Neural Network method for Inverse Modeling of Material Deformation
Allen, J.D., Jr.; Ivezic, N.D.; Zacharia, T.
1999-07-10
A method is described for inverse modeling of material deformation in applications of importance to the sheet metal forming industry. The method was developed in order to assess the feasibility of utilizing empirical data in the early stages of the design process as an alternative to conventional prototyping methods. Because properly prepared and employed artificial neural networks (ANN) were known to be capable of codifying and generalizing large bodies of empirical data, they were the natural choice for the application. The product of the work described here is a desktop ANN system that can produce in one pass an accurate die design for a user-specified part shape.
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
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.
Gao Yajun
2008-08-15
A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.
Inverse modeling methods for indoor airborne pollutant tracking: literature review and fundamentals.
Liu, X; Zhai, Z
2007-12-01
Reduction in indoor environment quality calls for effective control and improvement measures. Accurate and prompt identification of contaminant sources ensures that they can be quickly removed and contaminated spaces isolated and cleaned. This paper discusses the use of inverse modeling to identify potential indoor pollutant sources with limited pollutant sensor data. The study reviews various inverse modeling methods for advection-dispersion problems and summarizes the methods into three major categories: forward, backward, and probability inverse modeling methods. The adjoint probability inverse modeling method is indicated as an appropriate model for indoor air pollutant tracking because it can quickly find source location, strength and release time without prior information. The paper introduces the principles of the adjoint probability method and establishes the corresponding adjoint equations for both multi-zone airflow models and computational fluid dynamics (CFD) models. The study proposes a two-stage inverse modeling approach integrating both multi-zone and CFD models, which can provide a rapid estimate of indoor pollution status and history for a whole building. Preliminary case study results indicate that the adjoint probability method is feasible for indoor pollutant inverse modeling. The proposed method can help identify contaminant source characteristics (location and release time) with limited sensor outputs. This will ensure an effective and prompt execution of building management strategies and thus achieve a healthy and safe indoor environment. The method can also help design optimal sensor networks.
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
2016-12-01
A set of second-order differential equations describing the space-time behaviour 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 multicomponent observation data, is appropriate for directly inverting elastic parameters, medium density or wave velocities. Full wavefield 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 (FD) method to the dynamic inversion to improve the computational accuracy and speed up the performance. Numerical experiments indicated that the new FD 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 easily
Acoustic model order reduction for the lowest condition number in inverse method
NASA Astrophysics Data System (ADS)
Madoliat, Reza; Nouri, Nowrouz Mohammad; Rahrovi, Ali
2017-06-01
Acoustic sources with wide surfaces can be broken down in a fluid environment into smaller acoustic sources. In this study, a general model is presented, indicating the type, number, direction, position and strength of these sources in such a way that the main sound and the sound of the equivalent sources match each other acceptably. When the position and direction of the source is determined, the strength of the source can be found using the inverse method. However, since the solution is not unique in the inverse method, a different acoustic strength is obtained for the sources if different positions are selected. By selecting an arrangement of general sources and using an optimization algorithm, the least possible mismatch between the main sound and the sound of equivalent sources can be achieved. In the inverse method, it is important to reduce the effects of measurement errors. The sensor placement and acoustic model order reduction (AMOR) are studied for reducing these effects.
Odor emission rate estimation of indoor industrial sources using a modified inverse modeling method.
Li, Xiang; Wang, Tingting; Sattayatewa, Chakkrid; Venkatesan, Dhesikan; Noll, Kenneth E; Pagilla, Krishna R; Moschandreas, Demetrios J
2011-08-01
Odor emission rates are commonly measured in the laboratory or occasionally estimated with inverse modeling techniques. A modified inverse modeling approach is used to estimate source emission rates inside of a postdigestion centrifuge building of a water reclamation plant. Conventionally, inverse modeling methods divide an indoor environment in zones on the basis of structural design and estimate source emission rates using models that assume homogeneous distribution of agent concentrations within a zone and experimentally determined link functions to simulate airflows among zones. The modified approach segregates zones as a function of agent distribution rather than building design and identifies near and far fields. Near-field agent concentrations do not satisfy the assumption of homogeneous odor concentrations; far-field concentrations satisfy this assumption and are the only ones used to estimate emission rates. The predictive ability of the modified inverse modeling approach was validated with measured emission rate values; the difference between corresponding estimated and measured odor emission rates is not statistically significant. Similarly, the difference between measured and estimated hydrogen sulfide emission rates is also not statistically significant. The modified inverse modeling approach is easy to perform because it uses odor and odorant field measurements instead of complex chamber emission rate measurements.
Inversion of tsunami sources by the adjoint method in the presence of observational and model errors
NASA Astrophysics Data System (ADS)
Pires, C.; Miranda, P. M. A.
2003-04-01
The adjoint method is applied to the inversion of tsumani sources from tide-gauge observations in both idealized and realistic setups, with emphasis on the effects of observational, bathymetric and other model errors in the quality of the inversion. The method is developed in a way that allows for the direct optimization of seismic focal parameters, in the case of seismic tsunamis, through a 4-step inversion procedure that can be fully automated, consisting in (i) source area delimitation, by adjoint backward ray-tracing, (ii) adjoint optimization of the initial sea state, from a vanishing first-guess, (iii) non-linear adjustment of the fault model and (iv) final adjoint optimization in the fault parameter space. The methodology is systematically tested with synthetic data, showing its flexibility and robustness in the presence of significant amounts of error.
Proximal point methods for the inverse problem of identifying parameters in beam models
NASA Astrophysics Data System (ADS)
Jadamba, B.; Khan, A. A.; Paulhamus, M.; Sama, M.
2012-07-01
This paper studies the nonlinear inverse problem of identifying certain material parameters in the fourth-order boundary value problem representing the beam model. The inverse problem is solved by posing a convex optimization problem whose solution is an approximation of the sought parameters. The optimization problem is solved by the gradient based approaches, and in this setting, the most challenging aspect is the computation of the gradient of the objective functional. We present a detailed treatment of the adjoint stiffness matrix based approach for the gradient computation. We employ recently proposed self-adaptive inexact proximal point methods by Hager and Zhang [6] to solve the inverse problem. It is known that the regularization features of the proximal point methods are quite different from that of the Tikhonov regularization. We present a comparative analysis of the numerical efficiency of the used proximal point methods without using the Tikhonov regularization.
[Research advances in inverse methods used for modeling plant-atmosphere exchange].
Diao, Yiwei; Pei, Tiefan
2005-09-01
To estimate the source/sink and the vertical fluxes of mass and energy within and above plant canopies continues to be a critical research problem in biosphere-atmosphere exchange processes. The underlying approaches in such problem are to exploit the natural properties of turbulence within and above vegetation, such as Lagrangian inverse analysis, high order Eulerian closure model, and hybrid Eulerian-Lagrangian method. This paper introduced the recent development in multilayer turbulent transport methods to compute the distributions of the strengths of scalar sources and sinks within plant-atmosphere continuum, and in particular, focused on the so-called "inverse methods", and described above three methods and their characteristics in detail. The limitation and prospect of these methods were also mentioned.
Optimization based inversion method for the inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Mu, Huaiping; Li, Jingtao; Wang, Xueyao; Liu, Shi
2017-05-01
Precise estimation of the thermal physical properties of materials, boundary conditions, heat flux distributions, heat sources and initial conditions is highly desired for real-world applications. The inverse heat conduction problem (IHCP) analysis method provides an alternative approach for acquiring such parameters. The effectiveness of the inversion algorithm plays an important role in practical applications of the IHCP method. Different from traditional inversion models, in this paper a new inversion model that simultaneously highlights the measurement errors and the inaccurate properties of the forward problem is proposed to improve the inversion accuracy and robustness. A generalized cost function is constructed to convert the original IHCP into an optimization problem. An iterative scheme that splits a complicated optimization problem into several simpler sub-problems and integrates the superiorities of the alternative optimization method and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is developed for solving the proposed cost function. Numerical experiment results validate the effectiveness of the proposed inversion method.
Damage identification using inverse methods.
Friswell, Michael I
2007-02-15
This paper gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Inverse problems require the use of a model and the identification of uncertain parameters of this model. Damage is often local in nature and although the effect of the loss of stiffness may require only a small number of parameters, the lack of knowledge of the location means that a large number of candidate parameters must be included. This paper discusses a number of problems that exist with this approach to health monitoring, including modelling error, environmental effects, damage localization and regularization.
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.
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.
NASA Astrophysics Data System (ADS)
Hendricks Franssen, H.-J.; Alcolea, A.; Riva, M.; Bakr, M.; van de Wiel, N.; Stauffer, F.; Guadagnini, A.,
2009-04-01
While several inverse modeling methods for groundwater flow have been developed during the last decades, hardly any comparisons among them have been published. We present a comparison of the performance of seven inverse methods, the Regularized Pilot Points Method (both in its classical estimation (RPPM-CE) and Monte Carlo (MC) simulation (RPPM-CS) variants), the Monte-Carlo variant of the Representer Method (RM), the Sequential-Self Calibration method (SSC), the Zonation Method (ZM), the Moment Equations Method (MEM) and a recently developed Semi-Analytical Method (SAM). The aforementioned methods are applied to a two-dimensional synthetic set-up, depicting the steady-state groundwater flow around an extraction well in the presence of distributed recharge. Their relative performances were assessed in terms of characterization of (a) the log-transmissivity field, (b) the hydraulic head distribution and (c) the well catchment delineation with respect to the reference scenario. Simulations were performed for a mildly and strongly heterogeneous transmissivity field. Adopted comparison measures include the absolute mean error, the root mean square error and the average ensemble standard deviation (whenever a method allows evaluating it) of the log-transmissivity and hydraulic head distributions. In addition, the estimated median and reference well catchments were compared and the uncertainty associated with the estimated catchment was evaluated. We found that the MC-based methods (RPPM-CS, RM and SSC) yield very similar results in all tested scenarios, despite they use different parameterization schemes and different objective functions. The linear correlation coefficient between the estimates obtained by the different MC methods increases with the number of stochastic realizations adopted and attains values up to 0.99 for 500 stochastic realisations. For the mildly heterogeneous case, the other inverse methods (i.e., non MC) yielded results which were consistent with
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.
Global inverse modeling of CH4 sources and sinks: an overview of methods
NASA Astrophysics Data System (ADS)
Houweling, Sander; Bergamaschi, Peter; Chevallier, Frederic; Heimann, Martin; Kaminski, Thomas; Krol, Maarten; Michalak, Anna M.; Patra, Prabir
2017-01-01
The aim of this paper is to present an overview of inverse modeling methods that have been developed over the years for estimating the global sources and sinks of CH4. It provides insight into how techniques and estimates have evolved over time and what the remaining shortcomings are. As such, it serves a didactical purpose of introducing apprentices to the field, but it also takes stock of developments so far and reflects on promising new directions. The main focus is on methodological aspects that are particularly relevant for CH4, such as its atmospheric oxidation, the use of methane isotopologues, and specific challenges in atmospheric transport modeling of CH4. The use of satellite retrievals receives special attention as it is an active field of methodological development, with special requirements on the sampling of the model and the treatment of data uncertainty. Regional scale flux estimation and attribution is still a grand challenge, which calls for new methods capable of combining information from multiple data streams of different measured parameters. A process model representation of sources and sinks in atmospheric transport inversion schemes allows the integrated use of such data. These new developments are needed not only to improve our understanding of the main processes driving the observed global trend but also to support international efforts to reduce greenhouse gas emissions.
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
Inverse Monte Carlo method in a multilayered tissue model for diffuse reflectance spectroscopy.
Fredriksson, Ingemar; Larsson, Marcus; Strömberg, Tomas
2012-04-01
Model based data analysis of diffuse reflectance spectroscopy data enables the estimation of optical and structural tissue parameters. The aim of this study was to present an inverse Monte Carlo method based on spectra from two source-detector distances (0.4 and 1.2 mm), using a multilayered tissue model. The tissue model variables include geometrical properties, light scattering properties, tissue chromophores such as melanin and hemoglobin, oxygen saturation and average vessel diameter. The method utilizes a small set of presimulated Monte Carlo data for combinations of different levels of epidermal thickness and tissue scattering. The path length distributions in the different layers are stored and the effect of the other parameters is added in the post-processing. The accuracy of the method was evaluated using Monte Carlo simulations of tissue-like models containing discrete blood vessels, evaluating blood tissue fraction and oxygenation. It was also compared to a homogeneous model. The multilayer model performed better than the homogeneous model and all tissue parameters significantly improved spectral fitting. Recorded in vivo spectra were fitted well at both distances, which we previously found was not possible with a homogeneous model. No absolute intensity calibration is needed and the algorithm is fast enough for real-time processing.
NASA Astrophysics Data System (ADS)
Goncharsky, Alexander V.; Romanov, Sergey Y.
2017-02-01
We develop efficient iterative methods for solving inverse problems of wave tomography in models incorporating both diffraction effects and attenuation. In the inverse problem the aim is to reconstruct the velocity structure and the function that characterizes the distribution of attenuation properties in the object studied. We prove mathematically and rigorously the differentiability of the residual functional in normed spaces, and derive the corresponding formula for the Fréchet derivative. The computation of the Fréchet derivative includes solving both the direct problem with the Neumann boundary condition and the reversed-time conjugate problem. We develop efficient methods for numerical computations where the approximate solution is found using the detector measurements of the wave field and its normal derivative. The wave field derivative values at detector locations are found by solving the exterior boundary value problem with the Dirichlet boundary conditions. We illustrate the efficiency of this approach by applying it to model problems. The algorithms developed are highly parallelizable and designed to be run on supercomputers. Among the most promising medical applications of our results is the development of ultrasonic tomographs for differential diagnosis of breast cancer.
NASA Astrophysics Data System (ADS)
Mehl, S.; Foglia, L.; Hill, M. C.
2009-12-01
Methods for analyzing inverse modeling results can be separated into two categories: (1) linear methods, such as Cook’s D, which are computationally frugal and do not require additional model runs, and (2) nonlinear methods, such as cross validation, which are computationally more expensive because they generally require additional model runs. Depending on the type of nonlinear analysis performed, the additional runs can be the difference between 10’s of runs and 1000’s of runs. For example, cross-validation studies require the model to be recalibrated (the regression repeated) for each observation or set of observations analyzed. This can be computationally prohibitive if many observations or sets of observations are investigated and/or the model has many estimated parameters. A tradeoff exists between linear and nonlinear methods, with linear methods being computationally efficient, but the results being questioned when models are nonlinear. The trade offs between computational efficiency and accuracy are investigated by comparing results from several linear measures of observation importance (for example, Cook’s D, DFBETA’s) to their nonlinear counterparts based on cross validation. Examples from ground water models of the Maggia Valley in southern Switzerland are used to make comparisons. The models include representation of the stream-aquifer interaction and range from simple to complex, with associated modified Beale’s measure ranging from mildly nonlinear to highly nonlinear, respectively. These results demonstrate applicability and limitations of applying linear methods over a range of model complexity and linearity and can be used to better understand when the additional computation burden of nonlinear methods may be necessary.
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.
Estimating initial conditions for groundwater flow modeling using an adaptive inverse method
NASA Astrophysics Data System (ADS)
Hassane Maina, F.; Delay, F.; Ackerer, P.
2017-09-01
Due to continuous increases in water demand, the need for seasonal forecasts of available groundwater resources becomes inevitable. Hydrogeological models might provide a valuable tool for this kind of resource management. Because predictions over short time horizons are foreseen, the reliability of model outputs depends on accurate estimates of the initial conditions (ICs), as well as the estimated parameter values, boundary conditions and forcing terms (e.g., recharge, as well as sinks and sources). Here, we provide an inverse procedure for estimating these ICs. The procedure is based on an adaptive parameterization of the ICs that limits over-parameterization and involves the minimization of an ad hoc objective function. The quasi-Newton algorithm is used for the minimization, and the gradients are computed with an adjoint-state method. Two test cases based on a real aquifer that are designed to evaluate the capability of the method were addressed. It is assumed that the boundary conditions, hydraulic parameters and forcing terms are known from an existing hydrogeological model. In both test cases, the proposed method was quite successful in estimating the ICs and predicting head values that were not used in the calibration. 50 calibrations for each test case have been performed to quantify the reliability of the predictions.
Inverse-solution method for a class of non-classical cochlear models
de Boer, Egbert; Nuttall, Alfred L.
2009-01-01
Measurements of distortion-product (DP) waves inside the cochlea have led to a conception of wave propagation that is at variance with the “classical” attitude. Of the several alternatives that have been proposed to remedy this situation, the feed-forward model could be a promising one. This paper describes a method to apply the inverse solution with the aim to attain a feed-forward model that accurately reproduces a measured response. It is demonstrated that the computation method is highly successful. Subsequently, it is shown that in a feed-forward model a DP wave generated by a two-tone stimulus is almost exclusively a forward-traveling wave which property agrees with the nature of the experimental findings. However, the amplitude of the computed DP wave is only substantial in the region where the stimulation patterns of the two primary tones overlap. In addition, the model developed cannot explain coherent reflection for single tones. It has been suggested that a forward transversal DP wave induced by a (retrograde) compression wave could be involved in DP wave generation. This topic is critically evaluated. PMID:19354390
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)
Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.
2016-12-01
Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.
Fast Computation of the Inverse CMH Model
NASA Technical Reports Server (NTRS)
Patel, Umesh D.; Torre, Edward Della; Day, John H. (Technical Monitor)
2001-01-01
A fast computational method based on differential equation approach for inverse DOK model has been extended for the inverse CMH model. Also, a cobweb technique for calculating the inverse CMH model is also presented. The two techniques are differed from the point of view of flexibility and computation time.
NASA Astrophysics Data System (ADS)
Zhang, D.; Liao, Q.
2016-12-01
The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of
NASA Astrophysics Data System (ADS)
Boren, E. J.; Boschetti, L.; Johnson, D.
2016-12-01
With near-future droughts predicted to become both more frequent and more intense (Allen et al. 2015, Diffenbaugh et al. 2015), the estimation of satellite-derived vegetation water content would benefit a wide range of environmental applications including agricultural, vegetation, and fire risk monitoring. No vegetation water content thematic product is currently available (Yebra et al. 2013), but the successful launch of the Landsat 8 OLI and Sentinel 2A satellites, and the forthcoming Sentinel 2B, provide the opportunity for monitoring biophysical variables at a scale (10-30m) and temporal resolution (5 days) needed by most applications. Radiative transfer models (RTM) use a set of biophysical parameters to produce an estimated spectral response and - when used in inverse mode - provide a way to use satellite spectral data to estimate vegetation biophysical parameters, including water content (Zarco-Tejada et al. 2003). Using the coupled leaf and canopy level model PROSAIL5, and Landsat 8 OLI and Sentinel 2A MSI optical satellite data, the present research compares the results of three model inversion techniques: iterative optimization (OPT), look-up table (LUT), and artificial neural network (ANN) training. Ancillary biophysical data, needed for constraining the inversion process, were collected from various crop species grown in a controlled setting and under different water stress conditions. The measurements included fresh weight, dry weight, leaf area, and spectral leaf transmittance and reflectance in the 350-2500 nm range. Plot-level data, collected coincidently with satellite overpasses during three summer field campaigns in northern Idaho (2014 to 2016), are used to evaluate the results of the model inversion. Field measurements included fresh weight, dry weight, leaf area index, plant height, and top of canopy reflectance in the 350-2500 nm range. The results of the model inversion intercomparison exercised are used to characterize the uncertainties of
NASA Astrophysics Data System (ADS)
Hendricks Franssen, Harrie-Jan; Brunner, Philip; Eugster, Martin; Bauer, Peter; Kinzelbach, Wolfgang
The study area is the Chobe Enclave region in semi-arid Northern Botswana. Growing water demand in the local villages led to the development of different water supply scenarios one of which uses groundwater from a nearby aquifer. A regional groundwater flow model was established, both within a stochastic and a deterministic approach. In principle recharge can be derived from a surface water balance. The input data for the water balance, evapotranspiration and precipitation, were calculated using remotely sensed data. The calculation of evapotranspiration is based on the surface energy balance using multi-channel images from the Advanced Very High Resolution Radiometer (AVHRR). For several days of the year, actual ET is calculated and compared to station potential ET to yield crop coefficients. The crop coefficients are interpolated in time. Finally long-term ET is calculated by multiplying the crop coefficients with station potential ET. Precipitation is taken from station data and precipitation maps prepared by USAID using Meteosat images. As in most of the area surface runoff is small, subtracting evapotranspiration from precipitation yields recharge maps for the period 1990-2000. However, the values thus calculated are very inaccurate, as the errors both in precipitation and evapotranspiration estimates are large. Still, zones of different recharge and probable errors can be identified. The absolute value of the recharge flux in each zone is derived from the chloride method. Alternatively, the recharge flux was also estimated by the sequential self-calibrated method, a stochastic inverse modelling approach based on observed heads and pumping test data. Recharge values and transmissivities are estimated jointly in this method. The recharge zones derived from the water balance together with their stochastic properties are used as prior information. The method generates multiple equally likely solutions to the estimation problem and allows to assess the uncertainty
NASA Astrophysics Data System (ADS)
Yang, Yongying; Chai, Huiting; Li, Chen; Zhang, Yihui; Wu, Fan; Bai, Jian; Shen, Yibing
2017-05-01
Digitized evaluation of micro sparse defects on large fine optical surfaces is one of the challenges in the field of optical manufacturing and inspection. The surface defects evaluation system (SDES) for large fine optical surfaces is developed based on our previously reported work. In this paper, the electromagnetic simulation model based on Finite-Difference Time-Domain (FDTD) for vector diffraction theory is firstly established to study the law of microscopic scattering dark-field imaging. Given the aberration in actual optical systems, point spread function (PSF) approximated by a Gaussian function is introduced in the extrapolation from the near field to the far field and the scatter intensity distribution in the image plane is deduced. Analysis shows that both diffraction-broadening imaging and geometrical imaging should be considered in precise size evaluation of defects. Thus, a novel inverse-recognition calibration method is put forward to avoid confusion caused by diffraction-broadening effect. The evaluation method is applied to quantitative evaluation of defects information. The evaluation results of samples of many materials by SDES are compared with those by OLYMPUS microscope to verify the micron-scale resolution and precision. The established system has been applied to inspect defects on large fine optical surfaces and can achieve defects inspection of surfaces as large as 850 mm×500 mm with the resolution of 0.5 μm.
2016-02-10
AFRL-RX-WP-JA-2016-0305 MODEL-BASED INVERSE METHODS FOR SIZING CRACKS OF VARYING SHAPE AND LOCATION IN BOLT-HOLE EDDY CURRENT (BHEC...it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YY) 2...REPORT TYPE 3. DATES COVERED (From - To) 7 October 2015 Interim 6 May 2010 – 7 September 2015 4. TITLE AND SUBTITLE MODEL-BASED INVERSE METHODS FOR
NASA Astrophysics Data System (ADS)
Aldrin, John C.; Oneida, Erin K.; Shell, Eric B.; Sabbagh, Harold A.; Sabbagh, Elias; Murphy, R. Kim; Mazdiyasni, Siamack; Lindgren, Eric A.; Mooers, Ryan D.
2017-02-01
A model-based calibration process is introduced that estimates the state of the eddy current probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both transverse and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the amplitude/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with reasonable agreement. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states.
Long, J.C.S.; Doughty, C.; Hestir, K.; Martel, S.
1992-05-01
Fractured and heterogeneous reservoirs are complex and difficult to characterize. In many cases, the modeling approaches used for making predictions of behavior in such reservoirs have been unsatisfactory. In this paper we describe a new modeling approach which results in a model that has fractal-like qualities. This is an inverse approach which uses observations of reservoir behavior to create a model that can reproduce observed behavior. The model is described by an iterated function system (IFS) that creates a fractal-like object that can be mapped into a conductivity distribution. It may be possible to identify subclasses of Iterated Function Systems which describe geological facies. By limiting the behavior-based search for an IFS to the geologic subclasses, we can condition the reservoir model on geologic information. This technique is under development, but several examples provide encouragement for eventual application to reservoir prediction.
Inverse problems using reduced basis method
NASA Astrophysics Data System (ADS)
Gralla, Phil
Inverse Problems is a field of great interest for many applications, such as parameter identification and image reconstruction. The underlying models of inverse problems in many applications often involve Partial Differential Equations (PDEs). A Reduced Basis (RB) method for solving PDE based inverse problems is introduced in this thesis. The RB has been rigorously established as an efficient approach for solving PDEs in recent years. In this work, we investigate whether the RB method can be used as a regularization for solving ill-posed and nonlinear inverse problems using iterative methods. We rigorously analyze the RB method and prove convergence of the RB approximation to the exact solution. Furthermore, an iterative algorithm is proposed based on gradient method with RB regularization. We also implement the proposed method numerically and apply the algorithm to the inverse problem of Electrical Impedance Tomography (EIT) which is known to be a notoriously ill-posed and nonlinear. For the EIT example, we provide all necessary details and carefully explain each step of the RB method. We also investigate the limitations of the RB method for solving nonlinear inverse problems in general. We conclude that the RB method can be used to solve nonlinear inverse problems with appropriate assumptions however the assumptions are somewhat restrictive and may not be applicable for a wide range of problems.
NASA Astrophysics Data System (ADS)
Cooper, Matthew; Martin, Randall V.; Padmanabhan, Akhila; Henze, Daven K.
2017-04-01
Satellite observations offer information applicable to top-down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-Var modeling approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as "truth." We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top-down NOx emissions using models that do not have an adjoint.
