tube audio amplifiers led to an increased interest in mathematical modelling of such kind of amplifiers. The main purpose of this paper is to develop a novel global numerical approach in calculation of the harmonic distortion (HD) and intermodulation distortion (IM) of vacuum-triode audio amplifiers, suitable for applications using brute-force of modern computers. Since the 3/2 power law gives only the transcharacteristic inverse of a vacuum triode amplifier, unknown plate currents are determined in this paper iteratively using Newton's method. Using the resulting input/output pairs, harmonic distortions and intermodulations are calculated using discrete Fourier transform and three different analytical methods.
NASA Astrophysics Data System (ADS)
Gillet-Chaulet, F.; Gagliardini, O.; Nodet, M.; Ritz, C.; Durand, G.; Zwinger, T.; Seddik, H.; Greve, R.
2010-12-01
About a third of the current sea level rise is attributed to the release of Greenland and Antarctic ice, and their respective contribution is continuously increasing since the first diagnostic of the acceleration of their coastal outlet glaciers, a decade ago. Due to their related societal implications, good scenario of the ice sheets evolutions are needed to constrain the sea level rise forecast in the coming centuries. The quality of the model predictions depend primary on the good description of the physical processes involved and on a good initial state reproducing the main present observations (geometry, surface velocities and ideally the trend in elevation change). We model ice dynamics on the whole Greenland ice sheet using the full-Stokes finite element code Elmer. The finite element mesh is generated using the anisotropic mesh adaptation tool YAMS, and shows a high density around the major ice streams. For the initial state, we use an iterative procedure to compute the ice velocities, the temperature field, and the basal sliding coefficient field. The basal sliding coefficient is obtained with an inverse method by minimizing a cost function that measures the misfit between the present day surface velocities and the modelled surface velocities. We use two inverse methods for this: an inverse Robin problem recently proposed by Arthern and Gudmundsson (J. Glaciol. 2010), and a control method taking advantage of the fact that the Stokes equations are self adjoint in the particular case of a Newtonian rheology. From the initial states obtained by these two methods, we run transient simulations to evaluate the impact of the initial state of the Greenland ice sheet onto its related contribution to sea level rise for the next centuries.
NASA Astrophysics Data System (ADS)
Zhang, L.; Xu, M.; Huang, M.; Yu, G.
2009-11-01
Modeling ecosystem carbon cycle on the regional and global scales is crucial to the prediction of future global atmospheric CO2 concentration and thus global temperature which features large uncertainties due mainly to the limitations in our knowledge and in the climate and ecosystem models. There is a growing body of research on parameter estimation against available carbon measurements to reduce model prediction uncertainty at regional and global scales. However, the systematic errors with the observation data have rarely been investigated in the optimization procedures in previous studies. In this study, we examined the feasibility of reducing the impact of systematic errors on parameter estimation using normalization methods, and evaluated the effectiveness of three normalization methods (i.e. maximum normalization, min-max normalization, and z-score normalization) on inversing key parameters, for example the maximum carboxylation rate (Vcmax,25) at a reference temperature of 25°C, in a process-based ecosystem model for deciduous needle-leaf forests in northern China constrained by the leaf area index (LAI) data. The LAI data used for parameter estimation were composed of the model output LAI (truth) and various designated systematic errors and random errors. We found that the estimation of Vcmax,25 could be severely biased with the composite LAI if no normalization was taken. Compared with the maximum normalization and the min-max normalization methods, the z-score normalization method was the most robust in reducing the impact of systematic errors on parameter estimation. The most probable values of estimated Vcmax,25 inversed by the z-score normalized LAI data were consistent with the true parameter values as in the model inputs though the estimation uncertainty increased with the magnitudes of random errors in the observations. We concluded that the z-score normalization method should be applied to the observed or measured data to improve model parameter
NASA Astrophysics Data System (ADS)
Stukel, Michael R.; Landry, Michael R.; Ohman, Mark D.; Goericke, Ralf; Samo, Ty; Benitez-Nelson, Claudia R.
2012-03-01
Despite the increasing use of linear inverse modeling techniques to elucidate fluxes in undersampled marine ecosystems, the accuracy with which they estimate food web flows has not been resolved. New Markov Chain Monte Carlo (MCMC) solution methods have also called into question the biases of the commonly used L2 minimum norm (L 2MN) solution technique. Here, we test the abilities of MCMC and L 2MN methods to recover field-measured ecosystem rates that are sequentially excluded from the model input. For data, we use experimental measurements from process cruises of the California Current Ecosystem (CCE-LTER) Program that include rate estimates of phytoplankton and bacterial production, micro- and mesozooplankton grazing, and carbon export from eight study sites varying from rich coastal upwelling to offshore oligotrophic conditions. Both the MCMC and L 2MN methods predicted well-constrained rates of protozoan and mesozooplankton grazing with reasonable accuracy, but the MCMC method overestimated primary production. The MCMC method more accurately predicted the poorly constrained rate of vertical carbon export than the L 2MN method, which consistently overestimated export. Results involving DOC and bacterial production were equivocal. Overall, when primary production is provided as model input, the MCMC method gives a robust depiction of ecosystem processes. Uncertainty in inverse ecosystem models is large and arises primarily from solution under-determinacy. We thus suggest that experimental programs focusing on food web fluxes expand the range of experimental measurements to include the nature and fate of detrital pools, which play large roles in the model.
Multiphase inverse modeling: An Overview
Finsterle, S.
1998-03-01
Inverse modeling is a technique to derive model-related parameters from a variety of observations made on hydrogeologic systems, from small-scale laboratory experiments to field tests to long-term geothermal reservoir responses. If properly chosen, these observations contain information about the system behavior that is relevant to the performance of a geothermal field. Estimating model-related parameters and reducing their uncertainty is an important step in model development, because errors in the parameters constitute a major source of prediction errors. This paper contains an overview of inverse modeling applications using the ITOUGH2 code, demonstrating the possibilities and limitations of a formalized approach to the parameter estimation problem.
Magnain, Caroline; Elias, Mady; Frigerio, Jean-Marc
2008-07-01
In a previous article [J. Opt. Soc. Am. A 24, 2196 (2007)] we have modeled skin color using the radiative transfer equation, solved by the auxiliary function method. Three main parameters have been determined as being predominant in the diversity of skin color: the concentrations of melanosomes and of red blood cells and the oxygen saturation of blood. From the reflectance spectrum measured on real Caucasian skin, these parameters are now evaluated by minimizing the standard deviation on the adjusted wavelength range between the experimental spectrum and simulated spectra gathered in a database.
A Bayesian method for microseismic source inversion
NASA Astrophysics Data System (ADS)
Pugh, D. J.; White, R. S.; Christie, P. A. F.
2016-08-01
Earthquake source inversion is highly dependent on location determination and velocity models. Uncertainties in both the model parameters and the observations need to be rigorously incorporated into an inversion approach. Here, we show a probabilistic Bayesian method that allows formal inclusion of the uncertainties in the moment tensor inversion. This method allows the combination of different sets of far-field observations, such as P-wave and S-wave polarities and amplitude ratios, into one inversion. Additional observations can be included by deriving a suitable likelihood function from the uncertainties. This inversion produces samples from the source posterior probability distribution, including a best-fitting solution for the source mechanism and associated probability. The inversion can be constrained to the double-couple space or allowed to explore the gamut of moment tensor solutions, allowing volumetric and other non-double-couple components. The posterior probability of the double-couple and full moment tensor source models can be evaluated from the Bayesian evidence, using samples from the likelihood distributions for the two source models, producing an estimate of whether or not a source is double-couple. Such an approach is ideally suited to microseismic studies where there are many sources of uncertainty and it is often difficult to produce reliability estimates of the source mechanism, although this can be true of many other cases. Using full-waveform synthetic seismograms, we also show the effects of noise, location, network distribution and velocity model uncertainty on the source probability density function. The noise has the largest effect on the results, especially as it can affect other parts of the event processing. This uncertainty can lead to erroneous non-double-couple source probability distributions, even when no other uncertainties exist. Although including amplitude ratios can improve the constraint on the source probability
NASA Astrophysics Data System (ADS)
Shonkwiler, K. B.; Ham, J. M.; Williams, C.
2012-12-01
Development Initiative. Food and Agriculture Organization of the United Nations, Rome, Italy. [2] Loubet, B., Génermont, S., Ferrara, R., Bedos, C., Decuq, C., Personne, E., Fanucci, O., Durand, B., Rana, G., Cellier, P., 2010. An inverse model to estimate ammonia emissions from fields. Eur. J. Soil Sci. 61: 793-805. Panorama of a weather station (left) utilizing micrometeorological methods to aid in estimating emissions of methane and ammonia from an anaerobic livestock lagoon (center) at a commercial dairy in Northern Colorado, USA.
Relative risk regression models with inverse polynomials.
Ning, Yang; Woodward, Mark
2013-08-30
The proportional hazards model assumes that the log hazard ratio is a linear function of parameters. In the current paper, we model the log relative risk as an inverse polynomial, which is particularly suitable for modeling bounded and asymmetric functions. The parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal. The advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation. The utility of the method is further supported by analyzing two real data sets, addressing the specific question of the location of the minimum risk threshold.
Inverse methods-based estimation of plate coupling in a plate motion model governed by mantle flow
NASA Astrophysics Data System (ADS)
Ratnaswamy, V.; Stadler, G.; Gurnis, M.
2013-12-01
Plate motion is primarily controlled by buoyancy (slab pull) which occurs at convergent plate margins where oceanic plates undergo deformation near the seismogenic zone. Yielding within subducting plates, lateral variations in viscosity, and the strength of seismic coupling between plate margins likely have an important control on plate motion. Here, we wish to infer the inter-plate coupling for different subduction zones, and develop a method for inferring it as a PDE-constrained optimization problem, where the cost functional is the misfit in plate velocities and is constrained by the nonlinear Stokes equation. The inverse models have well resolved slabs, plates, and plate margins in addition to a power law rheology with yielding in the upper mantle. Additionally, a Newton method is used to solve the nonlinear Stokes equation with viscosity bounds. We infer plate boundary strength using an inexact Gauss-Newton method with line search for backtracking. Each inverse model is applied to two simple 2-D scenarios (each with three subduction zones), one with back-arc spreading and one without. For each case we examine the sensitivity of the inversion to the amount of surface velocity used: 1) full surface velocity data and 2) surface velocity data simplified using a single scalar average (2-D equivalent to an Euler pole) for each plate. We can recover plate boundary strength in each case, even in the presence of highly nonlinear flow with extreme variations in viscosity. Additionally, we ascribe an uncertainty in each plate's velocity and perform an uncertainty quantification (UQ) through the Hessian of the misfit in plate velocities. We find that as plate boundaries become strongly coupled, the uncertainty in the inferred plate boundary strength decreases. For very weak, uncoupled subduction zones, the uncertainty of inferred plate margin strength increases since there is little sensitivity between plate margin strength and plate velocity. This result is significant
Tsunami waveform inversion by adjoint methods
NASA Astrophysics Data System (ADS)
Pires, Carlos; Miranda, Pedro M. A.
2001-09-01
An adjoint method for tsunami waveform inversion is proposed, as an alternative to the technique based on Green's functions of the linear long wave model. The method has the advantage of being able to use the nonlinear shallow water equations, or other appropriate equation sets, and to optimize an initial state given as a linear or nonlinear function of any set of free parameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacement of tsunamigenic earthquakes. The proposed methodology is validated with experiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providing that the adjoint method is constrained in an appropriate manner. It is found, as in other methods, that the inversion skill of tsunami sources increases with the azimuthal and temporal coverage of assimilated tide gauge stations; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology to choose the subset of independent parameters that can be inverted with a given dataset of observations and to evaluate the error of the inversion process. The method is also applied to real tide gauge series, from the tsunami of the February 28, 1969, Gorringe Bank earthquake, suggesting some reasonable changes to the assumed focal parameters of that event. It is suggested that the method proposed may be able to deal with transient tsunami sources such as those generated by submarine landslides.
Error handling strategies in multiphase inverse modeling
Finsterle, S.; Zhang, Y.
2010-12-01
Parameter estimation by inverse modeling involves the repeated evaluation of a function of residuals. These residuals represent both errors in the model and errors in the data. In practical applications of inverse modeling of multiphase flow and transport, the error structure of the final residuals often significantly deviates from the statistical assumptions that underlie standard maximum likelihood estimation using the least-squares method. Large random or systematic errors are likely to lead to convergence problems, biased parameter estimates, misleading uncertainty measures, or poor predictive capabilities of the calibrated model. The multiphase inverse modeling code iTOUGH2 supports strategies that identify and mitigate the impact of systematic or non-normal error structures. We discuss these approaches and provide an overview of the error handling features implemented in iTOUGH2.
Oh, Geok Lian; Brunskog, Jonas
2014-08-01
Techniques have been studied for the localization of an underground source with seismic interrogation signals. Much of the work has involved defining either a P-wave acoustic model or a dispersive surface wave model to the received signal and applying the time-delay processing technique and frequency-wavenumber processing to determine the location of the underground tunnel. Considering the case of determining the location of an underground tunnel, this paper proposed two physical models, the acoustic approximation ray tracing model and the finite difference time domain three-dimensional (3D) elastic wave model to represent the received seismic signal. Two localization algorithms, beamforming and Bayesian inversion, are developed for each physical model. The beam-forming algorithms implemented are the modified time-and-delay beamformer and the F-K beamformer. Inversion is posed as an optimization problem to estimate the unknown position variable using the described physical forward models. The proposed four methodologies are demonstrated and compared using seismic signals recorded by geophones set up on ground surface generated by a surface seismic excitation. The examples show that for field data, inversion for localization is most advantageous when the forward model completely describe all the elastic wave components as is the case of the FDTD 3D elastic model.
An exact inverse method for subsonic flows
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1988-01-01
A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.
Application of the least-squares inversion method: Fourier series versus waveform inversion
NASA Astrophysics Data System (ADS)
Min, Dong-Joo; Shin, Jungkyun; Shin, Changsoo
2015-11-01
We describe an implicit link between waveform inversion and Fourier series based on inversion methods such as gradient, Gauss-Newton, and full Newton methods. Fourier series have been widely used as a basic concept in studies on seismic data interpretation, and their coefficients are obtained in the classical Fourier analysis. We show that Fourier coefficients can also be obtained by inversion algorithms, and compare the method to seismic waveform inversion algorithms. In that case, Fourier coefficients correspond to model parameters (velocities, density or elastic constants), whereas cosine and sine functions correspond to components of the Jacobian matrix, that is, partial derivative wavefields in seismic inversion. In the classical Fourier analysis, optimal coefficients are determined by the sensitivity of a given function to sine and cosine functions. In the inversion method for Fourier series, Fourier coefficients are obtained by measuring the sensitivity of residuals between given functions and test functions (defined as the sum of weighted cosine and sine functions) to cosine and sine functions. The orthogonal property of cosine and sine functions makes the full or approximate Hessian matrix become a diagonal matrix in the inversion for Fourier series. In seismic waveform inversion, the Hessian matrix may or may not be a diagonal matrix, because partial derivative wavefields correlate with each other to some extent, making them semi-orthogonal. At the high-frequency limits, however, the Hessian matrix can be approximated by either a diagonal matrix or a diagonally-dominant matrix. Since we usually deal with relatively low frequencies in seismic waveform inversion, it is not diagonally dominant and thus it is prohibitively expensive to compute the full or approximate Hessian matrix. By interpreting Fourier series with the inversion algorithms, we note that the Fourier series can be computed at an iteration step using any inversion algorithms such as the
NASA Astrophysics Data System (ADS)
Zidikheri, Meelis J.; Potts, Rodney J.
2015-09-01
A simple inversion scheme for optimizing volcanic emission dispersion model parameters with respect to satellite detections is presented in this paper. In this scheme, multiple dispersion model simulations, obtained by varying relevant model parameters, are created and compared against satellite detections using pattern correlation as a measure of model agreement with observations. It is shown that the scheme is successful in inferring emission source parameters such as those describing the vertical extent of the nascent sulfur dioxide emissions in the November 2010 Mount Merapi eruption in Java, Indonesia. These optimal parameter values then become a basis for improved forecasts of the transport of volcanic emissions.
NASA Astrophysics Data System (ADS)
Hanuš, J.; Ďurech, J.; Brož, M.; Warner, B. D.; Pilcher, F.; Stephens, R.; Oey, J.; Bernasconi, L.; Casulli, S.; Behrend, R.; Polishook, D.; Henych, T.; Lehký, M.; Yoshida, F.; Ito, T.
2011-06-01
Context. In the past decade, more than one hundred asteroid models were derived using the lightcurve inversion method. Measured by the number of derived models, lightcurve inversion has become the leading method for asteroid shape determination. Aims: Tens of thousands of sparse-in-time lightcurves from astrometric projects are publicly available. We investigate these data and use them in the lightcurve inversion method to derive new asteroid models. By having a greater number of models with known physical properties, we can gain a better insight into the nature of individual objects and into the whole asteroid population. Methods: We use sparse photometry from selected observatories from the AstDyS database (Asteroids - Dynamic Site), either alone or in combination with dense lightcurves, to determine new asteroid models by the lightcurve inversion method. We investigate various correlations between several asteroid parameters and characteristics such as the rotational state and diameter or family membership. We focus on the distribution of ecliptic latitudes of pole directions. We create a synthetic uniform distribution of latitudes, compute the method bias, and compare the results with the distribution of known models. We also construct a model for the long-term evolution of spins. Results: We present 80 new asteroid models derived from combined data sets where sparse photometry is taken from the AstDyS database and dense lightcurves are from the Uppsala Asteroid Photometric Catalogue (UAPC) and from several individual observers. For 18 asteroids, we present updated shape solutions based on new photometric data. For another 30 asteroids we present their partial models, i.e., an accurate period value and an estimate of the ecliptic latitude of the pole. The addition of new models increases the total number of models derived by the lightcurve inversion method to ~200. We also present a simple statistical analysis of physical properties of asteroids where we look
Methods for solving of inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Kobilskaya, E.; Lyashenko, V.
2016-10-01
A general mathematical model of the high-temperature thermodiffusion that occurs in a limited environment is considered. Based on this model a formulation of inverse problems for homogeneous and inhomogeneous parabolic equations is proposed. The inverse problem aims at identifying one or several unknown parameters of the mathematical model. These parameters allow maintaining the required temperature distribution and concentration of distribution of substance in the whole area or in part. For each case (internal, external heat source or a combination) the appropriate method for solving the inverse problem is proposed.
An inversion method for cometary atmospheres
NASA Astrophysics Data System (ADS)
Hubert, B.; Opitom, C.; Hutsemékers, D.; Jehin, E.; Munhoven, G.; Manfroid, J.; Bisikalo, D. V.; Shematovich, V. I.
2016-10-01
Remote observation of cometary atmospheres produces a measurement of the cometary emissions integrated along the line of sight. This integration is the so-called Abel transform of the local emission rate. The observation is generally interpreted under the hypothesis of spherical symmetry of the coma. Under that hypothesis, the Abel transform can be inverted. We derive a numerical inversion method adapted to cometary atmospheres using both analytical results and least squares fitting techniques. This method, derived under the usual hypothesis of spherical symmetry, allows us to retrieve the radial distribution of the emission rate of any unabsorbed emission, which is the fundamental, physically meaningful quantity governing the observation. A Tikhonov regularization technique is also applied to reduce the possibly deleterious effects of the noise present in the observation and to warrant that the problem remains well posed. Standard error propagation techniques are included in order to estimate the uncertainties affecting the retrieved emission rate. Several theoretical tests of the inversion techniques are carried out to show its validity and robustness. In particular, we show that the Abel inversion of real data is only weakly sensitive to an offset applied to the input flux, which implies that the method, applied to the study of a cometary atmosphere, is only weakly dependent on uncertainties on the sky background which has to be subtracted from the raw observations of the coma. We apply the method to observations of three different comets observed using the TRAPPIST telescope: 103P/ Hartley 2, F6/ Lemmon and A1/ Siding Spring. We show that the method retrieves realistic emission rates, and that characteristic lengths and production rates can be derived from the emission rate for both CN and C2 molecules. We show that the retrieved characteristic lengths can differ from those obtained from a direct least squares fitting over the observed flux of radiation, and
Wake Vortex Inverse Model User's Guide
NASA Technical Reports Server (NTRS)
Lai, David; Delisi, Donald
2008-01-01
NorthWest Research Associates (NWRA) has developed an inverse model for inverting landing aircraft vortex data. The data used for the inversion are the time evolution of the lateral transport position and vertical position of both the port and starboard vortices. The inverse model performs iterative forward model runs using various estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Forward model predictions of lateral transport and altitude are then compared with the observed data. Differences between the data and model predictions guide the choice of vortex parameter values, crosswind profile and circulation evolution in the next iteration. Iterations are performed until a user-defined criterion is satisfied. Currently, the inverse model is set to stop when the improvement in the rms deviation between the data and model predictions is less than 1 percent for two consecutive iterations. The forward model used in this inverse model is a modified version of the Shear-APA model. A detailed description of this forward model, the inverse model, and its validation are presented in a different report (Lai, Mellman, Robins, and Delisi, 2007). This document is a User's Guide for the Wake Vortex Inverse Model. Section 2 presents an overview of the inverse model program. Execution of the inverse model is described in Section 3. When executing the inverse model, a user is requested to provide the name of an input file which contains the inverse model parameters, the various datasets, and directories needed for the inversion. A detailed description of the list of parameters in the inversion input file is presented in Section 4. A user has an option to save the inversion results of each lidar track in a mat-file (a condensed data file in Matlab format). These saved mat-files can be used for post-inversion analysis. A description of the contents of the saved files is given in Section 5. An example of an inversion input
Walter, Donald A.; LeBlanc, Denis R.
2008-01-01
Historical weapons testing and disposal activities at Camp Edwards, which is located on the Massachusetts Military Reservation, western Cape Cod, have resulted in the release of contaminants into an underlying sand and gravel aquifer that is the sole source of potable water to surrounding communities. Ground-water models have been used at the site to simulate advective transport in the aquifer in support of field investigations. Reasonable models developed by different groups and calibrated by trial and error often yield different predictions of advective transport, and the predictions lack quantitative measures of uncertainty. A recently (2004) developed regional model of western Cape Cod, modified to include the sensitivity and parameter-estimation capabilities of MODFLOW-2000, was used in this report to evaluate the utility of inverse (statistical) methods to (1) improve model calibration and (2) assess model-prediction uncertainty. Simulated heads and flows were most sensitive to recharge and to the horizontal hydraulic conductivity of the Buzzards Bay and Sandwich Moraines and the Buzzards Bay and northern parts of the Mashpee outwash plains. Conversely, simulated heads and flows were much less sensitive to vertical hydraulic conductivity. Parameter estimation (inverse calibration) improved the match to observed heads and flows; the absolute mean residual for heads improved by 0.32 feet and the absolute mean residual for streamflows improved by about 0.2 cubic feet per second. Advective-transport predictions in Camp Edwards generally were most sensitive to the parameters with the highest precision (lowest coefficients of variation), indicating that the numerical model is adequate for evaluating prediction uncertainties in and around Camp Edwards. The incorporation of an advective-transport observation, representing the leading edge of a contaminant plume that had been difficult to match by using trial-and-error calibration, improved the match between an
NASA Astrophysics Data System (ADS)
Loubet, Benjamin; Carozzi, Marco
2015-04-01
Tropospheric ammonia (NH3) is a key player in atmospheric chemistry and its deposition is a threat for the environment (ecosystem eutrophication, soil acidification and reduction in species biodiversity). Most of the NH3 global emissions derive from agriculture, mainly from livestock manure (storage and field application) but also from nitrogen-based fertilisers. Inverse dispersion modelling has been widely used to infer emission sources from a homogeneous source of known geometry. When the emission derives from different sources inside of the measured footprint, the emission should be treated as multi-source problem. This work aims at estimating whether multi-source inverse dispersion modelling can be used to infer NH3 emissions from different agronomic treatment, composed of small fields (typically squares of 25 m side) located near to each other, using low-cost NH3 measurements (diffusion samplers). To do that, a numerical experiment was designed with a combination of 3 x 3 square field sources (625 m2), and a set of sensors placed at the centre of each field at several heights as well as at 200 m away from the sources in each cardinal directions. The concentration at each sensor location was simulated with a forward Lagrangian Stochastic (WindTrax) and a Gaussian-like (FIDES) dispersion model. The concentrations were averaged over various integration times (3 hours to 28 days), to mimic the diffusion sampler behaviour with several sampling strategy. The sources were then inferred by inverse modelling using the averaged concentration and the same models in backward mode. The sources patterns were evaluated using a soil-vegetation-atmosphere model (SurfAtm-NH3) that incorporates the response of the NH3 emissions to surface temperature. A combination emission patterns (constant, linear decreasing, exponential decreasing and Gaussian type) and strengths were used to evaluate the uncertainty of the inversion method. Each numerical experiment covered a period of 28
Inverse hydrochemical models of aqueous extracts tests
Zheng, L.; Samper, J.; Montenegro, L.
2008-10-10
Aqueous extract test is a laboratory technique commonly used to measure the amount of soluble salts of a soil sample after adding a known mass of distilled water. Measured aqueous extract data have to be re-interpreted in order to infer porewater chemical composition of the sample because porewater chemistry changes significantly due to dilution and chemical reactions which take place during extraction. Here we present an inverse hydrochemical model to estimate porewater chemical composition from measured water content, aqueous extract, and mineralogical data. The model accounts for acid-base, redox, aqueous complexation, mineral dissolution/precipitation, gas dissolution/ex-solution, cation exchange and surface complexation reactions, of which are assumed to take place at local equilibrium. It has been solved with INVERSE-CORE{sup 2D} and been tested with bentonite samples taken from FEBEX (Full-scale Engineered Barrier EXperiment) in situ test. The inverse model reproduces most of the measured aqueous data except bicarbonate and provides an effective, flexible and comprehensive method to estimate porewater chemical composition of clays. Main uncertainties are related to kinetic calcite dissolution and variations in CO2(g) pressure.
NASA Astrophysics Data System (ADS)
Xue, Haile; Shen, Xueshun; Chou, Jifan
2015-11-01
An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors (MEs) in past intervals. Given the analyses, the ME in each interval (6 h) between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year (2001-2005) GRAPES-GFS (Global Forecast System of the Global and Regional Assimilation and Prediction System) error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.
Use of ABIC and Invention of Inversion Methods
NASA Astrophysics Data System (ADS)
Fukahata, Y.; Yagi, Y.
2014-12-01
Bayesian inference is a powerful tool in inversion analyses of geophysical problems, because observed data are commonly inaccurate and insufficient in these problems. In Bayesian inference, we always encounter a problem in determining the relative weight between observed data and prior information. ABIC (Akaike's Bayesian Information Criterion) gives a useful solution to this problem particularly for linear inverse problems, by maximizing the marginal likelihood for the relative weight. In general, we subjectively construct a Bayesian model, which consists of a family of parametric models with different values of the relative weight giving different parametric models; ABIC enables us to objectively select a specific model among the parametric models. In principle, ABIC gives us an inverse solution that mostly follows observed data when we have enough amount of data with good accuracy, and gives us an inverse solution that mostly follows prior information when observed data are insufficient and/or inaccurate (see the attached image). In inversion analyses using ABIC, we do not manually adjust the relative weight. Hence, we quite easily obtain geophysically unrealistic results. Because of that, someone may think that inversion analyses using ABIC is difficult in dealing with or even unreliable. However, this characteristic is an excellent point of ABIC. If we obtain a geophysically unrealistic result, this implies that some problems are hidden in the inversion method. In this talk, we show an example of the invention of inversion methods inspired by ABIC: the importance of covariance components including modeling errors. As shown by this example, we can get closer to the true solution not by manually adjusting the relative weight to obtain a seemingly good-looking result, but by determining the relative weight statistically. It is a harder way to determine the relative weight statistically, but we should pursue this way to understand geophysical problems more
Geophysical Inversion With Multi-Objective Global Optimization Methods
NASA Astrophysics Data System (ADS)
Lelièvre, Peter; Bijani, Rodrigo; Farquharson, Colin
2016-04-01
We are investigating the use of Pareto multi-objective global optimization (PMOGO) methods to solve numerically complicated geophysical inverse problems. PMOGO methods can be applied to highly nonlinear inverse problems, to those where derivatives are discontinuous or simply not obtainable, and to those were multiple minima exist in the problem space. PMOGO methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. This allows a more complete assessment of the possibilities and provides opportunities to calculate statistics regarding the likelihood of particular model features. We are applying PMOGO methods to four classes of inverse problems. The first are discrete-body problems where the inversion determines values of several parameters that define the location, orientation, size and physical properties of an anomalous body represented by a simple shape, for example a sphere, ellipsoid, cylinder or cuboid. A PMOGO approach can determine not only the optimal shape parameters for the anomalous body but also the optimal shape itself. Furthermore, when one expects several anomalous bodies in the subsurface, a PMOGO inversion approach can determine an optimal number of parameterized bodies. The second class of inverse problems are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The third class of problems are lithological inversions, which are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the fourth class, surface geometry inversions, we consider a fundamentally different type of problem in which a model comprises wireframe surfaces representing contacts between rock units. The physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. Surface geometry inversion can be
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
Regeneration of stochastic processes: an inverse method
NASA Astrophysics Data System (ADS)
Ghasemi, F.; Peinke, J.; Sahimi, M.; Rahimi Tabar, M. R.
2005-10-01
We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.
Improved hybrid iterative optimization method for seismic full waveform inversion
NASA Astrophysics Data System (ADS)
Wang, Yi; Dong, Liang-Guo; Liu, Yu-Zhu
2013-06-01
In full waveform inversion (FWI), Hessian information of the misfit function is of vital importance for accelerating the convergence of the inversion; however, it usually is not feasible to directly calculate the Hessian matrix and its inverse. Although the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) or Hessian-free inexact Newton (HFN) methods are able to use approximate Hessian information, the information they collect is limited. The two methods can be interlaced because they are able to provide Hessian information for each other; however, the performance of the hybrid iterative method is dependent on the effective switch between the two methods. We have designed a new scheme to realize the dynamic switch between the two methods based on the decrease ratio (DR) of the misfit function (objective function), and we propose a modified hybrid iterative optimization method. In the new scheme, we compare the DR of the two methods for a given computational cost, and choose the method with a faster DR. Using these steps, the modified method always implements the most efficient method. The results of Marmousi and over thrust model testings indicate that the convergence with our modified method is significantly faster than that in the L-BFGS method with no loss of inversion quality. Moreover, our modified outperforms the enriched method by a little speedup of the convergence. It also exhibits better efficiency than the HFN method.
Geostatistical joint inversion of seismic and potential field methods
NASA Astrophysics Data System (ADS)
Shamsipour, Pejman; Chouteau, Michel; Giroux, Bernard
2016-04-01
Interpretation of geophysical data needs to integrate different types of information to make the proposed model geologically realistic. Multiple data sets can reduce uncertainty and non-uniqueness present in separate geophysical data inversions. Seismic data can play an important role in mineral exploration, however processing and interpretation of seismic data is difficult due to complexity of hard-rock geology. On the other hand, the recovered model from potential field methods is affected by inherent non uniqueness caused by the nature of the physics and by underdetermination of the problem. Joint inversion of seismic and potential field data can mitigate weakness of separate inversion of these methods. A stochastic joint inversion method based on geostatistical techniques is applied to estimate density and velocity distributions from gravity and travel time data. The method fully integrates the physical relations between density-gravity, on one hand, and slowness-travel time, on the other hand. As a consequence, when the data are considered noise-free, the responses from the inverted slowness and density data exactly reproduce the observed data. The required density and velocity auto- and cross-covariance are assumed to follow a linear model of coregionalization (LCM). The recent development of nonlinear model of coregionalization could also be applied if needed. The kernel function for the gravity method is obtained by the closed form formulation. For ray tracing, we use the shortest-path methods (SPM) to calculate the operation matrix. The jointed inversion is performed on structured grid; however, it is possible to extend it to use unstructured grid. The method is tested on two synthetic models: a model consisting of two objects buried in a homogeneous background and a model with stochastic distribution of parameters. The results illustrate the capability of the method to improve the inverted model compared to the separate inverted models with either gravity
NASA Astrophysics Data System (ADS)
Girault, M.; Maillet, D.; Bonthoux, F.; Galland, B.; Martin, P.; Braconnier, R.; Fontaine, J. R.
2008-02-01
A method is proposed for the estimation of time-varying emission rates of pollutant sources in a ventilated enclosure, through the resolution of an inverse forced convection problem. Unsteady transport-diffusion of the pollutant is considered, with the assumption of a stationary velocity field remaining unchanged during emission (passive contaminant). The pollutant transport equation is therefore linear with respect to concentration. The source's location is also supposed to be known. As the first step, a reduced model (RM) linking concentrations at a set of control points to emission rates of sources is identified from experimental data by using the modal identification method (MIM). This parameter estimation problem uses transient contaminant concentration measurements made at control points inside the ventilated enclosure, corresponding to increasing and decreasing steps of emission rates. Such experimental modelling allows us to avoid dealing with a CFD code involving turbulence modelling and to get rid of uncertainties about sensors position. In a second step, the identified RM is used to solve an inverse forced convection problem: from contaminant concentration measured at the same control points, rates of sources emitting simultaneously are estimated with a sequential in time algorithm using future time steps.
Putz, Ana-Maria; Putz, Mihai V
2012-01-01
The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands' assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature.
Putz, Ana-Maria; Putz, Mihai V.
2012-01-01
The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature. PMID:23443102
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M.; Tuma, M.
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Crosswell born inversion for heterogeneous velocity models
Hegge, R.F.; Herman, G.C.; Sevink, A.G.J.
1994-12-31
The application of high-frequency asymptotic Born inverse scattering methods to cross-well imaging is discussed and illustrated with a number of model studies for synthetic data. In particular, attention is given to imaging problems that are associated with typical cross-well geometries. A severe problem is the existence of multiple travel paths between sources and receivers that are particularly apparent if low-velocity layers are present. When this occurs, the high-frequency asymptotic imaging method is no longer valid and large artifacts in the images can result. However, it is concluded that, even in the case of multiple travel paths, good images can be obtained by omitting the singularities in the imaging formula and by combining the results for different source locations.
Development of an inverse method for coastal risk management
NASA Astrophysics Data System (ADS)
Idier, D.; Rohmer, J.; Bulteau, T.; Delvallée, E.
2013-04-01
Recent flooding events, like Katrina (USA, 2005) or Xynthia (France, 2010), illustrate the complexity of coastal systems and the limits of traditional flood risk analysis. Among other questions, these events raised issues such as: "how to choose flooding scenarios for risk management purposes?", "how to make a society more aware and prepared for such events?" and "which level of risk is acceptable to a population?". The present paper aims at developing an inverse approach that could seek to address these three issues. The main idea of the proposed method is the inversion of the usual risk assessment steps: starting from the maximum acceptable hazard level (defined by stakeholders as the one leading to the maximum tolerable consequences) to finally obtain the return period of this threshold. Such an "inverse" approach would allow for the identification of all the offshore forcing conditions (and their occurrence probability) inducing a threat for critical assets of the territory, such information being of great importance for coastal risk management. This paper presents the first stage in developing such a procedure. It focuses on estimation (through inversion of the flooding model) of the offshore conditions leading to the acceptable hazard level, estimation of the return period of the associated combinations, and thus of the maximum acceptable hazard level. A first application for a simplified case study (based on real data), located on the French Mediterranean coast, is presented, assuming a maximum acceptable hazard level. Even if only one part of the full inverse method has been developed, we demonstrate how the inverse method can be useful in (1) estimating the probability of exceeding the maximum inundation height for identified critical assets, (2) providing critical offshore conditions for flooding in early warning systems, and (3) raising awareness of stakeholders and eventually enhance preparedness for future flooding events by allowing them to assess
Inverse polynomial reconstruction method in DCT domain
NASA Astrophysics Data System (ADS)
Dadkhahi, Hamid; Gotchev, Atanas; Egiazarian, Karen
2012-12-01
The discrete cosine transform (DCT) offers superior energy compaction properties for a large class of functions and has been employed as a standard tool in many signal and image processing applications. However, it suffers from spurious behavior in the vicinity of edge discontinuities in piecewise smooth signals. To leverage the sparse representation provided by the DCT, in this article, we derive a framework for the inverse polynomial reconstruction in the DCT expansion. It yields the expansion of a piecewise smooth signal in terms of polynomial coefficients, obtained from the DCT representation of the same signal. Taking advantage of this framework, we show that it is feasible to recover piecewise smooth signals from a relatively small number of DCT coefficients with high accuracy. Furthermore, automatic methods based on minimum description length principle and cross-validation are devised to select the polynomial orders, as a requirement of the inverse polynomial reconstruction method in practical applications. The developed framework can considerably enhance the performance of the DCT in sparse representation of piecewise smooth signals. Numerical results show that denoising and image approximation algorithms based on the proposed framework indicate significant improvements over wavelet counterparts for this class of signals.
Inverse Modeling Via Linearized Functional Minimization
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Wohlberg, B.; Vesselinov, V. V.; Tartakovsky, D. M.
2014-12-01
We present a novel parameter estimation methodology for transient models of geophysical systems with uncertain, spatially distributed, heterogeneous and piece-wise continuous parameters.The methodology employs a bayesian approach to propose an inverse modeling problem for the spatial configuration of the model parameters.The likelihood of the configuration is formulated using sparse measurements of both model parameters and transient states.We propose using total variation regularization (TV) as the prior reflecting the heterogeneous, piece-wise continuity assumption on the parameter distribution.The maximum a posteriori (MAP) estimator of the parameter configuration is then computed by minimizing the negative bayesian log-posterior using a linearized functional minimization approach. The computation of the MAP estimator is a large-dimensional nonlinear minimization problem with two sources of nonlinearity: (1) the TV operator, and (2) the nonlinear relation between states and parameters provided by the model's governing equations.We propose a a hybrid linearized functional minimization (LFM) algorithm in two stages to efficiently treat both sources of nonlinearity.The relation between states and parameters is linearized, resulting in a linear minimization sub-problem equipped with the TV operator; this sub-problem is then minimized using the Alternating Direction Method of Multipliers (ADMM). The methodology is illustrated with a transient saturated groundwater flow application in a synthetic domain, stimulated by external point-wise loadings representing aquifer pumping, together with an array of discrete measurements of hydraulic conductivity and transient measurements of hydraulic head.We show that our inversion strategy is able to recover the overall large-scale features of the parameter configuration, and that the reconstruction is improved by the addition of transient information of the state variable.
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-31
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Joint Geophysical Inversion With Multi-Objective Global Optimization Methods
NASA Astrophysics Data System (ADS)
Lelievre, P. G.; Bijani, R.; Farquharson, C. G.
2015-12-01
Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem is essentially a geometry inversion, which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.
The quantum inverse scattering method with anyonic grading
NASA Astrophysics Data System (ADS)
Batchelor, M. T.; Foerster, A.; Guan, X.-W.; Links, J.; Zhou, H.-Q.
2008-11-01
We formulate the quantum inverse scattering method for the case of anyonic grading. This provides a general framework for constructing integrable models describing interacting hard-core anyons. Through this method we reconstruct the known integrable model of hard core anyons associated with the XXX model, and as a new application we construct the anyonic t - J model. The energy spectrum for each model is derived by means of a generalization of the algebraic Bethe ansatz. The grading parameters implementing the anyonic signature give rise to sector-dependent phase factors in the Bethe ansatz equations.
NASA Astrophysics Data System (ADS)
Jang, Hangilro; Kim, Hee Joon
2015-12-01
In transient electromagnetic (TEM) measurements, secondary fields that contain information on conductive targets such as hydrothermal mineral deposits in the seafloor can be measured in the absence of strong primary fields. A TEM system using a loop source is useful to the development of compact, autonomous instruments, which are well suited to submersible-based surveys. In this paper, we investigate the possibility of applying an in-loop TEM system to the detection of marine hydrothermal deposits through a one-dimensional modeling and inversion study. We examine step-off responses for a layered model and compare the characteristics of horizontal and vertical loop systems for detecting hydrothermal deposits. The feasibility study shows that TEM responses are very sensitive to a highly conductive layer. Time-domain target responses are larger and appear earlier in horizontal magnetic fields than in vertical ones, although the vertical field has 2-3 times larger magnitude than the horizontal one. An inverse problem is formulated with the Gauss-Newton method and solved with the damped and smoothness-constrained least-squares approach. The test example for a marine hydrothermal TEM survey demonstrated that the depth extent, conductivity and thickness of the highly conductive layer are well resolved.
A system model and inversion for synthetic aperture radar imaging.
Soumekh, M
1992-01-01
A system model and its corresponding inversion for synthetic aperture radar (SAR) imaging are presented. The system model incorporates the spherical nature of a radar's radiation pattern at far field. The inverse method based on this model performs a spatial Fourier transform (Doppler processing) on the recorded signals with respect to the available coordinates of a translational radar (SAR) or target (inverse SAR). It is shown that the transformed data provide samples of the spatial Fourier transform of the target's reflectivity function. The inverse method can be modified to incorporate deviations of the radar's motion from its prescribed straight line path. The effects of finite aperture on resolution, reconstruction, and sampling constraints for the imaging problem are discussed.
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T.; Graham, A.L.
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
NASA Astrophysics Data System (ADS)
Saunier, O.; Mathieu, A.; Didier, D.; Tombette, M.; Quélo, D.; Winiarek, V.; Bocquet, M.
2013-06-01
The Chernobyl nuclear accident and more recently the Fukushima accident highlighted that the largest source of error on consequences assessment is the source term including the time evolution of the release rate and its distribution between radioisotopes. Inverse modeling methods, which combine environmental measurements and atmospheric dispersion models, have proven efficient in assessing source term due to an accidental situation (Gudiksen, 1989; Krysta and Bocquet, 2007; Stohl et al., 2012a; Winiarek et al., 2012). Most existing approaches are designed to use air sampling measurements (Winiarek et al., 2012) and some of them also use deposition measurements (Stohl et al., 2012a; Winiarek et al., 2013) but none of them uses dose rate measurements. However, it is the most widespread measurement system, and in the event of a nuclear accident, these data constitute the main source of measurements of the plume and radioactive fallout during releases. This paper proposes a method to use dose rate measurements as part of an inverse modeling approach to assess source terms. The method is proven efficient and reliable when applied to the accident at the Fukushima Daiichi nuclear power plant (FD-NPP). The emissions for the eight main isotopes 133Xe, 134Cs, 136Cs, 137Cs, 137mBa, 131I, 132I and 132Te have been assessed. Accordingly, 103 PBq of 131I, 35.5 PBq of 132I, 15.5 PBq of 137Cs and 12 100 PBq of noble gases were released. The events at FD-NPP (such as venting, explosions, etc.) known to have caused atmospheric releases are well identified in the retrieved source term. The estimated source term is validated by comparing simulations of atmospheric dispersion and deposition with environmental observations. The result is that the model-measurement agreement for all of the monitoring locations is correct for 80% of simulated dose rates that are within a factor of 2 of the observed values. Changes in dose rates over time have been overall properly reconstructed, especially
NASA Astrophysics Data System (ADS)
Kerschberger, P.; Gehrer, A.
2010-08-01
In recent years an increased interest in pump-turbines has been recognized in the market. The rapid availability of pumped storage schemes and the benefits to the power system by peak lopping, providing reserve and rapid response for frequency control are becoming of growing advantage. In that context it is requested to develop pump-turbines that reliably stand dynamic operation modes, fast changes of the discharge rate by adjusting the variable diffuser vanes as well as fast changes from pump to turbine operation. Within the present study various flow patterns linked to the operation of a pump-turbine system are discussed. In that context pump and turbine mode are presented separately and different load cases at both operation modes are shown. In order to achieve modern, competitive pump-turbine designs it is further explained which design challenges should be considered during the geometry definition of a pump-turbine impeller. Within the present study a runner-blade profile for a low head pump-turbine has been developed. For the initial hydraulic runner-blade design, an inverse design method has been applied. Within this design procedure, a first blade geometry is generated by imposing the pressure loading-distribution and by means of an inverse 3D potential-flow-solution. The hydraulic behavior of both, pump-mode and turbine-mode is then evaluated by solving the full 3D Navier-Stokes equations in combination with a robust turbulence model. Based on this initial design the blade profile has been further optimized and redesigned considering various hydraulic pump-turbine requirements. Finally, the progress in hydraulic design is demonstrated by model test results which show a significant improvement in hydraulic performance compared to an existing reference design.
NASA Astrophysics Data System (ADS)
Huang, J.; Golombek, A.; Prinn, R.; Weiss, R.; Fraser, P.; Simmonds, P.; Dlugokencky, E. J.; Hall, B.; Elkins, J.; Steele, P.; Langenfelds, R.; Krummel, P.; Dutton, G.; Porter, L.
2008-09-01
Nitrous oxide (N2O) is an important ozone-depleting gas and greenhouse gas with multiple uncertain emission processes. Global nitrous oxide observations, the Model of Atmospheric Transport and Chemistry (MATCH) and an inverse method were used to optimally estimate N2O emissions from twelve source regions around the globe. MATCH was used with forecast center reanalysis winds at T62 resolution (192 longitude by 94 latitude surface grid, and 28 vertical levels) from 1 July 1996 to 30 June 2006. The average concentrations of N2O in the lowest four layers of the model were then compared with the monthly mean observations from four national/international networks measuring at 65 surface sites. A 12-month-running-mean smoother was applied to both the model results and the observations, due to the fact that the model was not able to reproduce the very small observed seasonal cycles. The inverse method was then used to solve for the time-averaged regional emissions of N2O for two time periods (1 January 1997 to 31 December 2001 and 1 January 2002 to 31 December 2005). The best estimate inversions assume that the model stratospheric destruction rates, which lead to a global N2O lifetime of 125 years, are correct. It also assumes normalized emission spatial distributions within each region from Bouwman et al. (1995). We conclude that global N2O emissions with 66% probability errors are 16.3-1.2+1.5 and 15.4-1.3+1.7 TgN (N2O) a-1, for 1997-2001 and 2001-2005 respectively. Emissions from the equator to 30°N increased significantly from the initial Bouwman et al. (1995) estimates while emissions from southern oceans (30°S-90°S) decreased significantly. The quoted uncertainties include both the measurement errors and modeling uncertainties estimated using a separate flexible 12-box model. We also found that 23 ± 4% of the N2O global total emissions come from the ocean, which is slightly smaller than the Bouwman et al. (1995) estimate. For the estimation of emissions from the
Frequency-domain elastic full-waveform multiscale inversion method based on dual-level parallelism
NASA Astrophysics Data System (ADS)
Li, Yuan-Yuan; Li, Zhen-Chun; Zhang, Kai; Zhang, Xuan
2015-12-01
The complexity of an elastic wavefield increases the nonlinearity of inversion. To some extent, multiscale inversion decreases the nonlinearity of inversion and prevents it from falling into local extremes. A multiscale strategy based on the simultaneous use of frequency groups and layer stripping method based on damped wave field improves the stability of inversion. A dual-level parallel algorithm is then used to decrease the computational cost and improve practicability. The seismic wave modeling of a single frequency and inversion in a frequency group are computed in parallel by multiple nodes based on multifrontal massively parallel sparse direct solver and MPI. Numerical tests using an overthrust model show that the proposed inversion algorithm can effectively improve the stability and accuracy of inversion by selecting the appropriate inversion frequency and damping factor in lowfrequency seismic data.
Significant uncertainty exists in the magnitude and variability of ammonia (NH3) emissions. NH3 emissions are needed as input for air quality modeling of aerosols and deposition of nitrogen compounds. Approximately 85% of NH3 emissions are estimated to come from agricultural ...