NASA Astrophysics Data System (ADS)
Duran, Lea; Jardani, Abderrahim; Fournier, Matthieu; Massei, Nicolas
2015-04-01
Karstic aquifers represent an important part of the water resources worldwide. Though they have been widely studied on many aspects, their geological and hydrogeological modeling is still complex. Geophysical methods can provide useful subsurface information for the characterization and mapping of karstic systems, especially when not accessible by speleology. The site investigated in this study is a sinkhole-spring system, with small diameter conduits that run within a chalk aquifer (Norville, in Upper Normandy, France). This site was investigated using several geophysical methods: electrical tomography, self-potential, mise-à-la-masse methods, and electromagnetic method (EM34). Coupling those results with boreholes data, a 3D geological model of the hydrogeological basin was established, including tectonic features as well as infiltration structures (sinkhole, covered dolines). The direction of the karstic conduits near the main sinkhole could be established, and the major fault was shown to be a hydraulic barrier. Also the average concentration of dolines on the basin could be estimated, as well as their depth. At last, several hypotheses could be made concerning the location of the main conduit network between the sinkhole and the spring, using previous hydrodynamic study of the site along with geophysical data. In order to validate the 3D geological model, an image-guided inversion of the apparent resistivity data was used. With this approach it is possible to use geological cross sections to constrain the inversion of apparent resistivity data, preserving both discontinuities and coherences in the inversion of the resistivity data. This method was used on the major fault, enabling to choose one geological interpretation over another (fault block structure near the fault, rather than important folding). The constrained inversion was also applied on covered dolines, to validate the interpretation of their shape and depth. Key words: Magnetic and electrical
Wang, Fei; Lin, Qi-zhong; Wang, Qin-jun; Li, Shuai
2011-05-01
The rapid identification of the minerals in the field is crucial in the remote sensing geology study and mineral exploration. The characteristic spectrum linear inversion modeling is able to obtain the mineral information quickly in the field study. However, the authors found that there was significant difference among the results of the model using the different kinds of spectra of the same sample. The present paper mainly studied the continuum based fast Fourier transform processing (CFFT) method and the characteristic spectrum linear inversion modeling (CSLM). On one hand, the authors obtained the optimal preferences of the CFFT method when applying it to rock samples: setting the CFFT low-pass frequency to 150 Hz. On the other hand, through the evaluation and study of the results of CSLM using different spectra, the authors found that the ASD spectra which were denoised in the CFFT method could provide better results when using them to extract the mineral information in the field.
Low Frequency Geoacoustic Inversion Method
2010-01-01
Inversion Method A. Tolstoy 1538 Hampton Hill Circle, McLean VA 22101 phone: (703) 760-0881 email: atolstoy@ieee.org Award Number: N00014-10-C...inversion method ( Tolstoy , ’10) with extension to slightly higher frequencies (up to 100Hz) and longer ranges (up 5km); � to apply the new LF...correlation value (see Tolstoy , ’93). A new feature for this effort includes software to check if the sampling has been fine enough to catch the “true
Low Frequency Geoacoustic Inversion Method
2011-09-01
DISTRIBUTION STATEMENT A: Distribution approved for public release, distribution is unlimited Low Frequency Geoacoustic Inversion Method A. Tolstoy ... Tolstoy , ’10), particularly the investigation of a new broadband method (the minimization method; see Tolstoy , ’12); � to apply the LF G.I. method...ADDRESS(ES) A. Tolstoy ,1538 Hampton Hill Circle,McLean,VA,22101 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND
NASA Astrophysics Data System (ADS)
Bellet, Michel; Massoni, Elisabeth; Boude, Serge
2004-06-01
Superplastic forming is a thermoforming-like process commonly applied to titanium and aluminum alloys at high temperature and in specific conditions. This paper presents the application of an inverse analysis technique to the identification of rheological and tribological parameters. The method consists of two steps. First, two different kinds of forming tests have been carried out for rheological and tribological identification, using specific mold shapes. Accurate instrumentation and measurements have been done in order to feed an experimental database (values of appropriate observables). In a second step, the development of an inverse method has been carried out. It consists of the minimization of an objective function representative of the distance — in a least squares sense — between measured and calculated values of the observables. The algorithm, which is coupled with the finite element model FORGE2®, is based on a Gauss-Newton method, including a sensitivity matrix calculated by the semi-analytical method.
NASA Astrophysics Data System (ADS)
Shin, Wae-Gyeong; Lee, Soo-Hong
Reliability of automotive parts has been one of the most interesting fields in the automotive industry. Especially small DC motor was issued because of the increasing adoption for passengers' safety and convenience. This study was performed to develop the accelerated life test method using Inverse power law model for small DC motors. The failure mode of small DC motor includes brush wear-out. Inverse power law model is applied effectively the electronic components to reduce the testing time and to achieve the accelerating test conditions. Accelerated life testing method was induced to bring on the brush wear-out as increasing voltage of motor. Life distribution of the small DC motor was supposed to follow Weibull distribution and life test time was calculated under the conditions of B10 life and 90% confidence level.
A model-assisted radio occultation data inversion method based on data ingestion into NeQuick
NASA Astrophysics Data System (ADS)
Shaikh, M. M.; Nava, B.; Kashcheyev, A.
2017-01-01
Inverse Abel transform is the most common method to invert radio occultation (RO) data in the ionosphere and it is based on the assumption of the spherical symmetry for the electron density distribution in the vicinity of an occultation event. It is understood that this 'spherical symmetry hypothesis' could fail, above all, in the presence of strong horizontal electron density gradients. As a consequence, in some cases wrong electron density profiles could be obtained. In this work, in order to incorporate the knowledge of horizontal gradients, we have suggested an inversion technique based on the adaption of the empirical ionospheric model, NeQuick2, to RO-derived TEC. The method relies on the minimization of a cost function involving experimental and model-derived TEC data to determine NeQuick2 input parameters (effective local ionization parameters) at specific locations and times. These parameters are then used to obtain the electron density profile along the tangent point (TP) positions associated with the relevant RO event using NeQuick2. The main focus of our research has been laid on the mitigation of spherical symmetry effects from RO data inversion without using external data such as data from global ionospheric maps (GIM). By using RO data from Constellation Observing System for Meteorology Ionosphere and Climate (FORMOSAT-3/COSMIC) mission and manually scaled peak density data from a network of ionosondes along Asian and American longitudinal sectors, we have obtained a global improvement of 5% with 7% in Asian longitudinal sector (considering the data used in this work), in the retrieval of peak electron density (NmF2) with model-assisted inversion as compared to the Abel inversion. Mean errors of NmF2 in Asian longitudinal sector are calculated to be much higher compared to American sector.
Low Frequency Geoacoustic Inversion Method
2012-09-30
DISTRIBUTION STATEMENT A: Distribution approved for public release, distribution is unlimited Low Frequency Geoacoustic Inversion Method A. Tolstoy ...recently featuring the minimization processor ( Tolstoy , ’10 and ’12); demonstration that horizontal arrays can be successfully used for G.I. with the...over twenty years, particularly for the suppression of sidelobes ( Tolstoy , ’93). For each the MFP values at sidelobes (non-true parameter values
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
Signal processing based method for modeling and solving inverse scattering problems
NASA Astrophysics Data System (ADS)
Ritter, Richard Shane
A mature and difficult problem, still preoccupying many research communities in different application areas, is the recovery of a quantitative image of some unknown penetrable strongly scattering object. In most fields, such as ground penetrating radar, seismic and medical applications, the problem is compounded by the availability of only limited angle and noisy data. One of the more common approximate solution methods is based on diffraction tomography that relies on the first Born approximation method, which limits applications to weakly scattering situations. More sophisticated methods are typically iterative in nature, computationally intense and may not converge. We have studied an alternative nonlinear filtering approach and developed a new way to implement it, as well as evaluating different filter functions to find an optimal form. We have applied this approach to a number of classes of objects and developed a user-friendly scattered field simulator as a resource for this and related inverse scattering problems. We also re-investigated the widely accepted limitations of the first Born approximation and found that when close to a scattering resonance, the first Born approximation can yield a good estimate of the object's scattering cross section. Tied to all of these imaging applications is the issue of limited data: how many sources and how many receivers are required for a given quality and reliability of the resulting image. We took a fundamental look at this issue in terms of the number of degrees of freedom of the entire source-measurement domain and deduced clear guidelines on the minimum data sets necessary that should be measured, in order to expect a reasonable image.
NASA Astrophysics Data System (ADS)
Haley, Craig; McLinden, Chris; Sioris, Christopher; Brohede, Samuel
Key to the retrieval of stratospheric minor species information from limb-scatter measurements are the selections of a radiative transfer model (RTM) and inversion method (solver). Here we assess the impact of choice of RTM and solver on the retrievals of stratospheric ozone and nitrogen dioxide from the OSIRIS instrument using the ‘Ozone Triplet' and Differential Optical Absorption Spectroscopy (DOAS) techniques that are used in the operational Level 2 processing algorithms. The RTMs assessed are LIMBTRAN, VECTOR, SCIARAYS, and SASKTRAN. The solvers studied include the Maximum A Posteriori (MAP), Maximum Likelihood (ML), Iterative Least Squares (ILS), and Chahine methods.
An AVAF inversion method for detecting hydrocarbons
NASA Astrophysics Data System (ADS)
Luo, Chunmei; Sen, Mrinal K.; Wang, Shangxu; Yuan, Sanyi
2017-10-01
Rock physics studies have shown that velocity dispersion is often associated with hydrocarbon deposit, which results in P-wave reflection coefficients varying with frequency. This effect is often neglected in the conventional amplitude versus angle or offset inversion, and thus error is introduced. Here we propose a method for inverting for dispersive velocity from the frequency-dependent P-wave reflection coefficients; the method is called amplitude variation with angle and frequency AVAF inversion. We employ forward modeling based on propagator matrices that include frequency-dependent elastic coefficients and a variant of the simulated annealing method called the heat-bath algorithm for inversion of layer parameters. In our application, the thickness of the dispersive layer is inverted for simultaneously. Synthetic and field data examples demonstrate the ability and usefulness of this method for detecting hydrocarbon bearing formations.
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)
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.
Variational Bayesian Approximation methods for inverse problems
NASA Astrophysics Data System (ADS)
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Forward model nonlinearity versus inverse model nonlinearity
Mehl, S.
2007-01-01
The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increased forward model nonlinearity increases inverse model nonlinearity. ?? 2007 National Ground Water Association.
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.
NASA Astrophysics Data System (ADS)
Dhananjay Dubey, Fnu
In this thesis, I applied Cauchy-type integral-based depth-to-basement estimation method to a variety of models to test the reliability of the method in different geological scenarios. I also inverted for three-dimensional (3D) subsurface anomalous density distribution with constrained model parameters in order to produce more compact inversion results. I demonstrated several single-block and multiple-block synthetic model results produced by constrained 3D gravity inversion. I also display results for Cauchy-type integral-based 3D depth-to-basement inversion of simple/complex basin models. The results from both methods are nicely consistent with true models at a very low misfit level and a fast convergence. A case study is presented at the end of our paper for both methods, and results for both methods are used to do interpretation jointly.
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.
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
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.
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.
An Inverse Model for TETRAD: Preliminary Results
Shook, George Michael; Renner, Joel Lawrence
2002-09-01
A model-independent parameter estimation model known as PEST has been linked to the reservoir simulator TETRAD. The method of inverse modeling is briefly reviewed, and the link between PEST and TETRAD is discussed. A single example is presented that illustrates the power of parameter estimation from well observations.
Inversion methods for interpretation of asteroid lightcurves
NASA Technical Reports Server (NTRS)
Kaasalainen, Mikko; Lamberg, L.; Lumme, K.
1992-01-01
We have developed methods of inversion that can be used in the determination of the three-dimensional shape or the albedo distribution of the surface of a body from disk-integrated photometry, assuming the shape to be strictly convex. In addition to the theory of inversion methods, we have studied the practical aspects of the inversion problem and applied our methods to lightcurve data of 39 Laetitia and 16 Psyche.
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.
NASA Astrophysics Data System (ADS)
Kesumastuti, Lintang; Marsono, Agus; Yatimantoro, Tatok; Pribadi, Sugeng
2017-07-01
This study performed W-Phase inversion for eight events with large magnitude (M>7) that occured in Indonesia for the period of 2006-2016 by using global data obtained from IRIS DMC (Incorporated Research Institutions for Seismology Data Management Center). The results of W-Phase inversion; both moment magnitude and focal mechanism were generally similar with the Global CMT (Centroid Moment Tensor) solutions. The result shows that maximum deviation of moment magnitude was 0,09 and the average of magnitudo deviation was 0.03625. Comparison of moment magnitude (Mw) indicates that seismic moments from Global CMT and W-Phase inversion are larger than that from body waves, especially for the 2010 Mentawai earthquake. Tsunami simulation was performed using two different source parameters and sea floor deformation, from Global CMT and W-Phase inversion to get arrival times and heights on the coasts to be validated by observation tide gauge data from IOC (Intergovernmental Oceanographic Commission). The simulation shows that these two models; Global CMT and W-Phase inversion yields similar tsunami arrival times and heights on the coasts, but they have a bit difference with the observation data for some tide gauge station.
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.
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.
FNAS/Rapid Spectral Inversion Methods
NASA Technical Reports Server (NTRS)
Poularikas, Alexander
1997-01-01
The purpose of this investigation was to study methods and ways for rapid inversion programs involving the correlated k-method, and to study the infrared observations of Saturn from the Cassini orbiter.
NASA Astrophysics Data System (ADS)
Dai, Meng-Xue; Chen, Jing-Bo; Cao, Jian
2017-07-01
Full-waveform inversion (FWI) is an ill-posed optimization problem which is sensitive to noise and initial model. To alleviate the ill-posedness of the problem, regularization techniques are usually adopted. The ℓ1-norm penalty is a robust regularization method that preserves contrasts and edges. The Orthant-Wise Limited-Memory Quasi-Newton (OWL-QN) method extends the widely-used limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to the ℓ1-regularized optimization problems and inherits the efficiency of L-BFGS. To take advantage of the ℓ1-regularized method and the prior model information obtained from sonic logs and geological information, we implement OWL-QN algorithm in ℓ1-regularized FWI with prior model information in this paper. Numerical experiments show that this method not only improve the inversion results but also has a strong anti-noise ability.
NASA Astrophysics Data System (ADS)
Cooper, M.; Martin, R.; Henze, D. K.
2016-12-01
Nitrogen oxide (NOx ≡ NO + NO2) emission inventories can be improved through top-down constraints provided by inverse modeling of observed nitrogen dioxide (NO2) columns. Here we compare two methods of inverse modeling for emissions of NOx from synthetic NO2 columns generated from known emissions using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-VAR approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We find that the standard mass balance algorithm can be improved by using an iterative process and using finite difference to calculate the local sensitivity of a change in NO2 columns to a change in emissions, resulting in a factor of two reduction in inversion error. In a simplified case study to recover local emission perturbations, horizontal smearing effects due to NOx transport were better resolved by the adjoint-based approach than by mass balance. For more complex emission changes that reflect real world scenarios, the iterative finite difference mass balance and adjoint methods produce similar top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of data sets that simulate satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint-based 4D-VAR method, it offers the ability to efficiently estimate top-down emissions using models that do not have an adjoint.
MODEL SELECTION FOR SPECTROPOLARIMETRIC INVERSIONS
Asensio Ramos, A.; Manso Sainz, R.; Martinez Gonzalez, M. J.; Socas-Navarro, H.; Viticchie, B.
2012-04-01
Inferring magnetic and thermodynamic information from spectropolarimetric observations relies on the assumption of a parameterized model atmosphere whose parameters are tuned by comparison with observations. Often, the choice of the underlying atmospheric model is based on subjective reasons. In other cases, complex models are chosen based on objective reasons (for instance, the necessity to explain asymmetries in the Stokes profiles) but it is not clear what degree of complexity is needed. The lack of an objective way of comparing models has, sometimes, led to opposing views of the solar magnetism because the inferred physical scenarios are essentially different. We present the first quantitative model comparison based on the computation of the Bayesian evidence ratios for spectropolarimetric observations. Our results show that there is not a single model appropriate for all profiles simultaneously. Data with moderate signal-to-noise ratios (S/Ns) favor models without gradients along the line of sight. If the observations show clear circular and linear polarization signals above the noise level, models with gradients along the line are preferred. As a general rule, observations with large S/Ns favor more complex models. We demonstrate that the evidence ratios correlate well with simple proxies. Therefore, we propose to calculate these proxies when carrying out standard least-squares inversions to allow for model comparison in the future.
Modelling and inversion -progress, problems, and challenges
NASA Astrophysics Data System (ADS)
Raiche, Art
1994-03-01
Researchers in the field of electromagnetic modelling and inversion have taken advantage of the impressive improvements of new computer hardware to explore exciting new initiatives and solid extensions of older ideas. Finite-difference time-stepping methods have been successfully applied to full-domain 3D models. Another new method combines time-stepping with spatial frequency solutions. The 2D model 3D source (2.5D) problem is also receiving fresh attention both for continental and sea floor applications. The 3D inversion problem is being attacked by several researchers using distorted Born approximation methods. Q-domain inversions using transformation to pseudo-wave field and travel time tomography have also been successfully tested for low contrast problems. Subspace methods have been successful in dramatically reducing the computational burden of the under-determined style of inversion. Static magnetic field interpretation methods are proving useful for delineating the position of closely-spaced multiple targets. Novel (“appeals to nature”) methods are also being investigated. Neural net algorithms have been tested for determining the depth and offset of buried pipes from EM ellipticity data. Genetic algorithms and simulated annealing have been tested for extremal model construction. The failure of researchers to take adequate account of the properties of the mathematical transformation from algorithms to the number domain represented by the computing process remains a major stumbling block. Structured programming, functional languages, and other software tools and methods are presented as an essential part of the serial process leading from EM theory to geological interpretation.
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
Methodology Using Inverse Methods for Pit Characterization in Multilayer Structures
NASA Astrophysics Data System (ADS)
Aldrin, John C.; Sabbagh, Harold A.; Sabbagh, Elias H.; Murphy, R. Kim; Concordia, Michael; Judd, David R.; Lindgren, Eric; Knopp, Jeremy
2006-03-01
This paper presents a methodology incorporating ultrasonic and eddy current data and NDE models to characterize pits in first and second layers. Approaches such as equivalent pit dimensions, approximate probe models, and iterative inversion schemes were designed to improve the reliability and speed of inverse methods for second layer pit characterization. A novel clutter removal algorithm was developed to compensate for coherent background noise. Validation was achieved using artificial and real pitting corrosion samples.
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)
Healy, D.; Kusznir, N.
2004-05-01
Recent discoveries of depth-dependent stretching and mantle exhumation at rifted continental margins require new models of margin formation. A two-dimensional coupled fluid mechanics/thermal kinematic model of sea-floor spreading initiation has been developed to predict the deformational and thermal evolution of rifted continental margins through time. The model can also include the effects of pre-breakup pure-shear stretching of continental lithosphere. Rifted margin lithosphere thinning and thermal evolution is dependent on ocean-ridge spreading rate (Vx), the mantle upwelling velocity beneath the ridge axis (Vz), and the pre-breakup lithosphere stretching factor (a). The model predicts the thinning of the upper crust, lower crust and lithospheric mantle of the continental margin, and the history of rifted margin subsidence, water depths and top basement heat-flow. We apply inverse methods to this new forward model of rifted margin formation to explore how successfully model input parameters may be extracted from observational data at rifted margins. The ability of the inverse method to find a unique solution has been established using synthetic data from forward modelling. Output parameters from the inversion are the horizontal and vertical velocities of sea-floor spreading, their variation with time, and the initial pre-breakup lithosphere stretching factor. Initial inversion tests used forward model predictions of the stretching of the upper crust, the whole crust and the whole lithosphere. These model predictions control the variation of crustal thickness and lithosphere temperature beneath the thinned continental margin and adjacent ocean, which in turn control margin subsidence and gravity anomaly. For application of the inversion procedure to observed data on rifted margins, the input data used are measured bathymetry, sediment thickness, gravity anomaly and upper crustal stretching. The forward problem is characterised by a non-linear relationship between
Abel inversion method for cometary atmospheres.
NASA Astrophysics Data System (ADS)
Hubert, Benoit; Opitom, Cyrielle; Hutsemekers, Damien; Jehin, Emmanuel; Munhoven, Guy; Manfroid, Jean; Bisikalo, Dmitry V.; Shematovich, Valery I.
2016-04-01
Remote observation of cometary atmospheres produces a measurement of the cometary emissions integrated along the line of sight joining the observing instrument and the gas of the coma. This integration is the so-called Abel transform of the local emission rate. We develop a method specifically adapted to the inversion of the Abel transform of cometary emissions, that retrieves the radial profile of the emission rate of any unabsorbed emission, under the hypothesis of spherical symmetry of the coma. The method uses weighted least squares fitting and analytical results. A Tikhonov regularization technique is applied to reduce the possible effects of noise and ill-conditioning, and standard error propagation techniques are implemented. Several theoretical tests of the inversion techniques are carried out to show its validity and robustness, and show that the method is only weakly dependent on any constant offset added to the data, which reduces the dependence of the retrieved emission rate on the background subtraction. We apply the method to observations of three different comets observed using the TRAPPIST instrument: 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 emission rate derived from the observed flux of CN emission at 387 nm and from the C2 emission at 514.1 nm of comet Siding Spring both present an easily-identifiable shoulder that corresponds to the separation between pre- and post-outburst gas. As a general result, we show that diagnosing properties and features of the coma using the emission rate is easier than directly using the observed flux. We also determine the parameters of a Haser model fitting the inverted data and fitting the line-of-sight integrated observation, for which we provide the exact analytical expression of the line-of-sight integration
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
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
Bayesian inverse modeling for quantitative precipitation estimation
NASA Astrophysics Data System (ADS)
Schinagl, Katharina; Rieger, Christian; Simmer, Clemens; Xie, Xinxin; Friederichs, Petra
2017-04-01
Polarimetric radars provide us with a richness of precipitation related measurements. Especially the high spatial and temporal resolution make the data an important information, e.g. for hydrological modeling. However, uncertainties in the precipitation estimates are large. Their systematic assessment and quantification is thus of great importance. Polarimetric radar observables like horizontal and vertical reflectivity ZH and ZV , cross-correlation coefficient ρHV and specific differential phase KDP are related to the drop size distribution (DSD) in the scan. This relation is described by forward operators which are integrals over the DSD and scattering terms. Given the polarimetric observables, the respective forward operators and assumptions about the measurement errors, we investigate the uncertainty in the DSD parameter estimation and based on it the uncertainty of precipitation estimates. We assume that the DSD follows a Gamma model, N(D) = N0Dμ exp(-ΛD), where all three parameters are variable. This model allows us to account for the high variability of the DSD. We employ the framework of Bayesian inverse methods to derive the posterior distribution of the DSD parameters. The inverse problem is investigated in a simulated environment (SE) using the COSMO-DE numerical weather prediction model. The advantage of the SE is that - unlike in a real world application - we know the parameters we want to estimate. Thus, building the inverse model into the SE gives us the opportunity of verifying our results against the COSMO-simulated DSD-values.
NASA Technical Reports Server (NTRS)
Fleming, H. E.
1977-01-01
Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.
NASA Technical Reports Server (NTRS)
Fleming, H. E.
1977-01-01
Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.
NASA Inverse Methods/Data Assimilation
NASA Technical Reports Server (NTRS)
Bennett, Andrew
2003-01-01
An overview of NASA's Third International Summer School on Inverse Methods and Data Assimilation which was conducted at Oregon State University from July 22 to August 2, 2002, is presented. Items listed include: a roster of attendees, a description of course content and talks given.
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
NASA Astrophysics Data System (ADS)
Voronina, Tatyana; Romanenko, Alexey; Loskutov, Artem
2017-04-01
The key point in the state-of-the-art in the tsunami forecasting is constructing a reliable tsunami source. In this study, we present an application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in the class of ill-posed problems. This approach is based on the least squares and the truncated singular value decomposition techniques. The tsunami wave propagation is considered within the scope of the linear shallow-water theory. As in inverse seismic problem, the numerical solutions obtained by mathematical methods become unstable due to the presence of noise in real data. A method of r-solutions makes it possible to avoid instability in the solution to the ill-posed problem under study. This method seems to be attractive from the computational point of view since the main efforts are required only once for calculating the matrix whose columns consist of computed waveforms for each harmonic as a source (an unknown tsunami source is represented as a part of a spatial harmonics series in the source area). Furthermore, analyzing the singular spectra of the matrix obtained in the course of numerical calculations one can estimate the future inversion by a certain observational system that will allow offering a more effective disposition for the tsunameters with the help of precomputations. In other words, the results obtained allow finding a way to improve the inversion by selecting the most informative set of available recording stations. The case study of the 6 February 2013 Solomon Islands tsunami highlights a critical role of arranging deep-water tsunameters for obtaining the inversion results. Implementation of the proposed methodology to the 16 September 2015 Chile tsunami has successfully produced tsunami source model
Distribution modeling of nonlinear inverse controllers under a Bayesian framework.
Herzallah, Randa; Lowe, David
2007-01-01
The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples.
Geoacoustic model inversion using artificial neural networks
NASA Astrophysics Data System (ADS)
Benson, Jeremy; Chapman, N. Ross; Antoniou, Andreas
2000-12-01
An inversion technique using artificial neural networks (ANNs) is described for estimating geoacoustic model parameters of the ocean bottom and information about the sound source from acoustic field data. The method is applied to transmission loss data from the TRIAL SABLE experiment that was carried out in shallow water off Nova Scotia. The inversion is designed to incorporate the a priori information available for the site in order to improve the estimation accuracy. The inversion scheme involves training feedforward ANNs to estimate the geoacoustic and geometric parameters using simulated input/output training pairs generated with a forward acoustic propagation model. The inputs to the ANNs are the spectral components of the transmission loss at each sensor of a vertical hydrophone array for the two lowest frequencies that were transmitted in the experiment, 35 and 55 Hz. The output is the set of environmental model parameters, both geometric and geoacoustic, corresponding to the received field. In order to decrease the training time, a separate network was trained for each parameter. The errors for the parallel estimation are 10% lower than for those obtained using a single network to estimate all the parameters simultaneously, and the training time is decreased by a factor of six. When the experimental data are presented to the ANNs the geometric parameters, such as source range and depth, are estimated with a high accuracy. Geoacoustic parameters, such as the compressional speed in the sediment and the sediment thickness, are found with a moderate accuracy.
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.
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
Current methods of radio occultation data inversion
NASA Technical Reports Server (NTRS)
Kliore, A. J.
1972-01-01
The methods of Abel integral transform and ray-tracing inversion have been applied to data received from radio occultation experiments as a means of obtaining refractive index profiles of the ionospheres and atmospheres of Mars and Venus. In the case of Mars, certain simplifications are introduced by the assumption of small refractive bending in the atmosphere. General inversion methods, independent of the thin atmosphere approximation, have been used to invert the data obtained from the radio occultation of Mariner 5 by Venus; similar methods will be used to analyze data obtained from Jupiter with Pioneers F and G, as well as from the other outer planets in the Outer Planet Grand Tour Missions.
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.
Inversion method of seismic forces at fault using finite element
NASA Astrophysics Data System (ADS)
Liu, D.; Xie, Z.; Geng, W.; Cai, Y.
2013-12-01
Fault slip inversion using seismic dislocation model has been discussed a lot. In this model, seismogenic fault is considered as an interface. However, geological surveys and seismic channel waves reveal that the fault usually possesses thickness. Rock compression tests also show that micro-cracks develop into a belt in which shear fracture plane takes place. Therefore, to simulate the fault as a narrow belt may be more reasonable to reflect mechanical behavior of earthquake source. This study proposes a method to inverse seismic forces at the fault with thickness. The fault is modeled by transversely isotropic material. Three-dimensional finite element models (FEMs) is used to calculate numerical Green's functions for displacements. The Green's functions are generated by imposing unit couples directly to the node pairs at the fault instead of dislocation. The unit couples are added separately in x, y, z directions of the finite element global coordinate system. A pure thrust earthquake is modeled by reducing shear modulus under tectonic stress field. Selected surface displacements induced by this earthquake are used as 'observation data' of the inversion. We combine numerical Green's functions with standard linear inverse methods with Laplace smoothing constraints to estimate seismic forces at the fault. The earthquake which is simulated by damage of shear modulus has the fault model with transversely isotropic material, therefore there exist no normal forces. When the fault material is isotropic and the earthquake is caused by the reduction of shear or Young's modulus, there are normal forces at the fault. This study shows that we can directly inverse three-dimensional seismic forces with the surface deformation caused by earthquakes. This method is feasible for heterogeneous materials and complicated geometry model. [1] Xie, Zhoumin, Inversion method of seismic stress drop by finite element scheme, Doctor Thesis, Peking University, 2013. [2] Hu, C., Zhou, Y
NASA Astrophysics Data System (ADS)
Mulquiney, John E.; Norton, John P.
1998-01-01
A new method for estimating time-varying fluxes of atmospheric trace gases using an atmospheric transport model and observed concentrations is presented. Specifically Kaiman filtering is used to estimate inputs from a state-space model identified using unit-pulse response functions from a transport model. The method is new in that no assumptions about initial concentrations in the model are required, although this in turn means that all flux processes must be explicitly modeled as inputs linearly related to concentrations. This also means that at least one extra measuring-site or other measurement variable (e.g. a linear combination of emissions) than the number of input-fluxes being estimated, is required to ensure a stable Kaiman filter.
NASA Astrophysics Data System (ADS)
Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean
2017-04-01
We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.
NASA Astrophysics Data System (ADS)
Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean
2017-01-01
We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.
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.
Radiation Source Mapping with Bayesian Inverse Methods
NASA Astrophysics Data System (ADS)
Hykes, Joshua Michael
We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution
Tissue elasticity measurement method using forward and inversion algorithms
NASA Astrophysics Data System (ADS)
Lee, Jong-Ha; Won, Chang-Hee; Park, Hee-Jun; Ku, Jeonghun; Heo, Yun Seok; Kim, Yoon-Nyun
2013-03-01
Elasticity is an important indicator of tissue health, with increased stiffness pointing to an increased risk of cancer. We investigated a tissue elasticity measurement method using forward and inversion algorithms for the application of early breast tumor identification. An optical based elasticity measurement system is developed to capture images of the embedded lesions using total internal reflection principle. From elasticity images, we developed a novel method to estimate the elasticity of the embedded lesion using 3-D finite-element-model-based forward algorithm, and neural-network-based inversion algorithm. The experimental results showed that the proposed characterization method can be diffierentiate the benign and malignant breast lesions.
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
Jinnai, H; Nishikawa, Y; Chen, S H; Koizumi, S; Hashimoto, T
2000-06-01
A method is proposed to determine the spectral function of the clipped-random-wave (CRW) model directly from scattering data. The spectral function f(k) (k is a wave number) gives the distribution of the magnitude of wave vectors of the sinusoidal waves that describes the essential features of the two-phase morphology. The proposed method involves "inverse clipping" of a correlation function to obtain f(k) and does not require any a priori assumptions for f(k). A critical test of the applicability of the inverse-clipping method was carried out by using three-component bicontinuous microemulsions. The method was then used to determine f(k) of the bicontinuous structure of a phase-separating polymer blend. f(k) for the polymer blend turned out to be a multipeaked function, while f(k) for the microemulsions exhibits a single broad maximum representing periodicity of the morphology. These results indicate the presence of the long-range regularity in the morphology of the polymer blend. Three-dimensional (3D) morphology corresponding to the scattering data of the polymer blend was generated using the CRW model together with the multipeaked f(k). Interface curvatures of the 3D morphology calculated from f(k) were measured and compared with those experimentally determined directly from the laser scanning confocal microscopy in the same blend.
NASA Astrophysics Data System (ADS)
Jinnai, Hiroshi; Nishikawa, Yukihiro; Chen, Sow-Hsin; Koizumi, Satoshi; Hashimoto, Takeji
2000-06-01
A method is proposed to determine the spectral function of the clipped-random-wave (CRW) model directly from scattering data. The spectral function f(k) (k is a wave number) gives the distribution of the magnitude of wave vectors of the sinusoidal waves that describes the essential features of the two-phase morphology. The proposed method involves ``inverse clipping'' of a correlation function to obtain f(k) and does not require any a priori assumptions for f(k). A critical test of the applicability of the inverse-clipping method was carried out by using three-component bicontinuous microemulsions. The method was then used to determine f(k) of the bicontinuous structure of a phase-separating polymer blend. f(k) for the polymer blend turned out to be a multipeaked function, while f(k) for the microemulsions exhibits a single broad maximum representing periodicity of the morphology. These results indicate the presence of the long-range regularity in the morphology of the polymer blend. Three-dimensional (3D) morphology corresponding to the scattering data of the polymer blend was generated using the CRW model together with the multipeaked f(k). Interface curvatures of the 3D morphology calculated from f(k) were measured and compared with those experimentally determined directly from the laser scanning confocal microscopy in the same blend.
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
Bridging the Gap - Interactive Inverse Groundwater Modeling
NASA Astrophysics Data System (ADS)
Singh, A.; Minsker, B.
2005-12-01
This paper presents a novel approach for solving the inverse problem of estimating heterogeneous aquifer parameters for a groundwater flow model, using interactive multi-objective evolutionary optimization. A hypothetical aquifer, for which the `true' parameter values (in this case hydraulic conductivity) are known, is used as a test case to demonstrate the usefulness of this method. It is shown that using automated calibration techniques without using expert interaction leads to parameter values that are not consistent with site knowledge. In such cases, it is desirable to incorporate expert knowledge in the inversion process to generate more reasonable estimates. An interactive approach is proposed within a multi-objective framework that allows the user to evaluate trade-offs between the expert knowledge and other measures of numerical errors. Using Pilot points and geostatistical parameters as decision variables, numerical optimization is combined with expert knowledge leading to conductivity fields that respect both the observation data and site knowledge that the expert may have. Early results indicate that this approach leads to parameter estimates that are much more consistent with site knowledge. A major issue with interactive approaches, however, is `human fatigue' in evaluating numerous potential solutions. One way of dealing with human fatigue is to use machine learning to model user preferences. This work presents initial results showing that machine learning models can be successfully used to augment user interaction, allowing the interactive genetic algorithm to find good solutions with much less user-effort.
The method of common search direction of joint inversion
NASA Astrophysics Data System (ADS)
Zhao, C.; Tang, R.
2013-12-01
In geophysical inversion, the first step is to construct an objective function. The second step is using the optimization algorithm to minimize the objective function, such as the gradient method and the conjugate gradient method. Compared with the former, the conjugate gradient method can find a better direction to make the error decreasing faster and has been widely used for a long time. At present, the joint inversion is generally using the conjugate gradient method. The most important thing of joint inversion is to construct the partial derivative matrix with respect to different physical properties. Then we should add the constraints among different physical properties into the integrated matrix and also use the cross gradient as constrained of joint inversion. There are two ways to apply the cross gradient into inverse process that can be added to the data function or the model function. One way is adding the cross gradient into data function. The partial derivative matrix will grow two times, meanwhile it's also requested to calculate the cross gradient of each grid and bring great computation cost.
Forward and inverse modelling of post-seismic deformation
NASA Astrophysics Data System (ADS)
Crawford, Ophelia; Al-Attar, David; Tromp, Jeroen; Mitrovica, Jerry X.
2017-02-01
We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.
Forward and inverse modelling of post-seismic deformation
NASA Astrophysics Data System (ADS)
Crawford, Ophelia; Al-Attar, David; Tromp, Jeroen; Mitrovica, Jerry X.
2016-11-01
We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and non-linear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.
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.
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.
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.
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.
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)
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 reduced basis Landweber method for nonlinear inverse problems
NASA Astrophysics Data System (ADS)
Garmatter, Dominik; Haasdonk, Bernard; Harrach, Bastian
2016-03-01
We consider parameter identification problems in parametrized partial differential equations (PDEs). These lead to nonlinear ill-posed inverse problems. One way of solving them is using iterative regularization methods, which typically require numerous amounts of forward solutions during the solution process. In this article we consider the nonlinear Landweber method and couple it with the reduced basis method as a model order reduction technique in order to reduce the overall computational time. In particular, we consider PDEs with a high-dimensional parameter space, which are known to pose difficulties in the context of reduced basis methods. We present a new method that is able to handle such high-dimensional parameter spaces by combining the nonlinear Landweber method with adaptive online reduced basis updates. It is then applied to the inverse problem of reconstructing the conductivity in the stationary heat equation.
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.
Inverse groundwater modeling with emphasis on model parameterization
NASA Astrophysics Data System (ADS)
Kourakos, George; Mantoglou, Aristotelis
2012-05-01
This study develops an inverse method aiming to circumvent the subjective decision regarding model parameterization and complexity in inverse groundwater modeling. The number of parameters is included as a decision variable along with parameter values. A parameterization based on B-spline surfaces (BSS) is selected to approximate transmissivity, and genetic algorithms were selected to perform error minimization. A transform based on linear least squares (LLS) is developed, so that different parameterizations may be combined by standard genetic algorithm operators. First, three applications, with isotropic, anisotropic, and zoned aquifer parameters, are examined in a single objective optimization problem and the estimated transmissivity is found to be near the true one. Interestingly, in the anisotropic case, the algorithm converged to a solution with an anisotropic distribution of control points. Next, a single objective optimization with regularization, penalizing complex models, is considered, and last, the problem is expressed in a multiobjective optimization framework (MOO), where the goals are simultaneous minimization of calibration error and model complexity. The result of MOO is a Pareto set of potential solutions where the user can examine the tradeoffs between calibration error and model complexity and select the most suitable model. By comparing calibration with prediction errors, it appears, that the most promising models are the ones near a region where the rate of decrease of calibration error as model complexity increases drops (bend of error curve). This is a useful result of practical interest in real inverse modeling applications.
Inversion method applied to the rotation curves of galaxies
NASA Astrophysics Data System (ADS)
Márquez-Caicedo, L. A.; Lora-Clavijo, F. D.; Sanabria-Gómez, J. D.
2017-07-01
We used simulated annealing, Montecarlo and genetic algorithm methods for matching both numerical data of density and velocity profiles in some low surface brigthness galaxies with theoretical models of Boehmer-Harko, Navarro-Frenk-White and Pseudo Isothermal Profiles for galaxies with dark matter halos. We found that Navarro-Frenk-White model does not fit at all in contrast with the other two models which fit very well. Inversion methods have been widely used in various branches of science including astrophysics (Charbonneau 1995, ApJS, 101, 309). In this work we have used three different parametric inversion methods (MonteCarlo, Genetic Algorithm and Simmulated Annealing) in order to determine the best fit of the observed data of the density and velocity profiles of a set of low surface brigthness galaxies (De Block et al. 2001, ApJ, 122, 2396) with three models of galaxies containing dark mattter. The parameters adjusted by the inversion methods were the central density and a characteristic distance in the Boehmer-Harko BH (Boehmer & Harko 2007, JCAP, 6, 25), Navarro-Frenk-White NFW (Navarro et al. 2007, ApJ, 490, 493) and Pseudo Isothermal Profile PI (Robles & Matos 2012, MNRAS, 422, 282). The results obtained showed that the BH and PI Profile dark matter galaxies fit very well for both the density and the velocity profiles, in contrast the NFW model did not make good adjustments to the profiles in any analized galaxy.
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.
A simple inverse design method for pump turbine
NASA Astrophysics Data System (ADS)
Yin, Junlian; Li, Jingjing; Wang, Dezhong; Wei, Xianzhu
2014-03-01
In this paper, a simple inverse design method is proposed for pump turbine. The main point of this method is that the blade loading distribution is first extracted from an existing model and then applied in the new design. As an example, the blade loading distribution of the runner designed with head 200m, was analyzed. And then, the combination of the extracted blade loading and a meridional passage suitable for 500m head is applied to design a new runner project. After CFD and model test, it is shown that the new runner performs very well in terms of efficiency and cavitation. Therefore, as an alternative, the inverse design method can be extended to other design applications.
Ocean tomography, inverse methods, and broadband ocean acoustics
NASA Astrophysics Data System (ADS)
Cornuelle, Bruce D.
2002-05-01
Ocean acoustic tomography, as proposed by Munk and Wunsch in 1979, and as implemented by the Ocean Tomography Group, uses ray travel times to estimate ocean sound speed and currents. Earlier work by Medwin (1970) and Hamilton (1977) used pulse travel times as measures of integrated sound speed along paths at short and long range, respectively. Munk and Wunsch (1979) recognized that broadband transmissions between many instruments could be used with inverse methods [Backus and Gilbert (1967); Liebelt (1967)] to reconstruct 3D ocean sound speed fields from the travel times along multiple paths. Inverse methods are widely used in ocean acoustics and in physical oceanography, and the modern challenge is to incorporate time dependence into the inverse methods to take advantage of the improving ocean dynamical models. In addition, the understanding of broadband acoustic propagation has improved to the point of refining the sensitivity kernel for travel time measurements beyond the simple geometrical optics of ray paths. This paper will review the evolving use of forward and inverse methods in acoustical oceanography, primarily with application to acoustic tomography.
Matrix methods for reflective inverse diffusion
NASA Astrophysics Data System (ADS)
Burgi, Kenneth W.; Marciniak, Michael A.; Nauyoks, Stephen E.; Oxley, Mark E.
2016-09-01
Reflective inverse diffusion is a method of refocusing light scattered by a rough surface. An SLM is used to shape the wavefront of a HeNe laser at 632.8-nm wavelength to produce a converging phase front after reflection. Iterative methods previously demonstrated intensity enhancements of the focused spot over 100 times greater than the surrounding background speckle. This proof-of-concept method was very time consuming and the algorithm started over each time the desired location of the focus spot in the observation plane was moved. Transmission matrices have been developed to control light scattered by transmission through a turbid media. Time varying phase maps are applied to an SLM and used to interrogate the phase scattering properties of the material. For each phase map, the resultant speckle intensity pattern is recorded less than 1 mm from the material surface and represents an observation plane of less than 0.02 mm2. Fourier transforms are used to extract the phase scattering properties of the material from the intensity measurements. We investigate the effectiveness this method for constructing the reflection matrix (RM) of a diffuse reflecting medium where the propagation distances and observation plane are almost 1,000 times greater than the previous work based on transmissive scatter. The RM performance is based on its ability to refocus reflectively scattered light to a single focused spot or multiple foci in the observation plane. Diffraction-based simulations are used to corroborate experimental results.
Inverse Modeling of Coastal Tides
1999-09-30
data in the tidal band. We have concluded that understanding this discrepancy and developing assimilation methods for baroclinic tides will require...Alexandre Kurapov to develop practical assimilation methods for coastal HF radar data. REFERENCES Bennett, A.F., B.S. Chua, and L.M. Leslie, Generalized
Inverse Modeling of Coastal Tides
1998-01-01
produced. We are also working with Profs. J. Allen and R. Miller on developing practical assimilation methods for the coastal problem. REFERENCES...40, 81--108, 1997. Egbert, G.D. and A.F. Bennett, Data assimilation methods for ocean tides, in Modern approaches to data assimilation in ocean
A statistical mechanical model for inverse melting
NASA Astrophysics Data System (ADS)
Feeney, Melissa R.; Debenedetti, Pablo G.; Stillinger, Frank H.
2003-08-01
Inverse melting is the situation in which a liquid freezes when it is heated isobarically. Both helium isotopes exhibit intervals of inverse melting at low temperature, and published data suggests that isotactic poly (4-methylpentene-1) also displays this unusual phase behavior. Here we propose a statistical mechanical model for inverse melting. It is a decorated modification of the Gaussian core model, in which particles possess a spectrum of thermally activated internal states. Excitation leads to a change in a particle's Gaussian interaction parameters, and this can result in a spatially periodic crystal possessing a higher entropy than the fluid with which it coexists. Numerical solution of the model, using integral equations and the hypernetted chain closure for the fluid phase, and the Einstein model for the solid phases, identifies two types of inverse melting. One mimics the behavior of the helium isotopes, for which the higher-entropy crystal is denser than the liquid. The other corresponds to inverse melting in poly(4-methylpentene-1), where the high-entropy crystal is less dense than the liquid with which it coexists.
Inverse modeling of human contrast response.
Katkov, Mikhail; Tsodyks, Misha; Sagi, Dov
2007-10-01
Mathematical singularities found in the Signal Detection Theory (SDT) based analysis of the 2-Alternative-Forced-Choice (2AFC) method [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Analysis of two-alternative force-choice Signal Detection Theory model. Journal of Mathematical Psychology, 50, 411-420; Katkov, M., Tsodyks, M., & Sagi, D. (2006b). Singularities in the inverse modeling of 2AFC contrast discrimination data. Vision Research, 46, 256-266; Katkov, M., Tsodyks, M., & Sagi, D. (2007). Singularities explained: Response to Klein. Vision Research, doi:10.1016/j.visres.2006.10.030] imply that contrast discrimination data obtained with the 2AFC method cannot always be used to reliably estimate the parameters of the underlying model (internal response and noise functions) with a reasonable number of trials. Here we bypass this problem with the Identification Task (IT) where observers identify one of N contrasts. We have found that identification data varies significantly between experimental sessions. Stable estimates using individual session data showed Contrast Response Functions (CRF) with high gain in the low contrast regime and low gain in the high contrast regime. Noise Amplitudes (NA) followed a decreasing function of contrast at low contrast levels, and were practically constant above some contrast level. The transition between these two regimes corresponded approximately to the position of the dipper in the Threshold versus Contrast (TvC) curves that were computed using the estimated parameters and independently measured using 2AFC.
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
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 ...
Jonsson, Ulf; Lindahl, Olof; Andersson, Britt
2014-12-01
To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency-dependent elastic modulus of the silicone rubber was modeled by a fourparameter fractional derivative viscoelastic model in the 100 to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5-mm-thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7%, 0.6%, and 0.7% for the silicone rubber samples with radial lengths of 38.0, 21.4, and 11.0 mm, respectively. The average complex elastic moduli of the samples were (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.
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 ...
Yao, Jie; Lesage, Anne-Cécile; Hussain, Fazle; Bodmann, Bernhard G.; Kouri, Donald J.
2014-12-15
The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green’s function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.
An inverse method to retrieve 3D radar reflectivity composites
NASA Astrophysics Data System (ADS)
Roca-Sancho, Jordi; Berenguer, Marc; Sempere-Torres, Daniel
2014-11-01
Dense radar networks offer the possibility of getting better Quantitative Precipitation Estimates (QPE) than those obtained with individual radars, as they allow increasing the coverage and improving quality of rainfall estimates in overlapping areas. Well-known sources of error such as attenuation by intense rainfall or errors associated with range can be mitigated through radar composites. Many compositing techniques are devoted to operational uses and do not exploit all the information that the network is providing. In this work an inverse method to obtain high-resolution radar reflectivity composites is presented. The method uses a model of radar sampling of the atmosphere that accounts for path attenuation and radar measurement geometry. Two significantly different rainfall situations are used to show detailed results of the proposed inverse method in comparison to other existing methodologies. A quantitative evaluation is carried out in a 12 h-event using two independent sources of information: a radar not involved in the composition process and a raingauge network. The proposed inverse method shows better performance in retrieving high reflectivity values and reproducing variability at convective scales than existing methods.
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
An inverse method using toroidal mode data
Willis, C.
1986-01-01
The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1%. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data.
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.
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.
Inverse method for estimating respiration rates from decay time series
NASA Astrophysics Data System (ADS)
Forney, D. C.; Rothman, D. H.
2012-09-01
Long-term organic matter decomposition experiments typically measure the mass lost from decaying organic matter as a function of time. These experiments can provide information about the dynamics of carbon dioxide input to the atmosphere and controls on natural respiration processes. Decay slows down with time, suggesting that organic matter is composed of components (pools) with varied lability. Yet it is unclear how the appropriate rates, sizes, and number of pools vary with organic matter type, climate, and ecosystem. To better understand these relations, it is necessary to properly extract the decay rates from decomposition data. Here we present a regularized inverse method to identify an optimally-fitting distribution of decay rates associated with a decay time series. We motivate our study by first evaluating a standard, direct inversion of the data. The direct inversion identifies a discrete distribution of decay rates, where mass is concentrated in just a small number of discrete pools. It is consistent with identifying the best fitting "multi-pool" model, without prior assumption of the number of pools. However we find these multi-pool solutions are not robust to noise and are over-parametrized. We therefore introduce a method of regularized inversion, which identifies the solution which best fits the data but not the noise. This method shows that the data are described by a continuous distribution of rates, which we find is well approximated by a lognormal distribution, and consistent with the idea that decomposition results from a continuum of processes at different rates. The ubiquity of the lognormal distribution suggest that decay may be simply described by just two parameters: a mean and a variance of log rates. We conclude by describing a procedure that estimates these two lognormal parameters from decay data. Matlab codes for all numerical methods and procedures are provided.
Inverse method for estimating respiration rates from decay time series
NASA Astrophysics Data System (ADS)
Forney, D. C.; Rothman, D. H.
2012-03-01
Long-term organic matter decomposition experiments typically measure the mass lost from decaying organic matter as a function of time. These experiments can provide information about the dynamics of carbon dioxide input to the atmosphere and controls on natural respiration processes. Decay slows down with time, suggesting that organic matter is composed of components (pools) with varied lability. Yet it is unclear how the appropriate rates, sizes, and number of pools vary with organic matter type, climate, and ecosystem. To better understand these relations, it is necessary to properly extract the decay rates from decomposition data. Here we present a regularized inverse method to identify an optimally-fitting distribution of decay rates associated with a decay time series. We motivate our study by first evaluating a standard, direct inversion of the data. The direct inversion identifies a discrete distribution of decay rates, where mass is concentrated in just a small number of discrete pools. It is consistent with identifying the best fitting "multi-pool" model, without prior assumption of the number of pools. However we find these multi-pool solutions are not robust to noise and are over-parametrized. We therefore introduce a method of regularized inversion, which identifies the solution which best fits the data but not the noise. This method shows that the data are described by a continuous distribution of rates which we find is well approximated by a lognormal distribution, and consistent with the idea that decomposition results from a continuum of processes at different rates. The ubiquity of the lognormal distribution suggest that decay may be simply described by just two parameters; a mean and a variance of log rates. We conclude by describing a procedure that estimates these two lognormal parameters from decay data. Matlab codes for all numerical methods and procedures are provided.
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)
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
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.
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.
Full Waveform Inversion Using the Adjoint Method for Earthquake Kinematics Inversion
NASA Astrophysics Data System (ADS)
Tago Pacheco, J.; Metivier, L.; Brossier, R.; Virieux, J.
2014-12-01
Extracting the information contained in seismograms for better description of the Earth structure and evolution is often based on only selected attributes of these signals. Exploiting the entire seismogram, Full Wave Inversion based on an adjoint estimation of the gradient and Hessian operators, has been recognized as a high-resolution imaging technique. Most of earthquake kinematics inversion are still based on the estimation of the Frechet derivatives for the gradient operator computation in linearized optimization. One may wonder the benefit of the adjoint formulation which avoids the estimation of these derivatives for the gradient estimation. Recently, Somala et al. (submitted) have detailed the adjoint method for earthquake kinematics inversion starting from the second-order wave equation in 3D media. They have used a conjugate gradient method for the optimization procedure. We explore a similar adjoint formulation based on the first-order wave equations while using different optimization schemes. Indeed, for earthquake kinematics inversion, the model space is the slip-rate spatio-temporal history over the fault. Seismograms obtained from a dislocation rupture simulation are linearly linked to this slip-rate distribution. Therefore, we introduce a simple systematic procedure based on Lagrangian formulation of the adjoint method in the linear problem of earthquake kinematics. We have developed both the gradient estimation using the adjoint formulation and the Hessian influence using the second-order adjoint formulation (Metivier et al, 2013, 2014). Since the earthquake kinematics is a linear problem, the minimization problem is quadratic, henceforth, only one solution of the Newton equations is needed with the Hessian impact. Moreover, the formal uncertainty estimation over slip-rate distribution could be deduced from this Hessian analysis. On simple synthetic examples for antiplane kinematic rupture configuration in 2D medium, we illustrate the properties of
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.
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.
An inverse dynamic method yielding flexible manipulator state trajectories
NASA Technical Reports Server (NTRS)
Kwon, Dong-Soo; Book, Wayne J.
1990-01-01
An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, torque is calculated in the time domain for a certain end point trajectory, as well as trajectories of all state variables. The open loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and its good experimental result is presented.
An inverse dynamic method yielding flexible manipulator state trajectories
NASA Technical Reports Server (NTRS)
Kwon, Dong-Soo; Book, Wayne J.
1990-01-01
An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, one can calculate torque in the time domain for a certain end-point trajectory, as well as trajectories of all state variables. The open-loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and experimental results are presented.
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.
An inverse method with regularity condition for transonic airfoil design
NASA Technical Reports Server (NTRS)
Zhu, Ziqiang; Xia, Zhixun; Wu, Liyi
1991-01-01
It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem, the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint on the prescribed pressure distribution. The same constraint exists at compressible speeds. Presented here is an inverse design method for transonic airfoils. In this method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition. Some design results are presented in order to demonstrate the capabilities of the method.
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.
NASA Astrophysics Data System (ADS)
Kim, Sun K.; Kim, Hee June; Lee, Woo Il
2003-07-01
The heat transfer coefficient during the thermoplastic composite tape lay-up process is estimated using an inverse method. This paper presents a simple inverse method using the parameter estimation technique combined with a suitable thermal transport model. The numerical simulation of the proposed thermal model is implemented by the finite element method. A small-scale tape lay-up system is built and experiments are conducted to measure temperature inside the composite during the process. The inverse method retrieves the unknown heat transfer coefficients by solving an optimization problem, which seeks consistency between the measured and computed temperatures.