Li, Ranran; Zou, Zhihong
2015-01-01
An integrated approach using the inverse method and Bayesian approach, combined with a lake eutrophication water quality model, was developed for parameter estimation and water environmental capacity (WEC) analysis. The model was used to support load reduction and effective water quality management in the Taihu Lake system in eastern China. Water quality was surveyed yearly from 1987 to 2010. Total nitrogen (TN) and total phosphorus (TP) were selected as water quality model variables. Decay rates of TN and TP were estimated using the proposed approach. WECs of TN and TP in 2011 were determined based on the estimated decay rates. Results showed that the historical loading was beyond the WEC, thus, reduction of nitrogen and phosphorus input is necessary to meet water quality goals. Then WEC and allowable discharge capacity (ADC) in 2015 and 2020 were predicted. The reduction ratios of ADC during these years were also provided. All of these enable decision makers to assess the influence of each loading and visualize potential load reductions under different water quality goals, and then to formulate a reasonable water quality management strategy. PMID:26426032
Inversion identities for inhomogeneous face models
NASA Astrophysics Data System (ADS)
Frahm, Holger; Karaiskos, Nikos
2014-10-01
We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions using the underlying integrable structure and crossing properties of the local Boltzmann weights. For the critical restricted solid-on-solid (RSOS) models these identities together with some information on the analytical properties of the transfer matrix determine the spectrum completely and allow to derive the Bethe equations for both periodic and general open boundary conditions.
Xia, J.; Miller, R.D.; Xu, Y.
2008-01-01
Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.
An Efficient Inverse Aerodynamic Design Method For Subsonic Flows
NASA Technical Reports Server (NTRS)
Milholen, William E., II
2000-01-01
Computational Fluid Dynamics based design methods are maturing to the point that they are beginning to be used in the aircraft design process. Many design methods however have demonstrated deficiencies in the leading edge region of airfoil sections. The objective of the present research is to develop an efficient inverse design method which is valid in the leading edge region. The new design method is a streamline curvature method, and a new technique is presented for modeling the variation of the streamline curvature normal to the surface. The new design method allows the surface coordinates to move normal to the surface, and has been incorporated into the Constrained Direct Iterative Surface Curvature (CDISC) design method. The accuracy and efficiency of the design method is demonstrated using both two-dimensional and three-dimensional design cases.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; Tartakovsky, Daniel M.
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Hybrid Adaptive Flight Control with Model Inversion Adaptation
NASA Technical Reports Server (NTRS)
Nguyen, Nhan
2011-01-01
This study investigates a hybrid adaptive flight control method as a design possibility for a flight control system that can enable an effective adaptation strategy to deal with off-nominal flight conditions. The hybrid adaptive control blends both direct and indirect adaptive control in a model inversion flight control architecture. The blending of both direct and indirect adaptive control provides a much more flexible and effective adaptive flight control architecture than that with either direct or indirect adaptive control alone. The indirect adaptive control is used to update the model inversion controller by an on-line parameter estimation of uncertain plant dynamics based on two methods. The first parameter estimation method is an indirect adaptive law based on the Lyapunov theory, and the second method is a recursive least-squares indirect adaptive law. The model inversion controller is therefore made to adapt to changes in the plant dynamics due to uncertainty. As a result, the modeling error is reduced that directly leads to a decrease in the tracking error. In conjunction with the indirect adaptive control that updates the model inversion controller, a direct adaptive control is implemented as an augmented command to further reduce any residual tracking error that is not entirely eliminated by the indirect adaptive control.
NASA Astrophysics Data System (ADS)
Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E.; Sweeney, C.; Turner, A. J.
2015-11-01
Understanding methane emissions from the Arctic, a fast warming carbon reservoir, is important for projecting changes in the global methane cycle under future climate scenarios. Here we optimize Arctic methane emissions with a nested-grid high-resolution inverse model by assimilating both high-precision surface measurements and column-average SCIAMACHY satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes are integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated by six different biogeochemical models. We find that, the global methane emissions during July 2004-June 2005 ranged from 496.4 to 511.5 Tg yr-1, with wetland methane emissions ranging from 130.0 to 203.3 Tg yr-1. The Arctic methane emissions during July 2004-June 2005 were in the range of 14.6-30.4 Tg yr-1, with wetland and lake emissions ranging from 8.8 to 20.4 Tg yr-1 and from 5.4 to 7.9 Tg yr-1 respectively. Canadian and Siberian lakes contributed most of the estimated lake emissions. Due to insufficient measurements in the region, Arctic methane emissions are less constrained in northern Russia than in Alaska, northern Canada and Scandinavia. Comparison of different inversions indicates that the distribution of global and Arctic methane emissions is sensitive to prior wetland emissions. Evaluation with independent datasets shows that the global and Arctic inversions improve estimates of methane mixing ratios in boundary layer and free troposphere. The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic.
Nonlinear inversion of pre-stack seismic data using variable metric method
NASA Astrophysics Data System (ADS)
Zhang, Fanchang; Dai, Ronghuo
2016-06-01
At present, the routine method to perform AVA (Amplitude Variation with incident Angle) inversion is based on the assumption that the ratio of S-wave velocity to P-wave velocity γ is a constant. However, this simplified assumption does not always hold, and it is necessary to use nonlinear inversion method to solve it. Based on Bayesian theory, the objective function for nonlinear AVA inversion is established and γ is considered as an unknown model parameter. Then, variable metric method with a strategy of periodically variational starting point is used to solve the nonlinear AVA inverse problem. The proposed method can keep the inverted reservoir parameters approach to the actual solution and has been performed on both synthetic and real data. The inversion results suggest that the proposed method can solve the nonlinear inverse problem and get accurate solutions even without the knowledge of γ.
A method for obtaining coefficients of compositional inverse generating functions
NASA Astrophysics Data System (ADS)
Kruchinin, Dmitry V.; Shablya, Yuriy V.; Kruchinin, Vladimir V.; Shelupanov, Alexander A.
2016-06-01
The aim of this paper is to show how to obtain expressions for coefficients of compositional inverse generating functions in explicit way. The method is based on the Lagrange inversion theorem and composita of generating functions. Also we give a method of obtaining expressions for coefficients of reciprocal generating functions and consider some examples.
Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination
Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos
2010-01-01
The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093
NASA Astrophysics Data System (ADS)
Saunier, O.; Mathieu, A.; Didier, D.; Tombette, M.; Quélo, D.; Winiarek, V.; Bocquet, M.
2013-11-01
The Chernobyl nuclear accident, and more recently the Fukushima accident, highlighted that the largest source of error on consequences assessment is the source term, including the time evolution of the release rate and its distribution between radioisotopes. Inverse modeling methods, which combine environmental measurements and atmospheric dispersion models, have proven efficient in assessing source term due to an accidental situation (Gudiksen, 1989; Krysta and Bocquet, 2007; Stohl et al., 2012a; Winiarek et al., 2012). Most existing approaches are designed to use air sampling measurements (Winiarek et al., 2012) and some of them also use deposition measurements (Stohl et al., 2012a; Winiarek et al., 2014). Some studies have been performed to use dose rate measurements (Duranova et al., 1999; Astrup et al., 2004; Drews et al., 2004; Tsiouri et al., 2012) but none of the developed methods were carried out to assess the complex source term of a real accident situation like the Fukushima accident. However, dose rate measurements are generated by the most widespread measurement system, and in the event of a nuclear accident, these data constitute the main source of measurements of the plume and radioactive fallout during releases. This paper proposes a method to use dose rate measurements as part of an inverse modeling approach to assess source terms. The method is proven efficient and reliable when applied to the accident at the Fukushima Daiichi Nuclear Power Plant (FD-NPP). The emissions for the eight main isotopes 133Xe, 134Cs, 136Cs, 137Cs, 137mBa, 131I, 132I and 132Te have been assessed. Accordingly, 105.9 PBq of 131I, 35.8 PBq of 132I, 15.5 PBq of 137Cs and 12 134 PBq of noble gases were released. The events at FD-NPP (such as venting, explosions, etc.) known to have caused atmospheric releases are well identified in the retrieved source term. The estimated source term is validated by comparing simulations of atmospheric dispersion and deposition with
Kong, Jude D; Jin, Chaochao; Wang, Hao
2015-12-01
In this paper, we improve the classic SEIR model by separating the juvenile group and the adult group to better describe the dynamics of childhood infectious diseases. We perform stability analysis to study the asymptotic dynamics of the new model, and perform sensitivity analysis to uncover the relative importance of the parameters on infection. The transmission rate is a key parameter in controlling the spread of an infectious disease as it directly determines the disease incidence. However, it is essentially impossible to measure the transmission rate for certain infectious diseases. We introduce an inverse method for our new model, which can extract the time-dependent transmission rate from either prevalence data or incidence data in existing open databases. Pre- and post-vaccination measles data sets from Liverpool and London are applied to estimate the time-varying transmission rate. From the Fourier transform of the transmission rate of Liverpool and London, we observe two spectral peaks with frequencies 1/year and 3/year. These dominant frequencies are robust with respect to different initial values. The dominant 1/year frequency is consistent with common belief that measles is driven by seasonal factors such as environmental changes and immune system changes and the 3/year frequency indicates the superiority of school contacts in driving measles transmission over other seasonal factors. Our results show that in coastal cities, the main modulator of the transmission of measles virus, paramyxovirus, is school seasons. On the other hand, in landlocked cities, both weather and school seasons have almost the same influence on paramyxovirus transmission.
Comparative study of inversion methods of three-dimensional NMR and sensitivity to fluids
NASA Astrophysics Data System (ADS)
Tan, Maojin; Wang, Peng; Mao, Keyu
2014-04-01
Three-dimensional nuclear magnetic resonance (3D NMR) logging can simultaneously measure transverse relaxation time (T2), longitudinal relaxation time (T1), and diffusion coefficient (D). These parameters can be used to distinguish fluids in the porous reservoirs. For 3D NMR logging, the relaxation mechanism and mathematical model, Fredholm equation, are introduced, and the inversion methods including Singular Value Decomposition (SVD), Butler-Reeds-Dawson (BRD), and Global Inversion (GI) methods are studied in detail, respectively. During one simulation test, multi-echo CPMG sequence activation is designed firstly, echo trains of the ideal fluid models are synthesized, then an inversion algorithm is carried on these synthetic echo trains, and finally T2-T1-D map is built. Futhermore, SVD, BRD, and GI methods are respectively applied into a same fluid model, and the computing speed and inversion accuracy are compared and analyzed. When the optimal inversion method and matrix dimention are applied, the inversion results are in good aggreement with the supposed fluid model, which indicates that the inversion method of 3D NMR is applieable for fluid typing of oil and gas reservoirs. Additionally, the forward modeling and inversion tests are made in oil-water and gas-water models, respectively, the sensitivity to the fluids in different magnetic field gradients is also examined in detail. The effect of magnetic gradient on fluid typing in 3D NMR logging is stuied and the optimal manetic gradient is choosen.
Full-waveform modeling and inversion of physical model data
NASA Astrophysics Data System (ADS)
Cai, Jian; Zhang, Jie
2016-08-01
Because full elastic waveform inversion requires considerable computation time for forward modeling and inversion, acoustic waveform inversion is often applied to marine data for reducing the computational time. To understand the validity of the acoustic approximation, we study data collected from an ultrasonic laboratory with a known physical model by applying elastic and acoustic waveform modeling and acoustic waveform inversion. This study enables us to evaluate waveform differences quantitatively between synthetics and real data from the same physical model and to understand the effects of different objective functions in addressing the waveform differences for full-waveform inversion. Because the materials used in the physical experiment are viscoelastic, we find that both elastic and acoustic synthetics differ substantially from the physical data over offset in true amplitude. If attenuation is taken into consideration, the amplitude versus offset (AVO) of viscoelastic synthetics more closely approximates the physical data. To mitigate the effect of amplitude differences, we apply trace normalization to both synthetics and physical data in acoustic full-waveform inversion. The objective function is equivalent to minimizing the phase differences with indirect contributions from the amplitudes. We observe that trace normalization helps to stabilize the inversion and obtain more accurate model solutions for both synthetics and physical data.
Inverse method for estimating shear stress in machining
NASA Astrophysics Data System (ADS)
Burns, T. J.; Mates, S. P.; Rhorer, R. L.; Whitenton, E. P.; Basak, D.
2016-01-01
An inverse method is presented for estimating shear stress in the work material in the region of chip-tool contact along the rake face of the tool during orthogonal machining. The method is motivated by a model of heat generation in the chip, which is based on a two-zone contact model for friction along the rake face, and an estimate of the steady-state flow of heat into the cutting tool. Given an experimentally determined discrete set of steady-state temperature measurements along the rake face of the tool, it is shown how to estimate the corresponding shear stress distribution on the rake face, even when no friction model is specified.
NASA Astrophysics Data System (ADS)
Tao, Yi; Sen, Mrinal K.; Zhang, Rui; Spikes, Kyle T.
2013-06-01
Non-uniqueness presents challenges to seismic inverse problems, especially for time-lapse inversion where multiple inversions are needed for different vintages of seismic data. For time-lapse applications, the focus typically is to detect relatively small changes in seismic attributes at limited locations and to relate these differences to changes in the underlying physical properties. We propose a robust inversion workflow where the baseline inversion uses a starting model, which combines a high-frequency fractal component and a low-frequency component from well log data. This starting model provides an estimate of the null space based on fractal statistics of well data. To further focus on the localized changes, the inverted elastic parameters from the baseline model and the difference between two time-lapse data are summed together to produce the virtual time-lapse seismic data. This is known as double-difference inversion, which focuses primarily on the areas where time-lapse changes occur. The misfit function uses both data and model norms so that the ill-posedness of the inverse problem can be regularized. We pre-process the seismic data using a local correlation-based warping algorithm to register the time-lapse datasets. Finally, very fast simulated annealing, a nonlinear global search method, is used to minimize the misfit function. We demonstrate the effectiveness of our method with synthetic data and field data from Cranfield site used for CO2 sequestration studies.
An inverse design method for 2D airfoil
NASA Astrophysics Data System (ADS)
Liang, Zhi-Yong; Cui, Peng; Zhang, Gen-Bao
2010-03-01
The computational method for aerodynamic design of aircraft is applied more universally than before, in which the design of an airfoil is a hot problem. The forward problem is discussed by most relative papers, but inverse method is more useful in practical designs. In this paper, the inverse design of 2D airfoil was investigated. A finite element method based on the variational principle was used for carrying out. Through the simulation, it was shown that the method was fit for the design.
Waveform Inversion of Synthetic Ocean Models in the Laplace Domain
NASA Astrophysics Data System (ADS)
Rosado, H.; Blacic, T. M.; Jun, H.; Shin, C.
2014-12-01
In seismic oceanography, the processed images show where small temperature changes (as little as 0.03°C) occur, although they do not give absolute temperatures. To get a 2-D temperature map, the data must be inverted for sound speed, which is then converted to temperature using equations of state. Full waveform inversion requires a starting model that is iteratively updated until the residuals converge. Global search algorithms such as Genetic Algorithm do not require a starting model close to the true model, but are computationally exhausting. Local search inversion is less expensive, but requires a reasonably accurate starting model. Unfortunately, most marine seismic data has little associated hydrographic data and so it is difficult to create starting models close enough to the true model for convergence throughout the target area. In addition, the band-limited nature of seismic data makes it inherently challenging to extract the long wavelength sound speed trend directly from seismic data. Laplace domain inversion (LDI) developed by Changsoo Shin and colleagues requires only a rudimentary starting model to produce smooth background sound speed models without requiring prior information about the medium. It works by transforming input data to the Laplace domain, and then examining the zero frequency component of the damped wavefield to extract a smooth sound speed model - basically, removing higher frequency fluctuations to expose background trends. This ability to use frequencies below those effectively propagated by the seismic source is what enables LDI to produce the smooth background trend from the data. We applied LDI to five synthetic data sets based on simplified models of oceanographic features. Using LDI, we were able to recover smoothed versions of our synthetic models, showing the viability of the method for creating sound speed profiles suitable for use as starting models for other methods of inversion that output more detailed models.
Determination of transient fluid temperature using the inverse method
NASA Astrophysics Data System (ADS)
Jaremkiewicz, Magdalena
2014-03-01
This paper proposes an inverse method to obtain accurate measurements of the transient temperature of fluid. A method for unit step and linear rise of temperature is presented. For this purpose, the thermometer housing is modelled as a full cylindrical element (with no inner hole), divided into four control volumes. Using the control volume method, the heat balance equations can be written for each of the nodes for each of the control volumes. Thus, for a known temperature in the middle of the cylindrical element, the distribution of temperature in three nodes and heat flux at the outer surface were obtained. For a known value of the heat transfer coefficient the temperature of the fluid can be calculated using the boundary condition. Additionally, results of experimental research are presented. The research was carried out during the start-up of an experimental installation, which comprises: a steam generator unit, an installation for boiler feed water treatment, a tray-type deaerator, a blow down flashvessel for heat recovery, a steam pressure reduction station, a boiler control system and a steam header made of martensitic high alloy P91 steel. Based on temperature measurements made in the steam header using the inverse method, accurate measurements of the transient temperature of the steam were obtained. The results of the calculations are compared with the real temperature of the steam, which can be determined for a known pressure and enthalpy.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; Tartakovsky, Daniel M.
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less
Models with inverse-square exchange
NASA Astrophysics Data System (ADS)
Ha, Z. N. C.; Haldane, F. D. M.
1992-10-01
A one-dimensional quantum N-body system of either fermions or bosons with SU(n) ``spins'' (or colors in particle physics language) interacting via inverse-square exchange is presented in this paper. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product-type wave function. The class of states we construct in this paper corresponds to the ground state and the low-energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e., the charge, spin velocities, etc.) explicitly. The correlation exponent and the compressibility are also found. As expected, the general harmonic relation [i.e., vS=(vNvJ)1/2] is satisfied among the charge and spin velocities.
Fast 3D inversion of airborne gravity-gradiometry data using Lanczos bidiagonalization method
NASA Astrophysics Data System (ADS)
Meng, Zhaohai; Li, Fengting; Zhang, Dailei; Xu, Xuechun; Huang, Danian
2016-09-01
We developed a new fast inversion method for to process and interpret airborne gravity gradiometry data, which was based on Lanczos bidiagonalization algorithm. Here, we describe the application of this new 3D gravity gradiometry inversion method to recover a subsurface density distribution model from the airborne measured gravity gradiometry anomalies. For this purpose, the survey area is divided into a large number of rectangular cells with each cell possessing a constant unknown density. It is well known that the solution of large linear gravity gradiometry is an ill-posed problem since using the smoothest inversion method is considerably time consuming. We demonstrate that the Lanczos bidiagonalization method can be an appropriate algorithm to solve a Tikhonov solver time cost function for resolving the large equations within a short time. Lanczos bidiagonalization is designed to make the very large gravity gradiometry forward modeling matrices to become low-rank, which will considerably reduce the running time of the inversion method. We also use a weighted generalized cross validation method to choose the appropriate Tikhonov parameter to improve inversion results. The inversion incorporates a model norm that allows us to attain the smoothing and depth of the solution; in addition, the model norm counteracts the natural decay of the kernels, which concentrate at shallow depths. The method is applied on noise-contaminated synthetic gravity gradiometry data to demonstrate its suitability for large 3D gravity gradiometry data inversion. The airborne gravity gradiometry data from the Vinton Salt Dome, USE, were considered as a case study. The validity of the new method on real data is discussed with reference to the Vinton Dome inversion result. The intermediate density values in the constructed model coincide well with previous results and geological information. This demonstrates the validity of the gravity gradiometry inversion method.
A Higher Order Iterative Method for Computing the Drazin Inverse
Soleymani, F.; Stanimirović, Predrag S.
2013-01-01
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747
Inverse problems of ultrasound tomography in models with attenuation
NASA Astrophysics Data System (ADS)
Goncharsky, Alexander V.; Romanov, Sergey Y.
2014-04-01
We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.
Inverse problems of ultrasound tomography in models with attenuation.
Goncharsky, Alexander V; Romanov, Sergey Y
2014-04-21
We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer. PMID:24694653
Inverse problems of ultrasound tomography in models with attenuation.
Goncharsky, Alexander V; Romanov, Sergey Y
2014-04-21
We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.
NASA Astrophysics Data System (ADS)
Jiang, Mingfeng; Xia, Ling; Shou, Guofa; Tang, Min
2007-03-01
Computing epicardial potentials from body surface potentials constitutes one form of ill-posed inverse problem of electrocardiography (ECG). To solve this ECG inverse problem, the Tikhonov regularization and truncated singular-value decomposition (TSVD) methods have been commonly used to overcome the ill-posed property by imposing constraints on the magnitudes or derivatives of the computed epicardial potentials. Such direct regularization methods, however, are impractical when the transfer matrix is large. The least-squares QR (LSQR) method, one of the iterative regularization methods based on Lanczos bidiagonalization and QR factorization, has been shown to be numerically more reliable in various circumstances than the other methods considered. This LSQR method, however, to our knowledge, has not been introduced and investigated for the ECG inverse problem. In this paper, the regularization properties of the Krylov subspace iterative method of LSQR for solving the ECG inverse problem were investigated. Due to the 'semi-convergence' property of the LSQR method, the L-curve method was used to determine the stopping iteration number. The performance of the LSQR method for solving the ECG inverse problem was also evaluated based on a realistic heart-torso model simulation protocol. The results show that the inverse solutions recovered by the LSQR method were more accurate than those recovered by the Tikhonov and TSVD methods. In addition, by combing the LSQR with genetic algorithms (GA), the performance can be improved further. It suggests that their combination may provide a good scheme for solving the ECG inverse problem.
Simple method for the synthesis of inverse patchy colloids
NASA Astrophysics Data System (ADS)
van Oostrum, P. D. J.; Hejazifar, M.; Niedermayer, C.; Reimhult, E.
2015-06-01
Inverse patchy colloids (IPC's) have recently been introduced as a conceptually simple model to study the phase-behavior of heterogeneously charged units. This class of patchy particles is referred to as inverse to highlight that the patches repel each other in contrast to the attractive interactions of conventional patches. IPCs demonstrate a complex interplay between attractions and repulsions that depend on their patch size and charge, their relative orientations as well as on charge of the substrate below; the resulting wide array of different types of aggregates that can be formed motivates their fabrication and use as model system. We present a novel method that does not rely on clean-room facilities and that is easily scalable to modify the surface of colloidal particles to create two polar regions with the opposite charge with respect to that of the equatorial region. The patch size is characterized by electron microscopy and fluorescently labeled to facilitate using confocal microscopy to study their phase behavior. We show that the pH can be used to tune the charges of the IPCs thus offering a tool to steer the self assembly.
Simple method for the synthesis of inverse patchy colloids.
van Oostrum, P D J; Hejazifar, M; Niedermayer, C; Reimhult, E
2015-06-17
Inverse patchy colloids (IPC's) have recently been introduced as a conceptually simple model to study the phase-behavior of heterogeneously charged units. This class of patchy particles is referred to as inverse to highlight that the patches repel each other in contrast to the attractive interactions of conventional patches. IPCs demonstrate a complex interplay between attractions and repulsions that depend on their patch size and charge, their relative orientations as well as on charge of the substrate below; the resulting wide array of different types of aggregates that can be formed motivates their fabrication and use as model system. We present a novel method that does not rely on clean-room facilities and that is easily scalable to modify the surface of colloidal particles to create two polar regions with the opposite charge with respect to that of the equatorial region. The patch size is characterized by electron microscopy and fluorescently labeled to facilitate using confocal microscopy to study their phase behavior. We show that the pH can be used to tune the charges of the IPCs thus offering a tool to steer the self assembly.
ERIC Educational Resources Information Center
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
Methods for solving ill-posed inverse problems
NASA Astrophysics Data System (ADS)
Alifanov, O. M.
1983-11-01
Various approaches to the solution of inverse problems of heat conduction are reviewed, including direct analytical and numerical methods, the method of iterative regularization, and algebraic and numerical methods regularized in accordance with the variational principle. The method of iterative regularization is shown to be the most versatile of the above approaches. The basic principles of this method are briefly examined, and methods are proposed for computing the gradients of discrepancies. An approach is proposed to the iterative solution of inverse problems with a specified order of smoothness.
Gradient-based methods for full waveform inversion
NASA Astrophysics Data System (ADS)
Métivier, L.; Brossier, R.; Operto, S.; Virieux, J.
2012-12-01
The minimization of the distance between recorded and synthetic seismograms (namely misfit function) for the reconstruction of subsurface velocity models leads to large-scale non-linear inverse problems. These problems are generally solved using gradient-based methods, such as the (preconditioned) steepest-descent method or the (preconditioned) non-linear conjugate gradient method, Gauss-Newton approach and more recently the l-BFGS quasi-Newton method. Except the Gauss-Newton approach, these methods only require the capability of computing (and storing) the gradient of the misfit function, efficiently performed through the adjoint state method, leading to the resolution of one forward problem and one adjoint problem per source. However, the inverse Hessian operator could be considered for compensating from target illumination variations coming from acquisition geometry and medium velocity variations. This operator acts as a filter in the model space when velocity is updated. For example, the l-BFGS method estimates an approximation of the inverse of the Hessian from gradients of previous iterations without no significant extra computational costs. Gauss-Newton approximation of the Hessian not only adds an extra computational cost but also neglects multi-scattering effects. Exact Newton methods will consider multi-scattering effects and may be more accurate than the l-BFGS approximation. For such investigation, we shall introduce the second-order adjoint formulation for the efficient estimation of the product of the Hessian operator and any vector in the model space. Using this product, we may update the velocity model through the resolution of the linear system associated with the computation of the Newton descent direction using a "matrix free" iterative linear solver such as the conjugate gradient method. This implementation could be performed for Newton approaches (and also the Gauss-Newton approximation) and requires an additional state and adjoint
Inverse Modelling of the Kawerau Geothermal Reservoir, NZ
White, S.P.
1995-01-01
In this paper we describe an existing model of the Kawerau geothermal field and attempts to improve this model using inverse modeling techniques. A match of model results to natural state temperatures and pressures at three reference depths are presented. These are used to form and ''objective function'' to be minimized by inverse modeling.
A fast and low-loss 3-D magnetotelluric inversion method with parallel structure
NASA Astrophysics Data System (ADS)
Zhang, K.; Zhang, L.
2013-12-01
The 2D assumption is valid in some cases of interpretation, the approximation does not work in most cases, especially in areas with complex geo-electrical structure. A number of 3D magentotelluric inversion methods has been proposed, including RRI, CG, QA, NLCG. Each of those methods has its own advantages and disadvantages. However, as the 3D dataset and mesh grid require greater computer memory and calculation time than 2D methods, the efficiency of the inversion scheme become a key concern of 3D inversions. We chose NLCG as the optimization method for inversion. A parameter matrix related with the current resisitivity model and data error is proposed to approximate the Hessian matrix. So four forward calculation can be avoided each iteration. In addition, OPENMP parallel API is utilized to establish an effecient parallel inversion structure based on frequency to reduce computation time. And both synthetic and field data are used to test the efficiency of the inversion and the preconditioning method. The model consists of four square prisms residing in a halfspace. The total computation time of invertion is 706s (use one PC). Fiugre 1 shows the inversion result. The abnormal bodies can be distinguished clearly. Field data from the NIHE dataset in China is used to verify the reliability and efficiency of the 3D inversion method. The total computation time is about 25 minutes after 60 iterations on one PC. Totally, four electrical layers can be corresponded to the four stratum in 3D AMT inversion model, and the faults can be seen clearly. In addition, we can get more information about fault and alteration interface from constrained inversion result. Finally, the inversion method is very fast and low-loss, so it can be used in modern PC (need only one PC) with few hardware constraints. (a): initial model; (b): inversion depth slices (1-4km); (c): fitting error (a): AMT 3D slice; (b): CSAMT 2D model; (c): TEM 1D model; (d): SIP 2D model; (e) AMT 3D constrained
Noncoherent matrix inversion methods for Scansar processing
NASA Astrophysics Data System (ADS)
Dendal, Didier
1995-11-01
The aim of this work is to develop some algebraic reconstruction techniques for low resolution power SAR imagery, as in the Scansar or QUICKLOOK imaging modes. The traditional reconstruction algorithms are indeed not well fit to low resolution power purposes, since Fourier constraints impose a computational load of the same order as the one of the usual SAR azimuthal resolution. Furthermore, the range migration balancing is superfluous, as it does not cover a tenth of the resolution cell in the less favorable situations. There are several possibilities for using matrices in the azimuthal direction. The most direct alternative leads to a matrix inversion. Unfortunately, the numerical conditioning of the problem is far from being excellent, since each line of the matrix is an image of the antenna radiating pattern with a shift between two successive lines corresponding to the distance covered by the SAR between two pulses transmission (a few meters for satellite ERS1). We'll show how it is possible to turn a very ill conditioned problem into an equivalent one, but without any divergence risk, by a technique of successive decimation by two (resolution power increased by two at each step). This technique leads to very small square matrices (two lines and two columns), the good numeric conditioning of which is certified by a well-known theorem of numerical analysis. The convergence rate of the process depends on the circumstances (mainly the distance between two impulses transmissions) and on the required accuracy, but five or six iterations already give excellent results. The process is applicable at four or five levels (number of decimations) which corresponds to initial matrices of 16 by 16 or 32 by 32. The azimuth processing is performed on the basis of the projection function concept (tomographic analogy of radar principles). This integrated information results from classical coherent range compression. The aperture synthesis is obtained by non-coherent processing
Inverse models: A necessary next step in ground-water modeling
Poeter, E.P.; Hill, M.C.
1997-01-01
Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.
Updated Results for the Wake Vortex Inverse Model
NASA Technical Reports Server (NTRS)
Robins, Robert E.; Lai, David Y.; Delisi, Donald P.; Mellman, George R.
2008-01-01
NorthWest Research Associates (NWRA) has developed an Inverse Model for inverting aircraft wake vortex data. The objective of the inverse modeling is to obtain estimates of the vortex circulation decay and crosswind vertical profiles, using time history measurements of the lateral and vertical position of aircraft vortices. The Inverse Model performs iterative forward model runs using estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Iterations are performed until a user-defined criterion is satisfied. Outputs from an Inverse Model run are the best estimates of the time history of the vortex circulation derived from the observed data, the vertical crosswind profile, and several vortex parameters. The forward model, named SHRAPA, used in this inverse modeling is a modified version of the Shear-APA model, and it is described in Section 2 of this document. Details of the Inverse Model are presented in Section 3. The Inverse Model was applied to lidar-observed vortex data at three airports: FAA acquired data from San Francisco International Airport (SFO) and Denver International Airport (DEN), and NASA acquired data from Memphis International Airport (MEM). The results are compared with observed data. This Inverse Model validation is documented in Section 4. A summary is given in Section 5. A user's guide for the inverse wake vortex model is presented in a separate NorthWest Research Associates technical report (Lai and Delisi, 2007a).
Application of Carbonate Reservoir using waveform inversion and reverse-time migration methods
NASA Astrophysics Data System (ADS)
Kim, W.; Kim, H.; Min, D.; Keehm, Y.
2011-12-01
Recent exploration targets of oil and gas resources are deeper and more complicated subsurface structures, and carbonate reservoirs have become one of the attractive and challenging targets in seismic exploration. To increase the rate of success in oil and gas exploration, it is required to delineate detailed subsurface structures. Accordingly, migration method is more important factor in seismic data processing for the delineation. Seismic migration method has a long history, and there have been developed lots of migration techniques. Among them, reverse-time migration is promising, because it can provide reliable images for the complicated model even in the case of significant velocity contrasts in the model. The reliability of seismic migration images is dependent on the subsurface velocity models, which can be extracted in several ways. These days, geophysicists try to obtain velocity models through seismic full waveform inversion. Since Lailly (1983) and Tarantola (1984) proposed that the adjoint state of wave equations can be used in waveform inversion, the back-propagation techniques used in reverse-time migration have been used in waveform inversion, which accelerated the development of waveform inversion. In this study, we applied acoustic waveform inversion and reverse-time migration methods to carbonate reservoir models with various reservoir thicknesses to examine the feasibility of the methods in delineating carbonate reservoir models. We first extracted subsurface material properties from acoustic waveform inversion, and then applied reverse-time migration using the inverted velocities as a background model. The waveform inversion in this study used back-propagation technique, and conjugate gradient method was used in optimization. The inversion was performed using the frequency-selection strategy. Finally waveform inversion results showed that carbonate reservoir models are clearly inverted by waveform inversion and migration images based on the
Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan
2016-06-01
In this paper, we investigate the full-waveform inversion in the frequency domain. We first test the inversion ability of three numerical optimization methods, i.e., the steepest-descent method, the Newton-CG method and the Gauss- Newton method, for a simple model. The results show that the Gauss-Newton method performs well and efficiently. Then numerical computations for a benchmark model named Marmousi model by the Gauss-Newton method are implemented. Parallel algorithm based on message passing interface (MPI) is applied as the inversion is a typical large-scale computational problem. Numerical computations show that the Gauss-Newton method has good ability to reconstruct the complex model.
Comparison of optimal design methods in inverse problems
NASA Astrophysics Data System (ADS)
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Estimating surface acoustic impedance with the inverse method.
Piechowicz, Janusz
2011-01-01
Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics. PMID:21939599
Computer modeling of inversion layer MOS solar cells and arrays
NASA Technical Reports Server (NTRS)
Ho, Fat Duen
1991-01-01
A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.
Homogenization method based on the inverse problem
Tota, A.; Makai, M.
2013-07-01
We present a method for deriving homogeneous multi-group cross sections to replace a heterogeneous region's multi-group cross sections; providing that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is developed using diffusion approximation to the neutron transport equation in a symmetrical slab geometry. Assuming that the boundary fluxes are given, two response matrices (RMs) can be defined. The first derives the boundary current from the boundary flux, the second derives the flux integral over the region from the boundary flux. Assuming that these RMs are known, we present a formula which reconstructs the multi-group cross-section matrix and the diffusion coefficients from the RMs of a homogeneous slab. Applying this formula to the RMs of a slab with multiple homogeneous regions yields a homogenization method; which produce such homogenized multi-group cross sections and homogenized diffusion coefficients, that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is based on the determination of the eigenvalues and the eigenvectors of the RMs. We reproduce the four-group cross section matrix and the diffusion constants from the RMs in numerical examples. We give conditions for replacing a heterogeneous region by a homogeneous one so that the boundary current and the region-averaged flux are preserved for a given boundary flux. (authors)
Inverse Modeling of Groundwater Flow for a Fractured Confined Aquifer
NASA Astrophysics Data System (ADS)
Zhang, Y.; Wang, D.
2013-12-01
A two-dimensional inverse method is developed to simultaneously estimate steady-state hydraulic conductivities, state variables, and boundary conditions (BC) for a fractured confined aquifer. Computation experiments were performed with five fractured models where each model is driven by dominantly lateral flow (true BC) through both fractures (Kf) and matrix (Km). From each model, observation data including hydraulic heads and Darcy fluxes were sampled without imposing measurement errors. These data were provided to inversion to estimate Kf and the unknown model BC. For the first 4 models, the same sampling data density was used, while Kf/Km ratio is fixed at 10. The 1st model contains a single vertical fracture, and the error of the estimated Kf is almost 0. The 2nd model contains a single horizontal fracture, and the error of the estimated Kf is 4.6%. The 3rd model contains a vertical and a horizontal fracture, and the error is 5.3%. The 4th model is same as the third, except that the fracture volume is 25 times greater, and the error is 0.70%. In this model, the highest BC estimation error occurred at the domain corners, where the inversion extrapolation error is the greatest (reduction of this error will be investigated in the future with local grid refinement and increased data density). The 5th model contains a set of diagonal fractures, two of which run from the left bottom corner to the right top corner and the other one runs from the left top corner to the right bottom corner. For this model, under a given data density, increasing Kf/Km (10 to 1,000,000) was tested. Kf estimation is found not to be sensitive to this variability - the largest Kf error is only 5.27%. For the same model, at Kf/Km =10, local sensitivity analysis using 1 percent scaled sensitivity (1ss) suggests that observed heads at different locations are important for estimating different parameters. A global inverse sensitivity analysis was then performed by increasing the number of the
The SOLA method for helioseismic inversion
NASA Astrophysics Data System (ADS)
Pijpers, F. P.; Thompson, M. J.
1994-01-01
The Subtractive Optimally Localized Averages (SOLA) method is a versatile and efficient technique for inverting helioseismic data. The SOLA method is based on explicit construction of Backus-Gilbert averaging kernels, but whereas the more usual formulations of the optimally localized averages (OLA) method use a multiplicative penalty function to localize the kernels, the distinctive idea of SOLA is that one specifies a desired target form for the kernels and then minimizes the integrated squared difference between the kernels and the target form. This allows great versatility in the choice of target form, and furthermore SOLA has the significant advantage of being computationally more efficient than the usual OLA formulations. A Gaussian target function is a useful choice, and we use the example of determining the Sun's internal rotation to explore how the parameter values (such as the Gaussian's width) should best be chosen. Some alternatives to using a Gaussian function as target function are discussed and applied to artificial data in a blind experiment. In particular we show that it is possible to invert directly for the gradient of the rotation. This may be of interest if there are localized large gradients in the rotation rate.
Forward and inverse modeling for jovian seismology
NASA Astrophysics Data System (ADS)
Jackiewicz, Jason; Nettelmann, Nadine; Marley, Mark; Fortney, Jonathan
2012-08-01
Jupiter is expected to pulsate in a spectrum of acoustic modes and recent re-analysis of a spectroscopic time series has identified a regular pattern in the spacing of the frequencies (Gaulme, P., Schmider, F.-X., Gay, J., Guillot, T., Jacob, C. [2011]. Astron. Astrophys. 531, A104). This exciting result can provide constraints on gross jovian properties and warrants a more in-depth theoretical study of the seismic structure of Jupiter. With current instrumentation, such as the SYMPA instrument (Schmider, F.X. [2007]. Astron. Astrophys. 474, 1073-1080) used for the Gaulme et al. (Gaulme, P., Schmider, F.-X., Gay, J., Guillot, T., Jacob, C. [2011]. Astron. Astrophys. 531, A104) analysis, we assume that, at minimum, a set of global frequencies extending up to angular degree ℓ=25 could be observed. In order to identify which modes would best constraining models of Jupiter's interior and thus help motivate the next generation of observations, we explore the sensitivity of derived parameters to this mode set. Three different models of the jovian interior are computed and the theoretical pulsation spectrum from these models for ℓ⩽25 is obtained. We compute sensitivity kernels and perform linear inversions to infer details of the expected discontinuities in the profiles in the jovian interior. We find that the amplitude of the sound-speed jump of a few percent in the inner/outer envelope boundary seen in two of the applied models should be reasonably inferred with these particular modes. Near the core boundary where models predict large density discontinuities, the location of such features can be accurately measured, while their amplitudes have more uncertainty. These results suggest that this mode set would be sufficient to infer the radial location and strength of expected discontinuities in Jupiter's interior, and place strong constraints on the core size and mass. We encourage new observations to detect these jovian oscillations.
INVERSE MODEL ESTIMATION AND EVALUATION OF SEASONAL NH 3 EMISSIONS
The presentation topic is inverse modeling for estimate and evaluation of emissions. The case study presented is the need for seasonal estimates of NH_{3} emissions for air quality modeling. The inverse modeling application approach is first described, and then the NH
Full waveform inverse modeling of GPR Data of layered media
NASA Astrophysics Data System (ADS)
Slob, E.
2012-04-01
Geophysical methods are increasingly being used to provide quantitative information of layered structures. Traditionally, geophysical data are inverted with the aid of a non-linear inverse modeling package. Full waveform inversion is then implemented by minimizing some penalty or objective function. The objective function is usually the measured data subtracted by the modeled data and the modeled data is modified to fit the measured data. Because the data is not touched, this is called a model-driven, or data-fitting problem. The objective function is non-quadratic making data fitting a hard task, generally requiring many iterations. Non-uniqueness of the solution leads to the question what the model quality is even when the data fit is very good. In this study, I explore an alternative method by finding a filter that allows for full waveform inverse modeling using reflection data only. The filter does not require model information and hence is completely different than solving a data fitting problem. The approach taken here creates the inverse model in two steps. First a true amplitude migration image of primary reflections is found directly from the data through an iterative procedure that converges very fast. Hence, it is a data-driven method. This image can be constructed for any point in space independently and therefore does not suffer from error propagation. The result of this step is a unique solution, but of course it is exact in terms of reflection amplitude as a function of one-way travel time. The second step is to find the electric permittivity from the image as a function of depth by assuming no magnetic contrasts occur in the layered model. Here the accuracy of the permittivity of the layer where the data is measured is crucial. Possible errors in this number lead to error propagation in the resulting permittivity profile as a function of depth. The present model is shown to work for one-dimensional media that do not dissipate energy. Extending the
A time domain sampling method for inverse acoustic scattering problems
NASA Astrophysics Data System (ADS)
Guo, Yukun; Hömberg, Dietmar; Hu, Guanghui; Li, Jingzhi; Liu, Hongyu
2016-06-01
This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally "direct" involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations.
Methodes entropiques appliquees au probleme inverse en magnetoencephalographie
NASA Astrophysics Data System (ADS)
Lapalme, Ervig
2005-07-01
This thesis is devoted to biomagnetic source localization using magnetoencephalography. This problem is known to have an infinite number of solutions. So methods are required to take into account anatomical and functional information on the solution. The work presented in this thesis uses the maximum entropy on the mean method to constrain the solution. This method originates from statistical mechanics and information theory. This thesis is divided into two main parts containing three chapters each. The first part reviews the magnetoencephalographic inverse problem: the theory needed to understand its context and the hypotheses for simplifying the problem. In the last chapter of this first part, the maximum entropy on the mean method is presented: its origins are explained and also how it is applied to our problem. The second part is the original work of this thesis presenting three articles; one of them already published and two others submitted for publication. In the first article, a biomagnetic source model is developed and applied in a theoretical con text but still demonstrating the efficiency of the method. In the second article, we go one step further towards a realistic modelization of the cerebral activation. The main priors are estimated using the magnetoencephalographic data. This method proved to be very efficient in realistic simulations. In the third article, the previous method is extended to deal with time signals thus exploiting the excellent time resolution offered by magnetoencephalography. Compared with our previous work, the temporal method is applied to real magnetoencephalographic data coming from a somatotopy experience and results agree with previous physiological knowledge about this kind of cognitive process.
NASA Astrophysics Data System (ADS)
Liu, B.; Li, S. C.; Nie, L. C.; Wang, J.; L, X.; Zhang, Q. S.
2012-12-01
Traditional inversion method is the most commonly used procedure for three-dimensional (3D) resistivity inversion, which usually takes the linearization of the problem and accomplish it by iterations. However, its accuracy is often dependent on the initial model, which can make the inversion trapped in local optima, even cause a bad result. Non-linear method is a feasible way to eliminate the dependence on the initial model. However, for large problems such as 3D resistivity inversion with inversion parameters exceeding a thousand, main challenges of non-linear method are premature and quite low search efficiency. To deal with these problems, we present an improved Genetic Algorithm (GA) method. In the improved GA method, smooth constraint and inequality constraint are both applied on the object function, by which the degree of non-uniqueness and ill-conditioning is decreased. Some measures are adopted from others by reference to maintain the diversity and stability of GA, e.g. real-coded method, and the adaptive adjustment of crossover and mutation probabilities. Then a generation method of approximately uniform initial population is proposed in this paper, with which uniformly distributed initial generation can be produced and the dependence on initial model can be eliminated. Further, a mutation direction control method is presented based on the joint algorithm, in which the linearization method is embedded in GA. The update vector produced by linearization method is used as mutation increment to maintain a better search direction compared with the traditional GA with non-controlled mutation operation. By this method, the mutation direction is optimized and the search efficiency is improved greatly. The performance of improved GA is evaluated by comparing with traditional inversion results in synthetic example or with drilling columnar sections in practical example. The synthetic and practical examples illustrate that with the improved GA method we can eliminate
Point source moment tensor inversion through a Bayesian hierarchical model
NASA Astrophysics Data System (ADS)
Mustać, Marija; Tkalčić, Hrvoje
2016-01-01
Characterization of seismic sources is an important aspect of seismology. Parameter uncertainties in such inversions are essential for estimating solution robustness, but are rarely available. We have developed a non-linear moment tensor inversion method in a probabilistic Bayesian framework that also accounts for noise in the data. The method is designed for point source inversion using waveform data of moderate-size earthquakes and explosions at regional distances. This probabilistic approach results in an ensemble of models, whose density is proportional to parameter probability distribution and quantifies parameter uncertainties. Furthermore, we invert for noise in the data, allowing it to determine the model complexity. We implement an empirical noise covariance matrix that accounts for interdependence of observational errors present in waveform data. After we demonstrate the feasibility of the approach on synthetic data, we apply it to a Long Valley Caldera, CA, earthquake with a well-documented anomalous (non-double-couple) radiation from previous studies. We confirm a statistically significant isotropic component in the source without a trade-off with the compensated linear vector dipoles component.
Linearized Functional Minimization for Inverse Modeling
Wohlberg, Brendt; Tartakovsky, Daniel M.; Dentz, Marco
2012-06-21
Heterogeneous aquifers typically consist of multiple lithofacies, whose spatial arrangement significantly affects flow and transport. The estimation of these lithofacies is complicated by the scarcity of data and by the lack of a clear correlation between identifiable geologic indicators and attributes. We introduce a new inverse-modeling approach to estimate both the spatial extent of hydrofacies and their properties from sparse measurements of hydraulic conductivity and hydraulic head. Our approach is to minimize a functional defined on the vectors of values of hydraulic conductivity and hydraulic head fields defined on regular grids at a user-determined resolution. This functional is constructed to (i) enforce the relationship between conductivity and heads provided by the groundwater flow equation, (ii) penalize deviations of the reconstructed fields from measurements where they are available, and (iii) penalize reconstructed fields that are not piece-wise smooth. We develop an iterative solver for this functional that exploits a local linearization of the mapping from conductivity to head. This approach provides a computationally efficient algorithm that rapidly converges to a solution. A series of numerical experiments demonstrates the robustness of our approach.
Tensile earthquakes: Theory, modeling, and inversion
NASA Astrophysics Data System (ADS)
VavryčUk, VáClav
2011-12-01
Tensile earthquakes are earthquakes which combine shear and tensile motions on a fault during the rupture process. The geometry of faulting is described by four angles: strike, dip, rake, and slope. The strike, dip, and rake define the orientation of the fault normal and the tangential component of the dislocation vector along the fault. The slope defines the deviation of the dislocation vector from the fault. The strike, dip, and rake are determined ambiguously from moment tensors similarly as for shear sources. The slope is determined uniquely and has the same value for both complementary solutions. The moment tensors of tensile earthquakes are characterized by significant non-double-couple (non-DC) components comprising both the compensated linear vector dipole (CLVD) and the isotropic (ISO) components. In isotropic media, the CLVD and ISO percentages should have the same sign and should depend linearly for earthquakes that occurred in the same focal area. The direction of the linear function between the CLVD and ISO defines the velocity ratio νP/νS in the focal area. The parameters of tensile earthquakes can be retrieved from their moment tensors. The procedure yields the angles describing the geometry of faulting as well as the νP/νS ratio in the focal area. The accuracy of the νP/νS ratio can be increased if a set of moment tensors of earthquakes that occurred in the same focal area is analyzed. The calculation of the νP/νS ratio from moment tensors is an auspicious method which might find applications in tomography of the focal area or in monitoring fluid flow during seismic activity. If the νP/νS ratio is found and well constrained, the parameters of tensile earthquakes can be inverted directly from observed data using a constrained nonlinear inversion. In this inversion, the parameter space can be limited by fixing the νP/νS ratio or forcing the νP/νS ratio to lie within some physically reasonable limits.