Comparison of iterative inverse coarse-graining methods
NASA Astrophysics Data System (ADS)
Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.
2016-10-01
Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.
Comparison of Optimal Design Methods in Inverse Problems
Banks, H. T.; Holm, Kathleen; Kappel, Franz
2011-01-01
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 (FIM). 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 criteria 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 [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762
Comparison of Optimal Design Methods in Inverse Problems.
Banks, H T; Holm, Kathleen; Kappel, Franz
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 (FIM). 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 criteria 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 [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].
Evaluation of simplified evaporation duct refractivity models for inversion problems
NASA Astrophysics Data System (ADS)
Saeger, J. T.; Grimes, N. G.; Rickard, H. E.; Hackett, E. E.
2015-10-01
To assess a radar system's instantaneous performance on any given day, detailed knowledge of the meteorological conditions is required due to the dependency of atmospheric refractivity on thermodynamic properties such as temperature, water vapor, and pressure. Because of the significant challenges involved in obtaining these data, recent efforts have focused on development of methods to obtain the refractivity structure inversely using radar measurements and radar wave propagation models. Such inversion techniques generally use simplified refractivity models in order to reduce the parameter space of the solution. Here the accuracy of three simple refractivity models is examined for the case of an evaporation duct. The models utilize the basic log linear shape classically associated with evaporation ducts, but each model depends on various parameters that affect different aspects of the profile, such as its shape and duct height. The model parameters are optimized using radiosonde data, and their performance is compared to these atmospheric measurements. The optimized models and data are also used to predict propagation using a parabolic equation code with the refractivity prescribed by the models and measured data, and the resulting propagation patterns are compared. The results of this study suggest that the best log linear model formulation for an inversion problem would be a two-layer model that contains at least three parameters: duct height, duct curvature, and mixed layer slope. This functional form permits a reasonably accurate fit to atmospheric measurements as well as embodies key features of the profile required for correct propagation prediction with as few parameters as possible.
A MEASURE-THEORETIC COMPUTATIONAL METHOD FOR INVERSE SENSITIVITY PROBLEMS I: METHOD AND ANALYSIS
Breidt, J.; Butler, T.; Estep, D.
2012-01-01
We consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map. This is a version of the model calibration or parameter estimation problem for a deterministic map. We assume that the uncertainty in the quantity of interest is represented by a random variable with a given distribution, and we use the law of total probability to express the inverse problem for the corresponding probability measure on the input space. Assuming that the map from the input space to the quantity of interest is smooth, we solve the generally ill-posed inverse problem by using the implicit function theorem to derive a method for approximating the set-valued inverse that provides an approximate quotient space representation of the input space. We then derive an efficient 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. PMID:23637467
Inverse modeling of soil infiltration process
NASA Astrophysics Data System (ADS)
Kuraz, Michal
2017-07-01
This paper presents an evaluation of the soil hydraulic parameters (SHP) for a mountainous podzolic soil profile. Due to the tickness of the top-soil layer only the SHPs for the lower layers can be identified using standard approaches - a single ring (SR) infiltration experiment and a Guelph permeameter (GP) measurement. The SHPs for the top soil layer were identified here by inverse modeling of the SR infiltration process, where, especially, the initial unsteady part of the experiment can provide very useful data for evaluating the retention curve parameters and the saturated hydraulic conductivity. This inverse analysis is the main topic of this paper. Since the infiltration process is a typical case of a model that describes the progressive breakthrough of the wetting curve, we made use of adaptive domain decomposition (dd-adaptivity) described by [1, 2, 3] for sequential activation and deactivation of the segments of our computational domain. Finally, we conducted a sensitivity analysis of our objective function on the SHP set.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...
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
Ko, Young-Rae; Hwang, Yoonkyu; Chae, Minji; Kim, Tae-Hyoung
2017-09-01
In this study, we present an identification-based direct construction of the inverse generalized Prandtl-Ishlinskii (P-I) model to facilitate inverse model-based feedforward compensation of asymmetric hysteresis nonlinearities. Compared with the derivation of the inverse model analytically from a generalized P-I model, this direct modeling approach has the following advantages. First, direct inverse model identification is formulated as a nonlinear optimization problem, which is not subject to the constraint condition on the generalized P-I model's threshold and density functions, where this is indispensable for the analytical model inversion procedure. Second, this approach may be a simple and attractive alternative when the identification precision of a generalized P-I model is limited by the constraint condition, which necessarily results in insufficient hysteresis compensation functionality for the analytically derived inverse model. Finally, direct inverse model identification can overcome the drawbacks of the analytical inversion method, including the accumulation of parameter estimation errors in an analytical inverse model because these parameters are computed from the generalized P-I model's parameters in a recursive manner. Our experimental results demonstrated that the implementation of open-loop control with the directly identified inverse generalized P-I model as a feedforward compensator achieved precise compensation for the asymmetric hysteresis nonlinearities of a piezoelectric stack actuator. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Matrix-inversion method: Applications to Möbius inversion adn deconvolution
NASA Astrophysics Data System (ADS)
Xie, Qian; Chen, Nan-Xian
1995-12-01
The purpose of this paper is threefold. The first is to show the matrix inversion method as a joint basis for the inversion of two important transforms: the Möbius and Laplace transforms. It is found that the Möbius transform is related to a multiplicative operator while the Laplace transform is related to an additive operator. The second is to show that the matrix inverison method is a useful tool for inverse problems not only in statistical physics but also in applied physics by means of adding two other applications, one the derivation of the Fuoss-Kirkwood formulas for relaxation spectra in studies of anelasticity and dielectrics and the other the reconstruction of real signal in signal processing. The third is to indicate the potentiality of the matrix inversion method as a rough algorithm for numerical solution of the convolution integral equation. The numerical examples given include the inversion of Laplace transform and the signal reconstruction with a Gaussian point spread kernel. (c) 1995 The American Physical Society
Geological realism in hydrogeological and geophysical inverse modeling: A review
NASA Astrophysics Data System (ADS)
Linde, Niklas; Renard, Philippe; Mukerji, Tapan; Caers, Jef
2015-12-01
Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.
An adaptive subspace trust-region method for frequency-domain seismic full waveform inversion
NASA Astrophysics Data System (ADS)
Zhang, Huan; Li, Xiaofan; Song, Hanjie; Liu, Shaolin
2015-05-01
Full waveform inversion is currently considered as a promising seismic imaging method to obtain high-resolution and quantitative images of the subsurface. It is a nonlinear ill-posed inverse problem, the main difficulty of which that prevents the full waveform inversion from widespread applying to real data is the sensitivity to incorrect initial models and noisy data. Local optimization theories including Newton's method and gradient method always lead the convergence to local minima, while global optimization algorithms such as simulated annealing are computationally costly. To confront this issue, in this paper we investigate the possibility of applying the trust-region method to the full waveform inversion problem. Different from line search methods, trust-region methods force the new trial step within a certain neighborhood of the current iterate point. Theoretically, the trust-region methods are reliable and robust, and they have very strong convergence properties. The capability of this inversion technique is tested with the synthetic Marmousi velocity model and the SEG/EAGE Salt model. Numerical examples demonstrate that the adaptive subspace trust-region method can provide solutions closer to the global minima compared to the conventional Approximate Hessian approach and the L-BFGS method with a higher convergence rate. In addition, the match between the inverted model and the true model is still excellent even when the initial model deviates far from the true model. Inversion results with noisy data also exhibit the remarkable capability of the adaptive subspace trust-region method for low signal-to-noise data inversions. Promising numerical results suggest this adaptive subspace trust-region method is suitable for full waveform inversion, as it has stronger convergence and higher convergence rate.
The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method
NASA Astrophysics Data System (ADS)
Voronina, T. A.; Romanenko, A. A.
2016-12-01
Application of the r-solution method to reconstructing the initial tsunami waveform is discussed. This methodology is based on the inversion of remote measurements of water-level data. The wave propagation is considered within the scope of a linear shallow-water theory. The ill-posed inverse problem in question is regularized by means of a least square inversion using the truncated Singular Value Decomposition method. As a result of the numerical process, an r-solution is obtained. The method proposed allows one to control the instability of a numerical solution and to obtain an acceptable result in spite of ill posedness of the problem. Implementation of this methodology to reconstructing of the initial waveform to 2013 Solomon Islands tsunami validates the theoretical conclusion for synthetic data and a model tsunami source: the inversion result strongly depends on data noisiness, the azimuthal and temporal coverage of recording stations with respect to the source area. Furthermore, it is possible to make a preliminary selection of the most informative set of the available recording stations used in the inversion process.
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.
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.
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.
Methodology for comparison of inverse heat conduction methods
NASA Astrophysics Data System (ADS)
Raynaud, M.; Beck, J. V.
1988-02-01
The inverse heat conduction problem involves the calculation of the surface heat flux from transient measured temperatures inside solids. The deviation of the estimated heat flux from the true heat flux due to stabilization procedures is called the deterministic bias. This paper defines two test problems that show the tradeoff between deterministic bias and sensitivity to measurement errors of inverse methods. For a linear problem, with the statistical assumptions of additive and uncorrelated errors having constant variance and zero mean, the second test case gives the standard deviation of the estimated heat flux. A methodology for the quantitative comparison of deterministic bias and standard deviation of inverse methods is proposed. Four numerical inverse methods are compared.
Jiang, Mingfeng; Xia, Ling; Shou, Guofa; Tang, Min
2007-03-07
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.
Non-cavitating propeller noise modeling and inversion
NASA Astrophysics Data System (ADS)
Kim, Dongho; Lee, Keunhwa; Seong, Woojae
2014-12-01
Marine propeller is the dominant exciter of the hull surface above it causing high level of noise and vibration in the ship structure. Recent successful developments have led to non-cavitating propeller designs and thus present focus is the non-cavitating characteristics of propeller such as hydrodynamic noise and its induced hull excitation. In this paper, analytic source model of propeller non-cavitating noise, described by longitudinal quadrupoles and dipoles, is suggested based on the propeller hydrodynamics. To find the source unknown parameters, the multi-parameter inversion technique is adopted using the pressure data obtained from the model scale experiment and pressure field replicas calculated by boundary element method. The inversion results show that the proposed source model is appropriate in modeling non-cavitating propeller noise. The result of this study can be utilized in the prediction of propeller non-cavitating noise and hull excitation at various stages in design and analysis.
Inverse modeling of April 2013 radioxenon detections
NASA Astrophysics Data System (ADS)
Hofman, Radek; Seibert, Petra; Philipp, Anne
2014-05-01
Significant concentrations of radioactive xenon isotopes (radioxenon) were detected by the International Monitoring System (IMS) for verification of the Comprehensive Nuclear-Test-Ban Treaty (CTBT) in April 2013 in Japan. Particularly, three detections of Xe-133 made between 2013-04-07 18:00 UTC and 2013-04-09 06:00 UTC at the station JPX38 are quite notable with respect to the measurement history of the station. Our goal is to analyze the data and perform inverse modeling under different assumptions. This work is useful with respect to nuclear test monitoring as well as for the analysis of and response to nuclear emergencies. Two main scenarios will be pursued: (i) Source location is assumed to be known (DPRK test site). (ii) Source location is considered unknown. We attempt to estimate the source strength and the source strength along with its plausible location compatible with the data in scenario (i) and (ii), respectively. We are considering also the possibility of a vertically distributed source. Calculations of source-receptor sensitivity (SRS) fields and the subsequent inversion are aimed at going beyond routine calculations performed by the CTBTO. For SRS calculations, we employ the Lagrangian particle dispersion model FLEXPART with high resolution ECMWF meteorological data (grid cell sizes of 0.5, 0.25 and ca. 0.125 deg). This is important in situations where receptors or sources are located in complex terrain which is the case of the likely source of detections-the DPRK test site. SRS will be calculated with convection enabled in FLEXPART which will also increase model accuracy. In the variational inversion procedure attention will be paid not only to all significant detections and their uncertainties but also to non-detections which can have a large impact on inversion quality. We try to develop and implement an objective algorithm for inclusion of relevant data where samples from temporal and spatial vicinity of significant detections are added in an
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
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…
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…
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.
New inversion methods for the Lorentz Integral Transform
NASA Astrophysics Data System (ADS)
Andreasi, D.; Leidemann, W.; Reiß, C.; Schwamb, M.
2005-06-01
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross-sections without explicit knowledge of final-state wave functions. The necessary inversion of the transform has to be treated with great care, since it constitutes a so-called ill-posed problem. In this work new inversion techniques for the Lorentz Integral Transform are introduced. It is shown that they all contain a regularization scheme, which is necessary to overcome the ill-posed problem. In addition, it is illustrated that the new techniques have a much broader range of application than the present standard inversion method of the Lorentz Integral Transform.
Inversion is the Solution to Dispersion: Modeling Tephra Fallout
NASA Astrophysics Data System (ADS)
Connor, C.
2005-12-01
Volcanologists increasingly rely on numerical simulations to understand the dynamics of erupting volcanoes. Mathematical models are often used to explain the geologic processes responsible for eruption deposits found in the geologic record, and to better characterize possible hazards from future volcanic activity. We wish to estimate parameters related to the dynamics of volcanic activity directly from field observations. For example, how well can we estimate the magnitude of an eruption from measurements of tephra deposits? One solution lies in coupling our numerical simulations of volcanic eruption phenomena to inversion methods that search for an optimal set of parameters that explains our observations. Here we use observations of tephra thickness and granulometry from the 1992 eruption of Cerro Negro volcano, Nicaragua, to test the performance of a numerical simulation of tephra fallout. The downhill simplex inversion method is used to search for optimal parameters, including the eruption column height, eruption mass, and wind velocity as a function of elevation about the volcanic vent, that produce deposits that best fit the thickness and grainsize variations observed on the tephra deposit. The computational efficiency of the model is greatly enhanced by parallelizing the numerical model. Through inversion, we estimate the column height and total mass of the eruption as 6500m +/- 750m and 3.1 x 1010 kg +/- 2.9 x 109 kg respectively. These parameter ranges agree well with observations made during the 1992 Cerro Negro eruption: 7000-7500 m maximum column height and 2.3 x 1010 kg mass erupted. Parameter uncertainty, reported as one standard deviation from the mean, is estimated using a Monte Carlo method. Inversion techniques such as the downhill simplex method provide an unbiased method for utilizing volcanological observations to evaluate and improve numerical simulations of volcanic activity. Such an approach is essential for evaluating numerical models used
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
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 damped Newton variational inversion method for SAR wind retrieval
NASA Astrophysics Data System (ADS)
Jiang, Zhuhui; Li, Yuanxiang; Yu, Fangjie; Chen, Ge; Yu, Wenxian
2017-01-01
The variational inversion for synthetic aperture radar (SAR) wind retrieval can take all sources' errors into account, but its iterative computation is very time consuming. For the wind vectors, (u, v) components are commonly used for variational inversion, but they are not intuitive for practical applications. In this paper, we modify the decomposition of wind vectors in the cost function into wind speed and wind direction and adopt the damped Newton method (DNVAR) to solve the cost function. Experimental results on simulated data show that DNVAR can effectively reduce background wind vector errors. Additionally, the average number of iterations is reduced drastically compared to prior arts. Furthermore, a detailed comparison between direct SAR wind retrieval (DIRECT) and DNVAR is performed. Simulations reveal that the DNVAR errors are smaller than the background wind vector errors in all considered cases. Thus, DNVAR could be employed to retrieve SAR sea surface wind. For practical applications, when the background wind speed is within moderate and high wind speed range, DNVAR has higher accuracy and is thus preferred. Otherwise, both DNVAR and DIRECT are feasible, considering the unknown actual errors of both background wind vectors and geophysical model function. Experimental results on Envisat/advanced synthetic aperture radar data show that the wind speed accuracy of DIRECT is largely affected by the background wind direction errors, but DNVAR can reduce the wind direction errors with minor effect on the wind speed errors in comparison with the background wind errors.
Parameter Selection Methods in Inverse Problem Formulation
2010-11-03
therapy levels, with u(t) = 0 for fully off and u(t) = 1, for fully on. Although HIV treatment is nearly always administered as combination therapy...Davidian, and E.S. Rosenberg, Model fitting and predic- tion with HIV treatment interruption data, CRSC-TR05-40, NCSU, October 2005; Bull. Math
Interactive Inverse Groundwater Modeling - Addressing User Fatigue
NASA Astrophysics Data System (ADS)
Singh, A.; Minsker, B. S.
2006-12-01
This paper builds on ongoing research on developing an interactive and multi-objective framework to solve the groundwater inverse problem. In this work we solve the classic groundwater inverse problem of estimating a spatially continuous conductivity field, given field measurements of hydraulic heads. The proposed framework is based on an interactive multi-objective genetic algorithm (IMOGA) that not only considers quantitative measures such as calibration error and degree of regularization, but also takes into account expert knowledge about the structure of the underlying conductivity field expressed as subjective rankings of potential conductivity fields by the expert. The IMOGA converges to the optimal Pareto front representing the best trade- off among the qualitative as well as quantitative objectives. However, since the IMOGA is a population-based iterative search it requires the user to evaluate hundreds of solutions. This leads to the problem of 'user fatigue'. We propose a two step methodology to combat user fatigue in such interactive systems. The first step is choosing only a few highly representative solutions to be shown to the expert for ranking. Spatial clustering is used to group the search space based on the similarity of the conductivity fields. Sampling is then carried out from different clusters to improve the diversity of solutions shown to the user. Once the expert has ranked representative solutions from each cluster a machine learning model is used to 'learn user preference' and extrapolate these for the solutions not ranked by the expert. We investigate different machine learning models such as Decision Trees, Bayesian learning model, and instance based weighting to model user preference. In addition, we also investigate ways to improve the performance of these models by providing information about the spatial structure of the conductivity fields (which is what the expert bases his or her rank on). Results are shown for each of these
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.
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.
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).
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.
Hydraulic Inverse Modeling Using Total-Variation Regularization with Relaxed Variable-Splitting
NASA Astrophysics Data System (ADS)
Lin, Y.; Vesselinov, V. V.; O'Malley, D.; Wohlberg, B.
2016-12-01
Inverse modeling seeks model parameters given a set of observed-state variables. For many practical hydrogeological problems, because the data coverage is limited, the inversion can be ill-posed and unstable. Typically, inverse analyses are applied to characterize aquifer heterogeneity where the hydraulic permeability is estimated throughout the model domain. To stabilize the inversion, regularization techniques can be employed to eliminate the ill-posedness. The most commonly used type of regularization include Tikhonov and Total-Variation (TV). The hydraulic tomographic analyses of aquifer heterogeneity with Tikhonov regularization tends to yield smoothed inversion results, while the ones with TV regularization can preserve the sharp contrast between low and high permeability regions. However, hydraulic inverse modeling with the conventional TV regularization can be computationally unstable and yield unwanted artifacts because of the non-differentiability of the TV norm. We develop a novel hydraulic inverse modeling method using a TV regularization with relaxed variable-splitting scheme to preserve sharp interfaces in piecewise-constant structures and improve the accuracy of inversion. We use an alternating-minimization algorithm to solve the minimization problem. Specifically, we decouple the original problem into two simple sub-problems: a standard inverse modeling sub-problem with the Tikhonov regularization, and a standard L2-TV sub-problem. We solve these two sub-problems using the standard linear solver and Alternating Direction Method of Multipliers (ADMM) iterative methods, respectively. Our new inversion algorithm is implemented in the MADS computational framework (http://mads.lanl.gov). The computational cost of our new inversion methods is comparable to those of conventional inversion approaches. Our numerical examples using synthetic data show that our new methods not only preserve sharp interfaces of subsurface permeability distribution, but also
The inverse gravimetric problem in gravity modelling
NASA Technical Reports Server (NTRS)
Sanso, F.; Tscherning, C. C.
1989-01-01
One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.
Saturation-inversion-recovery: A method for T1 measurement
NASA Astrophysics Data System (ADS)
Wang, Hongzhi; Zhao, Ming; Ackerman, Jerome L.; Song, Yiqiao
2017-01-01
Spin-lattice relaxation (T1) has always been measured by inversion-recovery (IR), saturation-recovery (SR), or related methods. These existing methods share a common behavior in that the function describing T1 sensitivity is the exponential, e.g., exp(- τ /T1), where τ is the recovery time. In this paper, we describe a saturation-inversion-recovery (SIR) sequence for T1 measurement with considerably sharper T1-dependence than those of the IR and SR sequences, and demonstrate it experimentally. The SIR method could be useful in improving the contrast between regions of differing T1 in T1-weighted MRI.
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.
Voxel inversion of airborne electromagnetic data for improved model integration
NASA Astrophysics Data System (ADS)
Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders
2014-05-01
Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054
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.
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.
Local constitutive behavior of paper determined by an inverse method
John M. Considine; C. Tim Scott; Roland Gleisner; Junyong Zhu
2006-01-01
The macroscopic behavior of paper is governed by small-scale behavior. Intuitively, we know that a small-scale defect with a paper sheet effectively determines the global behavior of the sheet. In this work, we describe a method to evaluate the local constitutive behavior of paper by using an inverse method.
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.
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
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
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
Towards an optimal inversion method for remote atmospheric sensing
NASA Technical Reports Server (NTRS)
King, J. I. F.
1969-01-01
The inference of atmospheric structure from satellite radiometric observations requires an inversion algorithm. A variety of techniques was spawned to meet these demands. One class, the nonlinear inversion methods, copes with the problem of data noise. Unlike linear techniques which require a priori data smoothing, the nonlinear method can be applied directly to raw data. The algorithm discriminates the noise input by resolving the inferences into two types of solution, associating the real roots with atmospheric structure while ascribing the imaginary roots to noise.
Accuracy evaluation of both Wallace-Bott and BEM-based paleostress inversion methods
NASA Astrophysics Data System (ADS)
Lejri, Mostfa; Maerten, Frantz; Maerten, Laurent; Soliva, Roger
2017-01-01
Four decades after their introduction, the validity of fault slip inversion methods based on Wallace (1951) and Bott (1959) hypothesis, which states that the slip on each fault surface has the same direction and sense as the maximum resolved shear stress, is still a subject of debate. According to some authors, this hypothesis is questionable since fault mechanical interactions induce slip reorientations as confirmed by geomechanical models. This leads us to ask as to what extent the Wallace-Bott simplifications are reliable as a basis hypothesis for stress inversion from fault slip data. In this paper, we compare two inversion methods; the first is based on the Wallace-Bott hypothesis, and the second relies on geomechanics and mechanical effects on fault heterogeneous slip distribution. In that context, a multi-parametric stress inversion study covering (i) the friction coefficients (μ), (ii) the full range of Andersonian state of stress and (iii) slip data sampling along the faults is performed. For each tested parameter, the results of the mechanical stress inversion and the Wallace-Bott (WB) based stress inversion for slip are compared in order to understand their respective effects. The predicted discrepancy between the solutions of both stress inversion methods (based on WB and mechanics) will then be used to explain the stress inversions results for the chimney Rock case study. It is shown that a high solution discrepancy is not always correlated with the misfit angle (ω) and can be found under specific configurations (R-, θ, μ, geometry) invalidating the WB solutions. We conclude that in most cases the mechanical stress inversion and the WB based stress inversion are both valid and complementary depending on the fault friction. Some exceptions (i.e. low fault friction, simple fault geometry and pure regimes) that may lead to wrong WB based stress inversion solutions are highlighted.
Magnetic interface forward and inversion method based on Padé approximation
NASA Astrophysics Data System (ADS)
Zhang, Chong; Huang, Da-Nian; Zhang, Kai; Pu, Yi-Tao; Yu, Ping
2016-12-01
The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on Padé approximation instead of the Taylor series expansion. Compared with the Taylor series, Padé's expansion's convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of Padé approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained.
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.
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
Inverting geodetic time series with a principal component analysis-based inversion method
NASA Astrophysics Data System (ADS)
Kositsky, A. P.; Avouac, J.-P.
2010-03-01
The Global Positioning System (GPS) system now makes it possible to monitor deformation of the Earth's surface along plate boundaries with unprecedented accuracy. In theory, the spatiotemporal evolution of slip on the plate boundary at depth, associated with either seismic or aseismic slip, can be inferred from these measurements through some inversion procedure based on the theory of dislocations in an elastic half-space. We describe and test a principal component analysis-based inversion method (PCAIM), an inversion strategy that relies on principal component analysis of the surface displacement time series. We prove that the fault slip history can be recovered from the inversion of each principal component. Because PCAIM does not require externally imposed temporal filtering, it can deal with any kind of time variation of fault slip. We test the approach by applying the technique to synthetic geodetic time series to show that a complicated slip history combining coseismic, postseismic, and nonstationary interseismic slip can be retrieved from this approach. PCAIM produces slip models comparable to those obtained from standard inversion techniques with less computational complexity. We also compare an afterslip model derived from the PCAIM inversion of postseismic displacements following the 2005 8.6 Nias earthquake with another solution obtained from the extended network inversion filter (ENIF). We introduce several extensions of the algorithm to allow statistically rigorous integration of multiple data sources (e.g., both GPS and interferometric synthetic aperture radar time series) over multiple timescales. PCAIM can be generalized to any linear inversion algorithm.
Adiabatic approximation for the Rabi model with broken inversion symmetry
NASA Astrophysics Data System (ADS)
Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi
2017-01-01
We study the properties and behavior of the Rabi model with broken inversion symmetry. Using an adiabatic approximation approach, we explore the high-frequency qubit and oscillator regimes, and obtain analytical solutions for the qubit-oscillator system. We demonstrate that, due to broken inversion symmetry, the positions of two potentials and zero-point energies in the oscillators become asymmetric and have a quadratic dependence on the mean dipole moments within the high-frequency oscillator regime. Furthermore, we find that there is a critical point above which the qubit-oscillator system becomes unstable, and the position of this critical point has a quadratic dependence on the mean dipole moments within the high-frequency qubit regime. Finally, we verify this critical point based on the method of semiclassical approximation.
Quantum inverse scattering and the lambda deformed principal chiral model
NASA Astrophysics Data System (ADS)
Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd
2017-07-01
The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current-current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard techniques of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin, we show that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.
A method of inversion of satellite magnetic anomaly data
NASA Technical Reports Server (NTRS)
Mayhew, M. A.
1977-01-01
A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.
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.
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
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…
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…
NASA Astrophysics Data System (ADS)
Itahashi, S.; Yumimoto, K.; Uno, I.; Kim, S.