Influence of Raman scattering on ocean color inversion models.
Westberry, Toby K; Boss, Emmanuel; Lee, Zhongping
2013-08-01
Raman scattering can be a significant contributor to the emergent radiance spectrum from the surface ocean. Here, we present an analytical approach to directly estimate the Raman contribution to remote sensing reflectance, and evaluate its effects on optical properties estimated from two common semianalytical inversion models. For application of the method to ocean color remote sensing, spectral irradiance products in the ultraviolet from the OMI instrument are merged with MODerate-resolution Imaging Spectroradiometer (MODIS) data in the visible. The resulting global fields of Raman-corrected optical properties show significant differences from standard retrievals, particularly for the particulate backscattering coefficient, b(bp), where average errors in clear ocean waters are ~50%. Given the interest in transforming b(bp) into biogeochemical quantities, Raman scattering must be accounted for in semianalytical inversion schemes. PMID:23913078
a method of gravity and seismic sequential inversion and its GPU implementation
NASA Astrophysics Data System (ADS)
Liu, G.; Meng, X.
2011-12-01
In this abstract, we introduce a gravity and seismic sequential inversion method to invert for density and velocity together. For the gravity inversion, we use an iterative method based on correlation imaging algorithm; for the seismic inversion, we use the full waveform inversion. The link between the density and velocity is an empirical formula called Gardner equation, for large volumes of data, we use the GPU to accelerate the computation. For the gravity inversion method , we introduce a method based on correlation imaging algorithm,it is also a interative method, first we calculate the correlation imaging of the observed gravity anomaly, it is some value between -1 and +1, then we multiply this value with a little density ,this value become the initial density model. We get a forward reuslt with this initial model and also calculate the correaltion imaging of the misfit of observed data and the forward data, also multiply the correaltion imaging result a little density and add it to the initial model, then do the same procedure above , at last ,we can get a inversion density model. For the seismic inveron method ,we use a mothod base on the linearity of acoustic wave equation written in the frequency domain,with a intial velociy model, we can get a good velocity result. In the sequential inversion of gravity and seismic , we need a link formula to convert between density and velocity ,in our method , we use the Gardner equation. Driven by the insatiable market demand for real time, high-definition 3D images, the programmable NVIDIA Graphic Processing Unit (GPU) as co-processor of CPU has been developed for high performance computing. Compute Unified Device Architecture (CUDA) is a parallel programming model and software environment provided by NVIDIA designed to overcome the challenge of using traditional general purpose GPU while maintaining a low learn curve for programmers familiar with standard programming languages such as C. In our inversion processing
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
ERIC Educational Resources Information Center
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
TOPEX/POSEIDON tides estimated using a global inverse model
NASA Technical Reports Server (NTRS)
Egbert, Gary D.; Bennett, Andrew F.; Foreman, Michael G. G.
1994-01-01
Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better
Solving inverse problems of identification type by optimal control methods
Lenhart, S.; Protopopescu, V.; Jiongmin Yong
1997-06-01
Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations.
Direct inversion methods for spectral amplitude modulation of femtosecond pulses.
Delgado-Aguillón, Jesús; Garduño-Mejía, Jesús; López-Téllez, Juan Manuel; Bruce, Neil C; Rosete-Aguilar, Martha; Román-Moreno, Carlos Jesús; Ortega-Martínez, Roberto
2014-04-01
In the present work, we applied an amplitude-spatial light modulator to shape the spectral amplitude of femtosecond pulses in a single step, without an iterative algorithm, by using an inversion method defined as the generalized retardance function. Additionally, we also present a single step method to shape the intensity profile defined as the influence matrix. Numerical and experimental results are presented for both methods.
Indium oxide inverse opal films synthesized by structure replication method
NASA Astrophysics Data System (ADS)
Amrehn, Sabrina; Berghoff, Daniel; Nikitin, Andreas; Reichelt, Matthias; Wu, Xia; Meier, Torsten; Wagner, Thorsten
2016-04-01
We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.
Computational methods for inverse problems in geophysics: inversion of travel time observations
Pereyra, V.; Keller, H.B.; Lee, W.H.K.
1980-01-01
General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.
Dispersion analysis with inverse dielectric function modelling.
Mayerhöfer, Thomas G; Ivanovski, Vladimir; Popp, Jürgen
2016-11-01
We investigate how dispersion analysis can profit from the use of a Lorentz-type description of the inverse dielectric function. In particular at higher angles of incidence, reflectance spectra using p-polarized light are dominated by bands from modes that have their transition moments perpendicular to the surface. Accordingly, the spectra increasingly resemble inverse dielectric functions. A corresponding description can therefore eliminate the complex dependencies of the dispersion parameters, allow their determination and facilitate a more accurate description of the optical properties of single crystals.
Dispersion analysis with inverse dielectric function modelling
NASA Astrophysics Data System (ADS)
Mayerhöfer, Thomas G.; Ivanovski, Vladimir; Popp, Jürgen
2016-11-01
We investigate how dispersion analysis can profit from the use of a Lorentz-type description of the inverse dielectric function. In particular at higher angles of incidence, reflectance spectra using p-polarized light are dominated by bands from modes that have their transition moments perpendicular to the surface. Accordingly, the spectra increasingly resemble inverse dielectric functions. A corresponding description can therefore eliminate the complex dependencies of the dispersion parameters, allow their determination and facilitate a more accurate description of the optical properties of single crystals.
NASA Astrophysics Data System (ADS)
Favier, L.; Zwinger, T.; Gillet-Chaulet, F.; Durand, G.; Gagliardini, O.
2012-04-01
Ice discharge and grounding line retreat in West Antarctica have been accelerated during the last decades. One of the most striking example is Pine Island Glacier (PIG) which accelerated dramatically over the last 30 years. Such rapid changes in this part of Antarctica are due to large modifications of ice dynamics which are nevertheless poorly understood, and badly represented in numerical models, as pointed out by the IPCC fourth assessment report. Here, a 3D full-Stokes model of a marine ice sheet is used to carry out prognostic simulations of PIG over the next two centuries. The flow problem is coupled with the evolution of the upper and lower free surfaces, and the position of the grounding line is determined by solving the contact problem between the ice-shelf/ice-sheet lower surface and the bedrock. The upper and lower surfaces, and the bathymetry provided on a 1 km grid (courtesy of A. Le Brocq) are used to produce the initial geometry of the entire PIG basin. The mesh refinement is a function of the surface velocities (also provided on a 1 km grid by A. Le Brocq) Hessian matrix and the distance to the grounding line. Surface velocities are also used to infer the basal drag through the resolution of an inverse Robin problem. The initial surface is first relaxed and the results are compared to the observed current surface elevation, surface velocity and change in surface elevation. A perturbation experiment is then performed for which the whole ice-shelf is instantaneously removed. This test can be seen as a worst case scenario as all the buttressing induced by the ice shelf is lost instantaneously. The effect of the ice-shelf disintegration for the following two centuries is discussed in terms of grounding line retreat and increase in sea level.
Aerosol Models for the CALIPSO Lidar Inversion Algorithms
NASA Technical Reports Server (NTRS)
Omar, Ali H.; Winker, David M.; Won, Jae-Gwang
2003-01-01
We use measurements and models to develop aerosol models for use in the inversion algorithms for the Cloud Aerosol Lidar and Imager Pathfinder Spaceborne Observations (CALIPSO). Radiance measurements and inversions of the AErosol RObotic NETwork (AERONET1, 2) are used to group global atmospheric aerosols using optical and microphysical parameters. This study uses more than 105 records of radiance measurements, aerosol size distributions, and complex refractive indices to generate the optical properties of the aerosol at more 200 sites worldwide. These properties together with the radiance measurements are then classified using classical clustering methods to group the sites according to the type of aerosol with the greatest frequency of occurrence at each site. Six significant clusters are identified: desert dust, biomass burning, urban industrial pollution, rural background, marine, and dirty pollution. Three of these are used in the CALIPSO aerosol models to characterize desert dust, biomass burning, and polluted continental aerosols. The CALIPSO aerosol model also uses the coarse mode of desert dust and the fine mode of biomass burning to build a polluted dust model. For marine aerosol, the CALIPSO aerosol model uses measurements from the SEAS experiment 3. In addition to categorizing the aerosol types, the cluster analysis provides all the column optical and microphysical properties for each cluster.
FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the
FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems
NASA Astrophysics Data System (ADS)
Vourc'h, Eric; Rodet, Thomas
2015-11-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods
NASA Astrophysics Data System (ADS)
Zhang, Dong; Zhang, Xiaolei; Yuan, Jianzheng; Ke, Rui; Yang, Yan; Hu, Ying
2016-01-01
The Laplace-Fourier domain full waveform inversion can simultaneously restore both the long and intermediate short-wavelength information of velocity models because of its unique characteristics of complex frequencies. This approach solves the problem of conventional frequency-domain waveform inversion in which the inversion result is excessively dependent on the initial model due to the lack of low frequency information in seismic data. Nevertheless, the Laplace-Fourier domain waveform inversion requires substantial computational resources and long computation time because the inversion must be implemented on different combinations of multiple damping constants and multiple frequencies, namely, the complex frequencies, which are much more numerous than the Fourier frequencies. However, if the entire target model is computed on every complex frequency for the Laplace-Fourier domain inversion (as in the conventional frequency domain inversion), excessively redundant computation will occur. In the Laplace-Fourier domain waveform inversion, the maximum depth penetrated by the seismic wave decreases greatly due to the application of exponential damping to the seismic record, especially with use of a larger damping constant. Thus, the depth of the area effectively inverted on a complex frequency tends to be much less than the model depth. In this paper, we propose a method for quantitative estimation of the effective inversion depth in the Laplace-Fourier domain inversion based on the principle of seismic wave propagation and mathematical analysis. According to the estimated effective inversion depth, we can invert and update only the model area above the effective depth for every complex frequency without loss of accuracy in the final inversion result. Thus, redundant computation is eliminated, and the efficiency of the Laplace-Fourier domain waveform inversion can be improved. The proposed method was tested in numerical experiments. The experimental results show that
Balancing aggregation and smoothing errors in inverse models
Turner, A. J.; Jacob, D. J.
2015-06-30
Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less
Balancing aggregation and smoothing errors in inverse models
Turner, A. J.; Jacob, D. J.
2015-01-13
Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less
Kılıç, Emre Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
Propeller sheet cavitation noise source modeling and inversion
NASA Astrophysics Data System (ADS)
Lee, Keunhwa; Lee, Jaehyuk; Kim, Dongho; Kim, Kyungseop; Seong, Woojae
2014-02-01
Propeller sheet cavitation is the main contributor to high level of noise and vibration in the after body of a ship. Full measurement of the cavitation-induced hull pressure over the entire surface of the affected area is desired but not practical. Therefore, using a few measurements on the outer hull above the propeller in a cavitation tunnel, empirical or semi-empirical techniques based on physical model have been used to predict the hull-induced pressure (or hull-induced force). In this paper, with the analytic source model for sheet cavitation, a multi-parameter inversion scheme to find the positions of noise sources and their strengths is suggested. The inversion is posed as a nonlinear optimization problem, which is solved by the optimization algorithm based on the adaptive simplex simulated annealing algorithm. Then, the resulting hull pressure can be modeled with boundary element method from the inverted cavitation noise sources. The suggested approach is applied to the hull pressure data measured in a cavitation tunnel of the Samsung Heavy Industry. Two monopole sources are adequate to model the propeller sheet cavitation noise. The inverted source information is reasonable with the cavitation dynamics of the propeller and the modeled hull pressure shows good agreement with cavitation tunnel experimental data.
Inverse Problems in Complex Models and Applications to Earth Sciences
NASA Astrophysics Data System (ADS)
Bosch, M. E.
2015-12-01
The inference of the subsurface earth structure and properties requires the integration of different types of data, information and knowledge, by combined processes of analysis and synthesis. To support the process of integrating information, the regular concept of data inversion is evolving to expand its application to models with multiple inner components (properties, scales, structural parameters) that explain multiple data (geophysical survey data, well-logs, core data). The probabilistic inference methods provide the natural framework for the formulation of these problems, considering a posterior probability density function (PDF) that combines the information from a prior information PDF and the new sets of observations. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires modeling several properties and structural parameters, which relate to each other according to dependency and independency notions. Thus, conditional probabilities across model components also factorize. A common setting proceeds by structuring the model parameter space in hierarchical layers. A primary layer (e.g. lithology) conditions a secondary layer (e.g. physical medium properties), which conditions a third layer (e.g. geophysical data). In general, less structured relations within model components and data emerge from the analysis of other inverse problems. They can be described with flexibility via direct acyclic graphs, which are graphs that map dependency relations between the model components. Examples of inverse problems in complex models can be shown at various scales. At local scale, for example, the distribution of gas saturation is inferred from pre-stack seismic data and a calibrated rock-physics model. At regional scale, joint inversion of gravity and magnetic data is applied
A new inversion method for (T2, D) 2D NMR logging and fluid typing
NASA Astrophysics Data System (ADS)
Tan, Maojin; Zou, Youlong; Zhou, Cancan
2013-02-01
One-dimensional nuclear magnetic resonance (1D NMR) logging technology has some significant limitations in fluid typing. However, not only can two-dimensional nuclear magnetic resonance (2D NMR) provide some accurate porosity parameters, but it can also identify fluids more accurately than 1D NMR. In this paper, based on the relaxation mechanism of (T2, D) 2D NMR in a gradient magnetic field, a hybrid inversion method that combines least-squares-based QR decomposition (LSQR) and truncated singular value decomposition (TSVD) is examined in the 2D NMR inversion of various fluid models. The forward modeling and inversion tests are performed in detail with different acquisition parameters, such as magnetic field gradients (G) and echo spacing (TE) groups. The simulated results are discussed and described in detail, the influence of the above-mentioned observation parameters on the inversion accuracy is investigated and analyzed, and the observation parameters in multi-TE activation are optimized. Furthermore, the hybrid inversion can be applied to quantitatively determine the fluid saturation. To study the effects of noise level on the hybrid method and inversion results, the numerical simulation experiments are performed using different signal-to-noise-ratios (SNRs), and the effect of different SNRs on fluid typing using three fluid models are discussed and analyzed in detail.
An equivalent source inversion method for imaging complex structures
NASA Astrophysics Data System (ADS)
Munk, Jens
Accurate subsurface imaging is of interest to geophysicists, having applications in geological mapping, underground void detection, ground contaminant mapping and land mine detection. The mathematical framework necessary to generate images of the subsurface from measurements of these fields describe the inverse problem, which is generally ill-posed and non-linear. Target scattering from an electromagnetic excitation results in a non-linear formulation, which is usually linearized using a weak scattering approximation. The equivalent source inversion method, in contrast, does not rely on a weak scattering approximation. The method combines the unknown total field and permittivity contrast into a single unknown distribution of "equivalent sources". Once determined, these sources are used to obtain an estimate of the total fields within the target or scatterer. The final step in the inversion is to use these fields in obtaining the desired physical property. Excellent reconstructions are obtained when the target is illuminated using multiple look angles and frequencies. Target reconstructions are further enhanced using various iterative algorithms. The general formulation of the method allow it to be used in conjunction with a number of geophysical applications. Specifically, the method can be applied to any geophysical technique incorporating a measured response to a known induced input. This is illustrated by formulating the method within resistivity electrical prospecting.
Efficiency of Pareto joint inversion of 2D geophysical data using global optimization methods
NASA Astrophysics Data System (ADS)
Miernik, Katarzyna; Bogacz, Adrian; Kozubal, Adam; Danek, Tomasz; Wojdyła, Marek
2016-04-01
Pareto joint inversion of two or more sets of data is a promising new tool of modern geophysical exploration. In the first stage of our investigation we created software enabling execution of forward solvers of two geophysical methods (2D magnetotelluric and gravity) as well as inversion with possibility of constraining solution with seismic data. In the algorithm solving MT forward solver Helmholtz's equations, finite element method and Dirichlet's boundary conditions were applied. Gravity forward solver was based on Talwani's algorithm. To limit dimensionality of solution space we decided to describe model as sets of polygons, using Sharp Boundary Interface (SBI) approach. The main inversion engine was created using Particle Swarm Optimization (PSO) algorithm adapted to handle two or more target functions and to prevent acceptance of solutions which are non - realistic or incompatible with Pareto scheme. Each inversion run generates single Pareto solution, which can be added to Pareto Front. The PSO inversion engine was parallelized using OpenMP standard, what enabled execution code for practically unlimited amount of threads at once. Thereby computing time of inversion process was significantly decreased. Furthermore, computing efficiency increases with number of PSO iterations. In this contribution we analyze the efficiency of created software solution taking under consideration details of chosen global optimization engine used as a main joint minimization engine. Additionally we study the scale of possible decrease of computational time caused by different methods of parallelization applied for both forward solvers and inversion algorithm. All tests were done for 2D magnetotelluric and gravity data based on real geological media. Obtained results show that even for relatively simple mid end computational infrastructure proposed solution of inversion problem can be applied in practice and used for real life problems of geophysical inversion and interpretation.
Lithological and Surface Geometry Joint Inversions Using Multi-Objective Global Optimization Methods
NASA Astrophysics Data System (ADS)
Lelièvre, Peter; Bijani, Rodrigo; Farquharson, Colin
2016-04-01
surfaces are set to a priori values. The inversion is tasked with calculating the geometry of the contact surfaces instead of some piecewise distribution of properties in a mesh. Again, no coupling measure is required and joint inversion is simplified. Both of these inverse problems involve high nonlinearity and discontinuous or non-obtainable derivatives. They can also involve the existence of multiple minima. Hence, one can not apply the standard descent-based local minimization methods used to solve typical minimum-structure inversions. Instead, we are applying Pareto multi-objective global optimization (PMOGO) methods, which generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. While there are definite advantages to PMOGO joint inversion approaches, the methods come with significantly increased computational requirements. We are researching various strategies to ameliorate these computational issues including parallelization and problem dimension reduction.
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-08-19
Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~101 to ~102 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less
Inverse distributed hydrological modelling of Alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2006-06-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2 in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. Application of a 2-dimensional numerical
Recent developments in the inversion by the method of relaxation
NASA Technical Reports Server (NTRS)
Chahine, M. T.
1972-01-01
The relaxation method for inverse solution of the full radiative transfer equation is generalized to solve for all the atmospheric parameters that appear in the integrand as functions or functionals, without any a priori information about the expected solution. Illustrations are presented using the 7.5 micron CH4 band for determining temperature profiles in the Jovian atmosphere, and the 6.3 micron band for determining the water vapor mixing ratio in the earth's atmosphere.
Inverse problems in the design, modeling and testing of engineering systems
NASA Technical Reports Server (NTRS)
Alifanov, Oleg M.
1991-01-01
Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.
The inverse problem for the simple dynamo model
NASA Astrophysics Data System (ADS)
Reshetnyak, Maxim
2016-04-01
The inverse solution of the 1D Parker dynamo equations is considered. The method [1] is based on minimization of the cost-function, which characterize deviation of the model solution properties from the desired ones. The output is the latitude distribution of the magnetic field generation sources: the α- and ω-effects. Minimization is made using the Monte-Carlo method. The details of the method, as well as some applications, which can be interesting for the broad dynamo community, are considered: conditions when the invisible for the observer at the surface of the planet toroidal part of the magnetic field is much larger than the poloidal counterpart. It is also demonstrated in what circumstances magnetic field in the both hemispheres has different properties (the so-called hemispherical dynamo), and simple physical explanation of this phenomenon is proposed. References [1] Reshetnyak M.Yu. Inverse problem in Parker's dynamo. Russ. J. Earth Sci. 2015. 15. ES4001, doi:10.2205/2015ES000558, arXiv:1511.06243
On the joint inversion of geophysical data for models of the coupled core-mantle system
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.
1991-01-01
Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.
Inverse modelling problems in linear algebra undergraduate courses
NASA Astrophysics Data System (ADS)
Martinez-Luaces, Victor E.
2013-10-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different presentations will be discussed. Finally, several results will be presented and some conclusions proposed.
Inversion method based on stochastic optimization for particle sizing.
Sánchez-Escobar, Juan Jaime; Barbosa-Santillán, Liliana Ibeth; Vargas-Ubera, Javier; Aguilar-Valdés, Félix
2016-08-01
A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem. PMID:27505357
Modelling and genetic algorithm based optimisation of inverse supply chain
NASA Astrophysics Data System (ADS)
Bányai, T.
2009-04-01
(Recycling of household appliances with emphasis on reuse options). The purpose of this paper is the presentation of a possible method for avoiding the unnecessary environmental risk and landscape use through unprovoked large supply chain of collection systems of recycling processes. In the first part of the paper the author presents the mathematical model of recycling related collection systems (applied especially for wastes of electric and electronic products) and in the second part of the work a genetic algorithm based optimisation method will be demonstrated, by the aid of which it is possible to determine the optimal structure of the inverse supply chain from the point of view economical, ecological and logistic objective functions. The model of the inverse supply chain is based on a multi-level, hierarchical collection system. In case of this static model it is assumed that technical conditions are permanent. The total costs consist of three parts: total infrastructure costs, total material handling costs and environmental risk costs. The infrastructure-related costs are dependent only on the specific fixed costs and the specific unit costs of the operation points (collection, pre-treatment, treatment, recycling and reuse plants). The costs of warehousing and transportation are represented by the material handling related costs. The most important factors determining the level of environmental risk cost are the number of out of time recycled (treated or reused) products, the number of supply chain objects and the length of transportation routes. The objective function is the minimization of the total cost taking into consideration the constraints. However a lot of research work discussed the design of supply chain [8], but most of them concentrate on linear cost functions. In the case of this model non-linear cost functions were used. The non-linear cost functions and the possible high number of objects of the inverse supply chain leaded to the problem of choosing a
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-06-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least squares ℓ2 sense and of a model coefficient norm in a ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multi-resolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the non-linear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-08-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least-squares ℓ2 sense and of a model coefficient norm in an ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multiresolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the nonlinear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Inverse distributed hydrological modelling of alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2005-12-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2) in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. A detailed covariance analysis was performed
Application of the hybrid method to inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Chen, Han-Taw; Chang, Shiuh-Ming
1990-04-01
The hybrid method involving the combined use of Laplace transform method and the FEM method is considerably powerful for solving one-dimensional linear heat conduction problems. In the present method, the time-dependent terms are removed from the problem using the Laplace transform method, and then the FEM is applied to the space domain. The transformed temperature is inverted numerically to obtain the result in the physical quantity. The estimation of the surface heat flux or temperature from transient measured temperatures inside the solid agrees well with the analytical solution of the direct problem without Beck's sensitivity analysis and a least-square criterion. Due to no time step, the present method can directly calculate the surface conditions of an inverse problem without step by step computation in the time domain until the specific time is reached.
[A hyperspectral subpixel target detection method based on inverse least squares method].
Li, Qing-Bo; Nie, Xin; Zhang, Guang-Jun
2009-01-01
In the present paper, an inverse least square (ILS) method combined with the Mahalanobis distance outlier detection method is discussed to detect the subpixel target from the hyperspectral image. Firstly, the inverse model for the target spectrum and all the pixel spectra was established, in which the accurate target spectrum was obtained previously, and then the SNV algorithm was employed to preprocess each original pixel spectra separately. After the pretreatment, the regressive coefficient of ILS was calculated with partial least square (PLS) algorithm. Each point in the vector of regressive coefficient corresponds to a pixel in the image. The Mahalanobis distance was calculated with each point in the regressive coefficient vector. Because Mahalanobis distance stands for the extent to which samples deviate from the total population, the point with Mahalanobis distance larger than the 3sigma was regarded as the subpixel target. In this algorithm, no other prior information such as representative background spectrum or modeling of background is required, and only the target spectrum is needed. In addition, the result of the detection is insensitive to the complexity of background. This method was applied to AVIRIS remote sensing data. For this simulation experiment, AVIRIS remote sensing data was free downloaded from the NASA official websit, the spectrum of a ground object in the AVIRIS hyperspectral image was picked up as the target spectrum, and the subpixel target was simulated though a linear mixed method. The comparison of the subpixel detection result of the method mentioned above with that of orthogonal subspace projection method (OSP) was performed. The result shows that the performance of the ILS method is better than the traditional OSP method. The ROC (receive operating characteristic curve) and SNR were calculated, which indicates that the ILS method possesses higher detection accuracy and less computing time than the OSP algorithm. PMID:19385196
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
NASA Astrophysics Data System (ADS)
Burger, Martin; Løseth Elvetun, Ole; Schlottbom, Matthias
2015-12-01
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to perturbed or not well resolved domains, and which allow for efficient discretizations not resolving any fine detail of those geometries. For forward problems in partial differential equations methods based on diffuse interface representations have gained strong attention in the last years, but so far they have not been considered systematically for inverse problems. In this work we introduce a diffuse domain method as a tool for the solution of variational inverse problems. As a particular example we study ECG inversion in further detail. ECG inversion is a linear inverse source problem with boundary measurements governed by an anisotropic diffusion equation, which naturally cries for solutions under changing geometries, namely the beating heart. We formulate a regularization strategy using Tikhonov regularization and, using standard source conditions, we prove convergence rates. A special property of our approach is that not only operator perturbations are introduced by the diffuse domain method, but more important we have to deal with topologies which depend on a parameter \\varepsilon in the diffuse domain method, i.e. we have to deal with \\varepsilon -dependent forward operators and \\varepsilon -dependent norms. In particular the appropriate function spaces for the unknown and the data depend on \\varepsilon . This prevents the application of some standard convergence techniques for inverse problems, in particular interpreting the perturbations as data errors in the original problem does not yield suitable results. We consequently develop a novel approach based on saddle-point problems. The numerical solution of the problem is discussed as well and results for several computational experiments are reported. In
Ray, J.; Lee, J.; Yadav, V.; Lefantzi, S.; Michalak, A. M.; van Bloemen Waanders, B.
2015-04-29
Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting.more » Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also
Inverse modeling with RZWQM2 to predict water quality
Technology Transfer Automated Retrieval System (TEKTRAN)
Agricultural systems models such as RZWQM2 are complex and have numerous parameters that are unknown and difficult to estimate. Inverse modeling provides an objective statistical basis for calibration that involves simultaneous adjustment of model parameters and yields parameter confidence intervals...
Inverse estimation of parameters for an estuarine eutrophication model
Shen, J.; Kuo, A.Y.
1996-11-01
An inverse model of an estuarine eutrophication model with eight state variables is developed. It provides a framework to estimate parameter values of the eutrophication model by assimilation of concentration data of these state variables. The inverse model using the variational technique in conjunction with a vertical two-dimensional eutrophication model is general enough to be applicable to aid model calibration. The formulation is illustrated by conducting a series of numerical experiments for the tidal Rappahannock River, a western shore tributary of the Chesapeake Bay. The numerical experiments of short-period model simulations with different hypothetical data sets and long-period model simulations with limited hypothetical data sets demonstrated that the inverse model can be satisfactorily used to estimate parameter values of the eutrophication model. The experiments also showed that the inverse model is useful to address some important questions, such as uniqueness of the parameter estimation and data requirements for model calibration. Because of the complexity of the eutrophication system, degrading of speed of convergence may occur. Two major factors which cause degradation of speed of convergence are cross effects among parameters and the multiple scales involved in the parameter system.
Towards inverse modeling of intratumor heterogeneity
NASA Astrophysics Data System (ADS)
Brutovsky, Branislav; Horvath, Denis
2015-08-01
Development of resistance limits efficiency of present anticancer therapies and preventing it remains a big challenge in cancer research. It is accepted, at the intuitive level, that resistance emerges as a consequence of the heterogeneity of cancer cells at the molecular, genetic and cellular levels. Produced by many sources, tumor heterogeneity is extremely complex time dependent statistical characteristics which may be quantified by measures defined in many different ways, most of them coming from statistical mechanics. In this paper, we apply the Markovian framework to relate population heterogeneity to the statistics of the environment. As, from an evolutionary viewpoint, therapy corresponds to a purposeful modi- fication of the cells' fitness landscape, we assume that understanding general relationship between the spatiotemporal statistics of a tumor microenvironment and intratumor heterogeneity will allow to conceive the therapy as an inverse problem and to solve it by optimization techniques. To account for the inherent stochasticity of biological processes at cellular scale, the generalized distancebased concept was applied to express distances between probabilistically described cell states and environmental conditions, respectively.
The inversion method of Matrix mineral bulk modulus based on Gassmann equation
NASA Astrophysics Data System (ADS)
Kai, L.; He, X.; Zhang, Z. H.
2015-12-01
In recent years, seismic rock physics has played an important role in oil and gas exploration. The seismic rock physics model can quantitatively describe the reservoir characteristics, such as lithologic association, pore structure, geological processes and so on. But the classic rock physics models need to determine the background parameter, that is, matrix mineral bulk modulus. An inaccurate inputs greatly influence the prediction reliability. By introducing different rock physics parameters, Gassmann equation is used to derive a reasonable modification. Two forms of Matrix mineral bulk modulus inversion methods including the linear regression method and Self-adapting inversion method are proposed. They effectively solve the value issues of Matrix mineral bulk modulus in different complex parameters conditions. Based on laboratory tests data, compared with the conventional method, the linear regression method is more simple and accurate. Meanwhile Self-adapting inversion method also has higher precision in the known rich rock physics parameters. Consequently, the modulus value was applied to reservoir fluid substitution, porosity inversion and S-wave velocity prediction. The introduction of Matrix mineral modulus base on Gassmann equations can effectively improve the reliability of the fluid impact prediction, and computational efficiency.
NASA Astrophysics Data System (ADS)
Amey, Ruth; Hooper, Andy
2016-04-01
Modelling the slip distribution along fault planes is an essential part of earthquake investigations. These models give insight into stress distribution and frictional properties of a fault, as well as being important for understanding seismic hazard. Here we present a new approach for constraining earthquake slip using geodetic data, and apply our method to the Mw 6.0 Napa Valley, California, earthquake of 24th August 2014. The method relies on the inclusion of a prior based on von Karman correlation. With the launch of ESA's satellite Sentinel-1A in 2014, the scientific community is now in a position to routinely investigate all large continental earthquakes using InSAR, and inverting for slip is a crucial part of that procedure. However, in order for the slip inversions to be useful we need to ensure that the inversion processes give results that are properly representing the slip distribution. Slip inversions are ill-posed and measurement noise results in unrealistically large fluctuations in the solution. To avoid this, an extra constraint such as minimum norm or Laplacian smoothing is usually employed to regularise the inversion. However, these constraints do not necessarily realistically represent earthquake slip. There is growing evidence that many aspects of earthquakes are self-similar and that earthquake slip distribution is well described by a von Karman autocorrelation function, which incorporates fractal properties through the Hurst parameter. We add this constraint to the slip inversion as a prior assumption using a Bayesian approach.
Comparison of carbon dioxide uptake between inverse and bottom-up models over the Mountain West
NASA Astrophysics Data System (ADS)
Brooks, B.; Desai, A. R.; Stephens, B. B.
2010-12-01
An essential objective of the North American Carbon Program (NACP) has been to constrain carbon cycle sources and sinks in particular through land surface model intercomparison. Many of these bottom-up models estimate fluxes of carbon dioxide using remotely sensed satellite products such as fraction of Photosynthetically Active Radiation (fPAR) and Leaf Area Index (LAI), which are difficult to calibrate over the complex terrain and heterogeneous land cover of the United States Mountain West. Inverse methods that retrieve fluxes by assimilating in situ CO2 concentrations offer a different approach for estimating carbon dioxide exchange. In this study we compare CO2 fluxes between several models that participated in the NACP Regional and Continental Interim Synthesis and CarbonTracker, a nested grid tracer transport inverse model, over a domain that encompasses the Regional Atmospheric Continuous CO2 Network in the Rocky Mountains (RACCOON). An inverse to bottom-up model comparison over the RACCOON domain allows us to address several key questions: 'How do inverse and bottom-up models differ in CO2 uptake?', 'Do the inverse model - bottom-up model mismatches exceed error estimates?', and 'Does filtering-out CO2 observations representing local flows before assimilation by the inverse model reduce such discrepancies?'
UCODE, a computer code for universal inverse modeling
Poeter, E.P.; Hill, M.C.
1999-01-01
This article presents the US Geological Survey computer program UCODE, which was developed in collaboration with the US Army Corps of Engineers Waterways Experiment Station and the International Ground Water Modeling Center of the Colorado School of Mines. UCODE performs inverse modeling, posed as a parameter-estimation problem, using nonlinear regression. Any application model or set of models can be used; the only requirement is that they have numerical (ASCII or text only) input and output files and that the numbers in these files have sufficient significant digits. Application models can include preprocessors and postprocessors as well as models related to the processes of interest (physical, chemical and so on), making UCODE extremely powerful for model calibration. Estimated parameters can be defined flexibly with user-specified functions. Observations to be matched in the regression can be any quantity for which a simulated equivalent value can be produced, thus simulated equivalent values are calculated using values that appear in the application model output files and can be manipulated with additive and multiplicative functions, if necessary. Prior, or direct, information on estimated parameters also can be included in the regression. The nonlinear regression problem is solved by minimizing a weighted least-squares objective function with respect to the parameter values using a modified Gauss-Newton method. Sensitivities needed for the method are calculated approximately by forward or central differences and problems and solutions related to this approximation are discussed. Statistics are calculated and printed for use in (1) diagnosing inadequate data or identifying parameters that probably cannot be estimated with the available data, (2) evaluating estimated parameter values, (3) evaluating the model representation of the actual processes and (4) quantifying the uncertainty of model simulated values. UCODE is intended for use on any computer operating
NASA Astrophysics Data System (ADS)
Hohage, Thorsten
1997-10-01
Convergence and logarithmic convergence rates of the iteratively regularized Gauss - Newton method in a Hilbert space setting are proven provided a logarithmic source condition is satisfied. This method is applied to an inverse potential and an inverse scattering problem, and the source condition is interpreted as a smoothness condition in terms of Sobolev spaces for the case where the domain is a circle. Numerical experiments yield convergence and convergence rates of the form expected by our general convergence theorem.
Nonlinear inversion for arbitrarily-oriented anisotropic models II: Inversion techniques
NASA Astrophysics Data System (ADS)
Bremner, P. M.; Panning, M. P.
2011-12-01
We present output models from inversion of a synthetic surface wave dataset. We implement new 3-D finite-frequency kernels, based on the Born approximation, to invert for upper mantle structure beneath western North America. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests were performed to achieve a robust inversion scheme. Four synthetic input models were created, to include: isotropic, constant strength anisotropic, variable strength anisotropic, and both anisotropic and isotropic together. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The object of this phase of the study was to determine appropriate nonlinear inversion schemes that adequately recover the input models. The synthetic dataset consists of collected seismic waveforms of 126 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150o centered about 44o lat, -110o lon (an arbitrary location within USArray coverage). Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π -prolate spheroidal wave function eigentapers (Slepian tapers) reduce noise biasing, and can provide error estimates in phase delay measurements. This study is a
Anthropomorphic Coding of Speech and Audio: A Model Inversion Approach
NASA Astrophysics Data System (ADS)
Feldbauer, Christian; Kubin, Gernot; Kleijn, W. Bastiaan
2005-12-01
Auditory modeling is a well-established methodology that provides insight into human perception and that facilitates the extraction of signal features that are most relevant to the listener. The aim of this paper is to provide a tutorial on perceptual speech and audio coding using an invertible auditory model. In this approach, the audio signal is converted into an auditory representation using an invertible auditory model. The auditory representation is quantized and coded. Upon decoding, it is then transformed back into the acoustic domain. This transformation converts a complex distortion criterion into a simple one, thus facilitating quantization with low complexity. We briefly review past work on auditory models and describe in more detail the components of our invertible model and its inversion procedure, that is, the method to reconstruct the signal from the output of the auditory model. We summarize attempts to use the auditory representation for low-bit-rate coding. Our approach also allows the exploitation of the inherent redundancy of the human auditory system for the purpose of multiple description (joint source-channel) coding.
A numerical method for solving a stochastic inverse problem for parameters.
Butler, T; Estep, D
2013-02-01
We review recent work (Briedt et al., 2011., 2012) on a new approach to the formulation and solution of the stochastic inverse parameter determination problem, i.e. determine the random variation of input parameters to a map that matches specified random variation in the output of the map, and then apply the various aspects of this method to the interesting Brusselator model. In this approach, the problem is formulated as an inverse problem for an integral equation using the Law of Total Probability. The solution method employs two steps: (1) we construct a systematic method for approximating set-valued inverse solutions and (2) we construct a computational approach to compute a measure-theoretic approximation of the probability measure on the input space imparted by the approximate set-valued inverse that solves the inverse problem. In addition to convergence analysis, we carry out an a posteriori error analysis on the computed probability distribution that takes into account all sources of stochastic and deterministic error. PMID:24347806
A numerical method for solving a stochastic inverse problem for parameters
Butler, T.; Estep, D.
2013-01-01
We review recent work (Briedt et al., 2011., 2012) on a new approach to the formulation and solution of the stochastic inverse parameter determination problem, i.e. determine the random variation of input parameters to a map that matches specified random variation in the output of the map, and then apply the various aspects of this method to the interesting Brusselator model. In this approach, the problem is formulated as an inverse problem for an integral equation using the Law of Total Probability. The solution method employs two steps: (1) we construct a systematic method for approximating set-valued inverse solutions and (2) we construct a computational approach to compute a measure-theoretic approximation of the probability measure on the input space imparted by the approximate set-valued inverse that solves the inverse problem. In addition to convergence analysis, we carry out an a posteriori error analysis on the computed probability distribution that takes into account all sources of stochastic and deterministic error. PMID:24347806
Coupled inverse geochemical and microbial reactive transport models in porous media
NASA Astrophysics Data System (ADS)
Samper, J.; Yang, C.
2007-12-01
Microbial processes play a major role in controlling geochemical conditions in subsurface systems. Various laboratory and in situ experiments have been performed to evaluate the relevance of microbial processes and derive key microbial parameters. Such experiments are often interpreted by suboptimal trial-and-error curve fitting. Here we present an inverse model for coupled flow, reactive solute transport, geochemical and microbial processes which overcomes the limitations of trial-and-error methods by making data interpretation in a systematic, objective, and efficient manner. It extends the capabilities of existing inverse models which deal mostly with flow and chemically-reactive solute transport. Our inverse model relies on the microbial reactive transport code BIOCORE of Samper et al. (2006a) and improves the inverse reactive transport model INVERSE- CORE of Dai and Samper (2004) by allowing the simultaneous estimation of geochemical and microbial parameters. The inverse model has been implemented in a finite element code, INVERSE-BIOCORE2D and its capabilities have been verified and tested with a synthetic experiment involving equilibrium speciation, kinetic sorption/desorption and kinetic biodegradation reactions. Model results indicate that both chemical and microbial parameters can be estimated accurately for error-free data. Estimation errors of microbial parameters are larger than those of kinetic sorption parameters and generally increase with increasing standard deviation of data noise. Estimation error of yield coefficient is the smallest among all microbial parameter and which does not depend on data noise. The inverse model has been used also to estimate microbial parameters of a laboratory experiment involving sucrose fermentation by yeast. Inverse estimation improves significantly the fit to measured data.
NASA Astrophysics Data System (ADS)
Rezaie, Mohammad; Moradzadeh, Ali; Kalate, Ali Nejati; Aghajani, Hamid
2016-09-01
Inversion of gravity data is one of the important steps in the interpretation of practical data. One of the most interesting geological frameworks for gravity data inversion is the detection of sharp boundaries between orebody and host rocks. The focusing inversion is able to reconstruct a sharp image of the geological target. This technique can be efficiently applied for the quantitative interpretation of gravity data. In this study, a new reweighted regularized method for the 3D focusing inversion technique based on Lanczos bidiagonalization method is developed. The inversion results of synthetic data show that the new method is faster than common reweighted regularized conjugate gradient method to produce an acceptable solution for focusing inverse problem. The new developed inversion scheme is also applied for inversion of the gravity data collected over the San Nicolas Cu-Zn orebody in Zacatecas State, Mexico. The inversion results indicate a remarkable correlation with the true structure of the orebody that is achieved from drilling data.
Bootstrap resampling as a tool for uncertainty analysis in 2-D magnetotelluric inversion modelling
NASA Astrophysics Data System (ADS)
Schnaidt, Sebastian; Heinson, Graham
2015-10-01
Uncertainty estimation is a vital part of geophysical numerical modelling. There exist a variety of methods aimed at uncertainty estimation, which are often complicated and difficult to implement. We present an inversion technique that produces multiple solutions, based on bootstrap resampling, to create a qualitative uncertainty measure for 2-D magnetotelluric inversion models. The approach is easy to implement, can be used with almost any inversion code, and does not require access to the inversion software's source code. It is capable of detecting the effect of data uncertainties on the model result rather than just analysing the effect of model variations on the model response. To obtain uncertainty estimates for an inversion model, the original data set is resampled repeatedly and alternate data set realizations are created and inverted. This ensemble of solutions is then statistically analysed to determine the variability between the different solutions. The process yields interpretable uncertainty maps for the inversion model and we demonstrate its effectiveness to qualitatively quantify uncertainty in synthetic model tests and a case study.
A method for determining void arrangements in inverse opals.
Blanford, C F; Carter, C B; Stein, A
2004-12-01
The periodic arrangement of voids in ceramic materials templated by colloidal crystal arrays (inverse opals) has been analysed by transmission electron microscopy. Individual particles consisting of an approximately spherical array of at least 100 voids were tilted through 90 degrees along a single axis within the transmission electron microscope. The bright-field images of these particles at high-symmetry points, their diffractograms calculated by fast Fourier transforms, and the transmission electron microscope goniometer angles were compared with model face-centred cubic, body-centred cubic, hexagonal close-packed, and simple cubic lattices in real and reciprocal space. The spatial periodicities were calculated for two-dimensional projections. The systematic absences in these diffractograms differed from those found in diffraction patterns from three-dimensional objects. The experimental data matched only the model face-centred cubic lattice, so it was concluded that the packing of the voids (and, thus, the polymer spheres that composed the original colloidal crystals) was face-centred cubic. In face-centred cubic structures, the stacking-fault displacement vector is a/6<211> . No stacking faults were observed when viewing the inverse opal structure along the orthogonal <110>-type directions, eliminating the possibility of a random hexagonally close-packed structure for the particles observed. This technique complements synchrotron X-ray scattering work on colloidal crystals by allowing both real-space and reciprocal-space analysis to be carried out on a smaller cross-sectional area.
Solving the structural inverse gravity problem by the modified gradient methods
NASA Astrophysics Data System (ADS)
Martyshko, P. S.; Akimova, E. N.; Misilov, V. E.
2016-09-01
New methods for solving the three-dimensional inverse gravity problem in the class of contact surfaces are described. Based on the approach previously suggested by the authors, new algorithms are developed. Application of these algorithms significantly reduces the number of the iterations and computing time compared to the previous ones. The algorithms have been numerically implemented on the multicore processor. The example of solving the structural inverse gravity problem for a model of four-layer medium (with the use of gravity field measurements) is constructed.
Estimates of tropical bromoform emissions using an inversion method
NASA Astrophysics Data System (ADS)
Ashfold, M. J.; Harris, N. R. P.; Manning, A. J.; Robinson, A. D.; Warwick, N. J.; Pyle, J. A.
2014-01-01
Bromine plays an important role in ozone chemistry in both the troposphere and stratosphere. When measured by mass, bromoform (CHBr3) is thought to be the largest organic source of bromine to the atmosphere. While seaweed and phytoplankton are known to be dominant sources, the size and the geographical distribution of CHBr3 emissions remains uncertain. Particularly little is known about emissions from the Maritime Continent, which have usually been assumed to be large, and which appear to be especially likely to reach the stratosphere. In this study we aim to reduce this uncertainty by combining the first multi-annual set of CHBr3 measurements from this region, and an inversion process, to investigate systematically the distribution and magnitude of CHBr3 emissions. The novelty of our approach lies in the application of the inversion method to CHBr3. We find that local measurements of a short-lived gas like CHBr3 can be used to constrain emissions from only a relatively small, sub-regional domain. We then obtain detailed estimates of CHBr3 emissions within this area, which appear to be relatively insensitive to the assumptions inherent in the inversion process. We extrapolate this information to produce estimated emissions for the entire tropics (defined as 20° S-20° N) of 225 Gg CHBr3 yr-1. The ocean in the area we base our extrapolations upon is typically somewhat shallower, and more biologically productive, than the tropical average. Despite this, our tropical estimate is lower than most other recent studies, and suggests that CHBr3 emissions in the coastline-rich Maritime Continent may not be stronger than emissions in other parts of the tropics.
NASA Astrophysics Data System (ADS)
Schuster, Thomas; Schöpfer, Frank
2010-08-01
The method of approximate inverse is a mollification method for stably solving inverse problems. In its original form it has been developed to solve operator equations in L2-spaces and general Hilbert spaces. We show that the method of approximate inverse can be extended to solve linear, ill-posed problems in Banach spaces. This paper is restricted to function spaces. The method itself consists of evaluations of dual pairings of the given data with reconstruction kernels that are associated with mollifiers and the dual of the operator. We first define what we mean by a mollifier in general Banach spaces and then investigate two settings more exactly: the case of Lp-spaces and the case of the Banach space of continuous functions on a compact set. For both settings we present the criteria turning the method of approximate inverse into a regularization method and prove convergence with rates. As an application we refer to x-ray diffractometry which is a technique of non-destructive testing that is concerned with computing the stress tensor of a specimen. Since one knows that the stress tensor is smooth, x-ray diffractometry can appropriately be modelled by a Banach space setting using continuous functions.
Inverse modeling analysis of soil dust sources over East Asia
NASA Astrophysics Data System (ADS)
Ku, Bonyang; Park, Rokjin J.
2011-10-01
Soil dust is the dominant aerosol by mass concentration in the troposphere and has considerable effects on air quality and climate. Parts of East Asia, including southern Mongolia, northern China, and the Taklamakan Desert, are important dust source regions. Accurate simulations of dust storm events are crucial for protecting human health and assessing the climatic impacts of dust events. However, even state-of-the-art aerosol models still contain large uncertainties in soil dust simulations, particularly for the dust emissions over East Asia. In this study, we attempted to reduce these uncertainties by using an inverse modeling technique to simulate dust emissions. We used the measured mass concentration of particles less than 10 μm in aerodynamic diameter (PM10) in the surface air over East Asia, in combination with an inverse model, to understand the dust sources. The global three-dimensional GEOS-Chem chemical transport model (CTM) was used as a forward model. The inverse model analysis yielded a 76% decrease in dust emissions from the southern region of the Gobi Desert, relative to the a priori result. The a posteriori dust emissions from the Taklamakan Desert and deserts in eastern and Inner Mongolia were two to three fold higher than the a priori dust emissions. The simulation results with the a posteriori dust sources showed much better agreement with these observations, indicating that the inverse modeling technique can be useful for estimation of the optimized dust emissions from individually sourced regions.
NASA Astrophysics Data System (ADS)
Marklein, R.; Langenberg, K. J.; Mayer, K.; Shlivinski, A.; Miao, J.; Zimmer, A.; Müller, W.; Schmitz, V.; Kohl, C.; Mletzko, U.
2005-04-01
This paper presents recent advances and future challenges of the application of different numerical modeling tools and linear and nonlinear inversion algorithms in ultrasonics and electromagnetics applied in NDE. The inversion methods considered in the presented work vary from linear schemes, e.g. SAFT/InASAFT and Diffraction Tomography/FT-SAFT, to nonlinear schemes, e.g. the Contrast Source Inversion. Inversion results are presented and compared for modeled and measured ultrasonic and electromagnetic data to locate voids and cracks as well as to locate aluminum tendon ducts in concrete, which is a typical GPR problem. Finite Integration Technique (FIT) and Domain Integral Equation (DIE) solvers are used as modeling tools.