2012-12-01
Air quality studies based on the chemical transport model have been provided many important results for promoting our knowledge of air pollution phenomena, however, discrepancies between modeling results and observation data are still important issue to overcome. One of the concerning issue would be an over-prediction of summertime tropospheric ozone in remote area of Japan. This problem has been pointed out in the model comparison study of both regional scale (e.g., MICS-Asia) and global scale model (e.g., TH-FTAP). Several reasons for this issue can be listed as, (i) the modeled reproducibility on the penetration of clean oceanic air mass, (ii) correct estimation of the anthropogenic NOx / VOC emissions over East Asia, (iii) the chemical reaction scheme used in model simulation. In this study, we attempt to inverse estimation of some important chemical reactions based on the combining system of DDM (decoupled direct method) sensitivity analysis and modeled Green's function approach. The decoupled direct method (DDM) is an efficient and accurate way of performing sensitivity analysis to model inputs, calculates sensitivity coefficients representing the responsiveness of atmospheric chemical concentrations to perturbations in a model input or parameter. The inverse solutions with the Green's functions are given by a linear, least-squares method but are still robust against nonlinearities, To construct the response matrix (i.e., Green's functions), we can directly use the results of DDM sensitivity analysis. The solution of chemical reaction constants which have relatively large uncertainties are determined with constraints of observed ozone concentration data over the remote area in Japan. Our inversed estimation demonstrated that the underestimation of reaction constant to produce HNO3 (NO2 + OH + M → HNO3 + M) in SAPRC99 chemical scheme, and the inversed results indicated the +29.0 % increment to this reaction. This estimation has good agreement when compared
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.
A hybrid inverse method for hydraulic tomography in fractured and karstic media
NASA Astrophysics Data System (ADS)
Wang, Xiaoguang; Jardani, Abderrahim; Jourde, Hervé
2017-08-01
We apply a stochastic Newton (SN) approach to solve a high-dimensional hydraulic inverse problem in highly heterogeneous geological media. By recognizing the connection between the cost function of deterministic optimizations and the posterior probability density of stochastic inversions, the Markov chain Monte Carlo (MCMC) sampler of SN is constructed by two parts: a deterministic part, which corresponds to a Newton step of deterministic optimization, and a stochastic part, which is a Gaussian distribution with the inverse of the local Hessian as the covariance matrix. The hybrid inverse method exploits the efficient tools for fast solution of deterministic inversions to improve the efficiency of the MCMC sampler. To address the ill-posedness of the inverse problem, a priori models, generated by a transition-probability geostatistical method, and conditioned to inter-well connection data, are used as regularization constraints. The effectiveness of the stochastic Newton method is first demonstrated by a synthetic test. The transmissivity field of the synthetic model is highly heterogeneous, and includes sharp variations. The inverse approach was then applied to a field hydraulic tomography investigation in a fractured and karstified aquifer to reconstruct its transmissivity field from a collection of real hydraulic head measurements. From the inversions, a series of transmissivity fields that produce good correlations between the inverted and the measured hydraulic heads were obtained. The inverse approach produced slightly different a posteriori transmissivity patterns for different a priori structure models of transmissivity; however, the trend and location of the high-transmissivity channels are consistent among various realizations. In addition, the uncertainty associated with each realization of the inverted transmissivity fields was quantified.
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.
Extrapolated Tikhonov method and inversion of 3D density images of gravity data
NASA Astrophysics Data System (ADS)
Wang, Zhu-Wen; Xu, Shi; Liu, Yin-Ping; Liu, Jing-Hua
2014-06-01
Tikhonov regularization (TR) method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method (EXTR) is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.
The application of the pilot points in groundwater numerical inversion model
NASA Astrophysics Data System (ADS)
Hu, Bin; Teng, Yanguo; Cheng, Lirong
2015-04-01
Numerical inversion simulation of groundwater has been widely applied in groundwater. Compared to traditional forward modeling, inversion model has more space to study. Zones and inversing modeling cell by cell are conventional methods. Pilot points is a method between them. The traditional inverse modeling method often uses software dividing the model into several zones with a few parameters needed to be inversed. However, distribution is usually too simple for modeler and result of simulation deviation. Inverse cell by cell will get the most actual parameter distribution in theory, but it need computational complexity greatly and quantity of survey data for geological statistical simulation areas. Compared to those methods, pilot points distribute a set of points throughout the different model domains for parameter estimation. Property values are assigned to model cells by Kriging to ensure geological units within the parameters of heterogeneity. It will reduce requirements of simulation area geological statistics and offset the gap between above methods. Pilot points can not only save calculation time, increase fitting degree, but also reduce instability of numerical model caused by numbers of parameters and other advantages. In this paper, we use pilot point in a field which structure formation heterogeneity and hydraulics parameter was unknown. We compare inversion modeling results of zones and pilot point methods. With the method of comparative analysis, we explore the characteristic of pilot point in groundwater inversion model. First, modeler generates an initial spatially correlated field given a geostatistical model by the description of the case site with the software named Groundwater Vistas 6. Defining Kriging to obtain the value of the field functions over the model domain on the basis of their values at measurement and pilot point locations (hydraulic conductivity), then we assign pilot points to the interpolated field which have been divided into 4
3D CSEM inversion based on goal-oriented adaptive finite element method
NASA Astrophysics Data System (ADS)
Zhang, Y.; Key, K.
2016-12-01
We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with
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
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
Dispersion analysis with inverse dielectric function modelling.
Mayerhöfer, Thomas G; Ivanovski, Vladimir; Popp, Jürgen
2016-11-05
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.
Inviscid transonic wing design using inverse methods in curvilinear coordinates
NASA Technical Reports Server (NTRS)
Gally, Thomas A.; Carlson, Leland A.
1987-01-01
An inverse wing design method has been developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.
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.
Nonlinear inversion for arbitrarily-oriented anisotropic models: Synthetic testing
NASA Astrophysics Data System (ADS)
Bremner, P. M.; Panning, M. P.
2010-12-01
We present an implementation of new 3-D finite-frequency kernels, based on the Born approximation, for inversion of a synthetic surface wave dataset. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests are performed to achieve a robust inversion scheme. Nonlinear inversion schemes are examined for adequate recovery of three input models to include: isotropic, anisotropic, and both anisotropic and isotropic input models. 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 focus of this study is on inverting for structure beneath western North America. The synthetic dataset consists of collected seismic waveforms of 128 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 150° centered about 44° lat, -110° lon (an arbitrary location within USArray coverage). The seismograms have been calculated within a simplified version of PREM in which the crust and 220 km discontinuity have been removed, dubbed PREM LIGHT, 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 400 km depth, coupled to a spherically symmetric inner sphere. The SEM solves the weak formulation of the seismic wave equation in the outer shell, and uses normal mode summation methods for the inner sphere. To validate the results of the SEM, seismograms are benchmarked against seismograms calculated with a 1-D normal mode summation. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π spheroidal wave function
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.
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
NASA Astrophysics Data System (ADS)
Pan, Qi; Liu, De-Jun; Guo, Zhi-Yong; Fang, Hua-Feng; Feng, Mu-Qun
2016-06-01
In the model of a horizontal straight pipeline of finite length, the segmentation of the pipeline elements is a significant factor in the accuracy and rapidity of the forward modeling and inversion processes, but the existing pipeline segmentation method is very time-consuming. This paper proposes a section segmentation method to study the characteristics of pipeline magnetic anomalies—and the effect of model parameters on these magnetic anomalies—as a way to enhance computational performance and accelerate the convergence process of the inversion. Forward models using the piece segmentation method and section segmentation method based on magnetic dipole reconstruction (MDR) are established for comparison. The results show that the magnetic anomalies calculated by these two segmentation methods are almost the same regardless of different measuring heights and variations of the inclination and declination of the pipeline. In the optimized inversion procedure the results of the simulation data calculated by these two methods agree with the synthetic data from the original model, and the inversion accuracies of the burial depths of the two methods are approximately equal. The proposed method is more computationally efficient than the piece segmentation method—in other words, the section segmentation method can meet the requirements for precision in the detection of pipelines by magnetic anomalies and reduce the computation time of the whole process.
Statistical method for resolving the photon-photoelectron-counting inversion problem
Wu Jinlong; Li Tiejun; Peng, Xiang; Guo Hong
2011-02-01
A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.
NASA Astrophysics Data System (ADS)
Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.
2017-07-01
The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.
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
Model selection in cognitive science as an inverse problem
NASA Astrophysics Data System (ADS)
Myung, Jay I.; Pitt, Mark A.; Navarro, Daniel J.
2005-03-01
How should we decide among competing explanations (models) of a cognitive phenomenon? This problem of model selection is at the heart of the scientific enterprise. Ideally, we would like to identify the model that actually generated the data at hand. However, this is an un-achievable goal as it is fundamentally ill-posed. Information in a finite data sample is seldom sufficient to point to a single model. Multiple models may provide equally good descriptions of the data, a problem that is exacerbated by the presence of random error in the data. In fact, model selection bears a striking similarity to perception, in that both require solving an inverse problem. Just as perceptual ambiguity can be addressed only by introducing external constraints on the interpretation of visual images, the ill-posedness of the model selection problem requires us to introduce external constraints on the choice of the most appropriate model. Model selection methods differ in how these external constraints are conceptualized and formalized. In this review we discuss the development of the various approaches, the differences between them, and why the methods perform as they do. An application example of selection methods in cognitive modeling is also discussed.
DAMIT: Database of Asteroid Models from Inversion Techniques
NASA Astrophysics Data System (ADS)
Kaasalainen, Mikko; Ďurech, Josef; Sidorin, Vojtěch
2014-12-01
DAMIT (Database of Asteroid Models from Inversion Techniques) is a database of three-dimensional models of asteroids computed using inversion techniques; it provides access to reliable and up-to-date physical models of asteroids, i.e., their shapes, rotation periods, and spin axis directions. Models from DAMIT can be used for further detailed studies of individual objects as well as for statistical studies of the whole set. The source codes for lightcurve inversion routines together with brief manuals, sample lightcurves, and the code for the direct problem are available for download.
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.
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.
Printer model inversion by constrained optimization
NASA Astrophysics Data System (ADS)
Cholewo, Tomasz J.
1999-12-01
This paper describes a novel method for finding colorant amounts for which a printer will produce a requested color appearance based on constrained optimization. An error function defines the gamut mapping method and black replacement method. The constraints limit the feasible solution region to the device gamut and prevent exceeding the maximum total area coverage. Colorant values corresponding to in-gamut colors are found with precision limited only by the accuracy of the device model. Out-of- gamut colors are mapped to colors within the boundary of the device gamut. This general approach, used in conjunction with different types of color difference equations, can perform a wide range of out-of-gamut mappings such as chroma clipping or for finding colors on gamut boundary having specified properties. We present an application of this method to the creation of PostScript color rendering dictionaries and ICC profiles.
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 full potential inverse method based on a density linearization scheme for wing design
NASA Technical Reports Server (NTRS)
Shankar, V.
1982-01-01
A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.
Gu, Guo-Ying; Yang, Mei-Ju; Zhu, Li-Min
2012-06-01
This paper presents a novel real-time inverse hysteresis compensation method for piezoelectric actuators exhibiting asymmetric hysteresis effect. The proposed method directly utilizes a modified Prandtl-Ishlinskii hysteresis model to characterize the inverse hysteresis effect of piezoelectric actuators. The hysteresis model is then cascaded in the feedforward path for hysteresis cancellation. It avoids the complex and difficult mathematical procedure for constructing an inversion of the hysteresis model. For the purpose of validation, an experimental platform is established. To identify the model parameters, an adaptive particle swarm optimization algorithm is adopted. Based on the identified model parameters, a real-time feedforward controller is implemented for fast hysteresis compensation. Finally, tests are conducted with various kinds of trajectories. The experimental results show that the tracking errors caused by the hysteresis effect are reduced by about 90%, which clearly demonstrates the effectiveness of the proposed inverse compensation method with the modified Prandtl-Ishlinskii model.
Constructing inverse probability weights for continuous exposures: a comparison of methods.
Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S
2014-03-01
Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
Inverse design of airfoils using a flexible membrane method
NASA Astrophysics Data System (ADS)
Thinsurat, Kamon
The Modified Garabedian Mc-Fadden (MGM) method is used to inversely design airfoils. The Finite Difference Method (FDM) for Non-Uniform Grids was developed to discretize the MGM equation for numerical solving. The Finite Difference Method (FDM) for Non-Uniform Grids has the advantage of being used flexibly with an unstructured grids airfoil. The commercial software FLUENT is being used as the flow solver. Several conditions are set in FLUENT such as subsonic inviscid flow, subsonic viscous flow, transonic inviscid flow, and transonic viscous flow to test the inverse design code for each condition. A moving grid program is used to create a mesh for new airfoils prior to importing meshes into FLUENT for the analysis of flows. For validation, an iterative process is used so the Cp distribution of the initial airfoil, the NACA0011, achieves the Cp distribution of the target airfoil, the NACA2315, for the subsonic inviscid case at M=0.2. Three other cases were carried out to validate the code. After the code validations, the inverse design method was used to design a shock free airfoil in the transonic condition and to design a separation free airfoil at a high angle of attack in the subsonic condition.
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.
Measurements of control rod worth by modified inverse kinetic method
Bobrov, A. A.; Lebedev, G. V. Nechaev, Yu. A.
2011-12-15
Results of control rod worth measurements on the Astra critical assembly at the Russian Research Centre Kurchatov Institute are presented. The measurements were carried out by the modified inverse kinetics method, which is based on the use of experimental information about the variation of neutron detector readings only after introducing a reactivity perturbation. Calculated corrections are not required. The results of measurements do not depend on the neutron detector position.
Globally Convergent Numerical Methods for Coefficient Inverse Problems
2008-09-23
Problems , 18, 209-219, 2002. 50. A.N. Tikhonov and V. Ya. Arsenin , Solutions of Ill - Posed Problems Winston & Sons. Washington...is because solutions of PDEs depend nonlinearly on their coefficients. The ill - posedness is a well known feature of inverse problems . This means that...ut (x, 0)‖L2(Ω) ≤ CK. Theorem 8.5 enables us to prove convergence of our method. Following the Tikhonov concept for ill - posed problems [50], we
Express method of construction of accurate inverse pole figures
NASA Astrophysics Data System (ADS)
Perlovich, Yu; Isaenkova, M.; Fesenko, V.
2016-04-01
With regard to metallic materials with the FCC and BCC crystal lattice a new method for constructing the X-ray texture inverse pole figures (IPF) by using tilt curves of spinning sample, characterized by high accuracy and rapidity (express), was proposed. In contrast to the currently widespread method to construct IPF using orientation distribution function (ODF), synthesized in several partial direct pole figures, the proposed method is based on a simple geometrical interpretation of a measurement procedure, requires a minimal operating time of the X-ray diffractometer.
NASA Astrophysics Data System (ADS)
Lin, Youzuo; Huang, Lianjie
2017-07-01
Reverse-time migration has the potential to image complex subsurface structures, including steeply-dipping fault zones, but the method requires an accurate velocity model. Acoustic- and elastic-waveform inversion is a promising tool for high-resolution velocity model building. Because of the ill-posedness of acoustic- and elastic-waveform inversion, it is a great challenge to obtain accurate velocity models containing sharp interfaces. To improve velocity model building, we develop an acoustic- and elastic-waveform inversion method with an interface-guided modified total-variation regularization scheme to improve the inversion accuracy and robustness, particularly for models with sharp interfaces and steeply-dipping fault zones with widths much smaller than the seismic wavelength. The new regularization scheme incorporates interface information into seismic full-waveform inversion. The interface information of subsurface interfaces is obtained iteratively using migration imaging during waveform inversion. Seismic migration is robust for subsurface imaging. Our new acoustic- and elastic-waveform inversion takes advantage of the robustness of migration imaging to improve velocity estimation. We use synthetic seismic data for a complex model containing sharp interfaces and several steeply-dipping fault zones to validate the improved capability of our new acoustic- and elastic-waveform inversion method. Our inversion results are much better than those produced without using interface-guided regularization. Acoustic- and elastic-waveform inversion with an interface-guided modified total-variation regularization scheme has the potential to accurately build subsurface velocity models with sharp interfaces and/or steep fault zones.
The Genetic Algorithm: A Robust Method for Stress Inversion
NASA Astrophysics Data System (ADS)
Thakur, P.; Srivastava, D. C.; Gupta, P. K.
2016-12-01
The knowledge of stress states in Earth`s crust is a fundamental objective in many tectonic, seismological and engineering geological studies. Geologists and geophysicists routinely practice methods for determination of the stress tensor from inversion of observations on the stress indicators, such as faults, earthquakes and calcite twin lamellae. While the stress inversion is essentially a nonlinear problem, it is commonly solved by linearization, under some assumptions, in most existing methods. These algorithms not only oversimplify the problem but are also vulnerable to entrapment of the solution in a local optimum. We propose a nonlinear heuristic technique, the genetic algorithm method, that searches the global optimum without making any linearizing assumption or simplification. The method mimics the natural evolutionary process of selection, crossover, mutation, and minimises the composite misfit function for searching the global optimum, the fittest stress tensor. The validity of the method is successfully tested on synthetic fault-slip observations in different tectonic settings and also in situations where the observations contain noisy data. These results are compared with those obtained from the other common methods. The genetic algorithm method is superior to other common methods, in particular, in the oblique tectonic settings where none of the principal stresses is directed vertically.
The inversion method in measuring noise emitted by machines in opencast mines of rock material.
Pleban, Dariusz; Piechowicz, Janusz; Kosała, Krzysztof
2013-01-01
The inversion method was used to test vibroacoustic processes in large-size machines used in opencast mines of rock material. When this method is used, the tested machine is replaced with a set of substitute sources, whose acoustic parameters are determined on the basis of sound pressure levels and phase shift angles of acoustic signals, measured with an array of 24 microphones. This article presents test results of a combine unit comprising a crusher and a vibrating sieve, for which an acoustic model of 7 substitute sources was developed with the inversion method.
NASA Astrophysics Data System (ADS)
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-09-01
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 the 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 2-D and a random hydraulic conductivity field in 3-D. 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 multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-09-01
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 the 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 ~10^{1} to ~10^{2} 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.
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-09-01
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
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-09-01
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 the 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 ~10^{1} to ~10^{2} 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.
Optimised spectral merge of the background model in seismic inversion
NASA Astrophysics Data System (ADS)
White, Roy; Zabihi Naeini, Ehsan
2017-01-01
The inversion of seismic reflection data to absolute impedance generates low-frequency deviations around the true impedance if the frequency content of the background impedance model does not merge seamlessly into the spectrum of the inverted seismic data. We present a systematic method of selecting a background model that minimises the mismatch between the background model and the relative impedance obtained by inverting the seismic data at wells. At each well a set of well-log relative impedances is formed by passing the impedance log through a set of zero-phase high-pass filters. The corresponding background models are constructed by passing the impedance log through the complementary zero-phase low-pass filters and a set of seismic relative impedances is computed by inverting the seismic data using these background models. If the inverted seismic data is to merge perfectly with the background model, it should correspond at the well to the well-log relative impedance. This correspondence is the basis of a procedure for finding the optimum combination of background model and inverted seismic data. It is difficult to predict the low-frequency content of inverted seismic data. These low frequencies are affected by the uncertainties in (1) measuring the low-frequency response of the seismic wavelet and (2) knowing how inversion protects the signal-to-noise ratio at low frequencies. Uncertainty (1) becomes acute for broadband seismic data; the low-frequency phase is especially difficult to estimate. Moreover we show that a mismatch of low-frequency phase is a serious source of inversion artefacts. We also show that relative impedance can estimate the low-frequency phase where a well tie cannot. Consequently we include a low-frequency phase shift, applied to the seismic relative impedances, in the search for the best spectral merge. The background models are specified by a low-cut corner frequency and the phase shifts by a phase intercept at zero frequency. A scan of
Stochastic reduced order models for inverse problems under uncertainty.
Warner, James E; Aquino, Wilkins; Grigoriu, Mircea D
2015-03-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.
Stochastic reduced order models for inverse problems under uncertainty
Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.
2014-01-01
This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115
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.
On comparing helioseismic two-dimensional inversion methods
NASA Technical Reports Server (NTRS)
Schou, J.; Christensen-Dalsgaard, J.; Thompson, M. J.
1994-01-01
We consider inversion techniques for investigating the structure and dynamics of the solar interior as functions of radius and latitude. In particular, we look at the problem of inferring the radial and latitudinal dependence of the Sun's internal rotation, using a fully two-dimensional least-squares inversion algorithm. Concepts such as averaging kernels, measures of resolution, and trade-off curves, which have previously been used in the one-dimensional case, are generalized to facilitate a comparison of two-dimensional methods. We investigate the weighting given to different modes and discuss the implications of this for observational strategies. As an illustration we use a mode set whose properties are similar to those expected for data from the GONG network.
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.
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.
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.
Modeling temperature inversion in southeastern Yellow Sea during winter 2016
NASA Astrophysics Data System (ADS)
Pang, Ig-Chan; Moon, Jae-Hong; Lee, Joon-Ho; Hong, Ji-Seok; Pang, Sung-Jun
2017-05-01
A significant temperature inversion with temperature differences larger than 3°C was observed in the southeastern Yellow Sea (YS) during February 2016. By analyzing in situ hydrographic profiles and results from a regional ocean model for the YS, this study examines the spatiotemporal evolution of the temperature inversion and its connection with wind-induced currents in winter. Observations reveal that in winter, when the northwesterly wind prevails over the YS, the temperature inversion occurs largely at the frontal zone southwest of Korea where warm/saline water of a Kuroshio origin meets cold/fresh coastal water. Our model successfully captures the temperature inversion observed in the winter of 2016 and suggests a close relation between northwesterly wind bursts and the occurrence of the large inversion. In this respect, the strong northwesterly wind drove cold coastal water southward in the upper layer via Ekman transport, which pushed the water mass southward and increased the sea level slope in the frontal zone in southeastern YS. The intensified sea level slope propagated northward away from the frontal zone as a shelf wave, causing a northward upwind flow response along the YS trough in the lower layer, thereby resulting in the large temperature inversion. Diagnostic analysis of the momentum balance shows that the westward pressure gradient, which developed with shelf wave propagation along the YS trough, was balanced with the Coriolis force in accordance with the northward upwind current in and around the inversion area.
Ellipsoidal head model for fetal magnetoencephalography: forward and inverse solutions
NASA Astrophysics Data System (ADS)
Gutiérrez, David; Nehorai, Arye; Preissl, Hubert
2005-05-01
Fetal magnetoencephalography (fMEG) is a non-invasive technique where measurements of the magnetic field outside the maternal abdomen are used to infer the source location and signals of the fetus' neural activity. There are a number of aspects related to fMEG modelling that must be addressed, such as the conductor volume, fetal position and orientation, gestation period, etc. We propose a solution to the forward problem of fMEG based on an ellipsoidal head geometry. This model has the advantage of highlighting special characteristics of the field that are inherent to the anisotropy of the human head, such as the spread and orientation of the field in relationship with the localization and position of the fetal head. Our forward solution is presented in the form of a kernel matrix that facilitates the solution of the inverse problem through decoupling of the dipole localization parameters from the source signals. Then, we use this model and the maximum likelihood technique to solve the inverse problem assuming the availability of measurements from multiple trials. The applicability and performance of our methods are illustrated through numerical examples based on a real 151-channel SQUID fMEG measurement system (SARA). SARA is an MEG system especially designed for fetal assessment and is currently used for heart and brain studies. Finally, since our model requires knowledge of the best-fitting ellipsoid's centre location and semiaxes lengths, we propose a method for estimating these parameters through a least-squares fit on anatomical information obtained from three-dimensional ultrasound images.
Ellipsoidal head model for fetal magnetoencephalography: forward and inverse solutions.
Gutiérrez, David; Nehorai, Arye; Preissl, Hubert
2005-05-07
Fetal magnetoencephalography (fMEG) is a non-invasive technique where measurements of the magnetic field outside the maternal abdomen are used to infer the source location and signals of the fetus' neural activity. There are a number of aspects related to fMEG modelling that must be addressed, such as the conductor volume, fetal position and orientation, gestation period, etc. We propose a solution to the forward problem of fMEG based on an ellipsoidal head geometry. This model has the advantage of highlighting special characteristics of the field that are inherent to the anisotropy of the human head, such as the spread and orientation of the field in relationship with the localization and position of the fetal head. Our forward solution is presented in the form of a kernel matrix that facilitates the solution of the inverse problem through decoupling of the dipole localization parameters from the source signals. Then, we use this model and the maximum likelihood technique to solve the inverse problem assuming the availability of measurements from multiple trials. The applicability and performance of our methods are illustrated through numerical examples based on a real 151-channel SQUID fMEG measurement system (SARA). SARA is an MEG system especially designed for fetal assessment and is currently used for heart and brain studies. Finally, since our model requires knowledge of the best-fitting ellipsoid's centre location and semiaxes lengths, we propose a method for estimating these parameters through a least-squares fit on anatomical information obtained from three-dimensional ultrasound images.
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.; ...
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
NASA Astrophysics Data System (ADS)
Sun, Jiajia; Li, Yaoguo
2014-05-01
Minimum-structure inversions using L2-norm measures have been widely applied to geophysical exploration problems. However, the smeared-out models resulting from L2-norm inversions are not always consistent with the real or expected geological structures, especially in regions where distinct interfaces between different rock units exist. To obtain sharp boundaries and blocky features, non-L2 inversions have been used successfully in geophysical imaging problems. In reality, however, both smooth and blocky features can be present in the subsurface physical properties or interfaces to be recovered. To deal with this situation, we develop a new method for adaptively recovering both smooth and blocky features in the constructed model from geophysical inversions. This method first detects different regions of the smoothness or blockiness in a model based on a sequence of inversions and then adaptively applies appropriate Lp model norm with different p values at different locations to complete the final inversion. We present two synthetic examples from basement inversion using gravity data and crosswell seismic traveltime tomography before demonstrating our method on a field data example at the U.S. Geological Survey Fractured Rock Research Site in central New Hampshire.
Computer Model Inversion and Uncertainty Quantification in the Geosciences
NASA Astrophysics Data System (ADS)
White, Jeremy T.
The subject of this dissertation is use of computer models as data analysis tools in several different geoscience settings, including integrated surface water/groundwater modeling, tephra fallout modeling, geophysical inversion, and hydrothermal groundwater modeling. The dissertation is organized into three chapters, which correspond to three individual publication manuscripts. In the first chapter, a linear framework is developed to identify and estimate the potential predictive consequences of using a simple computer model as a data analysis tool. The framework is applied to a complex integrated surface-water/groundwater numerical model with thousands of parameters. Several types of predictions are evaluated, including particle travel time and surface-water/groundwater exchange volume. The analysis suggests that model simplifications have the potential to corrupt many types of predictions. The implementation of the inversion, including how the objective function is formulated, what minimum of the objective function value is acceptable, and how expert knowledge is enforced on parameters, can greatly influence the manifestation of model simplification. Depending on the prediction, failure to specifically address each of these important issues during inversion is shown to degrade the reliability of some predictions. In some instances, inversion is shown to increase, rather than decrease, the uncertainty of a prediction, which defeats the purpose of using a model as a data analysis tool. In the second chapter, an efficient inversion and uncertainty quantification approach is applied to a computer model of volcanic tephra transport and deposition. The computer model simulates many physical processes related to tephra transport and fallout. The utility of the approach is demonstrated for two eruption events. In both cases, the importance of uncertainty quantification is highlighted by exposing the variability in the conditioning provided by the observations used for
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.
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.
NASA Astrophysics Data System (ADS)
Sahin, O. K.; Asci, M.
2014-12-01
At this study, determination of theoretical parameters for inversion process of Trabzon-Sürmene-Kutlular ore bed anomalies was examined. Making a decision of which model equation can be used for inversion is the most important step for the beginning. It is thought that will give a chance to get more accurate results. So, sections were evaluated with sphere-cylinder nomogram. After that, same sections were analyzed with cylinder-dike nomogram to determine the theoretical parameters for inversion process for every single model equations. After comparison of results, we saw that only one of them was more close to parameters of nomogram evaluations. But, other inversion result parameters were different from their nomogram parameters.
Inverse Kinematic Analysis of Human Hand Thumb Model
NASA Astrophysics Data System (ADS)
Toth-Tascau, Mirela; Pater, Flavius; Stoia, Dan Ioan; Menyhardt, Karoly; Rosu, Serban; Rusu, Lucian; Vigaru, Cosmina
2011-09-01
This paper deals with a kinematic model of the thumb of the human hand. The proposed model has 3 degrees of freedom being able to model the movements of the thumb tip with respect to the wrist joint centre. The kinematic equations are derived based on Denavit-Hartenberg Convention and solved in both direct and inverse way. Inverse kinematic analysis of human hand thumb model reveals multiple and connected solutions which are characteristic to nonlinear systems when the number of equations is greater than number of unknowns and correspond to natural movements of the finger.
Inverse modeling with RZWQM2 to predict water quality
USDA-ARS?s Scientific Manuscript database
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.
A Test of Maxwell's Z Model Using Inverse Modeling
NASA Technical Reports Server (NTRS)
Anderson, J. L. B.; Schultz, P. H.; Heineck, T.
2003-01-01
In modeling impact craters a small region of energy and momentum deposition, commonly called a "point source", is often assumed. This assumption implies that an impact is the same as an explosion at some depth below the surface. Maxwell's Z Model, an empirical point-source model derived from explosion cratering, has previously been compared with numerical impact craters with vertical incidence angles, leading to two main inferences. First, the flowfield center of the Z Model must be placed below the target surface in order to replicate numerical impact craters. Second, for vertical impacts, the flow-field center cannot be stationary if the value of Z is held constant; rather, the flow-field center migrates downward as the crater grows. The work presented here evaluates the utility of the Z Model for reproducing both vertical and oblique experimental impact data obtained at the NASA Ames Vertical Gun Range (AVGR). Specifically, ejection angle data obtained through Three-Dimensional Particle Image Velocimetry (3D PIV) are used to constrain the parameters of Maxwell's Z Model, including the value of Z and the depth and position of the flow-field center via inverse modeling.
A Test of Maxwell's Z Model Using Inverse Modeling
NASA Technical Reports Server (NTRS)
Anderson, J. L. B.; Schultz, P. H.; Heineck, T.
2003-01-01
In modeling impact craters a small region of energy and momentum deposition, commonly called a "point source", is often assumed. This assumption implies that an impact is the same as an explosion at some depth below the surface. Maxwell's Z Model, an empirical point-source model derived from explosion cratering, has previously been compared with numerical impact craters with vertical incidence angles, leading to two main inferences. First, the flowfield center of the Z Model must be placed below the target surface in order to replicate numerical impact craters. Second, for vertical impacts, the flow-field center cannot be stationary if the value of Z is held constant; rather, the flow-field center migrates downward as the crater grows. The work presented here evaluates the utility of the Z Model for reproducing both vertical and oblique experimental impact data obtained at the NASA Ames Vertical Gun Range (AVGR). Specifically, ejection angle data obtained through Three-Dimensional Particle Image Velocimetry (3D PIV) are used to constrain the parameters of Maxwell's Z Model, including the value of Z and the depth and position of the flow-field center via inverse modeling.
Effects of experimental and modeling errors on electrocardiographic inverse formulations.
Cheng, Leo K; Bodley, John M; Pullan, Andrew J
2003-01-01
The inverse problem of electrocardiology aims to reconstruct the electrical activity occurring within the heart using information obtained noninvasively on the body surface. Potentials obtained on the torso surface can be used as input for the inverse problem and an electrical image of the heart obtained. There are a number of different inverse algorithms currently used to produce electrical images of the heart. The relative performances of these inverse algorithms at this stage is largely unknown. Although there have been many simulation studies investigating the accuracy of each of these algorithms, to date, there has been no comprehensive study which compares a wide variety of inverse methods. By performing a detailed simulation study, we compare the performances of epicardial potential [Tikhonov, Truncated singular value decomposition (TSVD), and Greensite] and myocardial activation-based (critical point) inverse simulations along with different methods of choosing the appropriate level of regularization (optimal, L-curve, composite residual and smoothing operator, zero-crossing) to apply to each of these inverse methods. We also examine the effects of a variety of signal error, material property error, geometric error and a combination of these errors on each of the electrocardiographic inverse algorithms. Results from the simulation study show that the activation-based method is able to produce solutions which are more accurate and stable than potential-based methods especially in the presence of correlated errors such as geometric uncertainty. In general, the Greensite-Tikhonov method produced the most realistic potential-based solutions while the zero-crossing and L-curve were the preferred method for determining the regularization parameter. The presence of signal or material property error has little effect on the inverse solutions when compared with the large errors which resulted from the presence of any geometric error. In the presence of combined
Comparison of methods for inverse design of radiant enclosures.
Franca, Francis; Larsen, Marvin Elwood; Howell, John R.; Daun, Kyle; Leduc, Guillaume
2005-03-01
A particular inverse design problem is proposed as a benchmark for comparison of five solution techniques used in design of enclosures with radiating sources. The enclosure is three-dimensional and includes some surfaces that are diffuse and others that are specular diffuse. Two aspect ratios are treated. The problem is completely described, and solutions are presented as obtained by the Tikhonov method, truncated singular value decomposition, conjugate gradient regularization, quasi-Newton minimization, and simulated annealing. All of the solutions use a common set of exchange factors computed by Monte Carlo, and smoothed by a constrained maximum likelihood estimation technique that imposes conservation, reciprocity, and non-negativity. Solutions obtained by the various methods are presented and compared, and the relative advantages and disadvantages of these methods are summarized.
Inversion method for the restoration of chopped and nodded images
NASA Astrophysics Data System (ADS)
Bertero, Mario; Boccacci, Patrizia; Robberto, Massimo
1998-08-01
We present an iterative inversion method for the restoration of chopped and nodded images, typical of thermal IR astronomy with ground based telescopes. The method computes the smallest solution subjected to the constraint of positivity. The restored images exhibit artifacts, related to the chopping amplitude, which can be predicted by looking at the mathematical structure of the problem. However these effects can be strongly reduced by combing a few images taken with different chopping/nodding throws of small amplitude. Preliminary results on synthetic data are very promising. Restored images show high cosmetic quality and a typical restoration error smaller than 10 percent. We also present restorations of real images taken at the UKIRT telescope with the MAX camera. The availability of an image restoration method for mid-IR images would have a major impact on the telescope design and observing strategy at these wavelengths.
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.
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
UCODE, a computer code for universal inverse modeling
NASA Astrophysics Data System (ADS)
Poeter, Eileen P.; Hill, Mary C.
1999-05-01
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)
Rezaie, Mohammad; Moradzadeh, Ali; Kalate, Ali Nejati; Aghajani, Hamid
2017-01-01
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.
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
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.
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?'
Inferring stress from faulting: From early concepts to inverse methods
NASA Astrophysics Data System (ADS)
Célérier, Bernard; Etchecopar, Arnaud; Bergerat, Françoise; Vergely, Pierre; Arthaud, François; Laurent, Philippe
2012-12-01
We review the evolution of concepts on and methods of estimating the state of stress from fault movements. Theories of failure in isotropic materials suggested a simple geometrical construction of optimal principal stress directions from a fault plane and its associated slip. These optimal directions align shear stress and slip directions and maximize the difference between shear stress and frictional resistance on the fault plane. Optimal stress directions for calcite twinning are obtained by a similar construction, with the difference that they maximize shear stress. Force representation of seismic sources independently introduced pressure, P, and tension, T, axes at positions that also maximize shear stress on both nodal planes. Frictional slip theory and the constraint that slip and shear stress directions be parallel allowed to address reactivation of pre-existing faults. This suggested that stress could also be inverted from reactivated fault and slip data or earthquake focal mechanisms. Early methods relied on geometrical constructions as a substitute for calculations, whereas later methods relied on software as these calculations became tractable with the help of computers. Similar methods were developed for the inversion of stress from crystal twin gliding with non-optimal geometry, with a different criterion that relies on a threshold of the component of shear stress along the gliding line. Even though these methods seek a common stress tensor compatible with fault and slip data, their main use is to separate polyphase data into homogeneous subsets and help deciphering complex tectonic histories. Fault and slip data can also be analyzed to constrain the strain rather than the stress tensor. In most cases this involves a summation and yields an average strain for the considered rock volume. Stress inversion thus appears better suited for differentiating heterogeneous data whereas strain analysis appears better suited for homogenizing them.
Inverse modeling for heat conduction problem in human abdominal phantom.
Huang, Ming; Chen, Wenxi
2011-01-01
Noninvasive methods for deep body temperature measurement are based on the principle of heat equilibrium between the thermal sensor and the target location theoretically. However, the measurement position is not able to be definitely determined. In this study, a 2-dimensional mathematical model was built based upon some assumptions for the physiological condition of the human abdomen phantom. We evaluated the feasibility in estimating the internal organs temperature distribution from the readings of the temperature sensors arranged on the skin surface. It is a typical inverse heat conduction problem (IHCP), and is usually mathematically ill-posed. In this study, by integrating some physical and physiological a-priori information, we invoked the quasi-linear (QL) method to reconstruct the internal temperature distribution. The solutions of this method were improved by increasing the accuracy of the sensors and adjusting their arrangement on the outer surface, and eventually reached the state of converging at the best state accurately. This study suggests that QL method is able to reconstruct the internal temperature distribution in this phantom and might be worthy of a further study in an anatomical based model.
Gravity Inversion with Geological Modeling Constraint and Its Application in the Okinawa Trough
NASA Astrophysics Data System (ADS)
Zhang, S.
2014-12-01
The satellite altimetry gravity data is used to recover the 3D distribution of oceanic lithosphere density in the Okinawa Trough and its neighbor region. It's difficult to use only gravity data to invert complex geological structure and density distribution by 3D gravity Inversion method. In order to improve the vertical resolution of the density inversion result, 3D geological modeling method is used to build structural model for the inversion, prior constraint conditions can be applied to solve the non-unique problem. In the Okinawa Trough, it is proved by earthquake data that the Philippine plate dives beneath the Okinawa Trough, which result in the upwelling of mantel material and decrease of the crust thickness. The Benioff zone clearly shows the plate's subduction parameter, such as direction, dip, transformation. Therefore, a structural subduction model is created by geological modeling method and works as the initial model and as constraint condition in gravity inversion. The 3D gravity inversion result and seismology CMT data are both used to explain the oceanic lithosphere structure in the Okinawa Trough. The inversion result illustrates high density anomaly under the Okinawa Trough. Affected by small scale mantle convections, the continental lithosphere is separated, which result in the spreading of back-arc basin and the formation of the Okinawa Trough.
NASA Astrophysics Data System (ADS)
Henderson, Laura S.; Subbarao, Kamesh
2016-12-01
This work presents a case wherein the selection of models when producing synthetic light curves affects the estimation of the size of unresolved space objects. Through this case, "inverse crime" (using the same model for the generation of synthetic data and data inversion), is illustrated. This is done by using two models to produce the synthetic light curve and later invert it. It is shown here that the choice of model indeed affects the estimation of the shape/size parameters. When a higher fidelity model (henceforth the one that results in the smallest error residuals after the crime is committed) is used to both create, and invert the light curve model the estimates of the shape/size parameters are significantly better than those obtained when a lower fidelity model (in comparison) is implemented for the estimation. It is therefore of utmost importance to consider the choice of models when producing synthetic data, which later will be inverted, as the results might be misleadingly optimistic.
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.
A simple GPR full-waveform inversion method for investigating fractured rock hydrology
NASA Astrophysics Data System (ADS)
Sassen, D. S.; Everett, M. E.
2009-05-01
The 3-D geometry of fractures, along with the type and distribution of the fill material, substantially impacts bulk hydraulic properties. Coring is largely inadequate for a complete hydrologic characterization of fractured rock, and minimally invasive methods are desirable. A method is described for full-waveform inversion of GPR transmission data to quantitatively determine the fracture aperture and electromagnetic properties of the fill, based on a thin-layer model. This model is based on a plane wave assumption and assumes idealized geometry of the fracture, but it allows for quick exploration of the error space in inversion. Analysis of this method on synthetic data indicates that the properties of fractures with an aperture of greater than 5% of the dominant wavelength can be determined, when prior knowledge of the fracture orientation and electromagnetic properties of the background exist. This inversion method is applied to a study of the interaction of invasive brush vegetation with the shallow fractured rock hydrology of the Edward Aquifer of central Texas, USA. The transmission data are acquired with the transmitting antenna placed on the wall of a trench and the receiver moved out along the surface, and the background properties and fracture orientations are constrained by 3-D polarimetric GPR reflection data. The inversion results from field data show consistency with the location of fractures from reflection data.
Temporal rainfall estimation using input data reduction and model inversion
NASA Astrophysics Data System (ADS)
Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.
2016-12-01
Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a
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.
NASA Astrophysics Data System (ADS)
Lohman, R. B.; Simons, M.
2004-12-01
We examine inversions of geodetic data for fault slip and discuss how inferred results are affected by choices of regularization. The final goal of any slip inversion is to enhance our understanding of the dynamics governing fault zone processes through kinematic descriptions of fault zone behavior at various temporal and spatial scales. Important kinematic observations include ascertaining whether fault slip is correlated with topographic and gravitational anomalies, whether coseismic and postseismic slip occur on complementary or overlapping regions of the fault plane, and how aftershock distributions compare with areas of coseismic and postseismic slip. Fault slip inversions are generally poorly-determined inverse problems requiring some sort of regularization. Attempts to place inversion results in the context of understanding fault zone processes should be accompanied by careful treatment of how the applied regularization affects characteristics of the inferred slip model. Most regularization techniques involve defining a metric that quantifies the solution "simplicity". A frequently employed method defines a "simple" slip distribution as one that is spatially smooth, balancing the fit to the data vs. the spatial complexity of the slip distribution. One problem related to the use of smoothing constraints is the "smearing" of fault slip into poorly-resolved areas on the fault plane. In addition, even if the data is fit well by a point source, the fact that a point source is spatially "rough" will force the inversion to choose a smoother model with slip over a broader area. Therefore, when we interpret the area of inferred slip we must ask whether the slipping area is truly constrained by the data, or whether it could be fit equally well by a more spatially compact source with larger amplitudes of slip. We introduce an alternate regularization technique for fault slip inversions, where we seek an end member model that is the smallest region of fault slip that
NASA Astrophysics Data System (ADS)
Palmer, Paul I.; Barnett, J. J.; Eyre, J. R.; Healy, S. B.
2000-07-01
An optimal estimation inverse method is presented which can be used to retrieve simultaneously vertical profiles of temperature and specific humidity, in addition to surface pressure, from satellite-to-satellite radio occultation observations of the Earth's atmosphere. The method is a nonlinear, maximum a posteriori technique which can accommodate most aspects of the real radio occultation problem and is found to be stable and to converge rapidly in most cases. The optimal estimation inverse method has two distinct advantages over the analytic inverse method in that it accounts for some of the effects of horizontal gradients and is able to retrieve optimally temperature and humidity simultaneously from the observations. It is also able to account for observation noise and other sources of error. Combined, these advantages ensure a realistic retrieval of atmospheric quantities. A complete error analysis emerges naturally from the optimal estimation theory, allowing a full characterization of the solution. Using this analysis, a quality control scheme is implemented which allows anomalous retrieval conditions to be recognized and removed, thus preventing gross retrieval errors. The inverse method presented in this paper has been implemented for bending angle measurements derived from GPS/MET radio occultation observations of the Earth. Preliminary results from simulated data suggest that these observations have the potential to improve numerical weather prediction model analyses significantly throughout their vertical range.
Seismic imaging and inversion based on spectral-element and adjoint methods
NASA Astrophysics Data System (ADS)
Luo, Yang
One of the most important topics in seismology is to construct detailed tomographic images beneath the surface, which can be interpreted geologically and geochemically to understand geodynamic processes happening in the interior of the Earth. Classically, these images are usually produced based upon linearized traveltime anomalies involving several particular seismic phases, whereas nonlinear inversion fitting synthetic seismograms and recorded signals based upon the adjoint method becomes more and more favorable. The adjoint tomography, also referred to as waveform inversion, is advantageous over classical techniques in several aspects, such as better resolution, while it also has several drawbacks, e.g., slow convergence and lack of quantitative resolution analysis. In this dissertation, we focus on solving these remaining issues in adjoint tomography, from a theoretical perspective and based upon synthetic examples. To make the thesis complete by itself and easy to follow, we start from development of the spectral-element method, a wave equation solver that enables access to accurate synthetic seismograms for an arbitrary Earth model, and the adjoint method, which provides Frechet derivatives, also named as sensitivity kernels, of a given misfit function. Then, the sensitivity kernels for waveform misfit functions are illustrated, using examples from exploration seismology, in other words, for migration purposes. Next, we show step by step how these gradient derivatives may be utilized in minimizing the misfit function, which leads to iterative refinements on the Earth model. Strategies needed to speed up the inversion, ensure convergence and improve resolution, e.g., preconditioning, quasi-Newton methods, multi-scale measurements and combination of traveltime and waveform misfit functions, are discussed. Through comparisons between the adjoint tomography and classical tomography, we address the resolution issue by calculating the point-spread function, the
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.
A self-constrained inversion of magnetic data based on correlation method
NASA Astrophysics Data System (ADS)
Sun, Shida; Chen, Chao
2016-12-01
Geologically-constrained inversion is a powerful method for producing geologically reasonable solutions in geophysical exploration problems. But in many cases, except the observed geophysical data to be inverted, the geological information is insufficiently available for improving reliability of recovered models. To deal with these situations, self-constraints extracted from preprocessing observed data have been applied to constrain the inversion. In this paper, we present a self-constrained inversion method based on correlation method. In our approach the correlation results are first obtained by calculating the cross-correlation between theoretical data and horizontal gradients of the observed data. Subsequently, we propose two specific strategies to extract the spatial variation from the correlation results and then translate them into spatial weighting functions. Incorporating the spatial weighting functions into the model objective function, we obtain self-constrained solutions with higher reliability. We presented two synthetic and one field magnetic data example to test the validity. All results demonstrate that the solution from our self-constrained inversion can delineate the geological bodies with clearer boundaries and much more concentrated physical property.
Inversion of hierarchical Bayesian models using Gaussian processes.
Lomakina, Ekaterina I; Paliwal, Saee; Diaconescu, Andreea O; Brodersen, Kay H; Aponte, Eduardo A; Buhmann, Joachim M; Stephan, Klaas E
2015-09-01
Over the past decade, computational approaches to neuroimaging have increasingly made use of hierarchical Bayesian models (HBMs), either for inferring on physiological mechanisms underlying fMRI data (e.g., dynamic causal modelling, DCM) or for deriving computational trajectories (from behavioural data) which serve as regressors in general linear models. However, an unresolved problem is that standard methods for inverting the hierarchical Bayesian model are either very slow, e.g. Markov Chain Monte Carlo Methods (MCMC), or are vulnerable to local minima in non-convex optimisation problems, such as variational Bayes (VB). This article considers Gaussian process optimisation (GPO) as an alternative approach for global optimisation of sufficiently smooth and efficiently evaluable objective functions. GPO avoids being trapped in local extrema and can be computationally much more efficient than MCMC. Here, we examine the benefits of GPO for inverting HBMs commonly used in neuroimaging, including DCM for fMRI and the Hierarchical Gaussian Filter (HGF). Importantly, to achieve computational efficiency despite high-dimensional optimisation problems, we introduce a novel combination of GPO and local gradient-based search methods. The utility of this GPO implementation for DCM and HGF is evaluated against MCMC and VB, using both synthetic data from simulations and empirical data. Our results demonstrate that GPO provides parameter estimates with equivalent or better accuracy than the other techniques, but at a fraction of the computational cost required for MCMC. We anticipate that GPO will prove useful for robust and efficient inversion of high-dimensional and nonlinear models of neuroimaging data. Copyright © 2015. Published by Elsevier Inc.
Research on Inversion Models for Forest Height Estimation Using Polarimetric SAR Interferometry
NASA Astrophysics Data System (ADS)
Zhang, L.; Duan, B.; Zou, B.
2017-09-01
The forest height is an important forest resource information parameter and usually used in biomass estimation. Forest height extraction with PolInSAR is a hot research field of imaging SAR remote sensing. SAR interferometry is a well-established SAR technique to estimate the vertical location of the effective scattering center in each resolution cell through the phase difference in images acquired from spatially separated antennas. The manipulation of PolInSAR has applications ranging from climate monitoring to disaster detection especially when used in forest area, is of particular interest because it is quite sensitive to the location and vertical distribution of vegetation structure components. However, some of the existing methods can't estimate forest height accurately. Here we introduce several available inversion models and compare the precision of some classical inversion approaches using simulated data. By comparing the advantages and disadvantages of these inversion methods, researchers can find better solutions conveniently based on these inversion methods.
Inverse methods for stellarator error-fields and emission
NASA Astrophysics Data System (ADS)
Hammond, K. C.; Anichowski, A.; Brenner, P. W.; Diaz-Pacheco, R.; Volpe, F. A.; Wei, Y.; Kornbluth, Y.; Pedersen, T. S.; Raftopoulos, S.; Traverso, P.
2016-10-01
Work at the CNT stellarator at Columbia University has resulted in the development of two inverse diagnosis techniques that infer difficult-to-measure properties from simpler measurements. First, CNT's error-field is determined using a Newton-Raphson algorithm to infer coil misalignments based on measurements of flux surfaces. This is obtained by reconciling the computed flux surfaces (a function of coil misalignments) with the measured flux surfaces. Second, the plasma emissivity profile is determined based on a single CCD camera image using an onion-peeling method. This approach posits a system of linear equations relating pixel brightness to emission from a discrete set of plasma layers bounded by flux surfaces. Results for both of these techniques as applied to CNT will be shown, and their applicability to large modular coil stellarators will be discussed.
Multiresolution subspace-based optimization method for inverse scattering problems.
Oliveri, Giacomo; Zhong, Yu; Chen, Xudong; Massa, Andrea
2011-10-01
This paper investigates an approach to inverse scattering problems based on the integration of the subspace-based optimization method (SOM) within a multifocusing scheme in the framework of the contrast source formulation. The scattering equations are solved by a nested three-step procedure composed of (a) an outer multiresolution loop dealing with the identification of the regions of interest within the investigation domain through an iterative information-acquisition process, (b) a spectrum analysis step devoted to the reconstruction of the deterministic components of the contrast sources, and (c) an inner optimization loop aimed at retrieving the ambiguous components of the contrast sources through a conjugate gradient minimization of a suitable objective function. A set of representative reconstruction results is discussed to provide numerical evidence of the effectiveness of the proposed algorithmic approach as well as to assess the features and potentialities of the multifocusing integration in comparison with the state-of-the-art SOM implementation.
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.
2012-08-01
AFRL-RX-WP-TP-2012-0397 INVERSE PROBLEM FOR ELECTROMAGNETIC PROPAGATION IN A DIELECTRIC MEDIUM USING MARKOV CHAIN MONTE CARLO METHOD ...SUBTITLE INVERSE PROBLEM FOR ELECTROMAGNETIC PROPAGATION IN A DIELECTRIC MEDIUM USING MARKOV CHAIN MONTE CARLO METHOD (PREPRINT) 5a. CONTRACT...a stochastic inverse methodology arising in electromagnetic imaging. Nondestructive testing using guided microwaves covers a wide range of
A matrix-inversion method for gamma-source mapping from gamma-count data
Adsley, Ian; Burgess, Claire; Bull, Richard K
2013-07-01
In a previous paper it was proposed that a simple matrix inversion method could be used to extract source distributions from gamma-count maps, using simple models to calculate the response matrix. The method was tested using numerically generated count maps. In the present work a 100 kBq Co{sup 60} source has been placed on a gridded surface and the count rate measured using a NaI scintillation detector. The resulting map of gamma counts was used as input to the matrix inversion procedure and the source position recovered. A multi-source array was simulated by superposition of several single-source count maps and the source distribution was again recovered using matrix inversion. The measurements were performed for several detector heights. The effects of uncertainties in source-detector distances on the matrix inversion method are also examined. The results from this work give confidence in the application of the method to practical applications, such as the segregation of highly active objects amongst fuel-element debris. (authors)
Inverse Methods. Interdisciplinary Elements of Methodology, Computation, and Applications
NASA Astrophysics Data System (ADS)
Jacobsen, Bo Holm; Mosegaard, Klaus; Sibani, Paolo
Over the last few decades inversion concepts have become an integral part of experimental data interpretation in several branches of science. In numerous cases similar inversion-like techniques were developed independently in separate disciplines, sometimes based on different lines of reasoning, but not always to the same level of sophistication. This book is based on the Interdisciplinary Inversion Conference held at the University of Aarhus, Denmark. For scientists and graduate students in geophysics, astronomy, oceanography, petroleum geology, and geodesy, the book offers a wide variety of examples and theoretical background in the field of inversion techniques.