Moving lattice kinks and pulses: an inverse method.
Flach, S; Zolotaryuk, Y; Kladko, K
1999-05-01
We develop a general mapping from given kink or pulse shaped traveling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping-by definition an inverse method-to acoustic solitons in chains with nonlinear intersite interactions, nonlinear Klein-Gordon chains, reaction-diffusion equations, and discrete nonlinear Schrödinger systems. Potential functions can be found in a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least C2 functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.
NASA Astrophysics Data System (ADS)
Neupauer, Roseanna M.; Borchers, Brian; Wilson, John L.
2000-09-01
Inverse methods can be used to reconstruct the release history of a known source of groundwater contamination from concentration data describing the present-day spatial distribution of the contaminant plume. Using hypothetical release history functions and contaminant plumes, we evaluate the relative effectiveness of two proposed inverse methods, Tikhonov regularization (TR) and minimum relative entropy (MRE) inversion, in reconstructing the release history of a conservative contaminant in a one-dimensional domain [Skaggs and Kabala, 1994; Woodbury and Ulrych, 1996]. We also address issues of reproducibility of the solution and the appropriateness of models for simulating random measurement error. The results show that if error-free plume concentration data are available, both methods perform well in reconstructing a smooth source history function. With error-free data the MRE method is more robust than TR in reconstructing a nonsmooth source history function; however, the TR method is more robust if the data contain measurement error. Two error models were evaluated in this study, and we found that the particular error model does not affect the reliability of the solutions. The results for the TR method have somewhat greater reproducibility because, in some cases, its input parameters are less subjective than those of the MRE method; however, the MRE solution can identify regions where the data give little or no information about the source history function, while the TR solution cannot.
Estimates of tropical bromoform emissions using an inversion method
NASA Astrophysics Data System (ADS)
Ashfold, M. J.; Harris, N. R. P.; Manning, A. J.; Robinson, A. D.; Warwick, N. J.; Pyle, J. A.
2013-08-01
Bromine plays an important role in ozone chemistry in both the troposphere and stratosphere. When measured by mass, bromoform (CHBr3) is thought to be the largest organic source of bromine to the atmosphere. While seaweed and phytoplankton are known to be dominant sources, the size and the geographical distribution of CHBr3 emissions remains uncertain. Particularly little is known about emissions from the Maritime Continent, which have usually been assumed to be large, and which appear to be especially likely to reach the stratosphere. In this study we aim to use the first multi-annual set of CHBr3 measurements from this region, and an inversion method, to reduce this uncertainty. We find that local measurements of a short-lived gas like CHBr3 can only be used to constrain emissions from a relatively small, sub-regional domain. We then obtain detailed estimates of both the distribution and magnitude of CHBr3 emissions within this area. Our estimates appear to be relatively insensitive to the assumptions inherent in the inversion process. We extrapolate this information to produce estimated emissions for the entire tropics (defined as 20° S-20° N) of 225 GgCHBr3 y-1. This estimate is consistent with other recent studies, and suggests that CHBr3 emissions in the coastline-rich Maritime Continent may not be stronger than emissions in other parts of the tropics.
NASA Astrophysics Data System (ADS)
Illman, Walter A.; Berg, Steven J.; Zhao, Zhanfeng
2015-05-01
The robust performance of hydraulic tomography (HT) based on geostatistics has been demonstrated through numerous synthetic, laboratory, and field studies. While geostatistical inverse methods offer many advantages, one key disadvantage is its highly parameterized nature, which renders it computationally intensive for large-scale problems. Another issue is that geostatistics-based HT may produce overly smooth images of subsurface heterogeneity when there are few monitoring interval data. Therefore, some may question the utility of the geostatistical inversion approach in certain situations and seek alternative approaches. To investigate these issues, we simultaneously calibrated different groundwater models with varying subsurface conceptualizations and parameter resolutions using a laboratory sandbox aquifer. The compared models included: (1) isotropic and anisotropic effective parameter models; (2) a heterogeneous model that faithfully represents the geological features; and (3) a heterogeneous model based on geostatistical inverse modeling. The performance of these models was assessed by quantitatively examining the results from model calibration and validation. Calibration data consisted of steady state drawdown data from eight pumping tests and validation data consisted of data from 16 separate pumping tests not used in the calibration effort. Results revealed that the geostatistical inversion approach performed the best among the approaches compared, although the geological model that faithfully represented stratigraphy came a close second. In addition, when the number of pumping tests available for inverse modeling was small, the geological modeling approach yielded more robust validation results. This suggests that better knowledge of stratigraphy obtained via geophysics or other means may contribute to improved results for HT.
Optimized halftoning using dot diffusion and methods for inverse halftoning.
Mese, M; Vaidyanathan, P P
2000-01-01
Unlike the error diffusion method, the dot diffusion method for digital halftoning has the advantage of pixel-level parallelism. However, the image quality offered by error diffusion is still regarded as superior to most of the other known methods. We show how the dot diffusion method can be improved by optimization of the so-called class matrix. By taking the human visual characteristics into account we show that such optimization consistently results in images comparable to error diffusion, without sacrificing the pixel-level parallelism. Adaptive dot diffusion is also introduced and then a mathematical description of dot diffusion is derived. Furthermore, inverse halftoning of dot diffused images is discussed and two methods are proposed. The first one uses projection onto convex sets (POCS) and the second one uses wavelets. Of these methods, the wavelet method does not make use of the knowledge of the class matrix. Embedded multiresolution dot diffusion is also discussed, which is useful for rendering at different resolutions and transmitting images progressively.
Physical-Based Inversion for Subsurface Flow and Transport Modeling
NASA Astrophysics Data System (ADS)
Zhang, Y.; Jiao, J.; Wang, D.; Irsa, J.
2014-12-01
A new and computationally efficient fluid flow and transport inverse theory has been developed for characterizing, calibrating, and modeling aquifers. The theory is capable of simultaneous estimation of model boundary conditions (for simple transient problems, also the initial conditions) and fluid flow and transport parameters, i.e., spatially distributed permeabilities, source/sink rates, storativity, and dispersivity. The theory is robust to measurement errors and strong parameter variability. Effective parameters can be estimated to represent unresolved heterogeneity, e.g., sub-grid features and spatially variable recharge. The theory has been extended to new problems including parameter structure identification, unsaturated and variably saturated flows (e.g., directly estimating the soil retention functions), joint flow and transport inversion (e.g., containment source identification), uncertainty analysis (e.g., integrating subsurface static and dynamic data via geostatistical inversion), and high performance computing (e.g., solving large inversion systems with parallel computing). This presentation will summarize the body of the inversion research and discuss new directions for future work.
A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization
NASA Astrophysics Data System (ADS)
Liu, Shuang; Hu, Xiangyun; Liu, Tianyou
2014-07-01
Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.
New Advances for a joint 3D inversion of multiple EM methods
NASA Astrophysics Data System (ADS)
Meqbel, N. M.; Ritter, O.
2013-12-01
Electromagnetic (EM) methods are routinely applied to image the subsurface from shallow to regional structures. Individual EM methods differ in their sensitivities towards resistive and conductive structures as well as in their exploration depths. Joint 3D inversion of multiple EM data sets can result in significantly better resolution of subsurface structures than the individual inversions. Proper weighting between different EM data is essential, however. We present a recently developed weighting algorithm to combine magnetotelluric (MT), controlled source EM (CSEM) and DC-geoelectric (DC) data. It is well known that MT data are mostly sensible to regional conductive structures, whereas, CSEM and DC data are more suitable to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of each data residual are used to assess how much weight individual components of the total data gradient must have to achieve an equal contribution of all data sets in the inverse model. A numerically efficient way to search for appropriate weighting factors could be established by applying a bi-diagonalization procedure to the sensitivity matrix. Thereby, the original inverse problem can be projected onto a smaller dimension in which the search of weighting factors is numerically cheap. We demonstrate the efficiency of the proposed weighting schemes and explore the model domain with synthetic data sets.
Inverse rendering of faces with a 3D morphable model.
Aldrian, Oswald; Smith, William A P
2013-05-01
In this paper, we present a complete framework to inverse render faces with a 3D Morphable Model (3DMM). By decomposing the image formation process into geometric and photometric parts, we are able to state the problem as a multilinear system which can be solved accurately and efficiently. As we treat each contribution as independent, the objective function is convex in the parameters and a global solution is guaranteed. We start by recovering 3D shape using a novel algorithm which incorporates generalization error of the model obtained from empirical measurements. We then describe two methods to recover facial texture, diffuse lighting, specular reflectance, and camera properties from a single image. The methods make increasingly weak assumptions and can be solved in a linear fashion. We evaluate our findings on a publicly available database, where we are able to outperform an existing state-of-the-art algorithm. We demonstrate the usability of the recovered parameters in a recognition experiment conducted on the CMU-PIE database. PMID:23520253
Inverse problem for the current loop model: Possibilities and restrictions
NASA Astrophysics Data System (ADS)
Demina, I. M.; Farafonova, Yu. G.
2016-07-01
The possibilities of determining arbitrary current loop parameters based on the spatial structures of the magnetic field components generated by this loop on a sphere with a specified radius have been considered with the use of models. The model parameters were selected such that anomalies created by current loops on a sphere with a radius of 6378 km would be comparable in value with the different-scale anomalies of the observed main geomagnetic field (MGF). The least squares method was used to solve the inverse problem. Estimates close to the specified values were obtained for all current loop parameters except the current strength and radius. The radius determination error can reach ±120 km; at the same time, the magnetic moment value is determined with an accuracy of ±1%. The resolvability of the current force and radius can to a certain degree be improved by decreasing the observation sphere radius such that the ratio of the source distance to the current loop radius would be at least smaller than eight, which can be difficult to reach when modeling MGF.
A comparison of lidar inversion methods for cirrus applications
NASA Technical Reports Server (NTRS)
Elouragini, Salem; Flamant, Pierre H.
1992-01-01
Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.
More Bayesian Transdimensional Inversion for Thermal History Modelling (Invited)
NASA Astrophysics Data System (ADS)
Gallagher, K.
2013-12-01
Since the publication of Dodson (1973) quantifying the relationship between geochronogical ages and closure temperatures, an ongoing concern in thermochronology is reconstruction of thermal histories consistent with the measured data. Extracting this thermal history information is best treated as an inverse problem, given the complex relationship between the observations and the thermal history. When solving the inverse problem (i.e. finding thermal acceptable thermal histories), stochastic sampling methods have often been used, as these are relatively global when searching the model space. However, the issue remains how best to estimate those parts of the thermal history unconstrained by independent information, i.e. what is required to fit the data ? To solve this general problem, we use a Bayesian transdimensional Markov Chain Monte Carlo method and this has been integrated into user-friendly software, QTQt (Quantitative Thermochronology with Qt), which runs on both Macintosh and PC. The Bayesian approach allows us to consider a wide range of possible thermal history as general prior information on time, temperature (and temperature offset for multiple samples in a vertical profile). We can also incorporate more focussed geological constraints in terms of more specific priors. In this framework, it is the data themselves (and their errors) that determine the complexity of the thermal history solutions. For example, more precise data will justify a more complex solution, while more noisy data will be happy with simpler solutions. We can express complexity in terms of the number of time-temperature points defining the total thermal history. Another useful feature of this method is that was can easily deal with imprecise parameter values (e.g. kinetics, data errors), by drawing samples from a user specified probability distribution, rather than using a single value. Finally, the method can be applied to either single samples, or multiple samples (from a borehole or
Inversion of canopy reflectance models for estimation of vegetation parameters
NASA Technical Reports Server (NTRS)
Goel, Narendra S.
1987-01-01
One of the keys to successful remote sensing of vegetation is to be able to estimate important agronomic parameters like leaf area index (LAI) and biomass (BM) from the bidirectional canopy reflectance (CR) data obtained by a space-shuttle or satellite borne sensor. One approach for such an estimation is through inversion of CR models which relate these parameters to CR. The feasibility of this approach was shown. The overall objective of the research carried out was to address heretofore uninvestigated but important fundamental issues, develop the inversion technique further, and delineate its strengths and limitations.
An evolution equation modeling inversion of tulip flames
Dold, J.W.; Joulin, G.
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
Localization of incipient tip vortex cavitation using ray based matched field inversion method
NASA Astrophysics Data System (ADS)
Kim, Dongho; Seong, Woojae; Choo, Youngmin; Lee, Jeunghoon
2015-10-01
Cavitation of marine propeller is one of the main contributing factors of broadband radiated ship noise. In this research, an algorithm for the source localization of incipient vortex cavitation is suggested. Incipient cavitation is modeled as monopole type source and matched-field inversion method is applied to find the source position by comparing the spatial correlation between measured and replicated pressure fields at the receiver array. The accuracy of source localization is improved by broadband matched-field inversion technique that enhances correlation by incoherently averaging correlations of individual frequencies. Suggested localization algorithm is verified through known virtual source and model test conducted in Samsung ship model basin cavitation tunnel. It is found that suggested localization algorithm enables efficient localization of incipient tip vortex cavitation using a few pressure data measured on the outer hull above the propeller and practically applicable to the typically performed model scale experiment in a cavitation tunnel at the early design stage.
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hori, T.; Hirahara, K.; Hori, M.
2012-12-01
preconditioner, which uses a solution obtained by a lower resolution model generated in the same area to improve the convergence of the iterative solver. Also, the preconditioner is solved in single precision. As a result, the computation time is significantly reduced. Verification for our method is done by comparing the results with the analytical solution in a half-space (Okada, 1985.) As an application example, we performed an inversion analysis of fault slip in the 2011 Tohoku earthquake using Northeast Japan models generated by both our method and a conventional method (corresponding to Okada's analytical solution.) Our model has more than 150 million DOF and 4 layers with complex shape and different material properties. As a result, a significant difference in the results by the two models was seen, indicating the importance of introducing the layer shape of crust and heterogeneity of material in the models. The total computation time for Green's function is reduced by almost 1/7 because of the improvement of the computation method. We expect that this method will be a core technique of crustal deformation analysis. Our next plan is to take the ambiguity of the shape and the material property of the crust into consideration. Also, we would like to introduce viscoelasticity to the models.
Inversion of lidar signals with the slope method.
Kunz, G J; de Leeuw, G
1993-06-20
In homogeneous atmospheres, backscatter and extinction coefficients are commonly determined by the inversion of lidar signals by using the slope method, i.e., from a linear least-squares fit to the logarithm on the range-compensated lidar return. We investigate the accuracy of this method. A quantitative analysis is presented of the influence of white noise and atmospheric extinction on the accuracy of the slope method and on the maximum range of lidar systems. To meet this objective, we simulate lidar signals with extinction coefficients ranging from 10(-3) km(-1) to 10 km(-1) with different signal-to-noise ratios. It is shown that the backscatter coefficient can be determined by using the slope method with an ccuracy of better than ~ 10% if the extinction coefficient is smaller than 1 km(-1) and the signal-to-noise ratio is better than ~ 1000. The accuracy in the calculated extinction coefficient is only better than ~ 10% if the extinction is larger than 1 km(-1) and the signal-to-noise ratio is better than ~2000. If th atmospheric extinction coefficient is smaller than 0.1 km(-1), then it is not possible to invert the extinction from lidar measurements with an accuracy of 10% or better unless the signal-to-noise ratio isunrealistically high.
Inversion of Airborne Contaminants in a Regional Model
Akcelik, V.; Biros, G.; Draganescu, A.; Ghattas, O.; Hill, J.; van Bloemen Waanders, B.; /SLAC /Pennsylvania U. /Texas U. /Sandia
2007-01-10
We are interested in a DDDAS problem of localization of airborne contaminant releases in regional atmospheric transport models from sparse observations. Given measurements of the contaminant over an observation window at a small number of points in space, and a velocity field as predicted for example by a mesoscopic weather model, we seek an estimate of the state of the contaminant at the beginning of the observation interval that minimizes the least squares misfit between measured and predicted contaminant field, subject to the convection-diffusion equation for the contaminant. Once the ''initial'' conditions are estimated by solution of the inverse problem, we issue predictions of the evolution of the contaminant, the observation window is advanced in time, and the process repeated to issue a new prediction, in the style of 4D-Var. We design an appropriate numerical strategy that exploits the spectral structure of the inverse operator, and leads to efficient and accurate resolution of the inverse problem. Numerical experiments verify that high resolution inversion can be carried out rapidly for a well-resolved terrain model of the greater Los Angeles area.
Stochastic Time-lapse Seismic Inversion with a Hybrid Starting Model and Double-difference Data
NASA Astrophysics Data System (ADS)
Tao, Y.; Sen, M. K.; Zhang, R.; Spikes, K.
2012-12-01
We propose a robust stochastic time-lapse seismic inversion strategy with an application of monitoring a CO2 injection site. This workflow involves a baseline inversion using a hybrid starting model that combines a fractal prior and the low-frequency prior from well log data. This starting model extracts fractal statistics of the well data to provide an estimate of the null space. A second step of this workflow is to use a double-difference inversion scheme to focus on the local areas where time-lapse changes have occurred as a result of injecting CO2 into the reservoir. For this step, simulated data using the inverted prior from the baseline model and the difference between the baseline and repeat data are summed to produce the virtual repeat data. We use an error function that incorporates the model norms to regularize the inversion process. The seismic data are pre-processed using a local correlation based warping method to register different time-lapse datasets. The stochastic optimization method used here is very fast simulated annealing, where the updated model parameters are drawn from a temperature dependent Cauchy-like perturbation of current model parameters. Synthetic data show that double-difference inversion shows better result than a conventional two-pass approach. Inverted field data from Cranfield site shows time-lapse impedance changes that are consistent with CO2 injection effects.
An inverse model for magnetorheological dampers based on a restructured phenomenological model
NASA Astrophysics Data System (ADS)
Qian, Li-Jun; Liu, Bo; Chen, Peng; Bai, Xian-Xu
2016-04-01
Magnetorheological dampers (MRDs), a semi-active actuator based on MR effect, have great potential in vibration/shock control systems. However, it is difficult to establish its inverse model due to its intrinsic strong nonlinear hysteresis behaviors, and sequentially the precise, fast and effective control could not be realized effectively. This paper presents an inverse model for MRDs based on a restructured phenomenological model with incorporation of the "normalization" concept. The proposed inverse model of MRDs is validated by the simulation of the force tracking. The research results indicate that the inverse model could be applied for the damping force control with consideration of the strong nonlinear hysteresis behaviors of the MRDs.
Identification of dynamic stiffness matrices of elastomeric joints using direct and inverse methods
NASA Astrophysics Data System (ADS)
Noll, Scott; Dreyer, Jason T.; Singh, Rajendra
2013-08-01
New experiments are designed to permit direct comparison between direct and inverse identification methods of the dynamic stiffness matrices of elastomeric joints, including non-diagonal terms. The joints are constructed with combinations of inclined elastomeric cylinders to control non-diagonal terms in the stiffness matrix. The inverse experiment consists of an elastic metal beam end-supported by elastomeric joints coupling the in-plane transverse and longitudinal beam motion. A prior method is extended to identify the joint dynamic stiffness matrices of dimension 3 from limited modal measurements of the beam. The dynamic stiffness and loss factors of the elastomeric cylinders are directly measured in a commercial elastomer test machine in shear, compression, and inclined configurations and a coordinate transformation is used to estimate the kinematic non-diagonal stiffness terms. Agreement is found for both dynamic stiffness and loss factors between the direct and inverse methods at small displacements. Further, the identified joint properties are employed in a model that successfully predicts the modal parameters and accelerance spectra of the inverse experiment. This article provides valuable insight on the difficulties encountered when comparing system and elastomeric component test results.
Inverse modeling of FIB milling by dose profile optimization
NASA Astrophysics Data System (ADS)
Lindsey, S.; Waid, S.; Hobler, G.; Wanzenböck, H. D.; Bertagnolli, E.
2014-12-01
FIB technologies possess a unique ability to form topographies that are difficult or impossible to generate with binary etching through typical photo-lithography. The ability to arbitrarily vary the spatial dose distribution and therefore the amount of milling opens possibilities for the production of a wide range of functional structures with applications in biology, chemistry, and optics. However in practice, the realization of these goals is made difficult by the angular dependence of the sputtering yield and redeposition effects that vary as the topography evolves. An inverse modeling algorithm that optimizes dose profiles, defined as the superposition of time invariant pixel dose profiles (determined from the beam parameters and pixel dwell times), is presented. The response of the target to a set of pixel dwell times in modeled by numerical continuum simulations utilizing 1st and 2nd order sputtering and redeposition, the resulting surfaces are evaluated with respect to a target topography in an error minimization routine. Two algorithms for the parameterization of pixel dwell times are presented, a direct pixel dwell time method, and an abstracted method that uses a refineable piecewise linear cage function to generate pixel dwell times from a minimal number of parameters. The cage function method demonstrates great flexibility and efficiency as compared to the direct fitting method with performance enhancements exceeding ∼10× as compared to direct fitting for medium to large simulation sets. Furthermore, the refineable nature of the cage function enables solutions to adapt to the desired target function. The optimization algorithm, although working with stationary dose profiles, is demonstrated to be applicable also outside the quasi-static approximation. Experimental data confirms the viability of the solutions for 5 × 7 μm deep lens like structures defined by 90 pixel dwell times.
The independence of mass scales in inverse hierarchy models
NASA Astrophysics Data System (ADS)
Flores, Ricardo A.; Sher, Marc
1983-10-01
In inverse hierarchy models, one attempts to ``solve'' the hierarchy problem by generating a large scale X from a theory with only a smaller scale M. Einhorn and Jones have argued, however, that M and X are essentially independent scales, even though the ratio appears to be calculable. We consider a model in which the same phenomenon occurs, and show that it is identical to the more familiar ``near-Coleman-Weinberg'' models. As the latter clearly have two independent scales, one put in by hand and the other generated by dimensional transmutation, we argue that inverse hierarchy models also have two independent scales, thus agreeing with the more detailed analysis of Einhorn and Jones.
FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2013-10-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational
FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2012-09-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finance. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition
Research on inverse methods and optimization in Italy
NASA Technical Reports Server (NTRS)
Larocca, Francesco
1991-01-01
The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).
NASA Technical Reports Server (NTRS)
Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.
2005-01-01
In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article
NASA Astrophysics Data System (ADS)
Zhang, Chengjiao; Li, Xiaojie; Yang, Chenchen
2016-07-01
This paper introduces a modified method of characteristics and its application in forward and inversion simulations of underwater explosion. Compared with standard method of characteristics which is appropriate to homoentripic flow problem, the modified method can be also used to deal with isentropic flow problem such as underwater explosion. Underwater explosion of spherical TNT and composition B explosives are simulated by using the modified method, respectively. Peak pressures and flow field pressures are obtained, and they are coincident with those from empirical formulas. The comparison demonstrates the modified is feasible and reliable in underwater explosion simulation. Based on the modified method, inverse difference schemes and inverse method are introduced. Combined with the modified, the inverse schemes can be used to deal with gas-water interface inversion of underwater explosion. Inversion simulations of underwater explosion of the explosives are performed in water, and equation of state (EOS) of detonation product is not needed. The peak pressures from the forward simulations are provided as boundary conditions in the inversion simulations. Inversion interfaces are obtained and they are mainly in good agreement with those from the forward simulations in near field. The comparison indicates the inverse method and the inverse difference schemes are reliable and reasonable in interface inversion simulation.
Dynamic inverse models in human-cyber-physical systems
NASA Astrophysics Data System (ADS)
Robinson, Ryan M.; Scobee, Dexter R. R.; Burden, Samuel A.; Sastry, S. Shankar
2016-05-01
Human interaction with the physical world is increasingly mediated by automation. This interaction is characterized by dynamic coupling between robotic (i.e. cyber) and neuromechanical (i.e. human) decision-making agents. Guaranteeing performance of such human-cyber-physical systems will require predictive mathematical models of this dynamic coupling. Toward this end, we propose a rapprochement between robotics and neuromechanics premised on the existence of internal forward and inverse models in the human agent. We hypothesize that, in tele-robotic applications of interest, a human operator learns to invert automation dynamics, directly translating from desired task to required control input. By formulating the model inversion problem in the context of a tracking task for a nonlinear control system in control-a_ne form, we derive criteria for exponential tracking and show that the resulting dynamic inverse model generally renders a portion of the physical system state (i.e., the internal dynamics) unobservable from the human operator's perspective. Under stability conditions, we show that the human can achieve exponential tracking without formulating an estimate of the system's state so long as they possess an accurate model of the system's dynamics. These theoretical results are illustrated using a planar quadrotor example. We then demonstrate that the automation can intervene to improve performance of the tracking task by solving an optimal control problem. Performance is guaranteed to improve under the assumption that the human learns and inverts the dynamic model of the altered system. We conclude with a discussion of practical limitations that may hinder exact dynamic model inversion.
Modelling and genetic algorithm based optimisation of inverse supply chain
NASA Astrophysics Data System (ADS)
Bányai, T.
2009-04-01
(Recycling of household appliances with emphasis on reuse options). The purpose of this paper is the presentation of a possible method for avoiding the unnecessary environmental risk and landscape use through unprovoked large supply chain of collection systems of recycling processes. In the first part of the paper the author presents the mathematical model of recycling related collection systems (applied especially for wastes of electric and electronic products) and in the second part of the work a genetic algorithm based optimisation method will be demonstrated, by the aid of which it is possible to determine the optimal structure of the inverse supply chain from the point of view economical, ecological and logistic objective functions. The model of the inverse supply chain is based on a multi-level, hierarchical collection system. In case of this static model it is assumed that technical conditions are permanent. The total costs consist of three parts: total infrastructure costs, total material handling costs and environmental risk costs. The infrastructure-related costs are dependent only on the specific fixed costs and the specific unit costs of the operation points (collection, pre-treatment, treatment, recycling and reuse plants). The costs of warehousing and transportation are represented by the material handling related costs. The most important factors determining the level of environmental risk cost are the number of out of time recycled (treated or reused) products, the number of supply chain objects and the length of transportation routes. The objective function is the minimization of the total cost taking into consideration the constraints. However a lot of research work discussed the design of supply chain [8], but most of them concentrate on linear cost functions. In the case of this model non-linear cost functions were used. The non-linear cost functions and the possible high number of objects of the inverse supply chain leaded to the problem of choosing a
The generalized Phillips-Twomey method for NMR relaxation time inversion
NASA Astrophysics Data System (ADS)
Gao, Yang; Xiao, Lizhi; Zhang, Yi; Xie, Qingming
2016-10-01
The inversion of NMR relaxation time involves the Fredholm integral equation of the first kind. Due to its ill-posedness, numerical solutions to this type of equations are often found much less accurate and bear little resemblance to the true solution. There has been a strong interest in finding a well-posed method for this ill-posed problem since 1950s. In this paper, we prove the existence, the uniqueness, the stability and the convergence of the generalized Phillips-Twomey regularization method for solving this type of equations. Numerical simulations and core analyses arising from NMR transverse relaxation time inversion are conducted to show the effectiveness of the generalized Phillips-Twomey method. Both the simulation results and the core analyses agree well with the model and the realities.
Neural network fusion and inversion model for NDIR sensor measurement
NASA Astrophysics Data System (ADS)
Cieszczyk, Sławomir; Komada, Paweł
2015-12-01
This article presents the problem of the impact of environmental disturbances on the determination of information from measurements. As an example, NDIR sensor is studied, which can measure industrial or environmental gases of varying temperature. The issue of changes of influence quantities value appears in many industrial measurements. Developing of appropriate algorithms resistant to conditions changes is key problem. In the resulting mathematical model of inverse problem additional input variables appears. Due to the difficulties in the mathematical description of inverse model neural networks have been applied. They do not require initial assumptions about the structure of the created model. They provide correction of sensor non-linearity as well as correction of influence of interfering quantity. The analyzed issue requires additional measurement of disturbing quantity and its connection with measurement of primary quantity. Combining this information with the use of neural networks belongs to the class of sensor fusion algorithm.
Inverse problems in the modeling of vibrations of flexible beams
NASA Technical Reports Server (NTRS)
Banks, H. T.; Powers, R. K.; Rosen, I. G.
1987-01-01
The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.
NASA Astrophysics Data System (ADS)
Ke, Quanpeng
Heat flux and heat transfer coefficients at the interfaces of castings and molds are important parameters in the mold design and computer simulations of the solidification process in foundry operations. A better understanding of the heat flux and heat transfer coefficient between the solidifying casting and its mold can promote model design and improve the accuracy of computer simulation. The main purpose of the present dissertation involves the estimation of the heat flux and heat transfer coefficient at the interface of the molten metal and green sand. Since the inverse heat conduction method requires temperature measurement data to deduce the missing surface information, it is suitable for the present research. However, heat transfer inside green sand is complicated by the migration of water vapor and zonal temperature distribution results. This makes the solution of the inverse heat conduction problem more challenging. In this dissertation, Galerkin's method of Weighted Residual together with the front tracking technique is used in the development of a forward solver. Beck's future time step method incorporated with the Gaussian iterative minimization method is used as the inverse solver. The mathematical descriptions of the sensitivity coefficient for both the direct heat flux and direct heat transfer coefficient estimation are derived. The variations of the sensitivity coefficients with time are revealed. From the analysis of sensitivity coefficients, the concept of blank time period is proposed. This blank time period makes the inverse problem much more difficult. A total energy balance criterion is used to combat this. Numerical experiments confirmed the accuracy and robustness of both the direct heat flux estimation algorithm and the direct heat transfer coefficient estimation algorithm. Finally, some pouring experiments are carried out. The inverse algorithms are applied to the estimation of the heat flux and heat transfer coefficient at the interface of
Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.
2005-01-01
. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.
Why does inverse modeling of drainage inventories work?
NASA Astrophysics Data System (ADS)
White, Nicky; Roberts, Gareth
2016-04-01
We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. This approach builds upon a more general, non-linear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. We have tested both algorithms by inverting thousands of river profiles from Africa, Eurasia, the Americas, and Australia. For each continent, the drainage network was constructed from a digital elevation model and the fidelity of river profiles extracted from this network was carefully checked using satellite imagery. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Inverse modeling of these substantial inventories of river profiles suggests that drainage networks contain coherent signals that record the regional growth of elevation. In the second part of this presentation, we use spectral analysis of river profiles to suggest why drainage networks behave in a coherent, albeit non-linear, fashion. Our analysis implies that large-scale topographic signals injected into landscapes generate spectral slopes that are usually red (i.e. Brownian). At wavelengths shorter than tens of km, spectral slopes whiten which suggests that coherent topographic signals cease to exist at these shorter length scales. Our results suggest that inverse modeling of drainage networks can reveal useful information about landscape growth through space and time.
2.5D complex resistivity modeling and inversion using unstructured grids
NASA Astrophysics Data System (ADS)
Xu, Kaijun; Sun, Jie
2016-04-01
The characteristic of complex resistivity on rock and ore has been recognized by people for a long time. Generally we have used the Cole-Cole Model(CCM) to describe complex resistivity. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by CCM parameters such as direct resistivity(ρ0), chargeability(m), time constant(τ) and frequency dependence(c). Thus it is very important to obtain the complex parameters of geologic body. It is difficult to approximate complex structures and terrain using traditional rectangular grid. In order to enhance the numerical accuracy and rationality of modeling and inversion, we use an adaptive finite-element algorithm for forward modeling of the frequency-domain 2.5D complex resistivity and implement the conjugate gradient algorithm in the inversion of 2.5D complex resistivity. An adaptive finite element method is applied for solving the 2.5D complex resistivity forward modeling of horizontal electric dipole source. First of all, the CCM is introduced into the Maxwell's equations to calculate the complex resistivity electromagnetic fields. Next, the pseudo delta function is used to distribute electric dipole source. Then the electromagnetic fields can be expressed in terms of the primary fields caused by layered structure and the secondary fields caused by inhomogeneities anomalous conductivity. At last, we calculated the electromagnetic fields response of complex geoelectric structures such as anticline, syncline, fault. The modeling results show that adaptive finite-element methods can automatically improve mesh generation and simulate complex geoelectric models using unstructured grids. The 2.5D complex resistivity invertion is implemented based the conjugate gradient algorithm.The conjugate gradient algorithm doesn't need to compute the sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying vector. In addition, the inversion target zones are
Model Reduction of a Transient Groundwater-Flow Model for Bayesian Inverse Problems
NASA Astrophysics Data System (ADS)
Boyce, S. E.; Yeh, W. W.
2011-12-01
A Bayesian inverse problem requires many repeated model simulations to characterize an unknown parameter's posterior probability distribution. It is computationally infeasible to solve a Bayesian inverse problem of a discretized groundwater flow model with a high dimension parameter and state space. Model reduction has been shown to reduce the dimension of a groundwater model by several orders of magnitude and is well suited for Bayesian inverse problems. A projection-based model reduction approach is proposed to reduce the parameter and state dimensions of a groundwater model. Previous work has done this by using a greedy algorithm for the selection of parameter vectors that make up a basis and their corresponding steady-state solutions for a state basis. The proposed method extends this idea to include transient models by assembling sequentially though the greedy algorithm the parameter and state projection bases. The method begins with the parameter basis being a single vector that is equal to one or an accepted series of values. A set of state vectors that are solutions to the groundwater model using this parameter vector at appropriate times is called the parameter snapshot set. The appropriate times for the parameter snapshot set are determined by maximizing the set's minimum singular value. This optimization is a similar to those used in experimental design for maximizing information. The two bases are made orthonormal by a QR decomposition and applied to the full groundwater model to form a reduced model. The parameter basis is increased with a new parameter vector that maximizes the error between the full model and the reduced model at a set of observation times. The new parameter vector represents where the reduced model is least accurate in representing the original full model. The corresponding parameter snapshot set's appropriate times are found using a greedy algorithm. This sequentially chooses times that have maximum error between the full and
3D CSEM data inversion using Newton and Halley class methods
NASA Astrophysics Data System (ADS)
Amaya, M.; Hansen, K. R.; Morten, J. P.
2016-05-01
For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those
Theoretical study on the inverse modeling of deep body temperature measurement.
Huang, Ming; Chen, Wenxi
2012-03-01
We evaluated the theoretical aspects of monitoring the deep body temperature distribution with the inverse modeling method. A two-dimensional model was built based on anatomical structure to simulate the human abdomen. By integrating biophysical and physiological information, the deep body temperature distribution was estimated from cutaneous surface temperature measurements using an inverse quasilinear method. Simulations were conducted with and without the heat effect of blood perfusion in the muscle and skin layers. The results of the simulations showed consistently that the noise characteristics and arrangement of the temperature sensors were the major factors affecting the accuracy of the inverse solution. With temperature sensors of 0.05 °C systematic error and an optimized 16-sensor arrangement, the inverse method could estimate the deep body temperature distribution with an average absolute error of less than 0.20 °C. The results of this theoretical study suggest that it is possible to reconstruct the deep body temperature distribution with the inverse method and that this approach merits further investigation.
Pollution models and inverse distance weighting: Some critical remarks
NASA Astrophysics Data System (ADS)
de Mesnard, Louis
2013-03-01
When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model), and polluted rivers. The case where a station is confused with the reference point (or zero distance) is also discussed: in real cases this station imposes its measurement on the whole area regardless of the measurements made by other stations. This is a serious flaw when evaluating the mean pollution of an area. However, it is shown that this is not so in the case of a continuum of monitoring stations, and the measurement at the reference point and for the whole area may differ, which is satisfactory.
New 3D parallel SGILD modeling and inversion
Xie, G.; Li, J.; Majer, E.
1998-09-01
In this paper, a new parallel modeling and inversion algorithm using a Stochastic Global Integral and Local Differential equation (SGILD) is presented. The authors derived new acoustic integral equations and differential equation for statistical moments of the parameters and field. The new statistical moments integral equation on the boundary and local differential equations in domain will be used together to obtain mean wave field and its moments in the modeling. The new moments global Jacobian volume integral equation and the local Jacobian differential equations in domain will be used together to update the mean parameters and their moments in the inversion. A new parallel multiple hierarchy substructure direct algorithm or direct-iteration hybrid algorithm will be used to solve the sparse matrices and one smaller full matrix from domain to the boundary, in parallel. The SGILD modeling and imaging algorithm has many advantages over the conventional imaging approaches. The SGILD algorithm can be used for the stochastic acoustic, electromagnetic, and flow modeling and inversion, and are important for the prediction of oil, gas, coal, and geothermal energy reservoirs in geophysical exploration.
Full Waveform Inversion Methods for Source and Media Characterization before and after SPE5
NASA Astrophysics Data System (ADS)
Phillips-Alonge, K. E.; Knox, H. A.; Ober, C.; Abbott, R. E.
2015-12-01
The Source Physics Experiment (SPE) was designed to advance our understanding of explosion-source phenomenology and subsequent wave propagation through the development of innovative physics-based models. Ultimately, these models will be used for characterizing explosions, which can occur with a variety of yields, depths of burial, and in complex media. To accomplish this, controlled chemical explosions were conducted in a granite outcrop at the Nevada Nuclear Security Test Site. These explosions were monitored with extensive seismic and infrasound instrumentation both in the near and far-field. Utilizing this data, we calculate predictions before the explosions occur and iteratively improve our models after each explosion. Specifically, we use an adjoint-based full waveform inversion code that employs discontinuous Galerkin techniques to predict waveforms at station locations prior to the fifth explosion in the series (SPE5). The full-waveform inversions are performed using a realistic geophysical model based on local 3D tomography and inversions for media properties using previous shot data. The code has capabilities such as unstructured meshes that align with material interfaces, local polynomial refinement, and support for various physics and methods for implicit and explicit time-integration. The inversion results we show here evaluate these different techniques, which allows for model fidelity assessment (acoustic versus elastic versus anelastic, etc.). In addition, the accuracy and efficiency of several time-integration methods can be determined. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Schiller, Helmut
2007-05-01
The usage of inverse models to derive parameters of interest from measurements is widespread in science and technology. The operational usage of many inverse models became feasible just by emulation of the inverse model via a neural net (NN). This paper shows how NNs can be used to improve inversion accuracy by minimizing the sum of error squares. The procedure is very fast as it takes advantage of the Jacobian which is a byproduct of the NN calculation. An example from remote sensing is shown. It is also possible to take into account a non-diagonal covariance matrix of the measurement to derive the covariance matrix of the retrieved parameters.
Noncommutative Inverse Scattering Method for the Kontsevich System
NASA Astrophysics Data System (ADS)
Arthamonov, Semeon
2015-09-01
We formulate an analog of Inverse Scattering Method for integrable systems on noncommutative associative algebras. In particular, we define Hamilton flows, Casimir elements and noncommutative analog of the Lax matrix. The noncommutative Lax element generates infinite family of commuting Hamilton flows on an associative algebra. The proposed approach to integrable systems on associative algebras satisfies certain universal property, in particular, it incorporates both classical and quantum integrable systems as well as provides a basis for further generalization. We motivate our definition by explicit construction of noncommutative analog of Lax matrix for a system of differential equations on associative algebra recently proposed by Kontsevich. First, we present these equations in the Hamilton form by defining a bracket of Loday type on the group algebra of the free group with two generators. To make the definition more constructive, we utilize (with certain generalizations) the Van den Bergh approach to Loday brackets via double Poisson brackets. We show that there exists an infinite family of commuting flows generated by the noncommutative Lax element.
Inverse hydrological modelling of spatio-temporal rainfall patterns
NASA Astrophysics Data System (ADS)
Grundmann, Jens; Hörning, Sebastian; Bárdossy, András
2016-04-01
Distributed hydrological models are commonly used for simulating the non-linear response of a watershed to rainfall events for addressing different hydrological properties of the landscape. Such models are driven by spatial rainfall patterns for consecutive time steps, which are normally generated from point measurements using spatial interpolation methods. However, such methods fail in reproducing the true spatio-temporal rainfall patterns especially in data scarce regions with poorly gauged catchments or for highly dynamic, small scaled rainstorms which are not well recorded by existing monitoring networks. Consequently, uncertainties are associated with poorly identified spatio-temporal rainfall distribution in distributed rainfall-runoff-modelling since the amount of rainfall received by a catchment as well as the dynamics of the runoff generation of flood waves are underestimated. For addressing these challenges a novel methodology for inverse hydrological modelling is proposed using a Markov-Chain-Monte-Carlo framework. Thereby, potential candidates of spatio-temporal rainfall patterns are generated and selected according their ability to reproduce the observed surface runoff at the catchment outlet for a given transfer function in a best way. The Methodology combines the concept of random mixing of random spatial fields with a grid-based spatial distributed rainfall runoff model. The conditional target rainfall field is obtained as a linear combination of unconditional spatial random fields. The corresponding weights of the linear combination are selected such that the spatial variability of the rainfall amounts as well as the actual observed rainfall values are reproduced. The functionality of the methodology is demonstrated on a synthetic example. Thereby, the known spatio-temporal distribution of rainfall is reproduced for a given number of point observations of rainfall and the integral catchment response at the catchment outlet for a synthetic catchment
Group-theoretic models of the inversion process in bacterial genomes.
Egri-Nagy, Attila; Gebhardt, Volker; Tanaka, Mark M; Francis, Andrew R
2014-07-01
The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.
Markov Chain Monte Carlo Sampling Methods for 1D Seismic and EM Data Inversion
2008-09-22
This software provides several Markov chain Monte Carlo sampling methods for the Bayesian model developed for inverting 1D marine seismic and controlled source electromagnetic (CSEM) data. The current software can be used for individual inversion of seismic AVO and CSEM data and for joint inversion of both seismic and EM data sets. The structure of the software is very general and flexible, and it allows users to incorporate their own forward simulation codes and rockmore » physics model codes easily into this software. Although the softwae was developed using C and C++ computer languages, the user-supplied codes can be written in C, C++, or various versions of Fortran languages. The software provides clear interfaces for users to plug in their own codes. The output of this software is in the format that the R free software CODA can directly read to build MCMC objects.« less
Three-dimensional electromagnetic modeling and inversion on massively parallel computers
Newman, G.A.; Alumbaugh, D.L.
1996-03-01
This report has demonstrated techniques that can be used to construct solutions to the 3-D electromagnetic inverse problem using full wave equation modeling. To this point great progress has been made in developing an inverse solution using the method of conjugate gradients which employs a 3-D finite difference solver to construct model sensitivities and predicted data. The forward modeling code has been developed to incorporate absorbing boundary conditions for high frequency solutions (radar), as well as complex electrical properties, including electrical conductivity, dielectric permittivity and magnetic permeability. In addition both forward and inverse codes have been ported to a massively parallel computer architecture which allows for more realistic solutions that can be achieved with serial machines. While the inversion code has been demonstrated on field data collected at the Richmond field site, techniques for appraising the quality of the reconstructions still need to be developed. Here it is suggested that rather than employing direct matrix inversion to construct the model covariance matrix which would be impossible because of the size of the problem, one can linearize about the 3-D model achieved in the inverse and use Monte-Carlo simulations to construct it. Using these appraisal and construction tools, it is now necessary to demonstrate 3-D inversion for a variety of EM data sets that span the frequency range from induction sounding to radar: below 100 kHz to 100 MHz. Appraised 3-D images of the earth`s electrical properties can provide researchers opportunities to infer the flow paths, flow rates and perhaps the chemistry of fluids in geologic mediums. It also offers a means to study the frequency dependence behavior of the properties in situ. This is of significant relevance to the Department of Energy, paramount to characterizing and monitoring of environmental waste sites and oil and gas exploration.
Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models
Plant, Nathaniel G.; Holland, K. Todd
2011-01-01
A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.
Inversion of submesoscale patterns from a high-resolution Solomon Sea model: Feasibility assessment
NASA Astrophysics Data System (ADS)
Gaultier, Lucile; Djath, Bughsin'; Verron, Jacques; Brankart, Jean-Michel; Brasseur, Pierre; Melet, Angelique
2014-07-01
A high-resolution realistic numerical model of the Solomon Sea, which exhibits a high level of variability at mesoscales and submesoscales, is used to explore new avenues for data assimilation. Image data assimilation represents a powerful methodology to integrate information from high-resolution observations such as satellite sea surface temperature or chlorophyll, or high-resolution altimetric sea surface height that will be observed in the forthcoming SWOT mission. The present study investigates the feasibility and accuracy of the inversion of the dynamical submesoscale information contained in high-resolution images of sea surface temperature (SST) or salinity (SSS) to improve the estimation of oceanic surface currents. The inversion method is tested in the context of twin experiments, with SST and SSS data provided by a model of the Solomon Sea. For that purpose, synthetic tracer images are built by binarizing the norm of the gradient of SST, SSS or spiciness. The binarized tracer images are compared to the dynamical image which is derived from the Finite-Size Lyapunov Exponents. The adjustment of the dynamical image to the tracer image provides the optimal correction to be applied on the surface velocity field. The method is evaluated by comparing the result of the inversion to the reference model solution. The feasibility of the inversion of various images (SST, SSS, both SST and SSS or spiciness) is explored on two small areas of the Solomon Sea. We show that errors in the surface velocity field can be substantially reduced through the inversion of tracer images.
Inverse Modelling to Obtain Head Movement Controller Signal
NASA Technical Reports Server (NTRS)
Kim, W. S.; Lee, S. H.; Hannaford, B.; Stark, L.
1984-01-01
Experimentally obtained dynamics of time-optimal, horizontal head rotations have previously been simulated by a sixth order, nonlinear model driven by rectangular control signals. Electromyography (EMG) recordings have spects which differ in detail from the theoretical rectangular pulsed control signal. Control signals for time-optimal as well as sub-optimal horizontal head rotations were obtained by means of an inverse modelling procedures. With experimentally measured dynamical data serving as the input, this procedure inverts the model to produce the neurological control signals driving muscles and plant. The relationships between these controller signals, and EMG records should contribute to the understanding of the neurological control of movements.
Inversion methods for fast-ion velocity-space tomography in fusion plasmas
NASA Astrophysics Data System (ADS)
Jacobsen, A. S.; Stagner, L.; Salewski, M.; Geiger, B.; Heidbrink, W. W.; Korsholm, S. B.; Leipold, F.; Nielsen, S. K.; Rasmussen, J.; Stejner, M.; Thomsen, H.; Weiland, M.; the ASDEX Upgrade Team
2016-04-01
Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zeroth- and first-order Tikhonov regularization. The inversion methods are applied to fast-ion {{\\text{D}}α} measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high confidence regions, all methods agree that ions with pitch values close to zero, as well as ions with large pitch values, are ejected from the plasma center by the sawtooth crash, and that this ejection depletes the ion population with large pitch values more strongly.
Haynes, Mark; Verweij, Sacha A. M.; Moghaddam, Mahta; Carson, Paul L.
2014-01-01
A self-contained source characterization method for commercial ultrasound probes in transmission acoustic inverse scattering is derived and experimentally tested. The method is based on modified scattered field volume integral equations that are linked to the source-scattering transducer model. The source-scattering parameters are estimated via pair-wise transducer measurements and the nonlinear inversion of an acoustic propagation model that is derived. This combination creates a formal link between the transducer characterization and the inverse scattering algorithm. The method is tested with two commercial ultrasound probes in a transmission geometry including provisions for estimating the probe locations and aligning a robotic rotator. The transducer characterization results show that the nonlinear inversion fit the measured data well. The transducer calibration and inverse scattering algorithm are tested on simple targets. Initial images show that the recovered contrasts are physically consistent with expected values. PMID:24569251
Inverse problems and computational cell metabolic models: a statistical approach
NASA Astrophysics Data System (ADS)
Calvetti, D.; Somersalo, E.
2008-07-01
In this article, we give an overview of the Bayesian modelling of metabolic systems at the cellular and subcellular level. The models are based on detailed description of key biochemical reactions occurring in tissue, which may in turn be compartmentalized into cytosol and mitochondria, and of transports between the compartments. The classical deterministic approach which models metabolic systems as dynamical systems with Michaelis-Menten kinetics, is replaced by a stochastic extension where the model parameters are interpreted as random variables with an appropriate probability density. The inverse problem of cell metabolism in this setting consists of estimating the density of the model parameters. After discussing some possible approaches to solving the problem, we address the issue of how to assess the reliability of the predictions of a stochastic model by proposing an output analysis in terms of model uncertainties. Visualization modalities for organizing the large amount of information provided by the Bayesian dynamic sensitivity analysis are also illustrated.
A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.
Zhang, Kai; Wang, Zengfei; Zhang, Liming; Yao, Jun; Yan, Xia
2015-01-01
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
NASA Astrophysics Data System (ADS)
Iglesias, Marco A.
2016-02-01
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The general aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box (e.g. with commercial software). The proposed regularizing ensemble Kalman method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme (Hanke 1997 Inverse Problems 13 79-95) in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad hoc fixes, such as covariance localization, are implemented. The aim of this paper is to provide a detailed numerical investigation of the regularizing and convergence properties of the proposed regularizing ensemble Kalman scheme; the proof of these properties is an open problem. By means of numerical experiments, we investigate the conditions under which the proposed method inherits the regularizing properties of the LM scheme of (Hanke 1997 Inverse Problems 13 79-95) and is thus stable and suitable for its application in problems where the computation of the Fréchet derivative is not computationally feasible. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method
Toward Optimal and Scalable Dimension Reduction Methods for large-scale Bayesian Inversions
NASA Astrophysics Data System (ADS)
Bousserez, N.; Henze, D. K.
2015-12-01
Many inverse problems in geophysics are solved within the Bayesian framework, in which a prior probability density function of a quantity of interest is optimally updated using newly available observations. A maximum likelihood of the posterior probability density function is estimated using a model of the physics that relates the variables to be optimized to the observations. However, in many practical situations the number of observations is much smaller than the number of variables estimated, which leads to an ill-posed problem. In practice, this means that the data are informative only in a subspace of the initial space. It is both of theoretical and practical interest to characterize this "data-informed" subspace, since it allows a simple interpretation of the inverse solution and its uncertainty, but can also dramatically reduce the computational cost of the optimization by reducing the size of the problem. In this presentation the formalism of dimension reduction in Bayesian methods will be introduced, and different optimality criteria will be discussed (e.g., minimum error variances, maximum degree of freedom for signal). For each criterion, an optimal design for the reduced Bayesian problem will be proposed and compared with other suboptimal approaches. A significant advantage of our method is its high scalability owing to an efficient parallel implementation, making it very attractive for large-scale inverse problems. Numerical results from an Observation Simulation System Experiment (OSSE) consisting of a high spatial resolution (0.5°x0.7°) source inversion of methane over North America using observations from the Greenhouse gases Observing SATellite (GOSAT) instrument and the GEOS-Chem chemistry-transport model will illustrate the computational efficiency of our approach. Although only linear models are considered in this study, possible extensions to the non-linear case will also be discussed
NASA Technical Reports Server (NTRS)
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
Inverse-model-based cuffless blood pressure estimation using a single photoplethysmography sensor.
Suzuki, Arata
2015-07-01
This paper proposes an inverse-model-based cuffless method for estimating blood pressure using a single photoplethysmography sensor. The proposed method, which is based on the relationship between blood pressure and the features of pulse waves, employs an inverse estimation and uses the blood pressure as the explanatory variable. Using this method, the blood pressure can be estimated with high accuracy even in situations where the pulse wave features are scattered, as the method uses the dynamic signal-to-noise ratio of the Taguchi method. In order to verify the effectiveness of the proposed method, we employed it to measure the systolic blood pressure. It could be confirmed that the estimation accuracy of the proposed method is higher than that of similar methods.
New Y-function based MOSFET parameter extraction method from weak to strong inversion range
NASA Astrophysics Data System (ADS)
Henry, J. B.; Rafhay, Q.; Cros, A.; Ghibaudo, G.
2016-09-01
A new Y-function based MOSFET parameter extraction method is proposed. This method relies on explicit expressions of inversion charge and drain current versus Yc(=Qi√Cgc)-function and Y(=Id/√gm)-function, respectively, applicable from weak to strong inversion range. It enables a robust MOSFET parameter extraction even for low gate voltage overdrive, whereas conventional extraction techniques relying on strong inversion approximation fail.
Application of the Biot model to ultrasound in bone: inverse problem.
Sebaa, N; Fellah, Z A; Fellah, M; Ogam, E; Mitri, F G; Depollier, C; Lauriks, W
2008-07-01
This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimentally measured signals. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The ultrasonic propagation in cancellous bone is modelled using the Biot theory modified by the Johnson-Koplik-Dashen model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow waveforms. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.
Joint Inversion Modelling of Geophysical Data From Lough Neagh Basin
NASA Astrophysics Data System (ADS)
Vozar, J.; Moorkamp, M.; Jones, A. G.; Rath, V.; Muller, M. R.
2015-12-01
Multi-dimensional modelling of geophysical data collected in the Lough Neagh Basin is presented in the frame of the IRETHERM project. The Permo-Triassic Lough Neagh Basin, situated in the southeastern part of Northern Ireland, exhibits elevated geothermal gradient (~30 °C/km) in the exploratory drilled boreholes. This is taken to indicate good geothermal exploitation potential in the Sherwood Sandstone aquifer for heating, and possibly even electricity production, purposes. We have used a 3-D joint inversion framework for modelling the magnetotelluric (MT) and gravity data collected to the north of the Lough Neagh to derive robust subsurface geological models. Comprehensive supporting geophysical and geological data (e.g. borehole logs and reflection seismic images) have been used in order to analyze and model the MT and gravity data. The geophysical data sets were provided by the Geological Survey of Northern Ireland (GSNI). Considering correct objective function weighting in favor of noise-free MT response functions is particularly important in joint inversion. There is no simple way how to correct distortion effects the 3-D responses as can be done in 1-D or 2-D case. We have used the Tellus Project airborne EM data to constrain magnetotelluric data and correct them for near surface effects. The shallow models from airborne data are used to constrain the uppermost part of 3-D inversion model. Preliminary 3-D joint inversion modeling reveals that the Sherwood Sandstone Group and the Permian Sandstone Formation are imaged as a conductive zone at the depth range of 500 m to 2000 m with laterally varying thickness, depth, and conductance. The conductive target sediments become shallower and thinner to the north and they are laterally continuous. To obtain better characterization of thermal transport properties of investigated area we used porosity and resistivity data from the Annaghmore and Ballymacilroy boreholes to estimate the relations between porosity
Parallel Infrastructure Modeling and Inversion Module for E4D
2014-10-09
Electrical resistivity tomography ERT is a method of imaging the electrical conductivity of the subsurface. Electrical conductivity is a useful metric for understanding the subsurface because it is governed by geomechanical and geochemical properties that drive subsurface systems. ERT works by injecting current into the subsurface across a pair of electrodes, and measuring the corresponding electrical potential response across another pair of electrodes. Many such measurements are strategically taken across an array of electrodes to produce an ERT data set. These data are then processed through a computationally demanding process known as inversion to produce an image of the subsurface conductivity structure that gave rise to the measurements. Data can be inverted to provide 2D images, 3D images, or in the case of time-lapse 3D imaging, 4D images. ERT is generally not well suited for environments with buried electrically conductive infrastructure such as pipes, tanks, or well casings, because these features tend to dominate and degrade ERT images. This reduces or eliminates the utility of ERT imaging where it would otherwise be highly useful for, for example, imaging fluid migration from leaking pipes, imaging soil contamination beneath leaking subusurface tanks, and monitoring contaminant migration in locations with dense network of metal cased monitoring wells. The location and dimension of buried metallic infrastructure is often known. If so, then the effects of the infrastructure can be explicitly modeled within the ERT imaging algorithm, and thereby removed from the corresponding ERT image. However,there are a number of obstacles limiting this application. 1) Metallic infrastructure cannot be accurately modeled with standard codes because of the large contrast in conductivity between the metal and host material. 2) Modeling infrastructure in true dimension requires the computational mesh to be highly refined near the metal inclusions, which increases
Using informative priors in facies inversion: The case of C-ISR method
NASA Astrophysics Data System (ADS)
Valakas, G.; Modis, K.
2016-08-01
Inverse problems involving the characterization of hydraulic properties of groundwater flow systems by conditioning on observations of the state variables are mathematically ill-posed because they have multiple solutions and are sensitive to small changes in the data. In the framework of McMC methods for nonlinear optimization and under an iterative spatial resampling transition kernel, we present an algorithm for narrowing the prior and thus producing improved proposal realizations. To achieve this goal, we cosimulate the facies distribution conditionally to facies observations and normal scores transformed hydrologic response measurements, assuming a linear coregionalization model. The approach works by creating an importance sampling effect that steers the process to selected areas of the prior. The effectiveness of our approach is demonstrated by an example application on a synthetic underdetermined inverse problem in aquifer characterization.
Goal Directed Model Inversion: A Study of Dynamic Behavior
NASA Technical Reports Server (NTRS)
Colombano, Silvano P.; Compton, Michael; Raghavan, Bharathi; Lum, Henry, Jr. (Technical Monitor)
1994-01-01
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome 0 "would have been right if the outcome had been the desired one." The algorithm then proceeds as follows: (1) store the action that produced the wrong outcome as a "target" (2) redefine the wrong outcome as a desired goal (3) submit the new desired goal to the system (4) compare the new action with the target action and modify the system by using a suitable algorithm for credit assignment (Back propagation in our example) (5) resubmit the original goal. Prior publications by our group in this area focused on demonstrating empirical results based on the inverse kinematic problem for a simulated robotic arm. In this paper we apply the inversion process to much simpler analytic functions in order to elucidate the dynamic behavior of the system and to determine the sensitivity of the learning process to various parameters. This understanding will be necessary for the acceptance of GDMI as a practical tool.
Feedback control by online learning an inverse model.
Waegeman, Tim; Wyffels, Francis; Schrauwen, Francis
2012-10-01
A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made. PMID:24808008
NASA Technical Reports Server (NTRS)
Gutmann, Ethan D.; Small, Eric E.
2007-01-01
Soil hydraulic properties (SHPs) regulate the movement of water in the soil. This in turn plays an important role in the water and energy cycles at the land surface. At present, SHPS are commonly defined by a simple pedotransfer function from soil texture class, but SHPs vary more within a texture class than between classes. To examine the impact of using soil texture class to predict SHPS, we run the Noah land surface model for a wide variety of measured SHPs. We find that across a range of vegetation cover (5 - 80% cover) and climates (250 - 900 mm mean annual precipitation), soil texture class only explains 5% of the variance expected from the real distribution of SHPs. We then show that modifying SHPs can drastically improve model performance. We compare two methods of estimating SHPs: (1) inverse method, and (2) soil texture class. Compared to texture class, inverse modeling reduces errors between measured and modeled latent heat flux from 88 to 28 w/m(exp 2). Additionally we find that with increasing vegetation cover the importance of SHPs decreases and that the van Genuchten m parameter becomes less important, while the saturated conductivity becomes more important.
Risk evaluation of uranium mining: A geochemical inverse modelling approach
NASA Astrophysics Data System (ADS)
Rillard, J.; Zuddas, P.; Scislewski, A.
2011-12-01
It is well known that uranium extraction operations can increase risks linked to radiation exposure. The toxicity of uranium and associated heavy metals is the main environmental concern regarding exploitation and processing of U-ore. In areas where U mining is planned, a careful assessment of toxic and radioactive element concentrations is recommended before the start of mining activities. A background evaluation of harmful elements is important in order to prevent and/or quantify future water contamination resulting from possible migration of toxic metals coming from ore and waste water interaction. Controlled leaching experiments were carried out to investigate processes of ore and waste (leached ore) degradation, using samples from the uranium exploitation site located in Caetité-Bahia, Brazil. In experiments in which the reaction of waste with water was tested, we found that the water had low pH and high levels of sulphates and aluminium. On the other hand, in experiments in which ore was tested, the water had a chemical composition comparable to natural water found in the region of Caetité. On the basis of our experiments, we suggest that waste resulting from sulphuric acid treatment can induce acidification and salinization of surface and ground water. For this reason proper storage of waste is imperative. As a tool to evaluate the risks, a geochemical inverse modelling approach was developed to estimate the water-mineral interaction involving the presence of toxic elements. We used a method earlier described by Scislewski and Zuddas 2010 (Geochim. Cosmochim. Acta 74, 6996-7007) in which the reactive surface area of mineral dissolution can be estimated. We found that the reactive surface area of rock parent minerals is not constant during time but varies according to several orders of magnitude in only two months of interaction. We propose that parent mineral heterogeneity and particularly, neogenic phase formation may explain the observed variation of the
Reconstruction of multiple gastric electrical wave fronts using potential-based inverse methods
NASA Astrophysics Data System (ADS)
Kim, J. H. K.; Pullan, A. J.; Cheng, L. K.
2012-08-01
One approach for non-invasively characterizing gastric electrical activity, commonly used in the field of electrocardiography, involves solving an inverse problem whereby electrical potentials on the stomach surface are directly reconstructed from dense potential measurements on the skin surface. To investigate this problem, an anatomically realistic torso model and an electrical stomach model were used to simulate potentials on stomach and skin surfaces arising from normal gastric electrical activity. The effectiveness of the Greensite-Tikhonov or the Tikhonov inverse methods were compared under the presence of 10% Gaussian noise with either 84 or 204 body surface electrodes. The stability and accuracy of the Greensite-Tikhonov method were further investigated by introducing varying levels of Gaussian signal noise or by increasing or decreasing the size of the stomach by 10%. Results showed that the reconstructed solutions were able to represent the presence of propagating multiple wave fronts and the Greensite-Tikhonov method with 204 electrodes performed best (correlation coefficients of activation time: 90%; pacemaker localization error: 3 cm). The Greensite-Tikhonov method was stable with Gaussian noise levels up to 20% and 10% change in stomach size. The use of 204 rather than 84 body surface electrodes improved the performance; however, for all investigated cases, the Greensite-Tikhonov method outperformed the Tikhonov method.
A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty
Zhang, Kai; Wang, Zengfei; Zhang, Liming; Yao, Jun; Yan, Xia
2015-01-01
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model’s parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively ‘important’ elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient. PMID:26252392
Modeling and inversion Matlab algorithms for resistivity, induced polarization and seismic data
NASA Astrophysics Data System (ADS)
Karaoulis, M.; Revil, A.; Minsley, B. J.; Werkema, D. D.
2011-12-01
M. Karaoulis (1), D.D. Werkema (3), A. Revil (1,2), A., B. Minsley (4), (1) Colorado School of Mines, Dept. of Geophysics, Golden, CO, USA. (2) ISTerre, CNRS, UMR 5559, Université de Savoie, Equipe Volcan, Le Bourget du Lac, France. (3) U.S. EPA, ORD, NERL, ESD, CMB, Las Vegas, Nevada, USA . (4) USGS, Federal Center, Lakewood, 10, 80225-0046, CO. Abstract We propose 2D and 3D forward modeling and inversion package for DC resistivity, time domain induced polarization (IP), frequency-domain IP, and seismic refraction data. For the resistivity and IP case, discretization is based on rectangular cells, where each cell has as unknown resistivity in the case of DC modelling, resistivity and chargeability in the time domain IP modelling, and complex resistivity in the spectral IP modelling. The governing partial-differential equations are solved with the finite element method, which can be applied to both real and complex variables that are solved for. For the seismic case, forward modeling is based on solving the eikonal equation using a second-order fast marching method. The wavepaths are materialized by Fresnel volumes rather than by conventional rays. This approach accounts for complicated velocity models and is advantageous because it considers frequency effects on the velocity resolution. The inversion can accommodate data at a single time step, or as a time-lapse dataset if the geophysical data are gathered for monitoring purposes. The aim of time-lapse inversion is to find the change in the velocities or resistivities of each model cell as a function of time. Different time-lapse algorithms can be applied such as independent inversion, difference inversion, 4D inversion, and 4D active time constraint inversion. The forward algorithms are benchmarked against analytical solutions and inversion results are compared with existing ones. The algorithms are packaged as Matlab codes with a simple Graphical User Interface. Although the code is parallelized for multi
NASA Astrophysics Data System (ADS)
Gallovic, F.; Ampuero, J. P.
2015-12-01
Slip inversion methods differ in how the rupture model is parameterized and which regularizations or constraints are applied. However, there is still no consensus about which of the slip inversion methods are preferable and how reliable the inferred source models are due to the non-uniqueness or ill-posedness of the inverse problem. The 'Source Inversion Validation' (SIV) initiative aims to characterize and understand the performance of slip inversion methods (http://equake-rc.info/SIV/). Up to now, four benchmark test cases have been proposed, some of which were even conducted as blind tests. The next step is performing quantitative comparisons of the inverted rupture models. To this aim, we introduce a new comparison technique based on a Singular Value Decomposition (SVD) of the design matrix of the continuum inverse problem. We separate the range and null sub-spaces (representing resolved and unresolved features, respectively) by a selected 'cut-off' singular value, and compare different inverted models to the target (exact) model after projecting them on the range sub-space. This procedure effectively quantifies the ability of an inversion result to reproduce the resolvable features of the source. We find that even with perfect Green's functions the quality of an inverted model deteriorates with decreasing cut-off singular value due to applied regularization (smoothing and positivity constraints). Applying this approach to the inversion results of the SIV2a benchmark from various authors shows that the inferred source images are very similar to the target model when we consider a cut-off at ~1/10 of the largest singular value. Although the truncated model captures the overall rupture propagation, the final slip is biased significantly, showing distinct peaks below the stations lying above the rupture. We also show synthetic experiments to assess the role of station coverage, crustal velocity model, etc. on the conditioning of the slip inversion.
Depth-weighted Inverse and Imaging methods to study the Earth's Crust in Southern Italy
NASA Astrophysics Data System (ADS)
Fedi, M.
2012-04-01
Inversion means solving a set of geophysical equations for a spatial distribution of parameters (or functions) which could have produced an observed set of measurements. Imaging is instead a transformation of magnetometric data into a scaled 3D model resembling the true geometry of subsurface geologic features. While inversion theory allows many additional constraints, such as depth weighting, positivity, physical property bounds, smoothness, focusing, imaging methods of magnetic data derived under different theories are all found to reduce to either simple upward continuation or a depth-weighted upward continuation, with weights expressed in the general form of a power law of the altitude, with the half of the structural index as exponent. Note however that specifying the appropriate level of depth weighting is not just a problem in these imaging techniques but should also be considered in standard inversion methods. We will also investigate the relationship between imaging methods and multiscale methods. A multiscale analysis is well suitable to study potential fields because the way potential fields convey source information is strictly related to the scale of analysis. The stability of multiscale methods results from mixing, in a single operator, the wavenumber low-pass behaviour of the upward continuation transformation of the field with the enhancement high-pass properties of n-order derivative transformations. So, the complex reciprocal interference of several field components may be efficiently faced at several scales of the analysis and the depth to the sources may be estimated together with the homogeneity degrees of the field. We will describe the main aspects of both the kinds of interpretation under the study of multi-source models and apply either inversion or imaging techniques to the magnetic data of complex crustal areas of Southern Italy, such as the Campanian volcanic district and the Southern Apennines. The studied area includes a Pleistocene
A covariance-adaptive approach for regularized inversion in linear models
NASA Astrophysics Data System (ADS)
Kotsakis, Christopher
2007-11-01
The optimal inversion of a linear model under the presence of additive random noise in the input data is a typical problem in many geodetic and geophysical applications. Various methods have been developed and applied for the solution of this problem, ranging from the classic principle of least-squares (LS) estimation to other more complex inversion techniques such as the Tikhonov-Philips regularization, truncated singular value decomposition, generalized ridge regression, numerical iterative methods (Landweber, conjugate gradient) and others. In this paper, a new type of optimal parameter estimator for the inversion of a linear model is presented. The proposed methodology is based on a linear transformation of the classic LS estimator and it satisfies two basic criteria. First, it provides a solution for the model parameters that is optimally fitted (in an average quadratic sense) to the classic LS parameter solution. Second, it complies with an external user-dependent constraint that specifies a priori the error covariance (CV) matrix of the estimated model parameters. The formulation of this constrained estimator offers a unified framework for the description of many regularization techniques that are systematically used in geodetic inverse problems, particularly for those methods that correspond to an eigenvalue filtering of the ill-conditioned normal matrix in the underlying linear model. Our study lies on the fact that it adds an alternative perspective on the statistical properties and the regularization mechanism of many inversion techniques commonly used in geodesy and geophysics, by interpreting them as a family of `CV-adaptive' parameter estimators that obey a common optimal criterion and differ only on the pre-selected form of their error CV matrix under a fixed model design.
Ray, J.; Lee, J.; Yadav, V.; Lefantzi, S.; Michalak, A. M.; van Bloemen Waanders, B.
2014-08-20
We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO2 (ffCO2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less
Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions
Zhao, Yueqing; Lin, Rongfei; Šmarda, Zdenek; Khan, Yasir; Chen, Jinbiao; Wu, Qingbiao
2015-01-01
Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem. PMID:25884027
An initial inverse calibration of the ground-water flow model for the Hanford unconfined aquifer
Jacobson, E.A. . Desert Research Inst.); Freshly, M.D. )
1990-03-01
Large volumes of process cooling water are discharged to the ground form U.S. Department of Energy (DOE) nuclear fuel processing operations in the central portion of the Hanford Site in southeastern Washington. Over the years, these large volumes of waste water have recharged the unconfined aquifer at the Site. This artificial recharge has affected ground-water levels and contaminant movement in the unconfined aquifer. Ground-water flow and contaminant transport models have been applied to assess the impacts of site operations on the rate and direction of ground-water flow and contaminant transport in unconfined aquifer at the Hanford Site. The inverse calibration method developed by Neuman and modified by Jacobson was applied to improve calibration of a ground-water flow model of the unconfined aquifer at the Hanford Site. All information about estimates of hydraulic properties of the aquifer, hydraulic heads, boundary conditions, and discharges to and withdrawals form the aquifer is included in the inverse method to obtain an initial calibration of the ground-water flow model. The purpose of this report is to provide a description of the inverse method, its initial application to the unconfined aquifer at Hanford, and to present results of the initial inverse calibration. 28 refs., 19 figs., 1 tab.
NASA Astrophysics Data System (ADS)
He, Qinglong; Han, Bo; Chen, Yong; Li, Yang
2016-01-01
In this paper, we present an efficient inversion method to reconstruct the velocity and density model based on the acoustic wave equation. The inversion is performed in the frequency domain using the finite-difference contrast source inversion (FD-CSI) method. The full forward problem is required to be solved only once at the beginning of the inversion process, which makes the method very computationally efficient. Furthermore, the flexibility of the finite-difference operator ensures FD-CSI the capability of handling complex geophysical applications with inhomogeneous background media. Moreover, different parameters are automatically normalized, avoiding the numerical difficulty arising from the different magnitudes of the parameters. A variant of total variation regularization called multiplicative constraint is incorporated to resolve the sharp discontinuities of the parameters. We employ a two-phase inversion strategy to carry out the FD-CSI method. After simultaneously reconstructing the bulk modulus and density, we obtain a relatively reliable bulk modulus, which is used as the background in the next phase to retrieve more accurate bulk modulus and density. A simple experiment is carried out to present the capability of the FD-CSI method in dealing with the cross talk effect between different parameters. The application on the Marmousi model further emphasizes the performance of the method for more complex geophysical problems.
NASA Astrophysics Data System (ADS)
Li, Guo-Yang; Zheng, Yang; Liu, Yanlin; Destrade, Michel; Cao, Yanping
2016-11-01
A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.
Moissenet, Florent; Chèze, Laurence; Dumas, Raphaël
2012-06-01
Inverse dynamics combined with a constrained static optimization analysis has often been proposed to solve the muscular redundancy problem. Typically, the optimization problem consists in a cost function to be minimized and some equality and inequality constraints to be fulfilled. Penalty-based and Lagrange multipliers methods are common optimization methods for the equality constraints management. More recently, the pseudo-inverse method has been introduced in the field of biomechanics. The purpose of this paper is to evaluate the ability and the efficiency of this new method to solve the muscular redundancy problem, by comparing respectively the musculo-tendon forces prediction and its cost-effectiveness against common optimization methods. Since algorithm efficiency and equality constraints fulfillment highly belong to the optimization method, a two-phase procedure is proposed in order to identify and compare the complexity of the cost function, the number of iterations needed to find a solution and the computational time of the penalty-based method, the Lagrange multipliers method and pseudo-inverse method. Using a 2D knee musculo-skeletal model in an isometric context, the study of the cost functions isovalue curves shows that the solution space is 2D with the penalty-based method, 3D with the Lagrange multipliers method and 1D with the pseudo-inverse method. The minimal cost function area (defined as the area corresponding to 5% over the minimal cost) obtained for the pseudo-inverse method is very limited and along the solution space line, whereas the minimal cost function area obtained for other methods are larger or more complex. Moreover, when using a 3D lower limb musculo-skeletal model during a gait cycle simulation, the pseudo-inverse method provides the lowest number of iterations while Lagrange multipliers and pseudo-inverse method have almost the same computational time. The pseudo-inverse method, by providing a better suited cost function and an
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Inverse modeling analysis of soil dust emissions over East Asia
NASA Astrophysics Data System (ADS)
Ku, B.; Park, R.
2009-12-01
Soil dust is the most important aerosol by mass concentrations in the troposphere and has considerable effects on air quality and climate. East Asia including southern Mongolia and northern China is one of important source regions. Accurate simulations of dust storm outbreak would be thus crucial for protecting human health as well as for better assessing its climatic impacts. However, huge uncertainties in soil dust simulations especially for dust sources in East Asia are still present in the state-of-the-art aerosol models. We here attempt to reduce uncertainty with simulated dust sources by applying inverse modeling technique and gain better understanding on physical processes determining dust mobilization over East Asia. We used a 3-D global chemical transport model (GEOS-Chem) with DEAD dust mobilization scheme in 2001. In addition we implemented in the model a Shao dust emission scheme which uses different threshold friction velocity as a function of particle sizes. We first evaluated the model by comparing simulated aerosol concentrations against observations in China, Korea, and Japan. The model with the DEAD scheme overestimated PM10 mass concentrations close to dust source regions in China but underestimated observed PM10 in downwind regions such as Korea and Japan during dust storm breaks. These simulated discrepancies, however, were much reduced in the model with Shao scheme resulting from spatial changes in dust sources. To examine determining parameters of dust sources in those two schemes and underlying physical processes we conduct an inverse modeling analysis of dust emissions from 4 source regions (Inner Mongolia, Gobi, Taklamakan desert, Mongolian plateau). Our analysis yields optimized dust sources over East Aisa, which enable us to better quantify spatial and temporal distributions of dust aerosol concentrations and their contributions to both air quality and climate over East Asia.
Fast full waveform inversion with source encoding and second-order optimization methods
NASA Astrophysics Data System (ADS)
Castellanos, Clara; Métivier, Ludovic; Operto, Stéphane; Brossier, Romain; Virieux, Jean
2015-02-01
Full waveform inversion (FWI) of 3-D data sets has recently been possible thanks to the development of high performance computing. However, FWI remains a computationally intensive task when high frequencies are injected in the inversion or more complex wave physics (viscoelastic) is accounted for. The highest computational cost results from the numerical solution of the wave equation for each seismic source. To reduce the computational burden, one well-known technique is to employ a random linear combination of the sources, rather that using each source independently. This technique, known as source encoding, has shown to successfully reduce the computational cost when applied to real data. Up to now, the inversion is normally carried out using gradient descent algorithms. With the idea of achieving a fast and robust frequency-domain FWI, we assess the performance of the random source encoding method when it is interfaced with second-order optimization methods (quasi-Newton l-BFGS, truncated Newton). Because of the additional seismic modelings required to compute the Newton descent direction, it is not clear beforehand if truncated Newton methods can indeed further reduce the computational cost compared to gradient algorithms. We design precise stopping criteria of iterations to fairly assess the computational cost and the speed-up provided by the source encoding method for each optimization method. We perform experiment on synthetic and real data sets. In both cases, we confirm that combining source encoding with second-order optimization methods reduces the computational cost compared to the case where source encoding is interfaced with gradient descent algorithms. For the synthetic data set, inspired from the geology of Gulf of Mexico, we show that the quasi-Newton l-BFGS algorithm requires the lowest computational cost. For the real data set application on the Valhall data, we show that the truncated Newton methods provide the most robust direction of descent.
Model error estimation and correction by solving a inverse problem
NASA Astrophysics Data System (ADS)
Xue, Haile
2016-04-01
Nowadays, the weather forecasts and climate predictions are increasingly relied on numerical models. Yet, errors inevitably exist in model due to the imperfect numeric and parameterizations. From the practical point of view, model correction is an efficient strategy. Despite of the different complexity of forecast error correction algorithms, the general idea is to estimate the forecast errors by considering the NWP as a direct problem. Chou (1974) suggested an alternative view by considering the NWP as an inverse problem. The model error tendency term (ME) due to the model deficiency is assumed as an unknown term in NWP model, which can be discretized into short intervals (for example 6 hour) and considered as a constant or linear form in each interval. Given the past re-analyses and NWP model, the discretized MEs in the past intervals can be solved iteratively as a constant or linear-increased tendency term in each interval. These MEs can be further used as the online corrections. In this study, an iterative method for obtaining the MEs in past intervals was presented, and its convergence had been confirmed with sets of experiments in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August (JA) 2009 and January-February (JF) 2010. Then these MEs were used to get online model corretions based of systematic errors of GRAPES-GFS for July 2009 and January 2010. The data sets associated with initial condition and sea surface temperature (SST) used in this study are both based on NCEP final (FNL) data. According to the iterative numerical experiments, the following key conclusions can be drawn:(1) Batches of iteration test results indicated that the hour 6 forecast errors were reduced to 10% of their original value after 20 steps of iteration.(2) By offlinely comparing the error corrections estimated by MEs to the mean forecast errors, the patterns of estimated errors were considered to agree well with those
NASA Astrophysics Data System (ADS)
Jiang, Jun
This dissertation summarizes a procedure to design blades with finite thickness in three dimensions. In this inverse method, the prescribed quantities are the blade pressure loading shape, the inlet and outlet spanwise distributions of swirl, and the blade thickness distributions, and the primary calculated quantity is the blade geometry. The method is formulated in the fully inverse mode for design of three-dimensional blades in rotational and compressible flows whereby the blade shape is determined iteratively using the flow tangency condition along the blade surfaces. This technique is demonstrated here in the first instance for the design of two-dimensional cascaded and three-dimensional blades with finite thickness in inviscid and incompressible flows. In addition, the incoming flow is assumed irrotational so that the only vorticity present in the flowfield is the blade bound and shed vorticities. Design calculations presented for two-dimensional cascaded blades include an inlet guide vane, an impulse turbine blade, and a compressor blade. Consistency check is carried out for these cascaded blade design calculations using a panel analysis method and the analytical solution for the Gostelow profile. Free-vortex design results are also shown for fully three-dimensional blades with finite thickness such as an inlet guide vane, a rotor of axial-flow pumps, and a high-flow-coefficient pump inducer with design parameters typically found in industrial applications. These three-dimensional inverse design results are verified using Adamczyk's inviscid code.
TIME-LAPSE MODELING AND INVERSION OF CO2 SATURATION FOR SEQUESTRATION AND ENHANCED OIL RECOVERY
Mark A. Meadows
2004-11-19
In the fourth quarter of this DOE NETL project, they have developed an algorithm for generating time-lapse seismic anomalies from changes in fluid properties over time. This forward-modeling algorithm constitutes the first step in the inversion procedure of Phase III of the project. Examples were generated illustrating the flexibility of this approach. Additional activities in this reporting period included a trip by the Principal Investigator to the 7th International Conference on Greenhouse Gas Control Technologies (GHGT-7) in Vancouver, Canada, September 5-9, 2004. In the next quarter, they will work on the second step of the inversion procedure, namely, the inversion of the seismic time-lapse anomalies to obtain changes in fluid properties, and will continue investigating alternative methods for calculating properties of oil/brine/CO{sub 2} and brine/CO{sub 2} systems.
Irrigation Requirement Estimation Using Vegetation Indices and Inverse Biophysical Modeling
NASA Technical Reports Server (NTRS)
Bounoua, Lahouari; Imhoff, Marc L.; Franks, Shannon
2010-01-01
We explore an inverse biophysical modeling process forced by satellite and climatological data to quantify irrigation requirements in semi-arid agricultural areas. We constrain the carbon and water cycles modeled under both equilibrium, balance between vegetation and climate, and non-equilibrium, water added through irrigation. We postulate that the degree to which irrigated dry lands vary from equilibrium climate conditions is related to the amount of irrigation. The amount of water required over and above precipitation is considered as an irrigation requirement. For July, results show that spray irrigation resulted in an additional amount of water of 1.3 mm per occurrence with a frequency of 24.6 hours. In contrast, the drip irrigation required only 0.6 mm every 45.6 hours or 46% of that simulated by the spray irrigation. The modeled estimates account for 87% of the total reported irrigation water use, when soil salinity is not important and 66% in saline lands.
Sneutrino dark matter in gauged inverse seesaw models for neutrinos.
An, Haipeng; Dev, P S Bhupal; Cai, Yi; Mohapatra, R N
2012-02-24
Extending the minimal supersymmetric standard model to explain small neutrino masses via the inverse seesaw mechanism can lead to a new light supersymmetric scalar partner which can play the role of inelastic dark matter (IDM). It is a linear combination of the superpartners of the neutral fermions in the theory (the light left-handed neutrino and two heavy standard model singlet neutrinos) which can be very light with mass in ~5-20 GeV range, as suggested by some current direct detection experiments. The IDM in this class of models has keV-scale mass splitting, which is intimately connected to the small Majorana masses of neutrinos. We predict the differential scattering rate and annual modulation of the IDM signal which can be testable at future germanium- and xenon-based detectors.
Influence of head models on neuromagnetic fields and inverse source localizations
Ramon, Ceon; Haueisen, Jens; Schimpf, Paul H
2006-01-01
Background The magnetoencephalograms (MEGs) are mainly due to the source currents. However, there is a significant contribution to MEGs from the volume currents. The structure of the anatomical surfaces, e.g., gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the MEGs and the inverse source localizations. This was examined in detail with three different human head models. Methods Three finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissuetype model, (3) the Model 3 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. The lead fields and MEGs due to dipolar sources in the motor cortex were computed for all three models. The dipolar sources were oriented normal to the cortical surface and had a dipole moment of 100 μA meter. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. A set of 100 trial inverse runs was made covering the 3 cm cube motor cortex area in a random fashion. The Model 1 was used as a reference model. Results The reference model (Model 1), as expected, performed best in localizing the sources in the motor cortex area. The Model 3 performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The contour plots of the magnetic fields on top of the head were also different for all three models. The magnetic fields due to source currents were larger in magnitude as compared to the magnetic fields of volume currents. Discussion These results
Inverse planning optimization method for intensity modulated radiation therapy.
Lan, Yihua; Ren, Haozheng; Li, Cunhua; Min, Zhifang; Wan, Jinxin; Ma, Jianxin; Hung, Chih-Cheng
2013-10-01
In order to facilitate the leaf sequencing process in intensity modulated radiation therapy (IMRT), and design of a practical leaf sequencing algorithm, it is an important issue to smooth the planned fluence maps. The objective is to achieve both high-efficiency and high-precision dose delivering by considering characteristics of leaf sequencing process. The key factor which affects total number of monitor units for the leaf sequencing optimization process is the max flow value of the digraph which formulated from the fluence maps. Therefore, we believe that one strategy for compromising dose conformity and total number of monitor units in dose delivery is to balance the dose distribution function and the max flow value mentioned above. However, there are too many paths in the digraph, and we don't know the flow value of which path is the maximum. The maximum flow value among the horizontal paths was selected and used in the objective function of the fluence map optimization to formulate the model. The model is a traditional linear constrained quadratic optimization model which can be solved by interior point method easily. We believe that the smoothed maps from this model are more suitable for leaf sequencing optimization process than other smoothing models. A clinical head-neck case and a prostate case were tested and compared using our proposed model and the smoothing model which is based on the minimization of total variance. The optimization results with the same level of total number of monitor units (TNMU) show that the fluence maps obtained from our model have much better dose performance for the target/non-target region than the maps from total variance based on the smoothing model. This indicates that our model achieves better dose distribution when the algorithm suppresses the TNMU at the same level. Although we have just used the max flow value of the horizontal paths in the diagraph in the objective function, a good balance has been achieved between
Geostatistical Inverse Modeling for Natural Attenuation of Hydrocarbons in Groundwater
NASA Astrophysics Data System (ADS)
Hosseini, A. H.; Deutsch, C. V.; Mendoza, C. A.; Biggar, K. W.
2008-12-01
Parameter uncertainty for natural attenuation has been previously studied in the context of characterizing the uncertainty in the field measured biodegradation rate constant. Natural attenuation response variables (e.g. solute concentrations) should be stated in terms of a number of model parameters in such a way that (1) the most important mechanisms contributing to natural attenuation of petroleum hydrocarbons are simulated, (2) the independent variables (model parameters) and their uncertainty can be estimated using the available observations and prior information and (3) the model is not over-parameterized. Extensive sensitivity analyses show that the source term, aquifer heterogeneity and biodegradation rate of contaminants are the most important factors affecting the fate of dissolved petroleum hydrocarbon (PHC) contaminants in groundwater. A geostatistical inverse modeling approach is developed to quantify uncertainty in source geometry, source dissolution rate, aquifer heterogeneity and biodegradation rate constant. Multiple joint realizations of source geometry and aquifer transmissivity are constructed by distance function (DF) algorithm and sequential self calibration (SSC) approach. A gradient-based optimization approach is then adapted to condition the joint realizations to a number of observed concentrations recorded over a specific monitoring period. The conditioned joint realizations are then ranked based on their goodness of fit and used in the subsequent prediction of uncertainty in the response variables such as downstream concentrations, plume length and contaminant mass loaded into the aquifer. The inverse modeling approach and its associated calculation of sensitivity coefficients show that an extended monitoring period is significantly important in well-posedness of the problem; and an uncertainty in occurrence of the spill can have a minor impact on the modeling results as long as the observation data are collected while the contaminant
Robust phase sensitive inversion recovery imaging using a Markov random field model.
Garach, Ravindra M; Ji, Jim X; Ying, Lei; Ma, Jingfei
2004-01-01
This paper presents a novel method for phase sensitive inversion recovery (PSIR) imaging for improved T/sub 1/ contrast. This method models the phase of the complex magnetic resonance image using a statistical model based on Markov random fields. A computationally efficient optimization method is developed. Computer simulations and in-vivo brain imaging experiments show that the proposed method can produce PSIR images with enhanced T/sub 1/ contrast and it is robust against high levels of data noise even when rapid phase variations are presented.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Gu, Dasa; Wang, Yuhang; Smeltzer, Charles; Boersma, K. Folkert
2014-06-27
Inverse modeling using satellite observations of nitrogen dioxide (NO2) columns has been extensively used to estimate nitrogen oxides (NOx) emissions in China. Recently, the Global Ozone Monitoring Experiment-2 (GOME-2) and Ozone Monitoring Instrument (OMI) provide independent global NO2 column measurements on a nearly daily basis at around 9:30 and 13:30 local time across the equator, respectively. Anthropogenic NOx emission estimates by applying previously developed monthly inversion (MI) or daily inversion (DI) methods to these two sets of measurements show substantial differences. We improve the DI method by conducting model simulation, satellite retrieval, and inverse modeling sequentially on a daily basis. After each inversion, we update anthropogenic NOx emissions in the model simulation with the newly obtained a posteriori results. Consequently, the inversion-optimized emissions are used to compute the a priori NO2 profiles for satellite retrievals. As such, the a priori profiles used in satellite retrievals are now coupled to inverse modeling results. The improved procedure was applied to GOME-2 and OMI NO2 measurements in 2011. The new daily retrieval-inversion (DRI) method estimates an average NOx emission of 6.9 Tg N/yr over China, and the difference between using GOME-2 and OMI measurements is 0.4 Tg N/yr, which is significantly smaller than the difference of 1.3 Tg N/yr using the previous DI method. Using the more consistent DRI inversion results, we find that anthropogenic NOx emissions tend to be higher in winter and summer than spring (and possibly fall) and the weekday-to-weekend emission ratio tends to increase with NOx emission in China.
NASA Astrophysics Data System (ADS)
Monteiller, Vadim; Chevrot, Sébastien; Komatitsch, Dimitri; Wang, Yi
2015-08-01
We present a method for high-resolution imaging of lithospheric structures based on full waveform inversion of teleseismic waveforms. We model the propagation of seismic waves using our recently developed direct solution method/spectral-element method hybrid technique, which allows us to simulate the propagation of short-period teleseismic waves through a regional 3-D model. We implement an iterative quasi-Newton method based upon the L-BFGS algorithm, where the gradient of the misfit function is computed using the adjoint-state method. Compared to gradient or conjugate-gradient methods, the L-BFGS algorithm has a much faster convergence rate. We illustrate the potential of this method on a synthetic test case that consists of a crustal model with a crustal discontinuity at 25 km depth and a sharp Moho jump. This model contains short- and long-wavelength heterogeneities along the lateral and vertical directions. The iterative inversion starts from a smooth 1-D model derived from the IASP91 reference Earth model. We invert both radial and vertical component waveforms, starting from long-period signals filtered at 10 s and gradually decreasing the cut-off period down to 1.25 s. This multiscale algorithm quickly converges towards a model that is very close to the true model, in contrast to inversions involving short-period waveforms only, which always get trapped into a local minimum of the cost function.
NASA Astrophysics Data System (ADS)
Grigoriev, M.; Babich, L.
2015-09-01
The article represents the main noninvasive methods of heart electrical activity examination, theoretical bases of solution of electrocardiography inverse problem, application of different methods of heart examination in clinical practice, and generalized achievements in this sphere in global experience.
NASA Astrophysics Data System (ADS)
Miller, Eric L.; Willsky, Alan S.
1996-01-01
In this paper, we present an approach to the nonlinear inverse scattering problem using the extended Born approximation (EBA) on the basis of methods from the fields of multiscale and statistical signal processing. By posing the problem directly in the wavelet transform domain, regularization is provided through the use of a multiscale prior statistical model. Using the maximum a posteriori (MAP) framework, we introduce the relative Cramér-Rao bound (RCRB) as a tool for analyzing the level of detail in a reconstruction supported by a data set as a function of the physics, the source-receiver geometry, and the nature of our prior information. The MAP estimate is determined using a novel implementation of the Levenberg-Marquardt algorithm in which the RCRB is used to achieve a substantial reduction in the effective dimensionality of the inversion problem with minimal degradation in performance. Additional reduction in complexity is achieved by taking advantage of the sparse structure of the matrices defining the EBA in scale space. An inverse electrical conductivity problem arising in geophysical prospecting applications provides the vehicle for demonstrating the analysis and algorithmic techniques developed in this paper.
NASA Astrophysics Data System (ADS)
Dolman, A. J.; Shvidenko, A.; Schepaschenko, D.; Ciais, P.; Tchebakova, N.; Chen, T.; van der Molen, M. K.; Belelli Marchesini, L.; Maximov, T. C.; Maksyutov, S.; Schulze, E.-D.
2012-12-01
We determine the net land to atmosphere flux of carbon in Russia, including Ukraine, Belarus and Kazakhstan, using inventory-based, eddy covariance, and inversion methods. Our high boundary estimate is -342 Tg C yr-1 from the eddy covariance method, and this is close to the upper bounds of the inventory-based Land Ecosystem Assessment and inverse models estimates. A lower boundary estimate is provided at -1350 Tg C yr-1 from the inversion models. The average of the three methods is -613.5 Tg C yr-1. The methane emission is estimated separately at 41.4 Tg C yr-1. These three methods agree well within their respective error bounds. There is thus good consistency between bottom-up and top-down methods. The forests of Russia primarily cause the net atmosphere to land flux (-692 Tg C yr-1 from the LEA. It remains however remarkable that the three methods provide such close estimates (-615, -662, -554 Tg C yr-1) for net biome production (NBP), given the inherent uncertainties in all of the approaches. The lack of recent forest inventories, the few eddy covariance sites and associated uncertainty with upscaling and undersampling of concentrations for the inversions are among the prime causes of the uncertainty. The dynamic global vegetation models (DGVMs) suggest a much lower uptake at -91 Tg C yr-1, and we argue that this is caused by a high estimate of heterotrophic respiration compared to other methods.
NASA Astrophysics Data System (ADS)
Uliasz, M.; Schuh, A. E.
2011-12-01
Atmospheric transport modeling and its uncertainty play a crucial role in inversion studies with a goal to estimate fluxes of trace gases like carbon dioxide from available concentration measurements. Lagrangian particle models (e.g., CSU LPDM, STILT, FLEXPART) driven by regional meteorological models (e.g., WRF, RAMS) are state of the art tools in regional CO2 research including not only inversion studies, but also designing of tower network, or testing and supporting flight scenarios. They are typically used backward in time as an adjoint transport model providing, for each data point, influence functions (footprints) for surface fluxes and inflow fluxes across a domain perimeter. Modeling system used at CSU is based on SiB-RAMS (Regional Atmospheric Modeling System with Simple Biosphere model) providing meteorological fields for the LPDM (Lagrangian Particle Dispersion Model). Our LPDM can be run both in a forward and backward in time mode. Therefore, we recommend to use the comparison of forward and backward in time simulations as a method to evaluate internal model uncertainty. In addition the LPDM concentration fields can be compared to tracer concentrations simulated directly by RAMS, i.e. Eulerian grid model. We will discuss how simulated concentration fields, and in turn, the results of atmospheric inversions are affected by (1) model simplifications and optimizations, (2) time and space resolution of meteorological fields, and (3) selection of a domain for inversion study. The simulations are performed for the North America and smaller regional domains for a passive tracer and a tracers resulting from different CO2 fluxes (assimilation and respiration). Finally, we would like to propose a framework for inter comparison of different LPDMs coupled to regional meteorological models. This framework includes a sparse matrix format for influence functions to facilitate exchange and further applications of this product by different research groups.
Earthquake source tensor inversion with the gCAP method and 3D Green's functions
NASA Astrophysics Data System (ADS)
Zheng, J.; Ben-Zion, Y.; Zhu, L.; Ross, Z.
2013-12-01
We develop and apply a method to invert earthquake seismograms for source properties using a general tensor representation and 3D Green's functions. The method employs (i) a general representation of earthquake potency/moment tensors with double couple (DC), compensated linear vector dipole (CLVD), and isotropic (ISO) components, and (ii) a corresponding generalized CAP (gCap) scheme where the continuous wave trains are broken into Pnl and surface waves (Zhu & Ben-Zion, 2013). For comparison, we also use the waveform inversion method of Zheng & Chen (2012) and Ammon et al. (1998). Sets of 3D Green's functions are calculated on a grid of 1 km3 using the 3-D community velocity model CVM-4 (Kohler et al. 2003). A bootstrap technique is adopted to establish robustness of the inversion results using the gCap method (Ross & Ben-Zion, 2013). Synthetic tests with 1-D and 3-D waveform calculations show that the source tensor inversion procedure is reasonably reliable and robust. As initial application, the method is used to investigate source properties of the March 11, 2013, Mw=4.7 earthquake on the San Jacinto fault using recordings of ~45 stations up to ~0.2Hz. Both the best fitting and most probable solutions include ISO component of ~1% and CLVD component of ~0%. The obtained ISO component, while small, is found to be a non-negligible positive value that can have significant implications for the physics of the failure process. Work on using higher frequency data for this and other earthquakes is in progress.