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.
Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method
NASA Astrophysics Data System (ADS)
Zhang, Ren-Hui; Guo, Rong; Yang, Jun-Hu; Luo, Jia-Qi
2017-07-01
To improve the accuracy and reduce the calculation cost for the inverse problem of centrifugal pump impeller, the new inverse method based on proper orthogonal decomposition (POD) is proposed. The pump blade shape is parameterized by quartic Bezier curve, and the initial snapshots is generated by introducing the perturbation of the blade shape control parameters. The internal flow field and its hydraulic performance is predicted by CFD method. The snapshots vector includes the blade shape parameter and the distribution of blade load. The POD basis for the snapshots set are deduced by proper orthogonal decomposition. The sample vector set is expressed in terms of the linear combination of the orthogonal basis. The objective blade shape corresponding to the objective distribution of blade load is obtained by least square fit. The Iterative correction algorithm for the centrifugal pump blade inverse method based on POD is proposed. The objective blade load distributions are corrected according to the difference of the CFD result and the POD result. The two dimensional and three dimensional blade calculation cases show that the proposed centrifugal pump blade inverse method based on POD have good convergence and high accuracy, and the calculation cost is greatly reduced. After two iterations, the deviation of the blade load and the pump hydraulic performance are limited within 4.0% and 6.0% individually for most of the flow rate range. This paper provides a promising inverse method for centrifugal pump impeller, which will benefit the hydraulic optimization of centrifugal pump.
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.
Study of TEC fluctuation via stochastic models and Bayesian inversion
NASA Astrophysics Data System (ADS)
Bires, A.; Roininen, L.; Damtie, B.; Nigussie, M.; Vanhamäki, H.
2016-11-01
We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.
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.
Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model
NASA Astrophysics Data System (ADS)
Mejer Hansen, Thomas
2017-04-01
Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.
Efficient inversion and uncertainty quantification of a tephra fallout model
NASA Astrophysics Data System (ADS)
White, J. T.; Connor, C. B.; Connor, L.; Hasenaka, T.
2017-01-01
An efficient and effective inversion and uncertainty quantification approach is proposed for estimating eruption parameters given a data set collected from a tephra deposit. The approach is model independent and here is applied using Tephra2, a code that simulates advective and dispersive tephra transport and deposition. The Levenburg-Marquardt algorithm is combined with formal Tikhonov and subspace regularization to invert eruption parameters; a linear equation for conditional uncertainty propagation is used to estimate posterior parameter uncertainty. Both the inversion and uncertainty analysis support simultaneous analysis of the full eruption and wind field parameterization. The combined inversion/uncertainty quantification approach is applied to the 1992 eruption of Cerro Negro and the 2011 Kirishima-Shinmoedake eruption. While eruption mass uncertainty is reduced by inversion against tephra isomass data, considerable uncertainty remains for many eruption and wind field parameters, such as plume height. Supplementing the inversion data set with tephra granulometry data is shown to further reduce the uncertainty of most eruption and wind field parameters. The eruption mass of the 2011 Kirishima-Shinmoedake eruption is 0.82 × 1010 kg to 2.6 × 1010 kg, with 95% confidence; total eruption mass for the 1992 Cerro Negro eruption is 4.2 × 1010 kg to 7.3 × 1010 kg, with 95% confidence. These results indicate that eruption classification and characterization of eruption parameters can be significantly improved through this uncertainty quantification approach.
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.
Numerical methods for problems involving the Drazin inverse
NASA Technical Reports Server (NTRS)
Meyer, C. D., Jr.
1979-01-01
The objective was to try to develop a useful numerical algorithm for the Drazin inverse and to analyze the numerical aspects of the applications of the Drazin inverse relating to the study of homogeneous Markov chains and systems of linear differential equations with singular coefficient matrices. It is felt that all objectives were accomplished with a measurable degree of success.
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).
The Wing-Body Aeroelastic Analyses Using the Inverse Design Method
NASA Astrophysics Data System (ADS)
Lee, Seung Jun; Im, Dong-Kyun; Lee, In; Kwon, Jang-Hyuk
Flutter phenomenon is one of the most dangerous problems in aeroelasticity. When it occurs, the aircraft structure can fail in a few second. In recent aeroelastic research, computational fluid dynamics (CFD) techniques become important means to predict the aeroelastic unstable responses accurately. Among various flow equations like Navier-Stokes, Euler, full potential and so forth, the transonic small disturbance (TSD) theory is widely recognized as one of the most efficient theories. However, the small disturbance assumption limits the applicable range of the TSD theory to the thin wings. For a missile which usually has small aspect ratio wings, the influence of body aerodynamics on the wing surface may be significant. Thus, the flutter stability including the body effect should be verified. In this research an inverse design method is used to complement the aerodynamic deficiency derived from the fuselage. MGM (modified Garabedian-McFadden) inverse design method is used to optimize the aerodynamic field of a full aircraft model. Furthermore, the present TSD aeroelastic analyses do not require the grid regeneration process. The MGM inverse design method converges faster than other conventional aerodynamic theories. Consequently, the inverse designed aeroelastic analyses show that the flutter stability has been lowered by the body effect.
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 modelling of NOx emissions over eastern China: uncertainties due to chemical non-linearity
NASA Astrophysics Data System (ADS)
Gu, Dasa; Wang, Yuhang; Yin, Ran; Zhang, Yuzhong; Smeltzer, Charles
2016-10-01
Satellite observations of nitrogen dioxide (NO2) have often been used to derive nitrogen oxides (NOx = NO + NO2) emissions. A widely used inversion method was developed by Martin et al. (2003). Refinements of this method were subsequently developed. In the context of this inversion method, we show that the local derivative (of a first-order Taylor expansion) is more appropriate than the "bulk ratio" (ratio of emission to column) used in the original formulation for polluted regions. Using the bulk ratio can lead to biases in regions of high NOx emissions such as eastern China due to chemical non-linearity. Inverse modelling using the local derivative method is applied to both GOME-2 and OMI satellite measurements to estimate anthropogenic NOx emissions over eastern China. Compared with the traditional method using bulk ratio, the local derivative method produces more consistent NOx emission estimates between the inversion results using GOME-2 and OMI measurements. The results also show significant changes in the spatial distribution of NOx emissions, especially over high emission regions of eastern China. We further discuss a potential pitfall of using the difference of two satellite measurements to derive NOx emissions. Our analysis suggests that chemical non-linearity needs to be accounted for and that a careful bias analysis is required in order to use the satellite differential method in inverse modelling of NOx emissions.
3D Magnetization Vector Inversion of Magnetic Data: Improving and Comparing Methods
NASA Astrophysics Data System (ADS)
Liu, Shuang; Hu, Xiangyun; Zhang, Henglei; Geng, Meixia; Zuo, Boxin
2017-09-01
Magnetization vector inversion is an useful approach to invert for magnetic anomaly in the presence of significant remanent magnetization and self-demagnetization. However, magnetizations are usually obtained in many different directions under the influences of geophysical non-uniqueness. We propose an iteration algorithm of magnetization vector inversion (M-IDI) that one couple of magnetization direction is iteratively computed after the magnetization intensity is recovered from the magnitude magnetic anomaly. And we compare it with previous methods of (1) three orthogonal components inversion of total magnetization vector at Cartesian framework (MMM), (2) intensity, inclination and declination inversion at spherical framework (MID), (3) directly recovering the magnetization inclination and declination (M-IDCG) and (4) estimating the magnetization direction using correlation method (M-IDC) at the sequential inversion frameworks. The synthetic examples indicate that MMM returns multiply magnetization directions and MID results are strongly dependent on initial model and parameter weights. M-IDI computes faster than M-IDC and achieves a constant magnetization direction compared with M-IDCG. Additional priori information constraints can improve the results of MMM, MID and M-IDCG. Obtaining one magnetization direction, M-IDC and M-IDI are suitable for single and isolated anomaly. Finally, M-IDI and M-IDC are used to invert and interpret the magnetic anomaly of the Galinge iron-ore deposit (NW China) and the results are verified by information from drillholes and physical properties measurements of ore and rock samples. Magnetization vector inversion provides a comprehensive way to evaluate and investigate the remanent magnetization and self-demagnetization.
NASA Astrophysics Data System (ADS)
Zhao, Y.; Rathore, S.; Chen, J.; Hoversten, G. M.; Luo, J.
2016-12-01
Inverse problems in hydrogeological applications often require estimation of a large number of unknown parameters ranging from hundreds to millions. Such problems are computationally prohibitive. To efficiently deal with such high-dimensional problems, model reduction techniques are usually introduced to improve computational performance of traditional inversion method. In this study, we explored the feasibility and effectiveness of Principal Component Analysis (PCA) and Markov Chain Monte Carlo (MCMC) for model reduction using error-involved synthetic data. A 1-D groundwater pumping test is implemented on randomly generated hydraulic conductivity field, then computed head distribution adding random errors is treated as available data for inversing the original hydraulic conductivity field. We run full-dimensional inverse method a few times to generate training set for constructing experienced covariance matrix. Principal Component Analysis is implemented on the experienced covariance matrix to reduce dimensionality of the inverse problem. MCMC is implemented to draw samples from the reduced variable space for providing best estimate and quantifying uncertainty. The synthetic data study demonstrates that PCA-MCMC method can successfully provide reasonable estimate of hydraulic conductivity using biased data and effectively reduce computational time and storage usage. It is also noticed that a tradeoff exists between model simplicity and uncertainty quantification - a highly-reduced model causes narrower confidential intervals, sometimes implying insufficient uncertainty quantification. Thus the extent of model reduction should be wisely manipulated in light of specific problem requirements.
ENSO Diversity in Climate Models: A Linear Inverse Modeling Approach
NASA Astrophysics Data System (ADS)
Capotondi, A.; Sardeshmukh, P. D.
2013-12-01
As emphasized in a large recent literature, ENSO events differ in the longitudinal location of the largest sea surface temperature (SST) anomalies along the equator. These differences in peak longitude are associated with different atmospheric teleconnections and global-scale impacts, whose large societal relevance makes it very important to understand the origin and predictability of the various ENSO 'flavors'. In this study we use Linear Inverse Modeling (LIM) to examine ENSO diversity in a 1000-year pre-industrial control integration of the National Center for Atmospheric Research (NCAR) Community Climate System Model version 4 (CCSM4). We choose a pre-industrial control integration for its multi-century duration, and also to examine ENSO diversity in the context of natural variability. The NCAR-CCSM4 has relatively realistic ENSO variability, and a rich spectrum of ENSO diversity, and is thus well suited for studying the origin of ENSO flavors. In particular, the relative frequency of events peaking in the eastern and central equatorial Pacific ('EP' versus 'CP') undergoes inter-decadal modulations in this 1000-yr run. By constructing separate LIMs for the EP and CP epochs, as well as for the entire simulation, we examine to what extent the dominance of a specific ENSO flavor can be attributed to changes in the system dynamics (i.e in the LIM's linear operator) or is merely due to noise. Results from this study provide insights into the predictability of different ENSO types, establish a baseline for assessing ENSO changes due to global warming, and help define new dynamically meaningful ENSO metrics for evaluating climate models.
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
Iterated preconditioned LSQR method for inverse problems on unstructured grids
NASA Astrophysics Data System (ADS)
Arridge, S. R.; Betcke, M. M.; Harhanen, L.
2014-06-01
This article presents a method for solving large-scale linear inverse imaging problems regularized with a nonlinear, edge-preserving penalty term such as total variation or the Perona-Malik technique. Our method is aimed at problems defined on unstructured meshes, where such regularizers naturally arise in unfactorized form as a stiffness matrix of an anisotropic diffusion operator and factorization is prohibitively expensive. In the proposed scheme, the nonlinearity is handled with lagged diffusivity fixed point iteration, which involves solving a large-scale linear least squares problem in each iteration. Because the convergence of Krylov methods for problems with discontinuities is notoriously slow, we propose to accelerate it by means of priorconditioning (Bayesian preconditioning). priorconditioning is a technique that, through transformation to the standard form, embeds the information contained in the prior (Bayesian interpretation of a regularizer) directly into the forward operator and thence into the solution space. We derive a factorization-free preconditioned LSQR algorithm (MLSQR), allowing implicit application of the preconditioner through efficient schemes such as multigrid. The resulting method is also matrix-free i.e. the forward map can be defined through its action on a vector. We illustrate the performance of the method on two numerical examples. Simple 1D-deblurring problem serves to visualize the discussion throughout the paper. The effectiveness of the proposed numerical scheme is demonstrated on a three-dimensional problem in fluorescence diffuse optical tomography with total variation regularization derived algebraic multigrid preconditioner, which is the type of large scale, unstructured mesh problem, requiring matrix-free and factorization-free approaches that motivated the work here.
The genetic algorithm: A robust method for stress inversion
NASA Astrophysics Data System (ADS)
Thakur, Prithvi; Srivastava, Deepak C.; Gupta, Pravin K.
2017-01-01
The stress inversion of geological or geophysical observations is a nonlinear problem. In most existing methods, it is solved by linearization, under certain assumptions. These linear algorithms not only oversimplify the problem but also are vulnerable to entrapment of the solution in a local optimum. We propose the use of a nonlinear heuristic technique, the genetic algorithm, which searches the global optimum without making any linearizing assumption or simplification. The algorithm mimics the natural evolutionary processes of selection, crossover and mutation and, minimizes a composite misfit function for searching the global optimum, the fittest stress tensor. The validity and efficacy of the algorithm are demonstrated by a series of tests on synthetic and natural fault-slip observations in different tectonic settings and also in situations where the observations are noisy. It is shown that the genetic algorithm is superior to other commonly practised methods, in particular, in those tectonic settings where none of the principal stresses is directed vertically and/or the given data set is noisy.
Inverse method for flux characterization using infrared thermography in die forging
Lair, P.; Dumoulin, J.; Millan, P.
1998-02-20
In order to obtain high-quality pieces in advanced metallic alloys after hot die forging, a measurement methodology based on the association of infrared thermography with thermal inverse modelizations has been developed. It is based upon the maximum entropy principle. This report presents the method as well as numerical tests for the one-dimensional case. The two-dimensional case and results using some experimental data are also presented in both cases, where the noise influence is shown.
Numerical study of the inverse problem for the diffusion-reaction equation using optimization method
NASA Astrophysics Data System (ADS)
Soboleva, O. V.; Brizitskii, R. V.
2016-04-01
The model of transfer of substance with mixed boundary condition is considered. The inverse extremum problem of identification of the main coefficient in a nonstationary diffusion-reaction equation is formulated. The numerical algorithm based on the Newton-method of nonlinear optimization and finite difference discretization for solving this extremum problem is developed and realized on computer. The results of numerical experiments are discussed.
NASA Astrophysics Data System (ADS)
Rizzuti, G.; Gisolf, A.
2017-03-01
We study a reconstruction algorithm for the general inverse scattering problem based on the estimate of not only medium properties, as in more conventional approaches, but also wavefields propagating inside the computational domain. This extended set of unknowns is justified as a way to prevent local minimum stagnation, which is a common issue for standard methods. At each iteration of the algorithm, (i) the model parameters are obtained by solution of a convex problem, formulated from a special bilinear relationship of the data with respect to properties and wavefields (where the wavefield is kept fixed), and (ii) a better estimate of the wavefield is calculated, based on the previously reconstructed properties. The resulting scheme is computationally convenient since step (i) can greatly benefit from parallelization and the wavefield update (ii) requires modeling only in the known background model, which can be sped up considerably by factorization-based direct methods. The inversion method is successfully tested on synthetic elastic datasets.
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
NASA Astrophysics Data System (ADS)
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
The generalized Phillips-Twomey method for NMR relaxation time inversion.
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.
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.
New inverse method of centrifugal pump blade based on free form deformation
NASA Astrophysics Data System (ADS)
Zhang, R. H.; Guo, M.; Yang, J. H.; Liu, Y.; Li, R. N.
2013-12-01
In this research, a new inverse method for centrifugal pump blade based on free form deformation is proposed, the free form deformation is used to parametric the pump blade. The blade is implanted to a trivariate control volume which is equally subdivided by control lattice. The control volume can be deformed by moving the control lattice, thereupon the object is deformed. The flow in pump is solved by using a three dimensional turbulent model. The lattice deformation function is constructed according to the gradient distribution of fluid energy along the blade and its objective distribution. Deform the blade shape continually according to the flow solve, and we can get the objective blade shape. The calculation case shows that the proposed inverse method based on FFD method is rational.
Mirror Writing: Learning, Transfer, and Implications for Internal Inverse Models.
Latash, Mark L.
1999-06-01
In a study of the effects of practicing mirror writing, the effects of transfer to the nonpracticed hand and to nonpracticed phrases were assessed in 185 students. Large transfer effects were observed. An interpretation of those effects is based on a suggestion that the learning led to the creation of a new internal inverse model (or a modification of a pre-existent model) mapping the space of task variables onto the space of internal variables.
An inverse method for non linear ablative thermics with experimentation of automatic differentiation
NASA Astrophysics Data System (ADS)
Alestra, S.; Collinet, J.; Dubois, F.
2008-11-01
Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.
Kim, J HK; Du, P; Cheng, L K
2013-01-01
The use of cutaneous recordings to non-invasively characterize gastric slow wave had limited clinical acceptance, primarily due to the uncertainty in relating the recorded signal to the underlying gastric slow waves. In this study we aim to distinguish and quantitatively reconstruct different slow wave patterns using an inverse algorithm. Slow wave patterns corresponding to normal, retrograde and uncoupled activity at different frequencies were imposed on a model of the stomach surface. Gaussian noise (10% peak-to-peak) was added to cutaneous potentials and the Greensite-Tikhonov inverse method was used to reconstruct the potentials on the stomach. The effectiveness of the number or location of electrodes on the accuracy of the inverse solutions was investigated using four different electrode configurations. Results showed the reconstructed solutions were able to reliably distinguish the different slow wave patterns and waves with lower frequency were better correlated to the known solution than those with higher. The use of up to 228 electrodes improved the accuracy of the inverse solutions. However, the use of 120 electrodes concentrated around the stomach was able to achieve similar results. The most efficient electrode configuration for our model involved 120 electrodes with an inter-electrode distance of 32 mm. PMID:24137714
Kim, J H K; Du, P; Cheng, L K
2013-09-01
The use of cutaneous recordings to non-invasively characterize gastric slow waves has had limited clinical acceptance, primarily due to the uncertainty in relating the recorded signal to the underlying gastric slow waves. In this study we aim to distinguish and quantitatively reconstruct different slow wave patterns using an inverse algorithm. Slow wave patterns corresponding to normal, retrograde and uncoupled activity at different frequencies were imposed on a stomach surface model. Gaussian noise (10% peak-to-peak) was added to cutaneous potentials and the Greensite-Tikhonov inverse method was used to reconstruct the potentials on the stomach. The effectiveness of the number or location of electrodes on the accuracy of the inverse solutions was investigated using four different electrode configurations. Results showed the reconstructed solutions were able to reliably distinguish the different slow wave patterns and waves with lower frequency were better correlated to the known solution than those with higher. The use of up to 228 electrodes improved the accuracy of the inverse solutions. However, the use of 120 electrodes concentrated around the stomach was able to achieve similar results. The most efficient electrode configuration for our model involved 120 electrodes with an inter-electrode distance of 32 mm.
Viscoelastic modeling and inversion of a marine data set
Minkoff, S.E.; Symes, W.W.
1994-12-31
Deterministic waveform inversion in the p-{tau} domain permits estimation of the long-wavelength p-wave background velocity, the short-wavelength elastic parameter fluctuations, and the energy source for a marine data set from the Gulf of Mexico. The forward map is a convolutional model for p-wave primaries-only seismograms of viscoelastic, layered media. Two types of inversion (output least squares and differential semblance optimization) allow efficient estimation of various parameter combinations. Background velocities computed by differential semblance optimization were as consistent kinematically as those produced by interactive migration velocity analysis and gave somewhat more accurate depths. Source parameters obtained by output least squares inversion permitted considerably better fit to data than did those produced by as air gun modeling package. Output least squares inversion gave very short-scale detail of major reflectors closely resembling the detail derived from well logs. Despite evidence of considerable lateral heterogeneity in the shallow subsurface, estimates of deeper reflectors were remarkably consistent from midpoint to midpoint.
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
NASA Astrophysics Data System (ADS)
Ji, Hongzhu; Chen, Siying; Zhang, Yinchao; Chen, He; Guo, Pan; Chen, Hao
2017-02-01
A calibration method is proposed to invert the extinction coefficient for Fernald and Klett inversion by using the particle backscattering coefficient inversed with Raman and Elastic return signals. The calibration method is analyzed theoretically and experimentally, the inversion accuracy can be improved by removing the dependence on reference altitudes and intervals in conventional calibration methods, which resulted from the introduction of backscattering coefficient with relatively higher accuracy obtained by Raman-Mie inversion method. The standard deviation of this new calibration method can be reduced by about 20×, compared to that of the conventional calibration methods of Fernald and Klett inversion. And, the more stable effective inversed range with this new calibration method can be obtained by removing the dimple phenomenon in clouds position.
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.
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.
An optimal constrained linear inverse method for magnetic source imaging
Hughett, P.
1993-09-01
Magnetic source imaging is the reconstruction of the current distribution inside an inaccessible volume from magnetic field measurements made outside the volume. If the unknown current distribution is expressed as a linear combination of elementary current distributions in fixed positions, then the magnetic field measurements are linear in the unknown source amplitudes and both the least square and minimum mean square reconstructions are linear problems. This offers several advantages: The problem is well understood theoretically and there is only a single, global minimum. Efficient and reliable software for numerical linear algebra is readily available. If the sources are localized and statistically uncorrelated, then a map of expected power dissipation is equivalent to the source covariance matrix. Prior geological or physiological knowledge can be used to determine such an expected power map and thus the source covariance matrix. The optimal constrained linear inverse method (OCLIM) derived in this paper uses this prior knowledge to obtain a minimum mean square error estimate of the current distribution. OCLIM can be efficiently computed using the Cholesky decomposition, taking about a second on a workstation-class computer for a problem with 64 sources and 144 detectors. Any source and detector configuration is allowed as long as their positions are fixed a priori. Correlations among source and noise amplitudes are permitted. OCLIM reduces to the optimally weighted pseudoinverse method of Shim and Cho if the source amplitudes are independent and identically distributed and to the minimum-norm least squares estimate in the limit of no measurement noise or no prior knowledge of the source amplitudes. In the general case, OCLIM has better mean square error than either previous method. OCLIM appears well suited to magnetic imaging, since it exploits prior information, provides the minimum reconstruction error, and is inexpensive to compute.
Spectral curvature correction method based on inverse distance weighted interpolation
NASA Astrophysics Data System (ADS)
Jing, Juanjuan; Zhou, Jinsong; Li, Yacan; Feng, Lei
2016-10-01
Spectral curvature (smile effect) is universally existed in dispersive imaging spectrometer. Since most image processing systems considered all spatial pixels having the same wavelength, spectral curvature destroys the response consistence of the radiation energy in spatial dimension, it is necessary to correct the spectral curvature based on the spectral calibration data of the imaging spectrometer. Interpolation is widely used in resampling the measured spectra at the non-offset wavelength, but it is not versatile because the accuracy is different due to the spectral resolution changed. In the paper, we introduce the inverse distance weighted(IDW) method in spectrum resampling. First, calculate the Euclidean distance between the non-offset wavelength and the points near to it, the points number can be two, three, four or five, as many as you define. Then use the Euclidean distance to calculate the weight value of these points. Finally calculate the radiation of non-offset wavelength using the weight value and its corresponding radiation. The results turned out to be effective with the practical data acquired by the instrument, and it has the characteristics of versatility, simplicity, and fast.
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
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.
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.
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
Chen, Yu; Gao, Kai; Huang, Lianjie; Sabin, Andrew
2016-03-31
Accurate imaging and characterization of fracture zones is crucial for geothermal energy exploration. Aligned fractures within fracture zones behave as anisotropic media for seismic-wave propagation. The anisotropic properties in fracture zones introduce extra difficulties for seismic imaging and waveform inversion. We have recently developed a new anisotropic elastic-waveform inversion method using a modified total-variation regularization scheme and a wave-energy-base preconditioning technique. Our new inversion method uses the parameterization of elasticity constants to describe anisotropic media, and hence it can properly handle arbitrary anisotropy. We apply our new inversion method to a seismic velocity model along a 2D-line seismic data acquired at Eleven-Mile Canyon located at the Southern Dixie Valley in Nevada for geothermal energy exploration. Our inversion results show that anisotropic elastic-waveform inversion has potential to reconstruct subsurface anisotropic elastic parameters for imaging and characterization of fracture zones.
A method to calculate tunneling leakage currents in silicon inversion layers
NASA Astrophysics Data System (ADS)
Lujan, Guilherme S.; Sorée, Bart; Magnus, Wim; De Meyer, Kristin
2006-08-01
This paper proposes a quantum mechanical model for the calculation of tunneling leakage currents in a metal-oxide-semiconductor structure. The model incorporates both variational calculus and the transfer matrix method to compute the subband energies and the lifetimes of the inversion layer states. The use of variational calculus simplifies the subband energy calculation due to the analytical form of the wave functions, which offers an attractive perspective towards the calculation of the electron mobility in the channel. The model can be extended to high-k dielectrics with several layers. Good agreement between experimental data and simulation results is obtained for metal gate capacitors.
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.
Large scale 3-D modeling by integration of resistivity models and borehole data through inversion
NASA Astrophysics Data System (ADS)
Foged, N.; Marker, P. A.; Christansen, A. V.; Bauer-Gottwein, P.; Jørgensen, F.; Høyer, A.-S.; Auken, E.
2014-02-01
We present an automatic method for parameterization of a 3-D model of the subsurface, integrating lithological information from boreholes with resistivity models through an inverse optimization, with the objective of further detailing for geological models or as direct input to groundwater models. The parameter of interest is the clay fraction, expressed as the relative length of clay-units in a depth interval. The clay fraction is obtained from lithological logs and the clay fraction from the resistivity is obtained by establishing a simple petrophysical relationship, a translator function, between resistivity and the clay fraction. Through inversion we use the lithological data and the resistivity data to determine the optimum spatially distributed translator function. Applying the translator function we get a 3-D clay fraction model, which holds information from the resistivity dataset and the borehole dataset in one variable. Finally, we use k means clustering to generate a 3-D model of the subsurface structures. We apply the concept to the Norsminde survey in Denmark integrating approximately 700 boreholes and more than 100 000 resistivity models from an airborne survey in the parameterization of the 3-D model covering 156 km2. The final five-cluster 3-D model differentiates between clay materials and different high resistive materials from information held in resistivity model and borehole observations respectively.