Forward and Inverse Modeling of GPS Multipath for Snow Monitoring
NASA Astrophysics Data System (ADS)
Nievinski, Felipe Geremia
Snowpacks provide reservoirs of freshwater, storing solid precipitation and delaying runoff to be released later in the spring and summer when it is most needed. The goal of this dissertation is to develop the technique of GPS multipath reflectometry (GPS-MR) for ground-based measurement of snow depth. The phenomenon of multipath in GPS constitutes the reception of reflected signals in conjunction with the direct signal from a satellite. As these coherent direct and reflected signals go in and out of phase, signal-to-noise ratio (SNR) exhibits peaks and troughs that can be related to land surface characteristics. In contrast to other GPS reflectometry modes, in GPS-MR the poorly separated composite signal is collected utilizing a single antenna and correlated against a single replica. SNR observations derived from the newer L2-frequency civilian GPS signal (L2C) are used, as recorded by commercial off-the-shelf receivers and geodetic-quality antennas in existing GPS sites. I developed a forward/inverse approach for modeling GPS multipath present in SNR observations. The model here is unique in that it capitalizes on known information about the antenna response and the physics of surface scattering to aid in retrieving the unknown snow conditions in the antenna surroundings. This physically-based forward model is utilized to simulate the surface and antenna coupling. The statistically-rigorous inverse model is considered in two parts. Part I (theory) explains how the snow characteristics are parameterized; the observation/parameter sensitivity; inversion errors; and parameter uncertainty, which serves to indicate the sensing footprint where the reflection originates. Part II (practice) applies the multipath model to SNR observations and validates the resulting GPS retrievals against independent in situ measurements during a 1-3 year period in three different environments---grasslands, alpine, and forested. The assessment yields a correlation of 0.98 and an RMS error
NASA Astrophysics Data System (ADS)
Izumi, Tomoki; Takeuchi, Junichiro; Kawachi, Toshihiko; Fujihara, Masayuki
An inverse method to estimate the unsaturated hydraulic conductivity in seepage flow from field observations is presented. Considering the water movement in soil significantly affected by the soil temperature, the soil column of interest is assumed to be non-isothermal, and therefore the problem is based on coupled 1D water movement and thermal conduction equations. Since the saturated hydraulic conductivity could be definitely known, the inverse problem associated with the unsaturated hydraulic conductivity is reduced to that of identifying the relative hydraulic conductivity (RHC) from the hydro-geological information available. For functional representation of RHC, the free-form parameterized function is employed in lieu of the conventional fixed-form function. Values of the parameters included in the functions are optimally determined according to a simulation-optimization algorithm. For easy application of the method, a utilitarian observation system with simple instrumentation is specially contrived which implements collection of the hydro-geological data relatively easily in-situ available. Validity of the method developed is examined through its practical application to a real soil column in an upland crop field. The results show that the water movement model provides the forward solutions of high reproducibility, when coupled with thermal conduction model and calibrated through identifying the RHC by use of a free-form function.
Unrealistic parameter estimates in inverse modelling: A problem or a benefit for model calibration?
Poeter, E.P.; Hill, M.C.
1996-01-01
Estimation of unrealistic parameter values by inverse modelling is useful for constructed model discrimination. This utility is demonstrated using the three-dimensional, groundwater flow inverse model MODFLOWP to estimate parameters in a simple synthetic model where the true conditions and character of the errors are completely known. When a poorly constructed model is used, unreasonable parameter values are obtained even when using error free observations and true initial parameter values. This apparent problem is actually a benefit because it differentiates accurately and inaccurately constructed models. The problems seem obvious for a synthetic problem in which the truth is known, but are obscure when working with field data. Situations in which unrealistic parameter estimates indicate constructed model problems are illustrated in applications of inverse modelling to three field sites and to complex synthetic test cases in which it is shown that prediction accuracy also suffers when constructed models are inaccurate.
Efficient non-negative constrained model-based inversion in optoacoustic tomography
NASA Astrophysics Data System (ADS)
Ding, Lu; Luís Deán-Ben, X.; Lutzweiler, Christian; Razansky, Daniel; Ntziachristos, Vasilis
2015-09-01
The inversion accuracy in optoacoustic tomography depends on a number of parameters, including the number of detectors employed, discrete sampling issues or imperfectness of the forward model. These parameters result in ambiguities on the reconstructed image. A common ambiguity is the appearance of negative values, which have no physical meaning since optical absorption can only be higher or equal than zero. We investigate herein algorithms that impose non-negative constraints in model-based optoacoustic inversion. Several state-of-the-art non-negative constrained algorithms are analyzed. Furthermore, an algorithm based on the conjugate gradient method is introduced in this work. We are particularly interested in investigating whether positive restrictions lead to accurate solutions or drive the appearance of errors and artifacts. It is shown that the computational performance of non-negative constrained inversion is higher for the introduced algorithm than for the other algorithms, while yielding equivalent results. The experimental performance of this inversion procedure is then tested in phantoms and small animals, showing an improvement in image quality and quantitativeness with respect to the unconstrained approach. The study performed validates the use of non-negative constraints for improving image accuracy compared to unconstrained methods, while maintaining computational efficiency.
Image synthesis with graph cuts: a fast model proposal mechanism in probabilistic inversion
NASA Astrophysics Data System (ADS)
Zahner, Tobias; Lochbühler, Tobias; Mariethoz, Grégoire; Linde, Niklas
2016-02-01
Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with site-specific data, but also display the same type of patterns as those found in a training image. The training image can be seen as a conceptual model of the subsurface and is used as a non-parametric model of spatial variability. Inversion based on multiple-point statistics is challenging due to high nonlinearity and time-consuming geostatistical resimulation steps that are needed to create new model proposals. We propose an entirely new model proposal mechanism for geophysical inversion that is inspired by texture synthesis in computer vision. Instead of resimulating pixels based on higher-order patterns in the training image, we identify a suitable patch of the training image that replace a corresponding patch in the current model without breaking the patterns found in the training image, that is, remaining consistent with the given prior. We consider three cross-hole ground-penetrating radar examples in which the new model proposal mechanism is employed within an extended Metropolis Markov chain Monte Carlo (MCMC) inversion. The model proposal step is about 40 times faster than state-of-the-art multiple-point statistics resimulation techniques, the number of necessary MCMC steps is lower and the quality of the final model realizations is of similar quality. The model proposal mechanism is presently limited to 2-D fields, but the method is general and can be applied to a wide range of subsurface settings and geophysical data types.
NASA Astrophysics Data System (ADS)
Mohammad khaninezhad, M.; Jafarpour, B.
2012-12-01
Data limitation and heterogeneity of the geologic formations introduce significant uncertainty in predicting the related flow and transport processes in these environments. Fluid flow and displacement behavior in subsurface systems is mainly controlled by the structural connectivity models that create preferential flow pathways (or barriers). The connectivity of extreme geologic features strongly constrains the evolution of the related flow and transport processes in subsurface formations. Therefore, characterization of the geologic continuity and facies connectivity is critical for reliable prediction of the flow and transport behavior. The goal of this study is to develop a robust and geologically consistent framework for solving large-scale nonlinear subsurface characterization inverse problems under uncertainty about geologic continuity and structural connectivity. We formulate a novel inverse modeling approach by adopting a sparse reconstruction perspective, which involves two major components: 1) sparse description of hydraulic property distribution under significant uncertainty in structural connectivity and 2) formulation of an effective sparsity-promoting inversion method that is robust against prior model uncertainty. To account for the significant variability in the structural connectivity, we use, as prior, multiple distinct connectivity models. For sparse/compact representation of high-dimensional hydraulic property maps, we investigate two methods. In one approach, we apply the principle component analysis (PCA) to each prior connectivity model individually and combine the resulting leading components from each model to form a diverse geologic dictionary. Alternatively, we combine many realizations of the hydraulic properties from different prior connectivity models and use them to generate a diverse training dataset. We use the training dataset with a sparsifying transform, such as K-SVD, to construct a sparse geologic dictionary that is robust to
Three dimensional modeling and inversion of Borehole-surface Electrical Resistivity Data
NASA Astrophysics Data System (ADS)
Zhang, Y.; Liu, D.; Liu, Y.; Qin, M.
2013-12-01
After a long time of exploration, many oil fields have stepped into the high water-cut period. It is sorely needed to determining the oil-water distribution and water flooding front. Borehole-surface electrical resistivity tomography (BSERT) system is a low-cost measurement with wide measuring scope and small influence on the reservoir. So it is gaining more and more application in detecting water flooding areas and evaluating residual oil distribution in oil fields. In BSERT system, current is connected with the steel casing of the observation well. The current flows along the long casing and transmits to the surface through inhomogeneous layers. Then received electric potential difference data on the surface can be used to inverse the deep subsurface resistivity distribution. This study presents the 3D modeling and inversion method of electrical resistivity data. In an extensive literature, the steel casing is treated as a transmission line current source with infinite small radius and constant current density. However, in practical multi-layered formations with different resistivity, the current density along the casing is not constant. In this study, the steel casing is modeled by a 2.5e-7 ohm-m physical volume that the casing occupies in the finite element mesh. Radius of the casing can be set to a little bigger than the true radius, and this helps reduce the element number and computation time. The current supply point is set on the center of the top surface of the physical volume. The homogeneous formation modeling result shows the same precision as the transmission line current source model. The multi-layered formation modeling result shows that the current density along the casing is high in the low-resistivity layer, and low in the high-resistivity layer. These results are more reasonable. Moreover, the deviated and horizontal well can be simulated as simple as the vertical well using this modeling method. Based on this forward modeling method, the
Joining direct and indirect inverse calibration methods to characterize karst, coastal aquifers
NASA Astrophysics Data System (ADS)
De Filippis, Giovanna; Foglia, Laura; Giudici, Mauro; Mehl, Steffen; Margiotta, Stefano; Negri, Sergio
2016-04-01
Parameter estimation is extremely relevant for accurate simulation of groundwater flow. Parameter values for models of large-scale catchments are usually derived from a limited set of field observations, which can rarely be obtained in a straightforward way from field tests or laboratory measurements on samples, due to a number of factors, including measurement errors and inadequate sampling density. Indeed, a wide gap exists between the local scale, at which most of the observations are taken, and the regional or basin scale, at which the planning and management decisions are usually made. For this reason, the use of geologic information and field data is generally made by zoning the parameter fields. However, pure zoning does not perform well in the case of fairly complex aquifers and this is particularly true for karst aquifers. In fact, the support of the hydraulic conductivity measured in the field is normally much smaller than the cell size of the numerical model, so it should be upscaled to a scale consistent with that of the numerical model discretization. Automatic inverse calibration is a valuable procedure to identify model parameter values by conditioning on observed, available data, limiting the subjective evaluations introduced with the trial-and-error technique. Many approaches have been proposed to solve the inverse problem. Generally speaking, inverse methods fall into two groups: direct and indirect methods. Direct methods allow determination of hydraulic conductivities from the groundwater flow equations which relate the conductivity and head fields. Indirect methods, instead, can handle any type of parameters, independently from the mathematical equations that govern the process, and condition parameter values and model construction on measurements of model output quantities, compared with the available observation data, through the minimization of an objective function. Both approaches have pros and cons, depending also on model complexity. For
NASA Astrophysics Data System (ADS)
D'Auria, Luca; Fernandez, Jose; Puglisi, Giuseppe; Rivalta, Eleonora; Camacho, Antonio; Nikkhoo, Mehdi; Walter, Thomas
2016-04-01
The inversion of ground deformation and gravity data is affected by an intrinsic ambiguity because of the mathematical formulation of the inverse problem. Current methods for the inversion of geodetic data rely on both parametric (i.e. assuming a source geometry) and non-parametric approaches. The former are able to catch the fundamental features of the ground deformation source but, if the assumptions are wrong or oversimplified, they could provide misleading results. On the other hand, the latter class of methods, even if not relying on stringent assumptions, could suffer from artifacts, especially when dealing with poor datasets. In the framework of the EC-FP7 MED-SUV project we aim at comparing different inverse approaches to verify how they cope with basic goals of Volcano Geodesy: determining the source depth, the source shape (size and geometry), the nature of the source (magmatic/hydrothermal) and hinting the complexity of the source. Other aspects that are important in volcano monitoring are: volume/mass transfer toward shallow depths, propagation of dikes/sills, forecasting the opening of eruptive vents. On the basis of similar experiments already done in the fields of seismic tomography and geophysical imaging, we have devised a bind test experiment. Our group was divided into one model design team and several inversion teams. The model design team devised two physical models representing volcanic events at two distinct volcanoes (one stratovolcano and one caldera). They provided the inversion teams with: the topographic reliefs, the calculated deformation field (on a set of simulated GPS stations and as InSAR interferograms) and the gravity change (on a set of simulated campaign stations). The nature of the volcanic events remained unknown to the inversion teams until after the submission of the inversion results. Here we present the preliminary results of this comparison in order to determine which features of the ground deformation and gravity source
Quasiparticle density of states by inversion with maximum entropy method
NASA Astrophysics Data System (ADS)
Sui, Xiao-Hong; Wang, Han-Ting; Tang, Hui; Su, Zhao-Bin
2016-10-01
We propose to extract the quasiparticle density of states (DOS) of the superconductor directly from the experimentally measured superconductor-insulator-superconductor junction tunneling data by applying the maximum entropy method to the nonlinear systems. It merits the advantage of model independence with minimum a priori assumptions. Various components of the proposed method have been carefully investigated, including the meaning of the targeting function, the mock function, as well as the role and the designation of the input parameters. The validity of the developed scheme is shown by two kinds of tests for systems with known DOS. As a preliminary application to a Bi2Sr2CaCu2O8 +δ sample with its critical temperature Tc=89 K , we extract the DOS from the measured intrinsic Josephson junction current data at temperatures of T =4.2 K , 45 K , 55 K , 95 K , and 130 K . The energy gap decreases with increasing temperature below Tc, while above Tc, a kind of energy gap survives, which provides an angle to investigate the pseudogap phenomenon in high-Tc superconductors. The developed method itself might be a useful tool for future applications in various fields.
Method for the preparation of metal colloids in inverse micelles and product preferred by the method
Wilcoxon, Jess P.
1992-01-01
A method is provided for preparing catalytic elemental metal colloidal particles (e.g. gold, palladium, silver, rhodium, iridium, nickel, iron, platinum, molybdenum) or colloidal alloy particles (silver/iridium or platinum/gold). A homogeneous inverse micelle solution of a metal salt is first formed in a metal-salt solvent comprised of a surfactant (e.g. a nonionic or cationic surfactant) and an organic solvent. The size and number of inverse micelles is controlled by the proportions of the surfactant and the solvent. Then, the metal salt is reduced (by chemical reduction or by a pulsed or continuous wave UV laser) to colloidal particles of elemental metal. After their formation, the colloidal metal particles can be stabilized by reaction with materials that permanently add surface stabilizing groups to the surface of the colloidal metal particles. The sizes of the colloidal elemental metal particles and their size distribution is determined by the size and number of the inverse micelles. A second salt can be added with further reduction to form the colloidal alloy particles. After the colloidal elemental metal particles are formed, the homogeneous solution distributes to two phases, one phase rich in colloidal elemental metal particles and the other phase rich in surfactant. The colloidal elemental metal particles from one phase can be dried to form a powder useful as a catalyst. Surfactant can be recovered and recycled from the phase rich in surfactant.
NASA Astrophysics Data System (ADS)
Manning, A. J.; O'Doherty, S.; Jones, A. R.; Simmonds, P. G.; Derwent, R. G.
2011-01-01
Methane (CH4) and nitrous oxide (N2O) have strong radiative properties in the Earth's atmosphere and both are regulated through the United Nations Framework Convention on Climate Change. Through this convention the United Kingdom is obliged to report an inventory of annual emission estimates from 1990. This paper describes a methodology that estimates emissions of CH4 and N2O completely independent of the inventory values. Emissions have been estimated for each year 1990-2007 for the United Kingdom and for NW Europe. The methodology combines high-frequency observations from Mace Head, a monitoring site on the west coast of Ireland, with an atmospheric dispersion model and an inversion system. The sensitivities of the inversion method to the modeling assumptions are reported. The 20 year Northern Hemisphere midlatitude baseline mixing ratios, growth rates, and seasonal cycles of both gases are also presented. The results indicate reasonable agreement between the inventory and inversion results for the United Kingdom for N2O over the entire period. For CH4 the agreement is poor in the 1990s but good in the 2000s. The UK CH4 inventory reported reduction from 1990-1992 to 2005-2007 (over 50%) is dominated by changes to landfill and coal mine emissions and is more than double the corresponding drop in the inversion estimated emissions (24%). The inversion results suggest that the United Kingdom has met its Kyoto commitment (-12.5%) but by a smaller margin (-14.3%) than reported (-17.3%). The results for NW Europe with the United Kingdom removed show reasonable agreement in trend, on average the inversion results for N2O are 25% lower and for CH4 21% higher.
Application of direct inverse analogy method (DIVA) and viscous design optimization techniques
NASA Technical Reports Server (NTRS)
Greff, E.; Forbrich, D.; Schwarten, H.
1991-01-01
A direct-inverse approach to the transonic design problem was presented in its initial state at the First International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-1). Further applications of the direct inverse analogy (DIVA) method to the design of airfoils and incremental wing improvements and experimental verification are reported. First results of a new viscous design code also from the residual correction type with semi-inverse boundary layer coupling are compared with DIVA which may enhance the accuracy of trailing edge design for highly loaded airfoils. Finally, the capabilities of an optimization routine coupled with the two viscous full potential solvers are investigated in comparison to the inverse method.
NASA Astrophysics Data System (ADS)
Heng, Y.; Hoffmann, L.; Griessbach, S.; Rößler, T.; Stein, O.
2015-10-01
An inverse transport modeling approach based on the concepts of sequential importance resampling and parallel computing is presented to reconstruct altitude-resolved time series of volcanic emissions, which often can not be obtained directly with current measurement techniques. A new inverse modeling and simulation system, which implements the inversion approach with the Lagrangian transport model Massive-Parallel Trajectory Calculations (MPTRAC) is developed to provide reliable transport simulations of volcanic sulfur dioxide (SO2). In the inverse modeling system MPTRAC is used to perform two types of simulations, i. e., large-scale ensemble simulations for the reconstruction of volcanic emissions and final transport simulations. The transport simulations are based on wind fields of the ERA-Interim meteorological reanalysis of the European Centre for Medium Range Weather Forecasts. The reconstruction of altitude-dependent SO2 emission time series is also based on Atmospheric Infrared Sounder (AIRS) satellite observations. A case study for the eruption of the Nabro volcano, Eritrea, in June 2011, with complex emission patterns, is considered for method validation. Meteosat Visible and InfraRed Imager (MVIRI) near-real-time imagery data are used to validate the temporal development of the reconstructed emissions. Furthermore, the altitude distributions of the emission time series are compared with top and bottom altitude measurements of aerosol layers obtained by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite instruments. The final transport simulations provide detailed spatial and temporal information on the SO2 distributions of the Nabro eruption. The SO2 column densities from the simulations are in good qualitative agreement with the AIRS observations. Our new inverse modeling and simulation system is expected to become a useful tool to also study other volcanic
NASA Astrophysics Data System (ADS)
Borisov, Dmitry; Singh, Satish C.; Fuji, Nobuaki
2015-09-01
Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.
AVAZ inversion for fracture weakness parameters based on the rock physics model
NASA Astrophysics Data System (ADS)
Chen, Huaizhen; Yin, Xingyao; Qu, Shouli; Zhang, Guangzhi
2014-12-01
Subsurface fractures within many carbonates and unconventional resources play an important role in the storage and movement of fluid. The more reliably the detection of fractures could be performed, the more finely the reservoir description could be made. In this paper, we aim to propose a method which uses two important tools, a fractured anisotropic rock physics effective model and AVAZ (amplitude versus incident and azimuthal angle) inversion, to predict fractures from azimuthal seismic data. We assume that the rock, which contains one or more sets of vertical or sub-vertical fractures, shows transverse isotropy with a horizontal axis of symmetry (HTI). Firstly, we develop one improved fractured anisotropic rock physics effective model. Using this model, we estimate P-wave velocity, S-wave velocity and fracture weaknesses from well-logging data. Then the method is proposed to predict fractures from azimuthal seismic data based on AVAZ inversion, and well A is used to verify the reliability of the improved rock physics effective model. Results show that the estimated results are consistent with the real log value, and the variation of fracture weaknesses may detect the locations of fractures. The damped least squares method, which uses the estimated results as initial constraints during the inversion, is more stable. Tests on synthetic data show that fracture weaknesses parameters are still estimated reasonably with moderate noise. A test on real data shows that the estimated results are in good agreement with the drilling.
Natural vs. artificial groundwater recharge, quantification through inverse modeling
NASA Astrophysics Data System (ADS)
Hashemi, H.; Berndtsson, R.; Kompani-Zare, M.; Persson, M.
2012-08-01
Estimating the change in groundwater recharge from an introduced artificial recharge system is important in order to evaluate future water availability. This paper presents an inverse modeling approach to quantify the recharge contribution from both an ephemeral river channel and an introduced artificial recharge system based on floodwater spreading in arid Iran. The study used the MODFLOW-2000 to estimate recharge for both steady and unsteady-state conditions. The model was calibrated and verified based on the observed hydraulic head in observation wells and model precision, uncertainty, and model sensitivity were analyzed in all modeling steps. The results showed that in a normal year without extreme events the floodwater spreading system is the main contributor to recharge with 80% and the ephemeral river channel with 20% of total recharge in the studied area. Uncertainty analysis revealed that the river channel recharge estimation represents relatively more uncertainty in comparison to the artificial recharge zones. The model is also less sensitive to the river channel. The results show that by expanding the artificial recharge system the recharge volume can be increased even for small flood events while the recharge through the river channel increases only for major flood events.
Natural vs. artificial groundwater recharge, quantification through inverse modeling
NASA Astrophysics Data System (ADS)
Hashemi, H.; Berndtsson, R.; Kompani-Zare, M.; Persson, M.
2013-02-01
Estimating the change in groundwater recharge from an introduced artificial recharge system is important in order to evaluate future water availability. This paper presents an inverse modeling approach to quantify the recharge contribution from both an ephemeral river channel and an introduced artificial recharge system based on floodwater spreading in arid Iran. The study used the MODFLOW-2000 to estimate recharge for both steady- and unsteady-state conditions. The model was calibrated and verified based on the observed hydraulic head in observation wells and model precision, uncertainty, and model sensitivity were analyzed in all modeling steps. The results showed that in a normal year without extreme events, the floodwater spreading system is the main contributor to recharge with 80% and the ephemeral river channel with 20% of total recharge in the studied area. Uncertainty analysis revealed that the river channel recharge estimation represents relatively more uncertainty in comparison to the artificial recharge zones. The model is also less sensitive to the river channel. The results show that by expanding the artificial recharge system, the recharge volume can be increased even for small flood events, while the recharge through the river channel increases only for major flood events.
A boundary integral method for an inverse problem in thermal imaging
NASA Technical Reports Server (NTRS)
Bryan, Kurt
1992-01-01
An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.
McGrail, B. Peter
2001-10-31
A numerically based simulator was developed to assist in the interpretation of complex laboratory experiments examining transport processes of chemical and biological contaminants subject to nonlinear adsorption and/or source terms. The inversion is performed with any of three nonlinear regression methods, Marquardt-Levenberg, conjugate gradient, or quasi-Newton. The governing equations for the problem are solved by the method of finite-differences including any combination of three boundary conditions: (1) Dirichlet, (2) Neumann, and (3) Cauchy. The dispersive terms in the transport equations were solved using the second-order accurate in time and space Crank-Nicolson scheme, while the advective terms were handled using a third-order in time and space, total variation diminishing (TVD) scheme that damps spurious oscillations around sharp concentration fronts. The numerical algorithms were implemented in the computer code INVERTS, which runs on any standard personal computer. Apart from a comprehensive set of test problems, INVERTS was also used to model the elution of a nonradioactive tracer, {sup 185}Re, in a pressurized unsaturated flow (PUF) experiment with a simulated waste glass for low-activity waste immobilization. Interpretation of the elution profile was best described with a nonlinear kinetic model for adsorption.
Thomas, Edward V.; Stork, Christopher L.; Mattingly, John K.
2015-07-01
Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is traditionally solved by finding the set of transport model parameter values that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature pre dicted by the hypothesized model parameters. The weights are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. The traditional implicit (often inaccurate) assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. Here, an alternative method that accounts for correlated errors between channels is described and illustrated using an inverse problem based on the combination of gam ma and neutron multiplicity counting measurements.
FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2012-09-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finance. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition
FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2013-10-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational
Unified dark energy-dark matter model with inverse quintessence
Ansoldi, Stefano; Guendelman, Eduardo I. E-mail: guendel@bgu.ac.il
2013-05-01
We consider a model where both dark energy and dark matter originate from the coupling of a scalar field with a non-canonical kinetic term to, both, a metric measure and a non-metric measure. An interacting dark energy/dark matter scenario can be obtained by introducing an additional scalar that can produce non constant vacuum energy and associated variations in dark matter. The phenomenology is most interesting when the kinetic term of the additional scalar field is ghost-type, since in this case the dark energy vanishes in the early universe and then grows with time. This constitutes an ''inverse quintessence scenario'', where the universe starts from a zero vacuum energy density state, instead of approaching it in the future.
Electron electric dipole moment in Inverse Seesaw models
NASA Astrophysics Data System (ADS)
Abada, Asmaa; Toma, Takashi
2016-08-01
We consider the contribution of sterile neutrinos to the electric dipole moment of charged leptons in the most minimal realisation of the Inverse Seesaw mechanism, in which the Standard Model is extended by two right-handed neutrinos and two sterile fermion states. Our study shows that the two pairs of (heavy) pseudo-Dirac mass eigen-states can give significant contributions to the electron electric dipole moment, lying close to future experimental sensitivity if their masses are above the electroweak scale. The major contribution comes from two-loop diagrams with pseudo-Dirac neutrino states running in the loops. In our analysis we further discuss the possibility of having a successful leptogenesis in this framework, compatible with a large electron electric dipole moment.
Inverse hydrograph routing optimization model based on the kinematic wave approach
NASA Astrophysics Data System (ADS)
Saghafian, B.; Jannaty, M. H.; Ezami, N.
2015-08-01
This article presents and validates the inverse flood hydrograph routing optimization model under kinematic wave (KW) approximation in order to produce the upstream (inflow) hydrograph, given the downstream (outflow) hydrograph of a river reach. The cost function involves minimization of the error between the observed outflow hydrograph and the corresponding directly routed outflow hydrograph. Decision variables are the inflow hydrograph ordinates. The KW and genetic algorithm (GA) are coupled, representing the selected methods of direct routing and optimization, respectively. A local search technique is also enforced to achieve better agreement of the routed outflow hydrograph with the observed hydrograph. Computer programs handling the direct flood routing, cost function and local search are linked with the optimization model. The results show that the case study inflow hydrographs obtained by the GA were reconstructed with accuracy. It was also concluded that the coupled KW-GA model framework can perform inverse hydrograph routing with numerical stability.
NASA Astrophysics Data System (ADS)
Wang, D.; Zhang, Y.
2014-12-01
This research explores the interactions between data quantity, data quality and heterogeneity resolution on stochastic inversion of a physically based model. To further investigate aquifer heterogeneity, simulations are used to examine the impact of geostatistical models on inversion quality, as well as the spatial sensitivity to heterogeneity using local and global methods. The model domain is a two-dimensional steady-state confined aquifer with lateral flows through two hydrofacies with alternating patterns.To examine general effects, the control variable method was adopted to reveal the impact of three factors on estimated hydraulic conductivity (K) and hydraulic head boundary conditions (BCs): (1) data availability, (2) data error, and (3) characterization of heterogeneity. Results show that fewer data increase model sensitivity to measurement error and heterogeneity. Extremely large data errors can cause severe model deterioration, regardless of sufficient data availability or high resolution representation of heterogeneity. Smaller data errors can alleviate the bias caused by the limited observations. For heterogeneity resolution, once general patterns of geological structures are captured, its influence is minimal compared to the other factors.Next, two geostatistical models (spherical and exponential variograms), were used to explore the representation of heterogeneity under the same nugget effects. The results show that stochastic inversion based on the exponential variogram improves both the precision and accuracy of the inverse model, as compared to the spherical variogram. This difference is particularly important for determining accurate BCs through stochastic inversion.Last, sensitivity analysis was conducted to further investigate the effect of varying the K of each hydrofacies on model inversion. Results from the partial local method show that the inversion is more sensitive to perturbations of K in regions with high heterogeneity. Using the
Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace
Zhang, Cheng; Lai, Chun-Liang; Pettitt, B. Montgomery
2016-01-01
The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution. PMID:27453632
NASA Astrophysics Data System (ADS)
Rubin, Yoram; Chen, Xingyuan; Murakami, Haruko; Hahn, Melanie
2010-10-01
This paper addresses the inverse problem in spatially variable fields such as hydraulic conductivity in groundwater aquifers or rainfall intensity in hydrology. Common to all these problems is the existence of a complex pattern of spatial variability of the target variables and observations, the multiple sources of data available for characterizing the fields, the complex relations between the observed and target variables and the multiple scales and frequencies of the observations. The method of anchored distributions (MAD) that we propose here is a general Bayesian method of inverse modeling of spatial random fields that addresses this complexity. The central elements of MAD are a modular classification of all relevant data and a new concept called "anchors." Data types are classified by the way they relate to the target variable, as either local or nonlocal and as either direct or indirect. Anchors are devices for localization of data: they are used to convert nonlocal, indirect data into local distributions of the target variables. The target of the inversion is the derivation of the joint distribution of the anchors and structural parameters, conditional to all measurements, regardless of scale or frequency of measurement. The structural parameters describe large-scale trends of the target variable fields, whereas the anchors capture local inhomogeneities. Following inversion, the joint distribution of anchors and structural parameters is used for generating random fields of the target variable(s) that are conditioned on the nonlocal, indirect data through their anchor representation. We demonstrate MAD through a detailed case study that assimilates point measurements of the conductivity with head measurements from natural gradient flow. The resulting statistical distributions of the parameters are non-Gaussian. Similarly, the moments of the estimates of the hydraulic head are non-Gaussian. We provide an extended discussion of MAD vis à vis other inversion
Inverse modeling of tracer experiments in FEBEX compacted Ca-bentonite
NASA Astrophysics Data System (ADS)
Samper, Javier; Dai, Zhenxue; Molinero, Jorge; García-Gutiérrez, M.; Missana, T.; Mingarro, M.
Solute transport parameters of compacted Ca-bentonite used in the FEBEX Project were derived by García-Gutiérrez et al. (2001) from through- and in-diffusion experiments using analytical solutions for their interpretation. Here we expand their work and present the numerical interpretation of diffusion and permeation experiments by solving the inverse transport problem which is formulated as the minimization of a weighted least squares criterion measuring the differences between computed and measured concentration values. The inverse problem is solved with INVERSE-CORE 2 D© , a finite element code which accounts for both dissolved and sorbed concentration data, uses either the Golden section search or Gauss-Newton-Marquardt methods for minimizing the objective function and allows the estimation of transport and retardation parameters such as diffusion coefficient, total and kinematic porosity and distribution coefficients. Diffusion and permeation experiments performed on FEBEX compacted bentonite using tritium, cesium, selenium, and strontium have been effectively interpreted by inverse modeling. Estimated parameters are within the range of reported values for these tracers in bentonites. It has been found that failing to account for the role of sinters may lead to erroneous diffusion coefficients by a factor of 1.4. Possible ways to improve the design of in-diffusion and permeation experiments have been identified. The interpretation of the tritium permeation experiment requires the use of a double-porosity model with mobile porosity of 0.14 for a dry density of 1.18 g/cm 3.
Halloran, Jason P.; Erdemir, Ahmet
2011-01-01
Simulation-based prediction of specimen-specific biomechanical behavior commonly requires inverse analysis using geometrically consistent finite element (FE) models. Optimization drives such analyses but previous studies have highlighted a large computational cost dictated by iterative use of nonlinear FE models. The goal of this study was to evaluate the performance of a local regression-based adaptive surrogate modeling approach to decrease computational cost for both global and local optimization approaches using an inverse FE application. Nonlinear elastic material parameters for patient-specific heel-pad tissue were found, both with and without the surrogate model. Surrogate prediction replaced a FE simulation using local regression of previous simulations when the corresponding error estimate was less than a given tolerance. Performance depended on optimization type and tolerance value. The surrogate reduced local optimization expense up to 68%, but achieved accurate results for only 1 of 20 initial conditions. Conversely, up to a tolerance value of 20 N2, global optimization with the surrogate yielded consistent parameter predictions with a concurrent decrease in computational cost (up to 77%). However, the local optimization method without the surrogate, although sensitive to the initial conditions, was still on average seven times faster than the global approach. Our results help establish guide-lines for setting acceptable tolerance values while using an adaptive surrogate model for inverse FE analysis. Most important, the study demonstrates the benefits of a surrogate modeling approach for intensive FE-based iterative analysis. PMID:21544674
Three-dimensional modeling of Mount Vesuvius with sequential integrated inversion
NASA Astrophysics Data System (ADS)
Tondi, Rosaria; de Franco, Roberto
2003-05-01
A new image of Mount Vesuvius and the surrounding area is recovered from the tomographic inversion of 693 first P wave arrivals recorded by 314 receivers deployed along five profiles which intersect the crater, and gravity data collected in 17,598 stations on land and offshore. The final three-dimensional (3-D) velocity model presented here is determined by interpolation of five 2-D velocity sections obtained from sequential integrated inversion (SII) of seismic and gravity data. The inversion procedure adopts the "maximum likelihood" scheme in order to jointly optimize seismic velocities and densities. In this way we recover velocity and density models both consistent with seismic and gravity data information. The model parameterization of these 2-D models is chosen in order to keep the diagonal elements of the seismic resolution matrix in the order of 0.2-0.8. The highest values of resolution are detected under the volcano edifice. The imaged 6-km-thick crustal volume underlies a 25 × 45 km2 area. The interpolation is performed by choosing the right grid for a smoothing algorithm which prepares optimum models for asymptotic ray theory methods. Hence this model can be used as a reference model for a 3-D tomographic inversion of seismic data. The 3-D gravity modeling is straightforward. The results of this study clearly image the continuous structure of the Mesozoic carbonate basement top and the connection of the volcano conduit structure to two shallow depressions, which in terms of hazard prevention are the regions through which magma may more easily flow toward the surface and cause possible eruptions.
NASA Astrophysics Data System (ADS)
Kachar, H.; Mobasheri, M. R.; Abkar, A. A.; Rahim Zadegan, M.
2015-12-01
Increase of temperature with height in the troposphere is called temperature inversion. Parameters such as strength and depth are characteristics of temperature inversion. Inversion strength is defined as the temperature difference between the surface and the top of the inversion and the depth of inversion is defined as the height of the inversion from the surface. The common approach in determination of these parameters is the use of Radiosonde where these measurements are too sparse. The main objective of this study is detection and modeling the temperature inversion using MODIS thermal infrared data. There are more than 180 days per year in which the temperature inversion conditions are present in Kermanshah city. Kermanshah weather station was selected as the study area. 90 inversion days was selected from 2007 to 2008 where the sky was clear and the Radiosonde data were available. Brightness temperature for all thermal infrared bands of MODIS was calculated for these days. Brightness temperature difference between any of the thermal infrared bands of MODIS and band 31 was found to be sensitive to strength and depth of temperature inversion. Then correlation coefficients between these pairs and the inversion depth and strength both calculated from Radiosonde were evaluated. The results showed poor linear correlation. This was found to be due to the change of the atmospheric water vapor content and the relatively weak temperature inversion strength and depth occurring in Kermanshah. The polynomial mathematical models and Artificial intelligence algorithms were deployed for detection and modeling the temperature inversion. A model with the lowest terms and highest possible accuracy was obtained. The Model was tested using 20 independent test data. Results indicate that the inversion strength can be estimated with RMSE of 0.84° C and R2 of 0.90. Also inversion depth can be estimated with RMSE of 54.56 m and R2 of 0.86.
An inverse problem approach to modelling coastal effluent plumes
NASA Astrophysics Data System (ADS)
Lam, D. C. L.; Murthy, C. R.; Miners, K. C.
Formulated as an inverse problem, the diffusion parameters associated with length-scale dependent eddy diffusivities can be viewed as the unknowns in the mass conservation equation for coastal zone transport problems. The values of the diffusion parameters can be optimized according to an error function incorporated with observed concentration data. Examples are given for the Fickian, shear diffusion and inertial subrange diffusion models. Based on a new set of dyeplume data collected in the coastal zone off Bronte, Lake Ontario, it is shown that the predictions of turbulence closure models can be evaluated for different flow conditions. The choice of computational schemes for this diagnostic approach is based on tests with analytic solutions and observed data. It is found that the optimized shear diffusion model produced a better agreement with observations for both high and low advective flows than, e.g., the unoptimized semi-empirical model, Ky=0.075 σy1.2, described by Murthy and Kenney.
Yavari, Fatemeh; Mahdavi, Shirin; Towhidkhah, Farzad; Ahmadi-Pajouh, Mohammad-Ali; Ekhtiari, Hamed; Darainy, Mohammad
2016-04-01
Despite several pieces of evidence, which suggest that the human brain employs internal models for motor control and learning, the location of these models in the brain is not yet clear. In this study, we used transcranial direct current stimulation (tDCS) to manipulate right cerebellar function, while subjects adapt to a visuomotor task. We investigated the effect of this manipulation on the internal forward and inverse models by measuring two kinds of behavior: generalization of training in one direction to neighboring directions (as a proxy for inverse models) and localization of the hand position after movement without visual feedback (as a proxy for forward model). The experimental results showed no effect of cerebellar tDCS on generalization, but significant effect on localization. These observations support the idea that the cerebellum is a possible brain region for internal forward, but not inverse model formation. We also used a realistic human head model to calculate current density distribution in the brain. The result of this model confirmed the passage of current through the cerebellum. Moreover, to further explain some observed experimental results, we modeled the visuomotor adaptation process with the help of a biologically inspired method known as population coding. The effect of tDCS was also incorporated in the model. The results of this modeling study closely match our experimental data and provide further evidence in line with the idea that tDCS manipulates FM's function in the cerebellum.
An Inverse Method to Infer the Global Ocean Paleoventilation from the Atmospheric 14C Record
NASA Astrophysics Data System (ADS)
Marchal, O.; Hughen, K. A.; Muscheler, R.
2001-12-01
We present an inverse method to infer a record of global ocean ventilation (GOV) from records of atmospheric 14C activity (Δ 14C) and production. The method is based on the assimilation of activity and production data in a box model of the 14C cycle in the ocean-atmosphere-land biosphere system using the variational (adjoint) technique. It includes three components: (1) the model code that yields the value of the cost function (a measure of the misfit between observed and modelled Δ 14C); (2) the adjoint code that yields the partial derivatives of the cost function with respect to the parameters describing the temporal evolution of the GOV; and (3) an optimization procedure that yields the parameter values minimizing the cost function. Lagrange multipliers are introduced to simplify the calculation of the partial derivatives of the cost function and to construct the adjoint code directly from the model code. First we describe the method, outlining the formal similarities with the calculus of variation in analytical mechanics. Second we verify the method through the capability to recover a variety of GOV evolutions from the assimilation of artificial data ("twin experiments"). Third we apply the method to the Younger Dryas, using recent high-resolution records of Δ 14C from the Cariaco basin and of 10Be flux from Greenland ice cores. Our results give new insight into the role of the deep ocean circulation during this dramatic and rapid climate change in the circum North Atlantic area.
Resampling: An optimization method for inverse planning in robotic radiosurgery
Schweikard, Achim; Schlaefer, Alexander; Adler, John R. Jr.
2006-11-15
By design, the range of beam directions in conventional radiosurgery are constrained to an isocentric array. However, the recent introduction of robotic radiosurgery dramatically increases the flexibility of targeting, and as a consequence, beams need be neither coplanar nor isocentric. Such a nonisocentric design permits a large number of distinct beam directions to be used in one single treatment. These major technical differences provide an opportunity to improve upon the well-established principles for treatment planning used with GammaKnife or LINAC radiosurgery. With this objective in mind, our group has developed over the past decade an inverse planning tool for robotic radiosurgery. This system first computes a set of beam directions, and then during an optimization step, weights each individual beam. Optimization begins with a feasibility query, the answer to which is derived through linear programming. This approach offers the advantage of completeness and avoids local optima. Final beam selection is based on heuristics. In this report we present and evaluate a new strategy for utilizing the advantages of linear programming to improve beam selection. Starting from an initial solution, a heuristically determined set of beams is added to the optimization problem, while beams with zero weight are removed. This process is repeated to sample a set of beams much larger compared with typical optimization. Experimental results indicate that the planning approach efficiently finds acceptable plans and that resampling can further improve its efficiency.
An inverse method was developed to integrate satellite observations of atmospheric pollutant column concentrations and direct sensitivities predicted by a regional air quality model in order to discern biases in the emissions of the pollutant precursors.
Age-dependent forest carbon sink: Estimation via inverse modeling
NASA Astrophysics Data System (ADS)
Zhou, Tao; Shi, Peijun; Jia, Gensuo; Dai, Yongjiu; Zhao, Xiang; Shangguan, Wei; Du, Ling; Wu, Hao; Luo, Yiqi
2015-12-01
Forests have been recognized to sequester a substantial amount of carbon (C) from the atmosphere. However, considerable uncertainty remains regarding the magnitude and time course of the C sink. Revealing the intrinsic relationship between forest age and C sink is crucial for reducing uncertainties in prediction of forest C sink potential. In this study, we developed a stepwise data assimilation approach to combine a process-based Terrestrial ECOsystem Regional model, observations from multiple sources, and stochastic sampling to inversely estimate carbon cycle parameters including carbon sink at different forest ages for evergreen needle-leaved forests in China. The new approach is effective to estimate age-dependent parameter of maximal light-use efficiency (R2 = 0.99) and, accordingly, can quantify a relationship between forest age and the vegetation and soil C sinks. The estimated ecosystem C sink increases rapidly with age, peaks at 0.451 kg C m-2 yr-1 at age 22 years (ranging from 0.421 to 0.465 kg C m-2 yr-1), and gradually decreases thereafter. The dynamic patterns of C sinks in vegetation and soil are significantly different. C sink in vegetation first increases rapidly with age and then decreases. C sink in soil, however, increases continuously with age; it acts as a C source when the age is less than 20 years, after which it acts as a sink. For the evergreen needle-leaved forest, the highest C sink efficiency (i.e., C sink per unit net primary productivity) is approximately 60%, with age between 11 and 43 years. Overall, the inverse estimation of carbon cycle parameters can make reasonable estimates of age-dependent C sequestration in forests.
NASA Astrophysics Data System (ADS)
Fortin, W.; Holbrook, W. S.; Mallick, S.; Everson, E. D.; Tobin, H. J.; Keranen, K. M.
2014-12-01
Understanding the geologic composition of the Cascadia Subduction Zone (CSZ) is critically important in assessing seismic hazards in the Pacific Northwest. Despite being a potential earthquake and tsunami threat to millions of people, key details of the structure and fault mechanisms remain poorly understood in the CSZ. In particular, the position and character of the subduction interface remains elusive due to its relative aseismicity and low seismic reflectivity, making imaging difficult for both passive and active source methods. Modern active-source reflection seismic data acquired as part of the COAST project in 2012 provide an opportunity to study the transition from the Cascadia basin, across the deformation front, and into the accretionary prism. Coupled with advances in seismic inversion methods, this new data allow us to produce detailed velocity models of the CSZ and accurate pre-stack depth migrations for studying geologic structure. While still computationally expensive, current computing clusters can perform seismic inversions at resolutions that match that of the seismic image itself. Here we present pre-stack full waveform inversions of the central seismic line of the COAST survey offshore Washington state. The resultant velocity model is produced by inversion at every CMP location, 6.25 m laterally, with vertical resolution of 0.2 times the dominant seismic frequency. We report a good average correlation value above 0.8 across the entire seismic line, determined by comparing synthetic gathers to the real pre-stack gathers. These detailed velocity models, both Vp and Vs, along with the density model, are a necessary step toward a detailed porosity cross section to be used to determine the role of fluids in the CSZ. Additionally, the P-velocity model is used to produce a pre-stack depth migration image of the CSZ.
Inverse Optimization: A New Perspective on the Black-Litterman Model.
Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch
2012-12-11
The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views. PMID:25382873
Inverse Optimization: A New Perspective on the Black-Litterman Model.
Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch
2012-12-11
The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views.
Inverse Optimization: A New Perspective on the Black-Litterman Model
Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch.
2014-01-01
The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct “BL”-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new “BL”-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views. PMID:25382873
Lehikoinen, A.; Huttunen, J.M.J.; Finsterle, S.; Kowalsky, M.B.; Kaipio, J.P.
2009-08-01
We propose an approach for imaging the dynamics of complex hydrological processes. The evolution of electrically conductive fluids in porous media is imaged using time-lapse electrical resistance tomography. The related dynamic inversion problem is solved using Bayesian filtering techniques, that is, it is formulated as a sequential state estimation problem in which the target is an evolving posterior probability density of the system state. The dynamical inversion framework is based on the state space representation of the system, which involves the construction of a stochastic evolution model and an observation model. The observation model used in this paper consists of the complete electrode model for ERT, with Archie's law relating saturations to electrical conductivity. The evolution model is an approximate model for simulating flow through partially saturated porous media. Unavoidable modeling and approximation errors in both the observation and evolution models are considered by computing approximate statistics for these errors. These models are then included in the construction of the posterior probability density of the estimated system state. This approximation error method allows the use of approximate - and therefore computationally efficient - observation and evolution models in the Bayesian filtering. We consider a synthetic example and show that the incorporation of an explicit model for the model uncertainties in the state space representation can yield better estimates than a frame-by-frame imaging approach.
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Phan, Huy Phuong
2016-01-01
We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…
Hydrochlorofluorocarbon and hydrofluorocarbon emissions in East Asia determined by inverse modeling
NASA Astrophysics Data System (ADS)
Stohl, Andreas; Kim, J.; Li, S.; O'Doherty, S.; Zhou, L. X.; Saito, T.; Vollmer, M. K.; Wan, D.; Yao, B.; Yokouchi, Y.
2010-05-01
The emissions of three hydrochlorofluorocarbons, HCFC-22 (CHClF2), HCFC-141b (CH3CCl2F) and HCFC-142b (CH3CClF2) and three hydrofluorocarbons, HFC-23 (CHF3), HFC-134a (CH2FCF3) and HFC-152a (CH3CHF2) from five East Asian countries for the year 2008 are determined by inverse modeling. The inverse modeling is based on in-situ measurements of these halocarbons at the Japanese stations Cape Ochi-ishi and Hateruma, the Chinese station Shangdianzi and the South Korean station Gosan. For every station and every 3 hours, 20-day backward calculations were made with the Lagrangian particle dispersion model FLEXPART. The model output, the measurement data, bottom-up emission information and corresponding uncertainties were fed into an inversion algorithm to determine the regional emission fluxes. The model captures the observed variation of halocarbon mixing ratios very well for the two Japanese stations but has difficulties explaining the large observed variability at Shangdianzi, which is partly caused by small-scale transport from Beijing that is not adequately captured by the model. Based on HFC-23 measurements, the inversion algorithm could successfully identify the locations of factories known to produce HCFC-22 and emit HFC-23 as an unintentional byproduct. This lends substantial credibility to the inversion method and is, to our knowledge, the first time greenhouse gas emissions from point sources can be determined by inverse modeling using stations of a global network. The HFC-23 emissions thus determined will also be compared to emissions reported for some factories in the framework of Clean Development Mechanism projects. We report national emissions for China, North Korea, South Korea and Japan, as well as for the Taiwan region. Halocarbon emissions in China are much larger than the emissions in the other countries together and contribute a substantial fraction to the global emissions. Our estimates of Chinese emissions for the year 2008 are 64.9±6.5 kt/yr for
NASA Astrophysics Data System (ADS)
Frystacky, H.; Osorio-Murillo, C. A.; Over, M. W.; Kalbacher, T.; Gunnell, D.; Kolditz, O.; Ames, D.; Rubin, Y.
2013-12-01
The Method of Anchored Distributions (MAD) is a Bayesian technique for characterizing the uncertainty in geostatistical model parameters. Open-source software has been developed in a modular framework such that this technique can be applied to any forward model software via a driver. This presentation is about the driver that has been developed for OpenGeoSys (OGS), open-source software that can simulate many hydrogeological processes, including couple processes. MAD allows the use of multiple data types for conditioning the spatially random fields and assessing model parameter likelihood. For example, if simulating flow and mass transport, the inversion target variable could be hydraulic conductivity and the inversion data types could be head, concentration, or both. The driver detects from the OGS files which processes and variables are being used in a given project and allows MAD to prompt the user to choose those that are to be modeled or to be treated deterministically. In this way, any combination of processes allowed by OGS can have MAD applied. As for the software, there are two versions, each with its own OGS driver. A Windows desktop version is available as a graphical user interface and is ideal for the learning and teaching environment. High-throughput computing can even be achieved with this version via HTCondor if large projects want to be pursued in a computer lab. In addition to this desktop application, a Linux version is available equipped with MPI such that it can be run in parallel on a computer cluster. All releases can be downloaded from the MAD Codeplex site given below.
Determination of thermal load in film cooled bipropellant thrust chambers by an inverse method
NASA Astrophysics Data System (ADS)
Hinckel, J. N.; Savonov, R. I.; Patire, H.
2013-03-01
A method to obtain the heat load on the internal wall of a rocket thrust chamber using an inverse problem approach is described. According to the "classical" approach, the heat load on the internal wall of the chamber is assumed as the product of a heat transfer coefficient and the temperature difference of adiabatic wall temperature and local wall surface temperature. The time-dependent temperature distribution of the external wall of the thruster chamber is used to obtain empirical curve fittings to the temperature profile of the near wall flow field (adiabatic wall temperature) and the heat transfer coefficient profile. The applicability of the method is verified by applying it to three different problems; a model problem, an analytical solution, and a set of experimental data.
Love wave tomography in southern Africa from a two-plane-wave inversion method
NASA Astrophysics Data System (ADS)
Li, Aibing; Li, Lun
2015-08-01
Array measurements of surface wave phase velocity can be biased by multipath arrivals. A two-plane-wave (TPW) inversion method, in which the incoming wavefield is represented by the interference of two plane waves, is able to account for the multipath effect and solve for laterally varying phase velocity. Despite broad applications of the TPW method, its usage has been limited to Rayleigh waves. In this study, we have modified the TPW approach and applied it to Love waves. Main modifications include decomposing Love wave amplitude on the transverse component to x and y components in a local Cartesian system for each earthquake and using both components in the inversion. Such decomposition is also applied to the two plane waves to predict the incoming wavefield of an earthquake. We utilize fundamental mode Love wave data recorded at 85 broad-band stations from 69 distant earthquakes and solved for phase velocity in nine frequency bands with centre periods ranging from 34 to 100 s. The average phase velocity in southern Africa increases from 4.30 km s-1 at 34 s to 4.87 km s-1 at 100 s. Compared with predicted Love wave phase velocities from the published 1-D SV velocity model and radial anisotropy model in the region, these values are compatible from 34 to 50 s and slightly higher beyond 50 s, indicating radial anisotropy of VSH > VSV in the shallow upper mantle. A high Love wave velocity anomaly is imaged in the central and southern Kaapvaal craton at all periods, reflecting a cold and depleted cratonic lithosphere. A low velocity anomaly appears in the Bushveld Complex from 34 to 50 s, which can be interpreted as being caused by high iron content from an intracratonic magma intrusion. The modified TPW method provides a new way to measure Love wave phase velocities in a regional array, which are essential in developing radial anisotropic models and understanding the Earth structure in the crust and upper mantle.
Radiography of nonaxisymmetric objects: An onion-peeling inversion method
NASA Astrophysics Data System (ADS)
Schwierz-Iosefzon, T.; Notea, A.; Deutsch, M.
2002-09-01
An onion-peeling method for obtaining the linear attenuation coefficient distribution within a body from a single radiographic projection is presented. Unlike previous methods, which are applicable only to axi- or centrosymmetric objects, ours requires only mirror symmetry relative to the plane of the radiograph. An example of the use of the method is presented and discussed.
Design optimization of axial flow hydraulic turbine runner: Part I - an improved Q3D inverse method
NASA Astrophysics Data System (ADS)
Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji
2002-06-01
With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright
Inverse modeling of Texas NOx emissions using space-based and ground-based NO2 observations
NASA Astrophysics Data System (ADS)
Tang, W.; Cohan, D. S.; Lamsal, L. N.; Xiao, X.; Zhou, W.
2013-11-01
Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite-observed NO2 over rural regions. Satellite-based top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with decoupled direct method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2-based DKF inversion. The DKF inversions yield conflicting results: the satellite-based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.
Inverse modeling of Texas NOx emissions using space-based and ground-based NO2 observations
NASA Astrophysics Data System (ADS)
Tang, W.; Cohan, D.; Lamsal, L. N.; Xiao, X.; Zhou, W.
2013-07-01
Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellite-based top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite-based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.
Inverse Modeling of Texas NOx Emissions Using Space-Based and Ground-Based NO2 Observations
NASA Technical Reports Server (NTRS)
Tang, Wei; Cohan, D.; Lamsal, L. N.; Xiao, X.; Zhou, W.
2013-01-01
Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellitebased top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.
NASA Astrophysics Data System (ADS)
Garcia Juanatey, M. A.; Hübert, J.; Tryggvason, A.; Juhlin, C.; Pedersen, L. B.; Bauer, T. E.; Dehghannejad, M.
2012-12-01
Broadband MT data were acquired in the Skellefte district, an important mining area in northern Sweden, as part of the VINNOVA project "4D modeling of the Skellefte District". The project aims to provide a better understanding of the local and regional processes that took place in the past and, thus, provide a framework for new exploration strategies to target deeper deposits in the area. The new MT data, acquired in the central part of the district, consist of 36 stations along two parallel profiles that follow seismic reflection lines and potential field modeling studies in the area. The dimensionality and quality of the data set were carefully analyzed and 2D and 3D inversions were performed. 2D inversions provided a basis to compare with other MT surveys in the area and to some extent validate 3D inversion results. 3D inversion was deemed necessary given the complexity of the geological setting of the studied area. The algorithms used were the data space based REBOCC and WSINV3DMT methods. For the 2D inversion only the determinant of the impedance tensor was used, while for the 3D inversion all its elements were considered. Prior to 3D inversion, new error floors were calculated using individual 1D inversions of the off-diagonal components of the impedance tensor. The obtained models have an RMS value of ~2, and share the main regional features. A detailed comparison reveals the superiority of the 3D model, both in model structures and data fit. An interpretation of the 3D model is presented using also results from previous geophysical studies. The most interesting features in the model are conductors associated to prominent shear zones (from 1 to 12 km deep) and hydrothermally altered zones within the Skellefte Group rocks (between 250 and 6000 m depth). In addition, it is possible to identify faults associated to the transport of hydrothermal fluids that might be closely related to ore forming processes.
NASA Astrophysics Data System (ADS)
Zhao, Jingtao; Peng, Suping; Du, Wenfeng
2016-02-01
We consider sparsity-constraint inversion method for detecting seismic small-scale discontinuities, such as edges, faults and cavities, which provide rich information about petroleum reservoirs. However, where there is karstification and interference caused by macro-scale fault systems, these seismic small-scale discontinuities are hard to identify when using currently available discontinuity-detection methods. In the subsurface, these small-scale discontinuities are separately and sparsely distributed and their seismic responses occupy a very small part of seismic image. Considering these sparsity and non-smooth features, we propose an effective L 2-L 0 norm model for improvement of their resolution. First, we apply a low-order plane-wave destruction method to eliminate macro-scale smooth events. Then, based the residual data, we use a nonlinear structure-enhancing filter to build a L 2-L 0 norm model. In searching for its solution, an efficient and fast convergent penalty decomposition method is employed. The proposed method can achieve a significant improvement in enhancing seismic small-scale discontinuities. Numerical experiment and field data application demonstrate the effectiveness and feasibility of the proposed method in studying the relevant geology of these reservoirs.
Luan, Fu-Ming; Zhang, Xiao-Lei; Xiong, Hei-Gang; Zhang, Fang; Wang, Fang
2013-01-01
The present paper, based on the Qitai county of Xinjiang, selected 40 soil samples, and used two methods respectively, i.e. multiple linear stepwise regression (MLSR) and artificial neural network (ANNs), to establish the inversion and predieting model of soil organic matter (SOM) content and the model test from measured reflectance spectra and relative test were carried through to the models. Through quantitative analysis, the conclusions can be drawn as follows that the precision values of the different models vary from one to another, the model fitting effects order from high to low is that the integrated model for artificial neural networks (ANNs) is best, single artificial neural networks (ANNs) model is better, while stepwise multiple regression (MLSR) models are worse. Artificial neural networks (ANNs) has the strong abilities of linear and nonlinear approximation, while its integrated model for artificial neural networks (ANNs) is an important way to improve the inversion accuracy of soil organic matter (SOM) content, with the correlation coefficient up to 0.938, root mean square error and total root mean square error are minimum, being 2.13 and 1.404 respectively, and the predictive ability of the soil organic matter (SOM) content are very close to the measured spectrum, so the analysis results can achieve a more practical prediction accuracy for the best fitting model.
NASA Technical Reports Server (NTRS)
Smith, G. A.; Meyer, G.; Nordstrom, M.
1986-01-01
A new automatic flight control system concept suitable for aircraft with highly nonlinear aerodynamic and propulsion characteristics and which must operate over a wide flight envelope was investigated. This exact model follower inverts a complete nonlinear model of the aircraft as part of the feed-forward path. The inversion is accomplished by a Newton-Raphson trim of the model at each digital computer cycle time of 0.05 seconds. The combination of the inverse model and the actual aircraft in the feed-forward path alloys the translational and rotational regulators in the feedback path to be easily designed by linear methods. An explanation of the model inversion procedure is presented. An extensive set of simulation data for essentially the full flight envelope for a vertical attitude takeoff and landing aircraft (VATOL) is presented. These data demonstrate the successful, smooth, and precise control that can be achieved with this concept. The trajectory includes conventional flight from 200 to 900 ft/sec with path accelerations and decelerations, altitude changes of over 6000 ft and 2g and 3g turns. Vertical attitude maneuvering as a tail sitter along all axes is demonstrated. A transition trajectory from 200 ft/sec in conventional flight to stationary hover in the vertical attitude includes satisfactory operation through lift-cure slope reversal as attitude goes from horizontal to vertical at constant altitude. A vertical attitude takeoff from stationary hover to conventional flight is also demonstrated.
Forward- vs. Inverse Problems in Modeling Seismic Attenuation
NASA Astrophysics Data System (ADS)
Morozov, I. B.
2015-12-01
Seismic attenuation is an important property of wave propagation used in numerous applications. However, the attenuation is also a complex phenomenon, and it is important to differentiate between its two typical uses: 1) in forward problems, to model the amplitudes and spectral contents of waves required for hazard assessment and geotechnical engineering, and 2) in inverse problems, to determine the physical properties of the subsurface. In the forward-problem sense, the attenuation is successfully characterized in terms of empirical parameters of geometric spreading, radiation patterns, scattering amplitudes, t-star, alpha, kappa, or Q. Arguably, the predicted energy losses can be correct even if the underlying attenuation model is phenomenological and not sufficiently based on physics. An example of such phenomenological model is the viscoelasticity based on the correspondence principle and the Q-factor assigned to the material. By contrast, when used to invert for in situ material properties, models addressing the specific physics are required. In many studies (including in this session), a Q-factor is interpreted as a property of a point within the subsurface; however this property is only phenomenological and may be physically insufficient or inconsistent. For example, the bulk or shear Q at the same point can be different when evaluated from different wave modes. The cases of frequency-dependent Q are particularly prone of ambiguities such as trade-off with the assumed background geometric spreading. To rigorously characterize the in situ material properties responsible for seismic-wave attenuation, it is insufficient to only focus on the seismic energy loss. Mechanical models of the material need to be considered. Such models can be constructed by using Lagrangian mechanics. These models should likely contain no Q but will be based on parameters of microstructure such as heterogeneity, fractures, or fluids. I illustrate several such models based on viscosity
Affordable and personalized lighting using inverse modeling and virtual sensors
NASA Astrophysics Data System (ADS)
Basu, Chandrayee; Chen, Benjamin; Richards, Jacob; Dhinakaran, Aparna; Agogino, Alice; Martin, Rodney
2014-03-01
Wireless sensor networks (WSN) have great potential to enable personalized intelligent lighting systems while reducing building energy use by 50%-70%. As a result WSN systems are being increasingly integrated in state-ofart intelligent lighting systems. In the future these systems will enable participation of lighting loads as ancillary services. However, such systems can be expensive to install and lack the plug-and-play quality necessary for user-friendly commissioning. In this paper we present an integrated system of wireless sensor platforms and modeling software to enable affordable and user-friendly intelligent lighting. It requires ⇠ 60% fewer sensor deployments compared to current commercial systems. Reduction in sensor deployments has been achieved by optimally replacing the actual photo-sensors with real-time discrete predictive inverse models. Spatially sparse and clustered sub-hourly photo-sensor data captured by the WSN platforms are used to develop and validate a piece-wise linear regression of indoor light distribution. This deterministic data-driven model accounts for sky conditions and solar position. The optimal placement of photo-sensors is performed iteratively to achieve the best predictability of the light field desired for indoor lighting control. Using two weeks of daylight and artificial light training data acquired at the Sustainability Base at NASA Ames, the model was able to predict the light level at seven monitored workstations with 80%-95% accuracy. We estimate that 10% adoption of this intelligent wireless sensor system in commercial buildings could save 0.2-0.25 quads BTU of energy nationwide.
Inverse transport modeling of volcanic sulfur dioxide emissions using large-scale simulations
NASA Astrophysics Data System (ADS)
Heng, Yi; Hoffmann, Lars; Griessbach, Sabine; Rößler, Thomas; Stein, Olaf
2016-05-01
An inverse transport modeling approach based on the concepts of sequential importance resampling and parallel computing is presented to reconstruct altitude-resolved time series of volcanic emissions, which often cannot be obtained directly with current measurement techniques. A new inverse modeling and simulation system, which implements the inversion approach with the Lagrangian transport model Massive-Parallel Trajectory Calculations (MPTRAC) is developed to provide reliable transport simulations of volcanic sulfur dioxide (SO2). In the inverse modeling system MPTRAC is used to perform two types of simulations, i.e., unit simulations for the reconstruction of volcanic emissions and final forward simulations. Both types of transport simulations are based on wind fields of the ERA-Interim meteorological reanalysis of the European Centre for Medium Range Weather Forecasts. The reconstruction of altitude-dependent SO2 emission time series is also based on Atmospheric InfraRed Sounder (AIRS) satellite observations. A case study for the eruption of the Nabro volcano, Eritrea, in June 2011, with complex emission patterns, is considered for method validation. Meteosat Visible and InfraRed Imager (MVIRI) near-real-time imagery data are used to validate the temporal development of the reconstructed emissions. Furthermore, the altitude distributions of the emission time series are compared with top and bottom altitude measurements of aerosol layers obtained by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite instruments. The final forward simulations provide detailed spatial and temporal information on the SO2 distributions of the Nabro eruption. By using the critical success index (CSI), the simulation results are evaluated with the AIRS observations. Compared to the results with an assumption of a constant flux of SO2 emissions, our inversion approach leads to an improvement
NASA Astrophysics Data System (ADS)
Cerminara, Matteo; Esposti Ongaro, Tomaso; Valade, Sébastien; Harris, Andrew J. L.
2015-07-01
We present a coupled fluid-dynamic and electromagnetic model for volcanic ash plumes. In a forward approach, the model is able to simulate the plume dynamics from prescribed input flow conditions and generate the corresponding synthetic thermal infrared (TIR) image, allowing a comparison with field-based observations. An inversion procedure is then developed to retrieve vent conditions from TIR images, and to independently estimate the mass eruption rate. The adopted fluid-dynamic model is based on a one-dimensional, stationary description of a self-similar turbulent plume, for which an asymptotic analytical solution is obtained. The electromagnetic emission/absorption model is based on Schwarzschild's equation and on Mie's theory for disperse particles, and we assume that particles are coarser than the radiation wavelength (about 10 μm) and that scattering is negligible. In the inversion procedure, model parameter space is sampled to find the optimal set of input conditions which minimizes the difference between the experimental and the synthetic image. Application of the inversion procedure to an ash plume at Santiaguito (Santa Maria volcano, Guatemala) has allowed us to retrieve the main plume input parameters, namely mass flow rate, initial radius, velocity, temperature, gas mass ratio, entrainment coefficient and their related uncertainty. Moreover, by coupling with the electromagnetic model we have been able to obtain a reliable estimate of the equivalent Sauter diameter of the total particle size distribution. The presented method is general and, in principle, can be applied to the spatial distribution of particle concentration and temperature obtained by any fluid-dynamic model, either integral or multidimensional, stationary or time-dependent, single or multiphase. The method discussed here is fast and robust, thus indicating potential for applications to real-time estimation of ash mass flux and particle size distribution, which is crucial for model
NASA Astrophysics Data System (ADS)
Xiao, X.; Cohan, D. S.
2009-12-01
Substantial uncertainties in current emission inventories have been detected by the Texas Air Quality Study 2006 (TexAQS 2006) intensive field program. These emission uncertainties have caused large inaccuracies in model simulations of air quality and its responses to management strategies. To improve the quantitative understanding of the temporal, spatial, and categorized distributions of primary pollutant emissions by utilizing the corresponding measurements collected during TexAQS 2006, we implemented both the recursive Kalman filter and a batch matrix inversion 4-D data assimilation (FDDA) method in an iterative inverse modeling framework of the CMAQ-DDM model. Equipped with the decoupled direct method, CMAQ-DDM enables simultaneous calculation of the sensitivity coefficients of pollutant concentrations to emissions to be used in the inversions. Primary pollutant concentrations measured by the multiple platforms (TCEQ ground-based, NOAA WP-3D aircraft and Ronald H. Brown vessel, and UH Moody Tower) during TexAQS 2006 have been integrated for the use in the inverse modeling. Firstly pseudo-data analyses have been conducted to assess the two methods, taking a coarse spatial resolution emission inventory as a case. Model base case concentrations of isoprene and ozone at arbitrarily selected ground grid cells were perturbed to generate pseudo measurements with different assumed Gaussian uncertainties expressed by 1-sigma standard deviations. Single-species inversions have been conducted with both methods for isoprene and NOx surface emissions from eight states in the Southeastern United States by using the pseudo measurements of isoprene and ozone, respectively. Utilization of ozone pseudo data to invert for NOx emissions serves only for the purpose of method assessment. Both the Kalman filter and FDDA methods show good performance in tuning arbitrarily shifted a priori emissions to the base case “true” values within 3-4 iterations even for the nonlinear
Zhu, Lin; Dai, Zhenxue; Gong, Huili; Gable, Carl; Teatini, Pietro
2015-06-12
Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.
Model-based elastography: a survey of approaches to the inverse elasticity problem
Doyley, M M
2012-01-01
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This article reviews current approaches to elastography in three areas — quasi-static, harmonic, and transient — and describes inversion schemes for each elastographic imaging approach. Approaches include: first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials; and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper’s objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic, and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the transient behavior of soft tissue; and (3) developing better test procedures to evaluate the performance of modulus elastograms. PMID:22222839
Zhu, Lin; Dai, Zhenxue; Gong, Huili; Gable, Carl; Teatini, Pietro
2015-06-12
Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less
NASA Astrophysics Data System (ADS)
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
NASA Technical Reports Server (NTRS)
Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander
2013-01-01
The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.
Łęski, Szymon; Pettersen, Klas H; Tunstall, Beth; Einevoll, Gaute T; Gigg, John; Wójcik, Daniel K
2011-12-01
The recent development of large multielectrode recording arrays has made it affordable for an increasing number of laboratories to record from multiple brain regions simultaneously. The development of analytical tools for array data, however, lags behind these technological advances in hardware. In this paper, we present a method based on forward modeling for estimating current source density from electrophysiological signals recorded on a two-dimensional grid using multi-electrode rectangular arrays. This new method, which we call two-dimensional inverse Current Source Density (iCSD 2D), is based upon and extends our previous one- and three-dimensional techniques. We test several variants of our method, both on surrogate data generated from a collection of Gaussian sources, and on model data from a population of layer 5 neocortical pyramidal neurons. We also apply the method to experimental data from the rat subiculum. The main advantages of the proposed method are the explicit specification of its assumptions, the possibility to include system-specific information as it becomes available, the ability to estimate CSD at the grid boundaries, and lower reconstruction errors when compared to the traditional approach. These features make iCSD 2D a substantial improvement over the approaches used so far and a powerful new tool for the analysis of multielectrode array data. We also provide a free GUI-based MATLAB toolbox to analyze and visualize our test data as well as user datasets.
NASA Astrophysics Data System (ADS)
Schuster, David M.
1993-04-01
An inverse method has been developed to compute the structural stiffness properties of wings given a specified wing loading and aeroelastic twist distribution. The method directly solves for the bending and torsional stiffness distribution of the wing using a modal representation of these properties. An aeroelastic design problem involving the use of a computational aerodynamics method to optimize the aeroelastic twist distribution of a tighter wing operating at maneuver flight conditions is used to demonstrate the application of the method. This exercise verifies the ability of the inverse scheme to accurately compute the structural stiffness distribution required to generate a specific aeroelastic twist under a specified aeroelastic load.
Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states.
Decelle, Aurélien; Ricci-Tersenghi, Federico
2016-07-01
In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models). PMID:27575082
Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states
NASA Astrophysics Data System (ADS)
Decelle, Aurélien; Ricci-Tersenghi, Federico
2016-07-01
In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models).
Method for detecting a pericentric inversion in a chromosome
Lucas, Joe N.
2000-01-01
A method is provided for determining a clastogenic signature of a sample of chromosomes by quantifying a frequency of a first type of chromosome aberration present in the sample; quantifying a frequency of a second, different type of chromosome aberration present in the sample; and comparing the frequency of the first type of chromosome aberration to the frequency of the second type of chromosome aberration. A method is also provided for using that clastogenic signature to identify a clastogenic agent or dosage to which the cells were exposed.
Inverse analysis of water profile in starch by non-contact photopyroelectric method
NASA Astrophysics Data System (ADS)
Frandas, A.; Duvaut, T.; Paris, D.
2000-07-01
The photopyroelectric (PPE) method in a non-contact configuration was proposed to study water migration in starch sheets used for biodegradable packaging. A 1-D theoretical model was developed, allowing the study of samples having a water profile characterized by an arbitrary continuous function. An experimental setup was designed or this purpose which included the choice of excitation source, detection of signals, signal and data processing, and cells for conditioning the samples. We report here the development of an inversion procedure allowing for the determination of the parameters that influence the PPE signal. This procedure led to the optimization of experimental conditions in order to identify the parameters related to the water profile in the sample, and to monitor the dynamics of the process.
Variational methods for direct/inverse problems of atmospheric dynamics and chemistry
NASA Astrophysics Data System (ADS)
Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena
2013-04-01
We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the
Inverse Sensitivity/Uncertainty Methods Development for Nuclear Fuel Cycle Applications
NASA Astrophysics Data System (ADS)
Arbanas, G.; Dunn, M. E.; Williams, M. L.
2014-04-01
The Standardized Computer Analyses for Licensing Evaluation (SCALE) software package developed at the Oak Ridge National Laboratory includes codes that propagate uncertainties available in the nuclear data libraries to compute uncertainties in nuclear application performance parameters. We report on our recent efforts to extend this capability to develop an inverse sensitivity/uncertainty (IS/U) methodology that identifies the improvements in nuclear data that are needed to compute application responses within prescribed tolerances, while minimizing the cost of such data improvements. We report on our progress to date and present a simple test case for our method. Our methodology is directly applicable to thermal and intermediate neutron energy systems because it addresses the implicit neutron resonance self-shielding effects that are essential to accurate modeling of thermal and intermediate systems. This methodology is likely to increase the efficiency of nuclear data efforts.
Constraining the rheology of the lithosphere and upper mantle with geodynamic inverse modelling
NASA Astrophysics Data System (ADS)
Kaus, Boris; Baumann, Tobias
2016-04-01
The rheology of the lithosphere is of key importance for the physics of the lithosphere. Yet, it is probably the most uncertain parameter in geodynamics as experimental rock rheologies have to be extrapolated to geological conditions and as existing geophysical methods such as EET estimations make simplifying assumptions about the structure of the lithosphere. In many geologically interesting regions, such as the Alps, Andes or Himalaya, we actually have a significant amount of data already and as a result the geometry of the lithosphere is quite well constrained. Yet, knowing the geometry is only one part of the story, as we also need to have an accurate knowledge on the rheology and temperature structure of the lithosphere. Here, we discuss a relatively new method that we developed over the last few years, which is called geodynamic inversion. The basic principle of the method is simple: we compile available geophysical data into a realistic geometric model of the lithosphere and incorporate that into a thermo-mechanical numerical model of lithospheric deformation. In order to do so, we have to know the temperature structure, the density and the (nonlinear) rheological parameters for various parts of the lithosphere (upper crust, upper mantle, etc.). Rather than fixing these parameters we assume that they are all uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology, we first perform a geodynamic inversion of a synthetic forward model of intra-oceanic subduction with known parameters. This requires solving an inverse problem with 14-16 parameters, depending on whether temperature is assumed to be known or not. With the help of a massively parallel direct-search combined with a Markov Chain Monte Carlo method, solving the inverse problem
Evaluation of a Heterogeneity Preserving Inversion Method for Subsurface Unsaturated Flow
NASA Astrophysics Data System (ADS)
Zhang, Y.; Schaap, M. G.; Neuman, S. P.; Guadagnini, A.; Riva, M.
2013-12-01
is embedded in the inversion method through textural information. Our results show the benefit of our inverse modeling approach, assessed through minimization of the difference between observed and simulated water content dynamics, when compared against traditional zonation, with mean squared residual (MSR) decreasing by about 35% and Pearson correlation coefficient increasing from 0.9395 to 0.9612.
Dura-Bernal, Salvador; Li, Kan; Neymotin, Samuel A; Francis, Joseph T; Principe, Jose C; Lytton, William W
2016-01-01
Neural stimulation can be used as a tool to elicit natural sensations or behaviors by modulating neural activity. This can be potentially used to mitigate the damage of brain lesions or neural disorders. However, in order to obtain the optimal stimulation sequences, it is necessary to develop neural control methods, for example by constructing an inverse model of the target system. For real brains, this can be very challenging, and often unfeasible, as it requires repeatedly stimulating the neural system to obtain enough probing data, and depends on an unwarranted assumption of stationarity. By contrast, detailed brain simulations may provide an alternative testbed for understanding the interactions between ongoing neural activity and external stimulation. Unlike real brains, the artificial system can be probed extensively and precisely, and detailed output information is readily available. Here we employed a spiking network model of sensorimotor cortex trained to drive a realistic virtual musculoskeletal arm to reach a target. The network was then perturbed, in order to simulate a lesion, by either silencing neurons or removing synaptic connections. All lesions led to significant behvaioral impairments during the reaching task. The remaining cells were then systematically probed with a set of single and multiple-cell stimulations, and results were used to build an inverse model of the neural system. The inverse model was constructed using a kernel adaptive filtering method, and was used to predict the neural stimulation pattern required to recover the pre-lesion neural activity. Applying the derived neurostimulation to the lesioned network improved the reaching behavior performance. This work proposes a novel neurocontrol method, and provides theoretical groundwork on the use biomimetic brain models to develop and evaluate neurocontrollers that restore the function of damaged brain regions and the corresponding motor behaviors. PMID:26903796
Dura-Bernal, Salvador; Li, Kan; Neymotin, Samuel A.; Francis, Joseph T.; Principe, Jose C.; Lytton, William W.
2016-01-01
Neural stimulation can be used as a tool to elicit natural sensations or behaviors by modulating neural activity. This can be potentially used to mitigate the damage of brain lesions or neural disorders. However, in order to obtain the optimal stimulation sequences, it is necessary to develop neural control methods, for example by constructing an inverse model of the target system. For real brains, this can be very challenging, and often unfeasible, as it requires repeatedly stimulating the neural system to obtain enough probing data, and depends on an unwarranted assumption of stationarity. By contrast, detailed brain simulations may provide an alternative testbed for understanding the interactions between ongoing neural activity and external stimulation. Unlike real brains, the artificial system can be probed extensively and precisely, and detailed output information is readily available. Here we employed a spiking network model of sensorimotor cortex trained to drive a realistic virtual musculoskeletal arm to reach a target. The network was then perturbed, in order to simulate a lesion, by either silencing neurons or removing synaptic connections. All lesions led to significant behvaioral impairments during the reaching task. The remaining cells were then systematically probed with a set of single and multiple-cell stimulations, and results were used to build an inverse model of the neural system. The inverse model was constructed using a kernel adaptive filtering method, and was used to predict the neural stimulation pattern required to recover the pre-lesion neural activity. Applying the derived neurostimulation to the lesioned network improved the reaching behavior performance. This work proposes a novel neurocontrol method, and provides theoretical groundwork on the use biomimetic brain models to develop and evaluate neurocontrollers that restore the function of damaged brain regions and the corresponding motor behaviors. PMID:26903796
Leaf Area Index Retrieval From SPARC Data: Assessment Of Radiative Transfer Model Inversion
NASA Astrophysics Data System (ADS)
Dini, L.; Vuolo, F.; Randazzo, L.
2006-08-01
Leaf Area Index (LAI) is a key parameter for many biophysical and climatic models. In the field of interest of our research group, an accurate LAI estimation is needed for modelling crop water requirements for precision farming and agricultural resource management applications. The objective of this study is to assess the accuracy of LAI retrieval from EO data by means of a radiative transfer model inversion technique. To this aim multi-angular CHRIS/PROBA data, from SPARC 2003 and 2004 campaigns, has been employed in the inversion of PROSPECT-SAILH (P-SH) model by using a numerical optimisation technique based on the Marquardt-Levenberg (M-L) algorithm. From the same data set, the closer to nadir reflectance in the red and near-infrared bands has been selected in order to estimate LAI by using an empirical approach based on the CLAIR model. Such estimated LAI has been thus employed as prior information in the P-SH model. LAI values retrieved with this combined approach have been estimated with good accuracy for some type of crops (e.g. R2 = 0.80, RMSE=0.51 m2m-2 for Alfalfa canopies). Ongoing and future work includes further improvements of the M-L optimisation method and the implementation of a different optimisation method based on Genetic Algorithm GA.
Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
NASA Astrophysics Data System (ADS)
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver
A stochastic approach for model reduction and memory function design in hydrogeophysical inversion
NASA Astrophysics Data System (ADS)
Hou, Z.; Kellogg, A.; Terry, N.
2009-12-01
Geophysical (e.g., seismic, electromagnetic, radar) techniques and statistical methods are essential for research related to subsurface characterization, including monitoring subsurface flow and transport processes, oil/gas reservoir identification, etc. For deep subsurface characterization such as reservoir petroleum exploration, seismic methods have been widely used. Recently, electromagnetic (EM) methods have drawn great attention in the area of reservoir characterization. However, considering the enormous computational demand corresponding to seismic and EM forward modeling, it is usually a big problem to have too many unknown parameters in the modeling domain. For shallow subsurface applications, the characterization can be very complicated considering the complexity and nonlinearity of flow and transport processes in the unsaturated zone. It is warranted to reduce the dimension of parameter space to a reasonable level. Another common concern is how to make the best use of time-lapse data with spatial-temporal correlations. This is even more critical when we try to monitor subsurface processes using geophysical data collected at different times. The normal practice is to get the inverse images individually. These images are not necessarily continuous or even reasonably related, because of the non-uniqueness of hydrogeophysical inversion. We propose to use a stochastic framework by integrating minimum-relative-entropy concept, quasi Monto Carlo sampling techniques, and statistical tests. The approach allows efficient and sufficient exploration of all possibilities of model parameters and evaluation of their significances to geophysical responses. The analyses enable us to reduce the parameter space significantly. The approach can be combined with Bayesian updating, allowing us to treat the updated ‘posterior’ pdf as a memory function, which stores all the information up to date about the distributions of soil/field attributes/properties, then consider the
NASA Astrophysics Data System (ADS)
Deshpande, K.; Bust, G. S.; Clauer, C. R.; Kim, H.; Weimer, D. R.
2014-12-01
We have developed a high fidelity ``Satellite-beacon Ionospheric-scintillation Global Model of the upper Atmosphere" (SIGMA) which is a full 3D EM wave propagation model to simulate GPS scintillations globally. We demonstrate in this work that the results from this model can form a basic framework on the use of inverse method to understand the physics of high latitude irregularities using GPS scintillations. We are using SIGMA and an inverse method to understand the physics of the irregularities observed with GPS receivers from six different inter-hemispheric high latitude stations during a geomagnetic storm on 9 March 2012, and from Autonomous Adaptive Low-Power Instrument Platform (AAL-PIP) Antarctic stations during a substorm on 9 January 2014. We utilize ancillary observations from SuperDARN, ISRs, riometers etc. to obtain some of the input parameters of SIGMA. Further, we implement a uniform-grid SIGMA simulation or a non-linear optimization of the model to obtain the rest of the unknowns that give us the best fit with data. The input parameters of SIGMA thus derived represent the physical and propagation parameters related to the physics of the irregularity that produced those GNSS scintillations. Some of our findings from this investigation include that the spectral indices and outer scales for ionospheric heights of 350~km are higher than those at 120~km. The best fits we obtained from our inverse method mostly agree with the observations except for some cases, which might be because the spectral model we use is insufficient to describe irregularity physics. We need more auxiliary data in order to facilitate the possibility of accomplishing a unique solution to the inverse problem.
NASA Astrophysics Data System (ADS)
Liu, Qing Huo; Zhang, Zhong Qing
2000-07-01
We invert for the axisymmetric conductivity distribution from borehole electromagnetic induction measurements using a two-step linear inversion method based on a fast Fourier and Hankel transform enhanced extended Born approximation. In this method, the inverse problem is first cast as an under- determined linear least-norm problem for the induced electric current density; from the solution of this induced current density, the unknown conductivity distribution is then obtained by solving an over-determined linear problem using the newly developed, fast Fourier and Hankel transform enhanced extended Born approximation. Numerical results show that this inverse method is applicable to a very high conductivity contrast. It is a natural extension of the original two-step linear inversion method of Torres-Verdin and Habashy to axisymmetric media. In the first step, the CPU time costs O(N2). In the second step, the CPU time costs O(N log2 N) where N is the number of unknowns. Because of the fast Fourier and Hankel transform algorithm, this inverse method is actually more efficient than the conventional, brute-force first-order Born approximation.
SEASONAL NH 3 EMISSIONS FOR THE CONTINENTAL UNITED STATES: INVERSE MODEL ESTIMATION AND EVALUATION
An inverse modeling study has been conducted here to evaluate a prior estimate of seasonal ammonia (NH_{3}) emissions. The prior estimates were based on a previous inverse modeling study and two other bottom-up inventory studies. The results suggest that the prior estim...
Inverse modeling has been used extensively on the global scale to produce top-down estimates of emissions for chemicals such as CO and CH4. Regional scale air quality studies could also benefit from inverse modeling as a tool to evaluate current emission inventories; however, ...
ERIC Educational Resources Information Center
Losada, David E.; Barreiro, Alvaro
2003-01-01
Proposes an approach to incorporate term similarity and inverse document frequency into a logical model of information retrieval. Highlights include document representation and matching; incorporating term similarity into the measure of distance; new algorithms for implementation; inverse document frequency; and logical versus classical models of…
NASA Astrophysics Data System (ADS)
Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing
2016-06-01
The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations and large-scale models. We employ the inverse time dispersion transform (ITDT) to the third-order symplectic integration method to reduce the time-dispersion error. First, we adopt the pseudospectral algorithm for the spatial discretization and the third-order symplectic integration method for the temporal discretization. Then, we apply the ITDT to eliminate time-dispersion error from the synthetic data. As a post-processing method, the ITDT can be easily cascaded in traditional numerical simulations. We implement the ITDT in one typical exiting third-order symplectic scheme and compare its performances with the performances of the conventional second-order scheme and the rapid expansion method. Theoretical analyses and numerical experiments show that the ITDT can significantly reduce the time-dispersion error, especially for long travel times. The implementation of the ITDT requires some additional computations on correcting the time-dispersion error, but it allows us to use the maximum temporal interval under stability conditions; thus, its final computational efficiency would be higher than that of the traditional symplectic integration method for long-term simulations. With the aid of the ITDT, we can obtain much more accurate simulation results but with a lower computational cost.
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
NASA Astrophysics Data System (ADS)
Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar
2016-07-01
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the
Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm
NASA Astrophysics Data System (ADS)
Montesinos, Fuensanta G.; Blanco-Montenegro, Isabel; Arnoso, José
2016-04-01
We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).
Necpálová, Magdalena; Anex, Robert P.; Fienen, Michael N.; Del Grosso, Stephen J.; Castellano, Michael J.; Sawyer, John E.; Iqbal, Javed; Pantoja, Jose L.; Barker, Daniel W.
2015-01-01
The ability of biogeochemical ecosystem models to represent agro-ecosystems depends on their correct integration with field observations. We report simultaneous calibration of 67 DayCent model parameters using multiple observation types through inverse modeling using the PEST parameter estimation software. Parameter estimation reduced the total sum of weighted squared residuals by 56% and improved model fit to crop productivity, soil carbon, volumetric soil water content, soil temperature, N2O, and soil3NO− compared to the default simulation. Inverse modeling substantially reduced predictive model error relative to the default model for all model predictions, except for soil 3NO− and 4NH+. Post-processing analyses provided insights into parameter–observation relationships based on parameter correlations, sensitivity and identifiability. Inverse modeling tools are shown to be a powerful way to systematize and accelerate the process of biogeochemical model interrogation, improving our understanding of model function and the underlying ecosystem biogeochemical processes that they represent.
NASA Technical Reports Server (NTRS)
Truong-Loi, My-Linh; Saatchi, Sassan; Jaruwatanadilok, Sermsak
2012-01-01
A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha
Preliminary gravity inversion model of Frenchman Flat Basin, Nevada Test Site, Nevada
Phelps, G.A.; Graham, S.E.
2002-10-01
The depth of the basin beneath Frenchman Flat is estimated using a gravity inversion method. Gamma-gamma density logs from two wells in Frenchman Flat constrained the density profiles used to create the gravity inversion model. Three initial models were considered using data from one well, then a final model is proposed based on new information from the second well. The preferred model indicates that a northeast-trending oval-shaped basin underlies Frenchman Flat at least 2,100 m deep, with a maximum depth of 2,400 m at its northeast end. No major horst and graben structures are predicted. Sensitivity analysis of the model indicates that each parameter contributes the same magnitude change to the model, up to 30 meters change in depth for a 1% change in density, but some parameters affect a broader area of the basin. The horizontal resolution of the model was determined by examining the spacing between data stations, and was set to 500 square meters.
Preliminary gravity inversion model of Frenchman Flat Basin, Nevada Test Site, Nevada
Phelps, Geoffrey A.; Graham, Scott E.
2002-01-01
The depth of the basin beneath Frenchman Flat is estimated using a gravity inversion method. Gamma-gamma density logs from two wells in Frenchman Flat constrained the density profiles used to create the gravity inversion model. Three initial models were considered using data from one well, then a final model is proposed based on new information from the second well. The preferred model indicates that a northeast-trending oval-shaped basin underlies Frenchman Flat at least 2,100 m deep, with a maximum depth of 2,400 m at its northeast end. No major horst and graben structures are predicted. Sensitivity analysis of the model indicates that each parameter contributes the same magnitude change to the model, up to 30 meters change in depth for a 1% change in density, but some parameters affect a broader area of the basin. The horizontal resolution of the model was determined by examining the spacing between data stations, and was set to 500 square meters.
Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation
NASA Astrophysics Data System (ADS)
Poddar, Banibrata; Giurgiutiu, Victor
2016-04-01
Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.
Hydrochlorofluorocarbon and hydrofluorocarbon emissions in East Asia determined by inverse modeling
NASA Astrophysics Data System (ADS)
Stohl, A.; Kim, J.; Li, S.; O'Doherty, S.; Mühle, J.; Salameh, P. K.; Saito, T.; Vollmer, M. K.; Wan, D.; Weiss, R. F.; Yao, B.; Yokouchi, Y.; Zhou, L. X.
2010-04-01
The emissions of three hydrochlorofluorocarbons, HCFC-22 (CHClF2), HCFC-141b (CH3CCl2F) and HCFC-142b (CH3CClF2) and three hydrofluorocarbons, HFC-23 (CHF3), HFC-134a (CH2FCF3) and HFC-152a (CH3CHF2) from four East Asian countries and the Taiwan region for the year 2008 are determined by inverse modeling. The inverse modeling is based on in-situ measurements of these halocarbons at the Japanese stations Cape Ochi-ishi and Hateruma, the Chinese station Shangdianzi and the South Korean station Gosan. For every station and every 3 h, 20-day backward calculations were made with the Lagrangian particle dispersion model FLEXPART. The model output, the measurement data, bottom-up emission information and corresponding uncertainties were fed into an inversion algorithm to determine the regional emission fluxes. The model captures the observed variation of halocarbon mixing ratios very well for the two Japanese stations but has difficulties explaining the large observed variability at Shangdianzi, which is partly caused by small-scale transport from Beijing that is not adequately captured by the model. Based on HFC-23 measurements, the inversion algorithm could successfully identify the locations of factories known to produce HCFC-22 and emit HFC-23 as an unintentional byproduct. This lends substantial credibility to the inversion method. We report national emissions for China, North Korea, South Korea and Japan, as well as emissions for the Taiwan region. Halocarbon emissions in China are much larger than the emissions in the other countries together and contribute a substantial fraction to the global emissions. Our estimates of Chinese emissions for the year 2008 are 65.3±6.6 kt/yr for HCFC-22 (17% of global emissions extrapolated from Montzka et al., 2009), 12.1±1.6 kt/yr for HCFC-141b (22%), 7.3±0.7 kt/yr for HCFC-142b (17%), 6.2±0.7 kt/yr for HFC-23 (>50%), 12.9±1.7 kt/yr for HFC-134a (9% of global emissions estimated from Velders et al., 2009) and 3.4±0.5 kt
Hydrochlorofluorocarbon and hydrofluorocarbon emissions in East Asia determined by inverse modeling
NASA Astrophysics Data System (ADS)
Stohl, A.; Kim, J.; Li, S.; O'Doherty, S.; Salameh, P. K.; Saito, T.; Vollmer, M. K.; Wan, D.; Yao, B.; Yokouchi, Y.; Zhou, L. X.
2010-02-01
The emissions of three hydrochlorofluorocarbons, HCFC-22 (CHClF2), HCFC-141b (CH3CCl2F) and HCFC-142b (CH3CClF2) and three hydrofluorocarbons, HFC-23 (CHF3), HFC-134a (CH2FCF3) and HFC-152a (CH3CHF2) from five East Asian countries for the year 2008 are determined by inverse modeling. The inverse modeling is based on in-situ measurements of these halocarbons at the Japanese stations Cape Ochi-ishi and Hateruma, the Chinese station Shangdianzi and the South Korean station Gosan. For every station and every 3 h, 20-day backward calculations were made with the Lagrangian particle dispersion model FLEXPART. The model output, the measurement data, bottom-up emission information and corresponding uncertainties were fed into an inversion algorithm to determine the regional emission fluxes. The model captures the observed variation of halocarbon mixing ratios very well for the two Japanese stations but has difficulties explaining the large observed variability at Shangdianzi, which is partly caused by small-scale transport from Beijing that is not adequately captured by the model. Based on HFC-23 measurements, the inversion algorithm could successfully identify the locations of factories known to produce HCFC-22 and emit HFC-23 as an unintentional byproduct. This lends substantial credibility to the inversion method. We report national emissions for China, North Korea, South Korea and Japan, as well as emissions for the Taiwan region. Halocarbon emissions in China are much larger than the emissions in the other countries together and contribute a substantial fraction to the global emissions. Our estimates of Chinese emissions for the year 2008 are 65.3±6.6 kt/yr for HCFC-22 (17% of global emissions extrapolated from Montzka et al., 2009), 12.1±1.6 kt/yr for HCFC-141b (22%), 7.3±0.7 kt/yr for HCFC-142b (17%), 6.2±0.7 kt/yr for HFC-23 (>50%), 12.9±1.7 kt/yr for HFC-134a (9% of global emissions estimated from Velders et al., 2009) and 3.4±0.5 kt/yr for HFC-152a (7%).
Multiple tail models including inverse measures for structural design under uncertainties
NASA Astrophysics Data System (ADS)
Ramu, Palaniappan
Sampling-based reliability estimation with expensive computer models may be computationally prohibitive due to a large number of required simulations. One way to alleviate the computational expense is to extrapolate reliability estimates from observed levels to unobserved levels. Classical tail modeling techniques provide a class of models to enable this extrapolation using asymptotic theory by approximating the tail region of the cumulative distribution function (CDF). This work proposes three alternate tail extrapolation techniques including inverse measures that can complement classical tail modeling. The proposed approach, multiple tail models, applies the two classical and three alternate extrapolation techniques simultaneously to estimate inverse measures at the extrapolation regions and use the median as the best estimate. It is observed that the range of the five estimates can be used as a good approximation of the error associated with the median estimate. Accuracy and computational efficiency are competing factors in selecting sample size. Yet, as our numerical studies reveal, the accuracy lost to the reduction of computational power is very small in the proposed method. The method is demonstrated on standard statistical distributions and complex engineering examples.
A Study of the Parameters for Solar Structure Inversion Methods
NASA Astrophysics Data System (ADS)
Rabello-Soares, M. C.; Basu, Sarbani; Christensen-Dalsgaard, J.
The observed solar p-mode frequencies provide an extremely useful diagnostic of the internal structure of the Sun, and permit us to test in considerable detail the physics used in the theory of stellar structure. Two implementations of the optimally localized averages (OLA) method are amongst the most commonly used techniques for inverting helioseismic data, namely the Subtractive Optimally Localized Averages (SOLA) and Multiplicative Optimally Localized Averages (MOLA). In both of them, there are a number of parameters that must be chosen in order to find the solution. Proper choice of the parameters is very important to determine correctly the variation of the internal structure along the solar radius. In this work, we make a detailed analysis on the influence of each parameter on the solution and indicate how to arrive at an optimal set of parameters for a given data set.
NASA Technical Reports Server (NTRS)
Smith, C. B.
1982-01-01
The Fymat analytic inversion method for retrieving a particle-area distribution function from anomalous diffraction multispectral extinction data and total area is generalized to the case of a variable complex refractive index m(lambda) near unity depending on spectral wavelength lambda. Inversion tests are presented for a water-haze aerosol model. An upper-phase shift limit of 5 pi/2 retrieved an accurate peak area distribution profile. Analytical corrections using both the total number and area improved the inversion.
Hassaballah, Abdallah I.; Hassan, Mohsen A.; Mardi, Azizi N.; Hamdi, Mohd
2013-01-01
The determination of the myocardium’s tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle. PMID:24367544
TH-A-9A-06: Inverse Planning of Gamma Knife Radiosurgery Using Natural Physical Models
Riofrio, D; Ma, L; Zhou, J; Luan, S
2014-06-15
Purpose: Treatment-planning systems rely on computer intensive optimization algorithms in order to provide radiation dose localization. We are investigating a new optimization paradigm based on natural physical modeling and simulations, which tend to evolve in time and find the minimum energy state. In our research, we aim to match physical models with radiation therapy inverse planning problems, where the minimum energy state coincides with the optimal solution. As a prototype study, we have modeled the inverse planning of Gamma Knife radiosurgery using the dynamic interactions between charged particles and demonstrate the potential of the paradigm. Methods: For inverse planning of Gamma Knife radiosurgery: (1) positive charges are uniformly placed on the surface of tumors and critical structures. (2) The Gamma Knife dose kernels of 4mm, 8mm and 16mm radii are modeled as geometric objects with variable charges. (3) The number of shots per each kernel radii is obtained by solving a constrained integer-linear problem. (4) The shots are placed into the tumor volume and move under electrostatic forces. The simulation is performed until internal forces are zero or maximum iterations are reached. (5) Finally, non-negative least squares (NNLS) is used to calculate the beam-on times for each shot. Results: A 3D C-shaped tumor surrounding a spherical critical structure was used for testing the new optimization paradigm. These tests showed that charges spread out evenly covering the tumor while keeping distance from the critical structure, resulting in a high quality plan. Conclusion: We have developed a new paradigm for dose optimization based on the simulation of physical models. As prototype studies, we applied electrostatic models to Gamma Knife radiosurgery and demonstrated the potential of the new paradigm. Further research and fine-tuning of the model are underway. NSF CBET-0853157.
Neuman, S; Glascoe, L; Kosovic, B; Dyer, K; Hanley, W; Nitao, J; Gordon, R
2005-11-03
The rapid identification of contaminant plume sources and their characteristics in urban environments can greatly enhance emergency response efforts. Source identification based on downwind concentration measurements is complicated by the presence of building obstacles that can cause flow diversion and entrainment. While high-resolution computational fluid dynamics (CFD) simulations are available for predicting plume evolution in complex urban geometries, such simulations require large computational effort. We make use of an urban puff model, the Defence Science Technology Laboratory's (Dstl) Urban Dispersion Model (UDM), which employs empirically based puff splitting techniques. UDM enables rapid urban dispersion simulations by combining traditional Gaussian puff modeling with empirically deduced mixing and entrainment approximations. Here we demonstrate the preliminary reconstruction of an atmospheric release event using stochastic sampling algorithms and Bayesian inference together with the rapid UDM urban puff model based on point measurements of concentration. We consider source inversions for both a prototype isolated building and for observations and flow conditions taken during the Joint URBAN 2003 field campaign at Oklahoma City. The Markov Chain Monte Carlo (MCMC) stochastic sampling method is used to determine likely source term parameters and considers both measurement and forward model errors. It should be noted that the stochastic methodology is general and can be used for time-varying release rates and flow conditions as well as nonlinear dispersion problems. The results of inversion indicate the probability of a source being at a particular location with a particular release rate. Uncertainty in observed data, or lack of sufficient data, is inherently reflected in the shape and size of the probability distribution of source term parameters. Although developed and used independently, source inversion with both UDM and a finite-element CFD code can be
NASA Astrophysics Data System (ADS)
Fortin, Will F. J.
The utility and meaning of a geophysical dataset is dependent on good interpretation informed by high-quality data, processing, and attribute examination via technical methodologies. Active source marine seismic reflection data contains a great deal of information in the location, phase, and amplitude of both pre- and post-stack seismic reflections. Using pre- and post-stack data, this work has extracted useful information from marine reflection seismic data in novel ways in both the oceanic water column and the sub-seafloor geology. In chapter 1 we develop a new method for estimating oceanic turbulence from a seismic image. This method is tested on synthetic seismic data to show the method's ability to accurately recover both distribution and levels of turbulent diffusivity. Then we apply the method to real data offshore Costa Rica where we observe lee waves. Our results find elevated diffusivities near the seafloor as well as above the lee waves five times greater than surrounding waters and 50 times greater than open ocean diffusivities. Chapter 2 investigates subsurface geology in the Cascadia Subduction Zone and outlines a workflow for using pre-stack waveform inversion to produce highly detailed velocity models and seismic images. Using a newly developed inversion code, we achieve better imaging results as compared to the product of a standard, user-intensive method for building a velocity model. Our results image the subduction interface ~30 km farther landward than previous work and better images faults and sedimentary structures above the oceanic plate as well as in the accretionary prism. The resultant velocity model is highly detailed, inverted every 6.25 m with ~20 m vertical resolution, and will be used to examine the role of fluids in the subduction system. These results help us to better understand the natural hazards risks associated with the Cascadia Subduction Zone. Chapter 3 returns to seismic oceanography and examines the dynamics of nonlinear
Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods
Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev
2013-01-01
Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452
Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.
Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev
2013-05-01
Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.
A new method to inverse soil moisture based on thermal infrared and passive microwave remote sensing
NASA Astrophysics Data System (ADS)
Zhou, Zhuang; Kou, Xiaokang; Zhao, Shaojie; Jiang, Lingmei
2014-11-01
Soil moisture is one of the main factors in the water, energy and carbon cycles. It constitutes a major uncertainty in climate and hydrological models. By now, passive microwave remote sensing and thermal infrared remote sensing technology have been used to obtain and monitor soil moisture. However, as the resolution of passive microwave remote sensing is very low and the thermal infrared remote sensing method fails to provide soil temperature on cloudy days, it is hard to monitor the soil moisture accurately. To solve the problem, a new method has been tried in this research. Thermal infrared remote sensing and passive microwave remote sensing technology have been combined based on the delicate experiment. Since the soil moisture retrieved by passive microwave in general represents surface centimeters deep, which is different from deeper soil moisture estimated by thermal inertia method, a relationship between the two depths soil moisture has been established based on the experiment. The results show that there is a good relationship between the soil moisture estimated by passive microwave and thermal infrared remote sensing method. The correlation coefficient is 0.78 and RMSE (root mean square error) is 0.0195 · ?. This research provides a new possible method to inverse soil moisture.
Goal Directed Model Inversion: Learning Within Domain Constraints
NASA Technical Reports Server (NTRS)
Colombano, Silvano P.; Compton, Michael; Raghavan, Bharathi; Friedland, Peter (Technical Monitor)
1994-01-01
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: (1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e., would not need to learn everything from scratch as normally required at present; and (2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.
Goal Directed Model Inversion: Learning Within Domain Constraints
NASA Technical Reports Server (NTRS)
Colombano, Silvano P.; Compton, Michael; Raghavan, Bharathi; Lum, Henry, Jr. (Technical Monitor)
1994-01-01
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: 1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e. would not need to learn everything from scratch as normally required at present, and 2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.
Integro-differential method of solving the inverse coefficient heat conduction problem
NASA Astrophysics Data System (ADS)
Baranov, V. L.; Zasyad'Ko, A. A.; Frolov, G. A.
2010-03-01
On the basis of differential transformations, a stable integro-differential method of solving the inverse heat conduction problem is suggested. The method has been tested on the example of determining the thermal diffusivity on quasi-stationary fusion and heating of a quartz glazed ceramics specimen.
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
NASA Astrophysics Data System (ADS)
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
NASA Astrophysics Data System (ADS)
Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy
2014-05-01
Improving our understanding of the carbon cycle is an important component of modelling climate and the Earth system, and a variety of inverse modelling techniques have been used to combine process models with different types of observational data. Model data fusion, or inverse modelling, is the process of best combining our under- standing of the dynamics of a system, observations and our prior knowledge of the state of the system. We consider a simple model for the carbon budget allocation for terrestrial ecosystems, the Data Assimilation-Linked Ecosystem model (DALEC). DALEC is a box model simulating a large range of processes occurring at different time scales from days to millennia. Eddy covariance measurements of net ecosystem exchange of CO2 have been used intensively for over a decade to confront DALEC with real data to estimate model parameters and quantify uncertainty of the model predictions. The REgional FLux Estimation eXperiment (REFLEX), compared the strengths and weaknesses of various inverse modelling strategies (MCMC, ENKF) to estimate parameters and initial stocks for DALEC; most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. While other studies have tried to overcome this difficulty by adding complementary data streams or by considering longer observation windows no systematic analysis has been carried out so far to explain the large differences among results of REFLEX. One of the merits of DALEC is its simplicity that facilitates close mathematical scrutiny. Using variational techniques we quantify the ill-posedness of the inverse problem and we discuss various regularisation techniques. Using the tangent linear model we study the information content of multiple data sources and show how these multiple data sources help constraining initial carbon
Development of a Geocryologic Model of Permafrost From 2D Inversion of IP Profiling
NASA Astrophysics Data System (ADS)
Fortier, R.; Leblanc, A.
2004-05-01
Non-invasive investigation of permafrost along a planned route of pipeline, road or airstrip in cold regions involves the use of effective methods for detecting, characterizing, mapping and monitoring permafrost conditions on various spatial and temporal scales. Among the available near-surface geophysical methods, the electrical resistivity imaging is probably the most suitable method since the resistivity contrast between unfrozen and frozen ground can be one or two orders of magnitude. Induced polarization (IP) profiling was carried out to study the spatial distribution of ground ice in two permafrost mounds near Umiujaq in Nunavik, Canada. A dipole-dipole array was used to perform the IP profiling. Pseudo-sections of electrical resistivity and chargeability giving a misrepresented cross-section of the sub-surface were first draw. The inversion of IP profiling was also performed using DCIP2D developed by UBC-GIF for estimating the spatial distribution of electrical properties in the ground to create realistic models of sub-surface resistivity and chargeability cross-section. The inverse models show clearly the presence of ice-rich core in the permafrost mounds. The ice-rich cores are underlined by high resistivity values while the unfrozen zones show low resistivity values. The localisation of the permafrost table is highlighted by a strong contrast of resistivity while the permafrost base is marked by a transitional change in resistivity. In the hollow between the permafrost mounds, the models show low resistivity values characteristic of unfrozen zone. A synthetic resistivity sounding built from the most acceptable inverse model correlates well with electrical resistivity logging carried out in the permafrost mound during cone penetration tests. The inversion of IP profiling is fundamental for defining realistic models of sub-surface resistivity and chargeability. Electrical resistivity imaging is a appropriate near-surface geophysical method for permafrost
NASA Astrophysics Data System (ADS)
Ren, Zhiming; Liu, Yang; Zhang, Qunshan
2014-05-01
Full waveform inversion (FWI) has the potential to provide preferable subsurface model parameters. The main barrier of its applications to real seismic data is heavy computational amount. Numerical modelling methods are involved in both forward modelling and backpropagation of wavefield residuals, which spend most of computational time in FWI. We develop a time-space domain finite-difference (FD) method and adaptive variable-length spatial operator scheme in numerical simulation of viscoacoustic equation and extend them into the viscoacoustic FWI. Compared with conventional FD methods, different operator lengths are adopted for different velocities and quality factors, which can reduce the amount of computation without reducing accuracy. Inversion algorithms also play a significant role in FWI. In conventional single-scale methods, it is likely to converge to local minimums especially when the initial model is far from the real model. To tackle the problem, we introduce the second generation wavelet transform to implement the multiscale FWI. Compared to other multiscale methods, our method has advantages of ease of implementation and better time-frequency local analysis ability. The L2 norm is widely used in FWI and gives invalid model estimates when the data is contaminated with strong non-uniform noises. We apply the L1-norm and the Huber-norm criteria in the time-domain FWI to improve its antinoise ability. Our strategies have been successfully applied in synthetic experiments to both onshore and offshore reflection seismic data. The results of the viscoacoustic Marmousi example indicate that our new FWI scheme consumes smaller computer resources. In addition, the viscoacoustic Overthrust example shows its better convergence and more reasonable velocity and quality factor structures. All these results demonstrate that our method can improve inversion accuracy and computational efficiency of FWI.
Method of Minimax Optimization in the Coefficient Inverse Heat-Conduction Problem
NASA Astrophysics Data System (ADS)
Diligenskaya, A. N.; Rapoport, É. Ya.
2016-07-01
Consideration has been given to the inverse problem on identification of a temperature-dependent thermal-conductivity coefficient. The problem was formulated in an extremum statement as a problem of search for a quantity considered as the optimum control of an object with distributed parameters, which is described by a nonlinear homogeneous spatially one-dimensional Fourier partial equation with boundary conditions of the second kind. As the optimality criterion, the authors used the error (minimized on the time interval of observation) of uniform approximation of the temperature computed on the object's model at an assigned point of the segment of variation in the spatial variable to its directly measured value. Pre-parametrization of the sought control action, which a priori records its description accurate to assigning parameters of representation in the class of polynomial temperature functions, ensured the reduction of the problem under study to a problem of parametric optimization. To solve the formulated problem, the authors used an analytical minimax-optimization method taking account of the alternance properties of the sought optimum solutions based on which the algorithm of computation of the optimum values of the sought parameters is reduced to a system (closed for these unknowns) of equations fixing minimax deviations of the calculated values of temperature from those observed on the time interval of identification. The obtained results confirm the efficiency of the proposed method for solution of a certain range of applied problems. The authors have studied the influence of the coordinate of a point of temperature measurement on the exactness of solution of the inverse problem.
A combined direct/inverse three-dimensional transonic wing design method for vector computers
NASA Technical Reports Server (NTRS)
Weed, R. A.; Carlson, L. A.; Anderson, W. K.
1984-01-01
A three-dimensional transonic-wing design algorithm for vector computers is developed, and the results of sample computations are presented graphically. The method incorporates the direct/inverse scheme of Carlson (1975), a Cartesian grid system with boundary conditions applied at a mean plane, and a potential-flow solver based on the conservative form of the full potential equation and using the ZEBRA II vectorizable solution algorithm of South et al. (1980). The accuracy and consistency of the method with regard to direct and inverse analysis and trailing-edge closure are verified in the test computations.
A trade-off solution between model resolution and covariance in surface-wave inversion
Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.
2010-01-01
Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.
Kriging-based generation of optimal databases as forward and inverse surrogate models
NASA Astrophysics Data System (ADS)
Bilicz, S.; Lambert, M.; Gyimóthy, Sz
2010-07-01
Numerical methods are used to simulate mathematical models for a wide range of engineering problems. The precision provided by such simulators is usually fine, but at the price of computational cost. In some applications this cost might be crucial. This leads us to consider cheap surrogate models in order to reduce the computation time still meeting the precision requirements. Among all available surrogate models, we deal herein with the generation of an 'optimal' database of pre-calculated results combined with a simple interpolator. A database generation approach is investigated which is intended to achieve an optimal sampling. Such databases can be used for the approximate solution of both forward and inverse problems. Their structure carries some meta-information about the involved physical problem. In the case of the inverse problem, an approach for predicting the uncertainty of the solution (due to the applied surrogate model and/or the uncertainty of the measured data) is presented. All methods are based on kriging—a stochastic tool for function approximation. Illustrative examples are drawn from eddy current non-destructive evaluation.
Bedos, Carole; Rousseau-Djabri, Marie-France; Loubet, Benjamin; Durand, Brigitte; Flura, Dominique; Briand, Olivier; Barriuso, Enrique
2010-04-01
Few data sets of pesticide volatilization from plants at the field scale are available. In this work, we report measurements of fenpropidin and chlorothalonil volatilization on a wheat field using the aerodynamic gradient (AG) method and an inverse dispersion modeling approach (using the FIDES model). Other data necessary to run volatilization models are also reported: measured application dose, crop interception, plant foliage residue, upwind concentrations, and meteorological conditions. The comparison of the AG and inverse modeling methods proved the latter to be reliable and hence suitable for estimating volatilization rates with minimized costs. Different diurnal/nocturnal volatilization patterns were observed: fenpropidin volatilization peaked on the application day and then decreased dramatically, while chlorothalonil volatilization remained fairly stable over a week-long period. Cumulated emissions after 31 h reached 3.5 g ha(-1) and 5 g ha(-1), respectively (0.8% and 0.6% of the theoretical application dose). A larger difference in volatilization rates was expected given differences in vapor pressure, and for fenpropidin, volatilization should have continued given that 80% of the initial amount remained on plant foliage for 6 days. We thus ask if vapor pressure alone can accurately estimate volatilization just after application and then question the state of foliar residue. We identified adsorption, formulation, and extraction techniques as relevant explanations.
Bedos, Carole; Rousseau-Djabri, Marie-France; Loubet, Benjamin; Durand, Brigitte; Flura, Dominique; Briand, Olivier; Barriuso, Enrique
2010-04-01
Few data sets of pesticide volatilization from plants at the field scale are available. In this work, we report measurements of fenpropidin and chlorothalonil volatilization on a wheat field using the aerodynamic gradient (AG) method and an inverse dispersion modeling approach (using the FIDES model). Other data necessary to run volatilization models are also reported: measured application dose, crop interception, plant foliage residue, upwind concentrations, and meteorological conditions. The comparison of the AG and inverse modeling methods proved the latter to be reliable and hence suitable for estimating volatilization rates with minimized costs. Different diurnal/nocturnal volatilization patterns were observed: fenpropidin volatilization peaked on the application day and then decreased dramatically, while chlorothalonil volatilization remained fairly stable over a week-long period. Cumulated emissions after 31 h reached 3.5 g ha(-1) and 5 g ha(-1), respectively (0.8% and 0.6% of the theoretical application dose). A larger difference in volatilization rates was expected given differences in vapor pressure, and for fenpropidin, volatilization should have continued given that 80% of the initial amount remained on plant foliage for 6 days. We thus ask if vapor pressure alone can accurately estimate volatilization just after application and then question the state of foliar residue. We identified adsorption, formulation, and extraction techniques as relevant explanations. PMID:20199019
NASA Astrophysics Data System (ADS)
Zhang, Ying-Ying; Liu, De-Jun; Ai, Qing-Hui; Qin, Min-Jun
2014-10-01
Electrical resistivity tomography using a steel cased borehole as a long electrode is an advanced technique for geoelectrical survey based on the conventional mise-à-la-masse measurement. In most previous works, the steel casing is simplified as a transmission line current source with an infinitely small radius and constant current density. However, in practical stratified formations with different resistivity values, the current density along the casing cannot be constant. In this study, the steel casing is modeled by a conductive physical volume that the casing occupies in the finite element mesh. The current supply point is set on the center of the top surface of the physical volume. Synthetic modeling, using both a homogenous and layered formation, demonstrates reasonability of the forward modeling method proposed herein. Based on this forward modeling method, the inversion procedure can be implemented by using a freeware R3t (Lancaster University, UK). Inversion results of synthetic modeling data match fairly well with the defined target location and validate that the method works on the inversion of the casing-surface electrical resistivity data. Finally, a field example of Changqing oil field in China is carried out using the inversion method to image water flooding results and to discover wells with great potential to enhance residual oil recovery.
NASA Astrophysics Data System (ADS)
Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. R.
2013-04-01
This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.
Using a derivative-free optimization method for multiple solutions of inverse transport problems
Armstrong, Jerawan C.; Favorite, Jeffrey A.
2016-01-14
Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less
Freezing Time Estimation for a Cylindrical Food Using an Inverse Method
NASA Astrophysics Data System (ADS)
Hu, Yao Xing; Mihori, Tomoo; Watanabe, Hisahiko
Most of the published methods for estimating the freezing time require thermal properties of the product and any relevant heat transfer coefficients between the product and the cooling medium. However, the difficulty of obtaining thermal data for use in industrial freezing system of food has been pointed out. We have developed a new procedure for estimating the time to freeze a food of a slab by using the inverse method, which does not require the knowledge of thermal properties of the food being frozen. The method of applying inverse method to estimation of freezing time depends on the shape of the body to be frozen. In this paper, we explored the method of applying inverse method to the food body of cylindrical shape, using selected explicit expressions to describe the temperature profile. The temperature profile was found to be successfully approximated by a logarithmic function, with which an approximate equation to describe the freezing time was derived. An inversion procedure of estimating freezing time associated with the approximate equation, was validated via a numerical experiment.
Neural-network-based speed controller for induction motors using inverse dynamics model
NASA Astrophysics Data System (ADS)
Ahmed, Hassanein S.; Mohamed, Kamel
2016-08-01
Artificial Neural Networks (ANNs) are excellent tools for controller design. ANNs have many advantages compared to traditional control methods. These advantages include simple architecture, training and generalization and distortion insensitivity to nonlinear approximations and nonexact input data. Induction motors have many excellent features, such as simple and rugged construction, high reliability, high robustness, low cost, minimum maintenance, high efficiency, and good self-starting capabilities. In this paper, we propose a neural-network-based inverse model for speed controllers for induction motors. Simulation results show that the ANNs have a high tracing capability.
Frequency-domain seismic-wave modeling, migration, and full-waveform inversion
NASA Astrophysics Data System (ADS)
Xu, Kun
In the dissertation, I have proposed and developed new approaches for seismic modeling, migration, and full-waveform inversion in the frequency domain. For 3D scalar-wave simulations in the frequency-space domain, we develop a fourth-order compact finite-difference (FD) form with a high-order spatial accuracy (4-5 grid points per shortest wavelength), and optimal one-way wave-equation (OWWE) absorbing boundary conditions (ABCs) with only one outer layer; these strategies greatly reduce the total number of the model grid points, and thus the overall computational cost. For reverse-time migration (RTM) using the cross-correlation imaging condition in the time domain, extra disk storage or wavefield simulations are required to make the forward propagated source and backward-propagated receiver wavefields available at the same time. We propose a new method to implement RTM in the frequency domain. Using virtual sources for the backward propagation of the receiver wavefield, we can straightforwardly implement the excitation-time and cross-correlation imaging conditions at each frequency without any disk storage or I/O and with complete spatial coverage of the migrated images. As both time and frequency domains have their own advantages for the inversion, we implement a hybrid scheme to combine both advantages in elastic full-waveform inversion (FWI). We simulate the wavefields using a time-domain high-precision finite-element (FE) modeling parallelized over shots with the message passing interface (MPI), and implement the inversion in the frequency domain via Fourier transform. Thus, we can easily apply both frequency-selection and time-windowing techniques to reduce the nonlinearity in inversion. To decouple different parameters in elastic FWI, we propose a new multi-steplength gradient approach to assign individual weights separately for each parameter gradient, and search for an optimal steplength along the composite gradient direction. As variations in the results
NASA Astrophysics Data System (ADS)
Sun, J.; Shen, Z.; Burgmann, R.; Liang, F.
2012-12-01
We develop a three-step Maximum-A-Posterior probability (MAP) method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic solutions of earthquake rupture. The method originates from the Fully Bayesian Inversion (FBI) and the Mixed linear-nonlinear Bayesian inversion (MBI) methods , shares the same a posterior PDF with them and keeps most of their merits, while overcoming its convergence difficulty when large numbers of low quality data are used and improving the convergence rate greatly using optimization procedures. A highly efficient global optimization algorithm, Adaptive Simulated Annealing (ASA), is used to search for the maximum posterior probability in the first step. The non-slip parameters are determined by the global optimization method, and the slip parameters are inverted for using the least squares method without positivity constraint initially, and then damped to physically reasonable range. This step MAP inversion brings the inversion close to 'true' solution quickly and jumps over local maximum regions in high-dimensional parameter space. The second step inversion approaches the 'true' solution further with positivity constraints subsequently applied on slip parameters using the Monte Carlo Inversion (MCI) technique, with all parameters obtained from step one as the initial solution. Then the slip artifacts are eliminated from slip models in the third step MAP inversion with fault geometry parameters fixed. We first used a designed model with 45 degree dipping angle and oblique slip, and corresponding synthetic InSAR data sets to validate the efficiency and accuracy of method. We then applied the method on four recent large earthquakes in Asia, namely the 2010 Yushu, China earthquake, the 2011 Burma earthquake, the 2011 New Zealand earthquake and the 2008 Qinghai, China earthquake, and compared our results with those results from other groups. Our results show the effectiveness of
Ita, B. I.
2014-11-12
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
An inverse method to determine the mechanical properties of the iris in vivo
2014-01-01
Background Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment. Material and methods Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements. Results Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ1, α1, μ2 and α2 were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated. Conclusion Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment. PMID:24886660
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.
2015-07-01
This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated
Application of the flux noise reducing filter for CO2 inverse modelling
NASA Astrophysics Data System (ADS)
Maksyutov, Shamil; Yaremchuk, Alexey
2010-05-01
Recent atmospheric remote sensing products from AIRS and GOSAT provide large volume of the observations but with larger errors and variance as compared to in-situ measurements, so efficient noise reduction techniques are required for inverse modeling of the surface fluxes. Inverse models of the atmospheric transport optimize regional or grid resolving surface CO2 fluxes to fit transport model simulation optimally to the observations. The optimization problem appears to be ill-posed so it is usually solved by applying regularization techniques. Most widely used regularization methods apply constraints on flux deviation from prior and/or from adjacent regions of same surface type (land-ocean, vegetation type), and from adjacent time periods. Convenient method for solving the problem of limited dimension is based on singular value decomposition (SVD) of the transport matrix, because it can decompose the solution space into a combination of the independent singular vectors. Introducing a simple constraint on fluxes limits amplitude of the corresponding singular vectors with larger reduction for smaller singular values. However this amplitude reduction is not sufficient in practice for inverse modeling of the regional CO2 fluxes, when we have large underconstrained regions in tropics. Alternatively other means of the amplitude reduction are also used, such as truncation, when all amplitudes below threshold singular value are set to zero. We apply a filter which is less abrupt is less abrupt compared to truncation but still suppressing strongly small singular value related vectors. Setting strength of a constraint is often done empirically. To decide a proper value of the cut-off singular value we suggest analyzing a dependence of the singular vector amplitude vs the singular value and set the cut-off value aiming at retaining most of useful information from observation. A graphical tool based on a plot of amplitude spectra is proposed. Advantage of the technique is
Joint kinematic calculation based on clinical direct kinematic versus inverse kinematic gait models.
Kainz, H; Modenese, L; Lloyd, D G; Maine, S; Walsh, H P J; Carty, C P
2016-06-14
Most clinical gait laboratories use the conventional gait analysis model. This model uses a computational method called Direct Kinematics (DK) to calculate joint kinematics. In contrast, musculoskeletal modelling approaches use Inverse Kinematics (IK) to obtain joint angles. IK allows additional analysis (e.g. muscle-tendon length estimates), which may provide valuable information for clinical decision-making in people with movement disorders. The twofold aims of the current study were: (1) to compare joint kinematics obtained by a clinical DK model (Vicon Plug-in-Gait) with those produced by a widely used IK model (available with the OpenSim distribution), and (2) to evaluate the difference in joint kinematics that can be solely attributed to the different computational methods (DK versus IK), anatomical models and marker sets by using MRI based models. Eight children with cerebral palsy were recruited and presented for gait and MRI data collection sessions. Differences in joint kinematics up to 13° were found between the Plug-in-Gait and the gait 2392 OpenSim model. The majority of these differences (94.4%) were attributed to differences in the anatomical models, which included different anatomical segment frames and joint constraints. Different computational methods (DK versus IK) were responsible for only 2.7% of the differences. We recommend using the same anatomical model for kinematic and musculoskeletal analysis to ensure consistency between the obtained joint angles and musculoskeletal estimates.
An inverse method to recover the SFR and reddening properties from spectra of galaxies
NASA Astrophysics Data System (ADS)
Vergely, J.-L.; Lançon, A.; Mouhcine
2002-11-01
We develop a non-parametric inverse method to investigate the star formation rate, the metallicity evolution and the reddening properties of galaxies based on their spectral energy distributions (SEDs). This approach allows us to clarify the level of information present in the data, depending on its signal-to-noise ratio. When low resolution SEDs are available in the ultraviolet, optical and near-IR wavelength ranges together, we conclude that it is possible to constrain the star formation rate and the effective dust optical depth simultaneously with a signal-to-noise ratio of 25. With excellent signal-to-noise ratios, the age-metallicity relation can also be constrained. We apply this method to the well-known nuclear starburst in the interacting galaxy NGC 7714. We focus on deriving the star formation history and the reddening law. We confirm that classical extinction models cannot provide an acceptable simultaneous fit of the SED and the lines. We also confirm that, with the adopted population synthesis models and in addition to the current starburst, an episode of enhanced star formation that started more than 200 Myr ago is required. As the time elapsed since the last interaction with NGC 7715, based on dynamical studies, is about 100 Myr, our result reinforces the suggestion that this interaction might not have been the most important event in the life of NGC 7714.
Systematic hierarchical coarse-graining with the inverse Monte Carlo method
Lyubartsev, Alexander P.; Naômé, Aymeric; Vercauteren, Daniel P.; Laaksonen, Aatto
2015-12-28
We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730–3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.
Systematic hierarchical coarse-graining with the inverse Monte Carlo method
NASA Astrophysics Data System (ADS)
Lyubartsev, Alexander P.; Naômé, Aymeric; Vercauteren, Daniel P.; Laaksonen, Aatto
2015-12-01
We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730-3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hori, T.; Hirahara, K.; Hashimoto, C.; Hori, M.
2015-12-01
Inverse analysis of the coseismic/postseismic slip using postseismic deformation observation data is an important topic in geodetic inversion. Inverse analysis method may be improved by using numerical simulation (e.g. finite element (FE) method) of viscoelastic deformation, the model of which is of high-fidelity to the available high-resolution crustal data. The authors had been developing a large-scale simulation method using such FE high-fidelity models (HFM), assuming use of K computer, the current fastest supercomputer in Japan. In this study, we developed an inverse analysis method incorporating HFM, in which the asthenosphere viscosity and fault slip are estimated simultaneously, since the value of viscosity in the simulation is not trivial. We carried out numerical experiments using synthetic crustal deformation data. Based on Ichimura et al. (2013), we constructed an HFM in the domain of 2048x1536x850 km, which includes the Tohoku region in northeast Japan. We used the data set of JTOPO30 (2003), Koketsu et al. (2008) and CAMP standard model (Hashimoto et al. 2004) for the model geometry. The HFM is currently in 2km resolution, resulting in 0.5 billion degrees-of-freedom. The figure shows the overview of HFM. Synthetic crustal deformation data of three years after an earthquake in the location of GEONET, GPS/A observation points, and S-net were used. Inverse analysis was formulated as minimization of L2 norm of the difference between the FE simulation results and the observation data with respect to viscosity and fault slip, combining quasi-Newton algorithm with adjoint method. Coseismic slip was expressed by superposition of 53 subfaults, with four viscoelastic layers. We carried out 90 forward simulations, and the 57 parameters converged to the true values. Due to the fast computation method, it took only five hours using 2048 nodes (1/40 of entire resource) of K computer. In the future, we would like to also consider estimation of after slip and apply
NASA Astrophysics Data System (ADS)
Kirby, Jon F.
2014-09-01
The effective elastic thickness (Te) is a geometric measure of the flexural rigidity of the lithosphere, which describes the resistance to bending under the application of applied, vertical loads. As such, it is likely that its magnitude has a major role in governing the tectonic evolution of both continental and oceanic plates. Of the several ways to estimate Te, one has gained popularity in the 40 years since its development because it only requires gravity and topography data, both of which are now readily available and provide excellent coverage over the Earth and even the rocky planets and moons of the solar system. This method, the ‘inverse spectral method’, develops measures of the relationship between observed gravity and topography data in the spatial frequency (wavenumber) domain, namely the admittance and coherence. The observed measures are subsequently inverted against the predictions of thin, elastic plate models, giving estimates of Te and other lithospheric parameters. This article provides a review of inverse spectral methodology and the studies that have used it. It is not, however, concerned with the geological or geodynamic significance or interpretation of Te, nor does it discuss and compare Te results from different methods in different provinces. Since the three main aspects of the subject are thin elastic plate flexure, spectral analysis, and inversion methods, the article broadly follows developments in these. The review also covers synthetic plate modelling, and concludes with a summary of the controversy currently surrounding inverse spectral methods, whether or not the large Te values returned in cratonic regions are artefacts of the method, or genuine observations.
Seismology on a Comet: Calibration Measurements, Modeling and Inversion
NASA Astrophysics Data System (ADS)
Faber, C.; Hoppe, J.; Knapmeyer, M.; Fischer, H.; Seidensticker, K. J.
2011-12-01
The Mission Rosetta was launched to comet 67P/Churyumov-Gerasimenko in 2004. It will finally reach the comet and will deliver the Lander Philae at the surface of the nucleus in November 2014. The Lander carries ten experiments, one of which is the Surface Electric Sounding and Acoustic Monitoring Experiment (SESAME). Part of this experiment is the Comet Acoustic Surface Sounding Experiment (CASSE) housed in the three feet of the lander. The primary goal of CASSE is to determine the elastic parameters of the surface material, like the Young's modulus and the Poisson ratio. Additional goals are the determination of shallow structure, quantification of porosity, and the location of activity spots and thermally and impact caused cometary activity. We conduct calibration measurements with accelerometers identical to the flight model. The goal of these measurements is to develop inversion procedures for travel times and to estimate the expected accuracy that CASSE can achieve in terms of elastic wave velocity, elastic parameters, and source location. The experiments are conducted mainly on sandy soil, in dry, wet or frozen conditions, and apart from buildings with their reflecting walls and artificial noise sources. We expect that natural sources, like thermal cracking at sunrise and sunset, can be located to an accuracy of about 10 degrees in direction and a few decimeters (1σ) in distance if occurring within the sensor triangle and from first arrivals alone. The accuracy of the direction is essentially independent of the distance, whereas distance determination depends critically on the identification of later arrivals. Determination of elastic wave velocities on the comet will be conducted with controlled sources at known positions and are likely to achieve an accuracy of σ=15% for the velocity of the first arriving wave. Limitations are due to the fixed source-receiver geometry and the wavelength emitted by the CASSE piezo-ceramic sources. In addition to the
Inverse modelling of radionuclide release rates using gamma dose rate observations
NASA Astrophysics Data System (ADS)
Hamburger, Thomas; Stohl, Andreas; von Haustein, Christoph; Thummerer, Severin; Wallner, Christian
2014-05-01
Severe accidents in nuclear power plants such as the historical accident in Chernobyl 1986 or the more recent disaster in the Fukushima Dai-ichi nuclear power plant in 2011 have drastic impacts on the population and environment. The hazardous consequences reach out on a national and continental scale. Environmental measurements and methods to model the transport and dispersion of the released radionuclides serve as a platform to assess the regional impact of nuclear accidents - both, for research purposes and, more important, to determine the immediate threat to the population. However, the assessments of the regional radionuclide activity concentrations and the individual exposure to radiation dose underlie several uncertainties. For example, the accurate model representation of wet and dry deposition. One of the most significant uncertainty, however, results from the estimation of the source term. That is, the time dependent quantification of the released spectrum of radionuclides during the course of the nuclear accident. The quantification of the source terms of severe nuclear accidents may either remain uncertain (e.g. Chernobyl, Devell et al., 1995) or rely on rather rough estimates of released key radionuclides given by the operators. Precise measurements are mostly missing due to practical limitations during the accident. Inverse modelling can be used to realise a feasible estimation of the source term (Davoine and Bocquet, 2007). Existing point measurements of radionuclide activity concentrations are therefore combined with atmospheric transport models. The release rates of radionuclides at the accident site are then obtained by improving the agreement between the modelled and observed concentrations (Stohl et al., 2012). The accuracy of the method and hence of the resulting source term depends amongst others on the availability, reliability and the resolution in time and space of the observations. Radionuclide activity concentrations are observed on a
NASA Astrophysics Data System (ADS)
Davoine, X.; Bocquet, M.
2007-03-01
The reconstruction of the Chernobyl accident source term has been previously carried out using core inventories, but also back and forth confrontations between model simulations and activity concentration or deposited activity measurements. The approach presented in this paper is based on inverse modelling techniques. It relies both on the activity concentration measurements and on the adjoint of a chemistry-transport model. The location of the release is assumed to be known, and one is looking for a source term available for long-range transport that depends both on time and altitude. The method relies on the maximum entropy on the mean principle and exploits source positivity. The inversion results are mainly sensitive to two tuning parameters, a mass scale and the scale of the prior errors in the inversion. To overcome this hardship, we resort to the statistical L-curve method to estimate balanced values for these two parameters. Once this is done, many of the retrieved features of the source are robust within a reasonable range of parameter values. Our results favour the acknowledged three-step scenario, with a strong initial release (26 to 27 April), followed by a weak emission period of four days (28 April-1 May) and again a release, longer but less intense than the initial one (2 May-6 May). The retrieved quantities of iodine-131, caesium-134 and caesium-137 that have been released are in good agreement with the latest reported estimations. Yet, a stronger apportionment of the total released activity is ascribed to the first period and less to the third one. Finer chronological details are obtained, such as a sequence of eruptive episodes in the first two days, likely related to the modulation of the boundary layer diurnal cycle. In addition, the first two-day release surges are found to have effectively reached an altitude up to the top of the domain (5000 m).
NASA Astrophysics Data System (ADS)
Davoine, X.; Bocquet, M.
2007-01-01
The reconstruction of the Chernobyl accident source term has been previously carried out using core inventories, but also back and forth confrontations between model simulations and activity concentration or deposited activity measurements. The approach presented in this paper is based on inverse modelling techniques. It relies both on the activity concentration measurements and on the adjoint of a chemistry-transport model. The location of the release is assumed to be known, and one is looking for a source term available for long-range transport that depends both on time and altitude. The method relies on the maximum entropy on the mean principle and exploits source positivity. The inversion results are mainly sensitive to two tuning parameters, a mass scale and the scale of the prior errors in the inversion. To overcome this hardship, we resort to the statistical L-curve method to estimate balanced values for these two parameters. Once this is done, many of the retrieved features of the source are robust within a reasonable range of parameter values. Our results favour the acknowledged three-step scenario, with a strong initial release (26 to 27 April), followed by a weak emission period of four days (28 April-1 May) and again a release, longer but less intense than the initial one (2 May-6 May). The retrieved quantities of iodine-131, caesium-134 and caesium-137 that have been released are in good agreement with the latest reported estimations. Yet, a stronger apportionment of the total released activity is ascribed to the first period and less to the third one. Finer chronological details are obtained, such as a sequence of eruptive episodes in the first two days, likely related to the modulation of the boundary layer diurnal cycle. In addition, the first two-day release surges are found to have effectively reached an altitude up to the top of the domain (5000 m).
Inverse modeling of Asian (222)Rn flux using surface air (222)Rn concentration.
Hirao, Shigekazu; Yamazawa, Hiromi; Moriizumi, Jun
2010-11-01
When used with an atmospheric transport model, the (222)Rn flux distribution estimated in our previous study using soil transport theory caused underestimation of atmospheric (222)Rn concentrations as compared with measurements in East Asia. In this study, we applied a Bayesian synthesis inverse method to produce revised estimates of the annual (222)Rn flux density in Asia by using atmospheric (222)Rn concentrations measured at seven sites in East Asia. The Bayesian synthesis inverse method requires a prior estimate of the flux distribution and its uncertainties. The atmospheric transport model MM5/HIRAT and our previous estimate of the (222)Rn flux distribution as the prior value were used to generate new flux estimates for the eastern half of the Eurasian continent dividing into 10 regions. The (222)Rn flux densities estimated using the Bayesian inversion technique were generally higher than the prior flux densities. The area-weighted average (222)Rn flux density for Asia was estimated to be 33.0 mBq m(-2) s(-1), which is substantially higher than the prior value (16.7 mBq m(-2) s(-1)). The estimated (222)Rn flux densities decrease with increasing latitude as follows: Southeast Asia (36.7 mBq m(-2) s(-1)); East Asia (28.6 mBq m(-2) s(-1)) including China, Korean Peninsula and Japan; and Siberia (14.1 mBq m(-2) s(-1)). Increase of the newly estimated fluxes in Southeast Asia, China, Japan, and the southern part of Eastern Siberia from the prior ones contributed most significantly to improved agreement of the model-calculated concentrations with the atmospheric measurements. The sensitivity analysis of prior flux errors and effects of locally exhaled (222)Rn showed that the estimated fluxes in Northern and Central China, Korea, Japan, and the southern part of Eastern Siberia were robust, but that in Central Asia had a large uncertainty.
Forward and inverse electroencephalographic modeling in health and in acute traumatic brain injury
Irimia, Andrei; Goh, S.Y. Matthew; Torgerson, Carinna M.; Chambers, Micah C.; Kikinis, Ron; Van Horn, John D.
2013-01-01
Objective EEG source localization is demonstrated in three cases of acute traumatic brain injury (TBI) with progressive lesion loads using anatomically faithful models of the head which account for pathology. Methods Multimodal magnetic resonance imaging (MRI) volumes were used to generate head models via the finite element method (FEM). A total of 25 tissue types—including 6 types accounting for pathology— were included. To determine the effects of TBI upon source localization accuracy, a minimum-norm operator was used to perform inverse localization and to determine the accuracy of the latter. Results The importance of using a more comprehensive number of tissue types is confirmed in both health and in TBI. Pathology omission is found to cause substantial inaccuracies in EEG forward matrix calculations, with lead field sensitivity being underestimated by as much as ~200% in (peri-) contusional regions when TBI-related changes are ignored. Failing to account for such conductivity changes is found to misestimate substantial localization error by up to 35 mm. Conclusions Changes in head conductivity profiles should be accounted for when performing EEG modeling in acute TBI. Significance Given the challenges of inverse localization in TBI, this framework can benefit neurotrauma patients by providing useful insights on pathophysiology. PMID:23746499
NASA Astrophysics Data System (ADS)
Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L.
2012-12-01
This study aims at demonstrating the possibility of calibrating hydrologic parameters using surface flux and streamflow observations in version 4 of the Community Land Model (CLM4). Previously we showed that surface flux and streamflow calculations are sensitive to several key hydrologic parameters in CLM4, and discussed the necessity and possibility of parameter calibration. In this study, we evaluate performances of several different inversion strategies, including least-square fitting, quasi Monte-Carlo (QMC) sampling based Bayesian updating, and a Markov-Chain Monte-Carlo (MCMC) Bayesian inversion approach. The parameters to be calibrated include the surface and subsurface runoff generation parameters and vadose zone soil water parameters. We discuss the effects of surface flux and streamflow observations on the inversion results and compare their consistency and reliability using both monthly and daily observations at various flux tower and MOPEX sites. We find that the sampling-based stochastic inversion approaches behaved consistently - as more information comes in, the predictive intervals of the calibrated parameters as well as the misfits between the calculated and observed observations decrease. In general, the parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or streamflow observations. We also evaluated the possibility of probabilistic model averaging for more consistent parameter estimation.
Improving GNSS-R sea level determination through inverse modeling of SNR data
NASA Astrophysics Data System (ADS)
Strandberg, Joakim; Hobiger, Thomas; Haas, Rüdiger
2016-08-01
This paper presents a new method for retrieving sea surface heights from Global Navigation Satellite Systems reflectometry (GNSS-R) data by inverse modeling of SNR observations from a single geodetic receiver. The method relies on a B-spline representation of the temporal sea level variations in order to account for its continuity. The corresponding B-spline coefficients are determined through a nonlinear least squares fit to the SNR data, and a consistent choice of model parameters enables the combination of multiple GNSS in a single inversion process. This leads to a clear increase in precision of the sea level retrievals which can be attributed to a better spatial and temporal sampling of the reflecting surface. Tests with data from two different coastal GNSS sites and comparison with colocated tide gauges show a significant increase in precision when compared to previously used methods, reaching standard deviations of 1.4 cm at Onsala, Sweden, and 3.1 cm at Spring Bay, Tasmania.
Baghani, Ali; Salcudean, Septimiu; Honarvar, Mohammad; Sahebjavaher, Ramin S; Rohling, Robert; Sinkus, Ralph
2011-08-01
In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques. PMID:21813354
Baghani, Ali; Salcudean, Septimiu; Honarvar, Mohammad; Sahebjavaher, Ramin S; Rohling, Robert; Sinkus, Ralph
2011-08-01
In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques.
Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods
Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti
2012-01-01
Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell’s equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions than have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called Minimum Norm Estimates (MNE), promote source estimates with a small ℓ2 norm. Here, we consider a more general class of priors based on mixed-norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as Mixed-Norm Estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ1/ℓ2 mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ1/ℓ2 norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furhermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data. PMID:22421459
Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods
NASA Astrophysics Data System (ADS)
Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti
2012-04-01
Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ2 norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ1/ℓ2 mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ1/ℓ2 norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.
NASA Astrophysics Data System (ADS)
Filippi, Anthony Matthew
For complex systems, sufficient a priori knowledge is often lacking about the mathematical or empirical relationship between cause and effect or between inputs and outputs of a given system. Automated machine learning may offer a useful solution in such cases. Coastal marine optical environments represent such a case, as the optical remote sensing inverse problem remains largely unsolved. A self-organizing, cybernetic mathematical modeling approach known as the group method of data handling (GMDH), a type of statistical learning network (SLN), was used to generate explicit spectral inversion models for optically shallow coastal waters. Optically shallow water light fields represent a particularly difficult challenge in oceanographic remote sensing. Several algorithm-input data treatment combinations were utilized in multiple experiments to automatically generate inverse solutions for various inherent optical property (IOP), bottom optical property (BOP), constituent concentration, and bottom depth estimations. The objective was to identify the optimal remote-sensing reflectance Rrs(lambda) inversion algorithm. The GMDH also has the potential of inductive discovery of physical hydro-optical laws. Simulated data were used to develop generalized, quasi-universal relationships. The Hydrolight numerical forward model, based on radiative transfer theory, was used to compute simulated above-water remote-sensing reflectance Rrs(lambda) psuedodata, matching the spectral channels and resolution of the experimental Naval Research Laboratory Ocean PHILLS (Portable Hyperspectral Imager for Low-Light Spectroscopy) sensor. The input-output pairs were for GMDH and artificial neural network (ANN) model development, the latter of which was used as a baseline, or control, algorithm. Both types of models were applied to in situ and aircraft data. Also, in situ spectroradiometer-derived Rrs(lambda) were used as input to an optimization-based inversion procedure. Target variables
Doughty, C.A.
1996-05-01
The hydrologic properties of heterogeneous geologic media are estimated by simultaneously inverting multiple observations from well-test data. A set of pressure transients observed during one or more interference tests is compared to the corresponding values obtained by numerically simulating the tests using a mathematical model. The parameters of the mathematical model are varied and the simulation repeated until a satisfactory match to the observed pressure transients is obtained, at which point the model parameters are accepted as providing a possible representation of the hydrologic property distribution. Restricting the search to parameters that represent fractal hydrologic property distributions can improve the inversion process. Far fewer parameters are needed to describe heterogeneity with a fractal geometry, improving the efficiency and robustness of the inversion. Additionally, each parameter set produces a hydrologic property distribution with a hierarchical structure, which mimics the multiple scales of heterogeneity often seen in natural geological media. Application of the IFS inverse method to synthetic interference-test data shows that the method reproduces the synthetic heterogeneity successfully for idealized heterogeneities, for geologically-realistic heterogeneities, and when the pressure data includes noise.
NASA Astrophysics Data System (ADS)
Alkhalifah, Tariq; Choi, Yunseok
2012-12-01
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.