Large-scale 3-D modeling by integration of resistivity models and borehole data through inversion
NASA Astrophysics Data System (ADS)
Foged, N.; Marker, P. A.; Christansen, A. V.; Bauer-Gottwein, P.; Jørgensen, F.; Høyer, A.-S.; Auken, E.
2014-11-01
We present an automatic method for parameterization of a 3-D model of the subsurface, integrating lithological information from boreholes with resistivity models through an inverse optimization, with the objective of further detailing of geological models, or as direct input into groundwater models. The parameter of interest is the clay fraction, expressed as the relative length of clay units in a depth interval. The clay fraction is obtained from lithological logs and the clay fraction from the resistivity is obtained by establishing a simple petrophysical relationship, a translator function, between resistivity and the clay fraction. Through inversion we use the lithological data and the resistivity data to determine the optimum spatially distributed translator function. Applying the translator function we get a 3-D clay fraction model, which holds information from the resistivity data set and the borehole data set in one variable. Finally, we use k-means clustering to generate a 3-D model of the subsurface structures. We apply the procedure to the Norsminde survey in Denmark, integrating approximately 700 boreholes and more than 100 000 resistivity models from an airborne survey in the parameterization of the 3-D model covering 156 km2. The final five-cluster 3-D model differentiates between clay materials and different high-resistivity materials from information held in the resistivity model and borehole observations, respectively.
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.
The appropriateness of ignorance in the inverse kinetic Ising model
NASA Astrophysics Data System (ADS)
Dunn, Benjamin; Battistin, Claudia
2017-03-01
We develop efficient ways to consider and correct for the effects of hidden units for the paradigmatic case of the inverse kinetic Ising model with fully asymmetric couplings. We identify two sources of error in reconstructing the connectivity among the observed units while ignoring part of the network. One leads to a systematic bias in the inferred parameters, whereas the other involves correlations between the visible and hidden populations and has a magnitude that depends on the coupling strength. We estimate these two terms using a mean field approach and derive self-consistent equations for the couplings accounting for the systematic bias. Through application of these methods on simple networks of varying relative population size and connectivity strength, we assess how and under what conditions the hidden portion can influence inference and to what degree it can be crudely estimated. We find that for weak to moderately coupled systems, the effects of the hidden units is a simple rotation that can be easily corrected for. For strongly coupled systems, the non-systematic term becomes large and can no longer be safely ignored, further highlighting the importance of understanding the average strength of couplings for a given system of interest.
Yitembe, Bertrand Russel; Crevecoeur, Guillaume; Van Keer, Roger; Dupre, Luc
2011-05-01
The EEG is a neurological diagnostic tool with high temporal resolution. However, when solving the EEG inverse problem, its localization accuracy is limited because of noise in measurements and available uncertainties of the conductivity value in the forward model evaluations. This paper proposes the reduced conductivity dependence (RCD) method for decreasing the localization error in EEG source analysis by limiting the propagation of the uncertain conductivity values to the solutions of the inverse problem. We redefine the traditional EEG cost function, and in contrast to previous approaches, we introduce a selection procedure of the EEG potentials. The selected potentials are, as low as possible, affected by the uncertainties of the conductivity when solving the inverse problem. We validate the methodology on the widely used three-shell spherical head model with a single electrical dipole and multiple dipoles as source model. The proposed RCD method enhances the source localization accuracy with a factor ranging between 2 and 4, dependent on the dipole location and the noise in measurements. © 2011 IEEE
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.
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
Anatomy of Higgs mass in supersymmetric inverse seesaw models
NASA Astrophysics Data System (ADS)
Chun, Eung Jin; Mummidi, V. Suryanarayana; Vempati, Sudhir K.
2014-09-01
We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops.
Sediment Acoustics: Wideband Model, Reflection Loss and Ambient Noise Inversion
2009-09-30
between 1 and 10 kHz. The model is also capable of explaining the apparent discrepancy between the data and the Kramers- Kronig relationship (K-K...of in-situ measurements of sediment sound speed and attenuation from SAX99, SAX04 and SW06 with the commonly used Kramers- Kronig equation (black...inverse quality factor. The data is overlaid by the Kramers- Kronig estimate of sound speed from measured attenuation, by both the commonly used equation
Han, Jijun; Yang, Deqiang; Sun, Houjun; Xin, Sherman Xuegang
2017-01-01
Inverse method is inherently suitable for calculating the distribution of source current density related with an irregularly structured electromagnetic target field. However, the present form of inverse method cannot calculate complex field-tissue interactions. A novel hybrid inverse/finite-difference time domain (FDTD) method that can calculate the complex field-tissue interactions for the inverse design of source current density related with an irregularly structured electromagnetic target field is proposed. A Huygens' equivalent surface is established as a bridge to combine the inverse and FDTD method. Distribution of the radiofrequency (RF) magnetic field on the Huygens' equivalent surface is obtained using the FDTD method by considering the complex field-tissue interactions within the human body model. The obtained magnetic field distributed on the Huygens' equivalent surface is regarded as the next target. The current density on the designated source surface is derived using the inverse method. The homogeneity of target magnetic field and specific energy absorption rate are calculated to verify the proposed method.
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.
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.
Inverse modeling of biomass smoke emissions using the TOMS AI
NASA Astrophysics Data System (ADS)
Zhang, S. Y.; Penner, J. E.; Torres, O.
2003-12-01
Results of inverse modeling of biomass smoke emissions using the TOMS AI and a three-dimensional transport model are presented. The IMPACT model with DAO meteorology data in 1997 are utilized to obtain aerosol spatial and temporal distributions. Two absorbing aerosol types are considered, including biomass smoke and mineral dust. First, a radiative transfer model is applied to generate the modeled AI. Then a Bayesian inverse technique is applied to optimize the difference between the modeled AI and the EP TOMS AI in the same period by regulating monthly a priori biomass smoke emissions, while the dust emissions are fixed. The modeled AI with a posteriori emissions generally is in better agreement with the EP TOMS AI. The annual global a posteriori source increases by about 13% for the year 1997 (6.31 Tg/yr BC) in the base scenario, with a larger adjustment of monthly regional emissions. Five sensitivity scenarios are carried out, including sensitivity to the a priori uncertainties, the height of the smoke layer, the cloud screening criteria of the daily EP TOMS AI, the adjustment of emissions in a lumped region outside of the major biomass burning regions, and the covariances between observations. Results suggest that a posteriori annual global emissions in the sensitivity scenarios are within 15% of that of the base scenario. However, the difference of annual a posteriori emissions between the sensitivity scenarios and the base scenario can be as large as 50% on regional scale. We are also applying the inverse model technique to the year 2000 to compare with biomass emissions deduced from an analysis based on burned areas.
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.
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.
A Gibbs sampler for inequality-constrained geostatistical interpolation and inverse modeling
NASA Astrophysics Data System (ADS)
Michalak, Anna M.
2008-09-01
Interpolation and inverse modeling problems are ubiquitous in environmental sciences. In many applications, the parameters being estimated or mapped have physical constraints, such as nonnegativity (e.g. concentration, hydraulic conductivity), solubility limits, censored data (e.g. due to dry wells or detection limits), and other physical boundaries or missing data. Geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters, but these methods typically cannot enforce physical constraints. This paper describes a statistically rigorous and computationally efficient Gibbs sampler, a Markov chain Monte Carlo technique, based on an a priori truncated Gaussian distribution model, which allows for multiple and variable physical constraints to be enforced within a geostatistical framework. Sample interpolation and inverse modeling applications confirm that estimates, uncertainty bounds and conditional simulations reflect the specified constraints, leading to conclusions that are more consistent with the underlying conceptual model, and provide a more accurate measure of the posterior uncertainty of the parameters being estimated. In addition, especially in inverse modeling applications, a posteriori confidence bounds are narrower even in areas where constraints are not imposed. The method is applicable in multiple dimensions, for data with or without measurement error, and with any variogram model.
NASA Astrophysics Data System (ADS)
Ren, Tao; Modest, Michael F.; Fateev, Alexander; Clausen, Sønnik
2015-01-01
In this study, we present an inverse calculation model based on the Levenberg-Marquardt optimization method to reconstruct temperature and species concentration from measured line-of-sight spectral transmissivity data for homogeneous gaseous media. The high temperature gas property database HITEMP 2010 (Rothman et al. (2010) [1]), which contains line-by-line (LBL) information for several combustion gas species, such as CO2 and H2O, was used to predict gas spectral transmissivities. The model was validated by retrieving temperatures and species concentrations from experimental CO2 and H2O transmissivity measurements. Optimal wavenumber ranges for CO2 and H2O transmissivity measured across a wide range of temperatures and concentrations were determined according to the performance of inverse calculations. Results indicate that the inverse radiation model shows good feasibility for measurements of temperature and gas concentration.
Advanced model of eddy-current NDE inverse problem with sparse grid algorithm
NASA Astrophysics Data System (ADS)
Zhou, Liming; Sabbagh, Harold A.; Sabbagh, Elias H.; Murphy, R. Kim; Bernacchi, William
2017-02-01
In model-based inverse problem, some unknown parameters need to be estimated. These parameters are used not only to characterize the physical properties of cracks, but also to describe the position of the probes (such as lift off and angles) in the calibration. After considering the effect of the position of the probes in the inverse problem, the accuracy of the inverse result will be improved. With increasing the number of the parameters in the inverse problems, the burden of calculations will increase exponentially in the traditional full grid method. The sparse grid algorithm, which was introduced by Sergey A. Smolyak, was used in our work. With this algorithm, we obtain a powerful interpolation method that requires significantly fewer support nodes than conventional interpolation on a full grid. In this work, we combined sparse grid toolbox TASMANIAN, which is produced by Oak Ridge National Laboratory, and professional eddy-current NDE software, VIC-3D R◯, to solve a specific inverse problem. An advanced model based on our previous one is used to estimate length and depth of the crack, lift off and two angles of the position of probes. Considering the calibration process, pseudorandom noise is considered in the model and statistical behavior is discussed.
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.
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
Modeling and inversion of dispersion curves of surface waves in shallow site investigations
NASA Astrophysics Data System (ADS)
Pei, Donghong
2007-12-01
The shallow S-wave velocity structure is very important for the seismic design of engineered structures and facilities, seismic hazard evaluation of a region, comprehensive earthquake preparedness, development of the national seismic hazard map, and seismic-resistant design of buildings. The use of surface waves for the characterization of the shallow subsurface involves three steps: (a) acquisition of high-frequency broadband seismic surface wave records generated either by active sources or passive ambient noise (microtremors or microseisms), (b) extraction of phase dispersion curves from the recorded seismic signals, and (c) derivation of S-wave velocity profiles either using inversion algorithms or manually error and trial forward modeling. The first two steps have been successfully achieved by several techniques. However, the third step (inversion) needs more improvements. An accurate and automatic inversion method is needed to generate shallow S-wave velocity profiles. With the achievement of a fast forward modeling method, this study focuses on the inversion of phase velocity dispersion curves of surface waves contained in ambient seismic noise for a one dimensional, flat-layered S-wave velocity structure. For the forward modeling, we present a new more efficient algorithm, called the fast generalized R/T (reflection and transmission) coefficient method, to calculate the phase velocity of surface waves for a layered earth model. The fast method is based on but is more efficient than the traditional ones. The improvements by this study include (1) computation of the generalized reflection and transmission coefficients without calculation of the modified reflection and transmission coefficients; (2) presenting an analytic solution for the inverse of the 4X4 layer matrix E. Compared with traditional R/T methods, the fast generalized R/T coefficient method, when applied on Rayleigh waves, significantly improves the speed of computation, cutting the computational
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.
NASA Astrophysics Data System (ADS)
Mackay, Neill; Wilson, Chris; Zika, Jan
2017-04-01
The Overturning in the Subpolar North Atlantic Program (OSNAP) aims to quantify the subpolar AMOC and its variability, including associated fluxes of heat and freshwater, using a combination of observations and models. In contribution OSNAP, we have developed a novel inverse method that diagnoses the interior mixing and advective flux at the boundary of an enclosed volume in the ocean. This Regional Thermohaline Inverse Method (RTHIM) operates in salinity-temperature (S-T) coordinates, a framework which allows us to gain insights into water mass transformation within the control volume and boundary fluxes of heat and freshwater. RTHIM will use multiple long-term observational datasets and reanalyses, including Argo, to provide a set of inverse estimates to be used to understand the sub-annual transport timescales sampled by the OSNAP array. Having validated the method using the NEMO model, we apply RTHIM to an Arctic domain using temperature and salinity and surface flux data from reanalyses. We also use AVISO surface absolute geostrophic velocities which, combined with thermal wind balance, provide an initial estimate for the inflow and outflow through the boundary. We diagnose the interior mixing in S-T coordinates and the boundary flow, calculating the transformation rates of well-known water masses and the individual contributions to these rates from surface flux processes, boundary flow and interior mixing. Outputs from RTHIM are compared with similar metrics from previous literature on the region. The inverse solution reproduces an observed pattern of warm, saline Atlantic waters entering the Arctic volume and cooler, fresher waters leaving. Meanwhile, surface fluxes act to create waters at the extremes of the S-T distribution and interior mixing acts in opposition, creating water masses at intermediate S-T and destroying them at the extremes. RTHIM has the potential to be compared directly with the OSNAP array observations by defining a domain boundary which
The application of inverse methods to spatially-distributed acoustic sources
NASA Astrophysics Data System (ADS)
Holland, K. R.; Nelson, P. A.
2013-10-01
Acoustic inverse methods, based on the output of an array of microphones, can be readily applied to the characterisation of acoustic sources that can be adequately modelled as a number of discrete monopoles. However, there are many situations, particularly in the fields of vibroacoustics and aeroacoustics, where the sources are distributed continuously in space over a finite area (or volume). This paper is concerned with the practical problem of applying inverse methods to such distributed source regions via the process of spatial sampling. The problem is first tackled using computer simulations of the errors associated with the application of spatial sampling to a wide range of source distributions. It is found that the spatial sampling criterion for minimising the errors in the radiated far-field reconstructed from the discretised source distributions is strongly dependent on acoustic wavelength but is only weakly dependent on the details of the source field itself. The results of the computer simulations are verified experimentally through the application of the inverse method to the sound field radiated by a ducted fan. The un-baffled fan source with the associated flow field is modelled as a set of equivalent monopole sources positioned on the baffled duct exit along with a matrix of complimentary non-flow Green functions. Successful application of the spatial sampling criterion involves careful frequency-dependent selection of source spacing, and results in the accurate reconstruction of the radiated sound field. Discussions of the conditioning of the Green function matrix which is inverted are included and it is shown that the spatial sampling criterion may be relaxed if conditioning techniques, such as regularisation, are applied to this matrix prior to inversion.
Analytic model approach to the inversion of scattering data. [to obtain ozone profile
NASA Technical Reports Server (NTRS)
Green, A. E. S.; Klenk, K. F.
1977-01-01
An analytic model approach is applied to several simple atmospheric inversion problems. This method gives a sharp determination of aerosol size distribution parameters. It is shown that this analytic approach, together with ground level point sampling data measurements, can be used to infer information on the tropospheric ozone profile.
Inverse modeling of geochemical and mechanical compaction in sedimentary basins
NASA Astrophysics Data System (ADS)
Colombo, Ivo; Porta, Giovanni Michele; Guadagnini, Alberto
2015-04-01
We study key phenomena driving the feedback between sediment compaction processes and fluid flow in stratified sedimentary basins formed through lithification of sand and clay sediments after deposition. Processes we consider are mechanic compaction of the host rock and the geochemical compaction due to quartz cementation in sandstones. Key objectives of our study include (i) the quantification of the influence of the uncertainty of the model input parameters on the model output and (ii) the application of an inverse modeling technique to field scale data. Proper accounting of the feedback between sediment compaction processes and fluid flow in the subsurface is key to quantify a wide set of environmentally and industrially relevant phenomena. These include, e.g., compaction-driven brine and/or saltwater flow at deep locations and its influence on (a) tracer concentrations observed in shallow sediments, (b) build up of fluid overpressure, (c) hydrocarbon generation and migration, (d) subsidence due to groundwater and/or hydrocarbons withdrawal, and (e) formation of ore deposits. Main processes driving the diagenesis of sediments after deposition are mechanical compaction due to overburden and precipitation/dissolution associated with reactive transport. The natural evolution of sedimentary basins is characterized by geological time scales, thus preventing direct and exhaustive measurement of the system dynamical changes. The outputs of compaction models are plagued by uncertainty because of the incomplete knowledge of the models and parameters governing diagenesis. Development of robust methodologies for inverse modeling and parameter estimation under uncertainty is therefore crucial to the quantification of natural compaction phenomena. We employ a numerical methodology based on three building blocks: (i) space-time discretization of the compaction process; (ii) representation of target output variables through a Polynomial Chaos Expansion (PCE); and (iii) model
NASA Astrophysics Data System (ADS)
Yuan, S.; Fuji, N.; Singh, S. C.; Borisov, D.
2016-12-01
We present a novel methodology to invert seismic data locally through the combination of wavefield injection and extrapolation method. Seismic full waveform inversion has proved its promising resolving power in seismology community for these decades. However, the computational cost for 3D practical scale elastic or viscoelastic waveform inversion remains still challenging. The computational cost is much more severe for time-lapse surveys, which requires real-time model estimation on a daily or weekly basis. Besides, changes of the structures during time-lapse surveys are likely to occur within a smaller area, such as oil and gas reservoir or CO2 injection wells. We propose methods that effectively and quantitatively image the localized structure change relatively far from source and receiver arrays. We thus have to perform both forward modeling and waveform inversions inside the region that contain neither source nor receiver. Firstly, we look for the equivalent source expression inside the region of interest by wavefield injection method. Secondly, we extrapolate wavefield from physical receivers to an array of virtual receivers by using correlation-type representation theorem. In this paper, we present elastic 2D numerical examples of our methods and quantitatively evaluate errors of obtained models, in comparison with those from full-model inversions. The results show that the proposed localized waveform inversion is more efficient, accurate and robust even under existence of errors in both initial models and data.
2D TEM Modeling and Inversion by Adaptive Born Forward Mapping
NASA Astrophysics Data System (ADS)
Lee, T.; Seo, M.; Cho, I. K.; Ko, K. B.; You, Y. J.
2014-12-01
In the airborne electromagnetic survey, vast data are acquired with the development of precise measuring equipment and the automation of data acquisition. In this study we developed fast and accurate two-dimensional (2D) modeling and inversion algorithm based on the adaptive born forward mapping (ABFM) method, which is recently emerging for fast time-domain electromagnetic (TEM) modeling. The ABFM method is an approximation method that takes into consideration the true electrical conductivity distribution of subsurface media and is different from the conventional Born approximation that uses the constant electric conductivity. One of the most important points of the ABFM method is how to set a suitable sensitivity function. In this study, the known 1D sensitivity function was expanded into 2D sensitivity function to effectively approximate the dispersive behavior of electromagnetic field. By comparing the analytic solution and approximate ABFM solution for layered earth models, we found that the two solutions correspond to each other well. This implies that the 2D sensitivity function suggested in this study is suitable and that the ABFM method has very excellent accuracy in 2D TEM modeling even though it is an approximation method. Furthermore, a 2D inversion algorithm was developed with respect to the apparent conductivity data of TEM based on ABFM. To enhance the resolution and stability, the smoothness-constrained least-squares method with ACB constraint was employed. The inversion of calculated data for various models produced a reasonable model close to the true model. It is expected that the method will be extensively applicable to TEM modeling and inversion without difficulty in the future.
[A method for solution of the multi-objective inverse problems under uncertainty].
Pisarev, A S; Samsonova, M G
2013-01-01
We describe a method to solve multi-objective inverse problems under uncertainty. The method was tested on non-linear models of dynamic series and population dynamics, as well as on the spatiotemporal model of gene expression in terms of non-linear differential equations. We consider how to identify model parameters when experimental data contain additive noise and measurements are performed in discrete time points. We formulate the multi-objective problem of optimization under uncertainty. In addition to a criterion of least squares difference we applied a criterion which is based on the integral of trajectories of the system spatiotemporal dynamics, as well as a heuristic criterion CHAOS based on the decision tree method. The optimization problem is formulated using a fuzzy statement and is constrained by penalty functions based on the normalized membership functions of a fuzzy set of model solutions. This allows us to reconstruct the expression pattern of hairy gene in Drosophila even-skipped mutants that is in good agreement with experimental data. The reproducibility of obtained results is confirmed by solution of inverse problems using different global optimization methods with heuristic strategies.
Efficient inversion of three-dimensional finite element models of volcano deformation
NASA Astrophysics Data System (ADS)
Charco, M.; Galán del Sastre, P.
2014-03-01
Numerical techniques, as such as finite element method, allow for the inclusion of features, such as topography and/or mechanical heterogeneities, for the interpretation of volcanic deformation. However, models based on these numerical techniques usually are not suitable to be included in non-linear estimations of source parameters based on explorative optimization schemes because they require a calculation of the numerical approach for every evaluation of the misfit function. We present a procedure for finite element (FE) models that can be combined with explorative inversion schemes. The methodology is based on including a body force term representing an infinitesimal source in the model formulation that is responsible for pressure (volume) changes in the medium. This provides significant savings in both the time required for mesh generation and actual computational time of the numerical approach. Furthermore, we develop an inversion algorithm to estimate those parameters that characterize the changes in location and pressure (volume) of deformation sources. Both provide FE inversions in a single step, avoiding remeshing and assembly of the linear system of algebraic equations that define the numerical approach and/or the automatic mesh generation. After providing the theoretical basis for the model, the numerical approach and the algorithm for the inversions, we test the methodology using a synthetic example in a stratovolcano. Our results suggest that the FE inversion methodology can be considered suitable for efficiently save time in quantitative interpretations of volcano deformation.
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
Healy, Richard W.; Scanlon, Bridget R.
2010-01-01
Simulation models are widely used in all types of hydrologic studies, and many of these models can be used to estimate recharge. Models can provide important insight into the functioning of hydrologic systems by identifying factors that influence recharge. The predictive capability of models can be used to evaluate how changes in climate, water use, land use, and other factors may affect recharge rates. Most hydrological simulation models, including watershed models and groundwater-flow models, are based on some form of water-budget equation, so the material in this chapter is closely linked to that in Chapter 2. Empirical models that are not based on a water-budget equation have also been used for estimating recharge; these models generally take the form of simple estimation equations that define annual recharge as a function of precipitation and possibly other climatic data or watershed characteristics.Model complexity varies greatly. Some models are simple accounting models; others attempt to accurately represent the physics of water movement through each compartment of the hydrologic system. Some models provide estimates of recharge explicitly; for example, a model based on the Richards equation can simulate water movement from the soil surface through the unsaturated zone to the water table. Recharge estimates can be obtained indirectly from other models. For example, recharge is a parameter in groundwater-flow models that solve for hydraulic head (i.e. groundwater level). Recharge estimates can be obtained through a model calibration process in which recharge and other model parameter values are adjusted so that simulated water levels agree with measured water levels. The simulation that provides the closest agreement is called the best fit, and the recharge value used in that simulation is the model-generated estimate of recharge.
Significance of the model considering mixed grain-size for inverse analysis of turbidites
NASA Astrophysics Data System (ADS)
Nakao, K.; Naruse, H.; Tokuhashi, S., Sr.
2016-12-01
A method for inverse analysis of turbidity currents is proposed for application to field observations. Estimation of initial condition of the catastrophic events from field observations has been important for sedimentological researches. For instance, there are various inverse analyses to estimate hydraulic conditions from topography observations of pyroclastic flows (Rossano et al., 1996), real-time monitored debris-flow events (Fraccarollo and Papa, 2000), tsunami deposits (Jaffe and Gelfenbaum, 2007) and ancient turbidites (Falcini et al., 2009). These inverse analyses need forward models and the most turbidity current models employ uniform grain-size particles. The turbidity currents, however, are the best characterized by variation of grain-size distribution. Though there are numerical models of mixed grain-sized particles, the models have difficulty in feasibility of application to natural examples because of calculating costs (Lesshaft et al., 2011). Here we expand the turbidity current model based on the non-steady 1D shallow-water equation at low calculation costs for mixed grain-size particles and applied the model to the inverse analysis. In this study, we compared two forward models considering uniform and mixed grain-size particles respectively. We adopted inverse analysis based on the Simplex method that optimizes the initial conditions (thickness, depth-averaged velocity and depth-averaged volumetric concentration of a turbidity current) with multi-point start and employed the result of the forward model [h: 2.0 m, U: 5.0 m/s, C: 0.01%] as reference data. The result shows that inverse analysis using the mixed grain-size model found the known initial condition of reference data even if the condition where the optimization started is deviated from the true solution, whereas the inverse analysis using the uniform grain-size model requires the condition in which the starting parameters for optimization must be in quite narrow range near the solution. The
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.
Shinnery oak bidirectional reflectance properties and canopy model inversion
NASA Technical Reports Server (NTRS)
Deering, Donald W.; Eck, Thomas F.; Grier, Toby
1992-01-01
Field measurements are presented, together with the results of a 3D canopy-model inversion for sand shinnery oak community in western Texas. The spectral bidirectional radiance measurements were in three spectral channels encompassing both the complete land surface and sky hemispheres. The changes in canopy reflectance that occur with variations in solar zenith angle and view direction for two seasons of the year were evaluated, and the 3D radiation-interaction model was inverted to estimate the oak leaf area index and canopy density from the reflectance data.
GARCH modelling of covariance in dynamical estimation of inverse solutions
NASA Astrophysics Data System (ADS)
Galka, Andreas; Yamashita, Okito; Ozaki, Tohru
2004-12-01
The problem of estimating unobserved states of spatially extended dynamical systems poses an inverse problem, which can be solved approximately by a recently developed variant of Kalman filtering; in order to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH modelling of covariance, well known in econometrics, with Kalman filtering. We formulate this algorithm for spatiotemporal systems governed by stochastic diffusion equations and demonstrate its feasibility by presenting a numerical simulation designed to imitate the situation of the generation of electroencephalographic recordings by the human cortex.
Aircraft automatic flight control system with model inversion
NASA Technical Reports Server (NTRS)
Smith, G. A.; Meyer, George
1990-01-01
A simulator study was conducted to verify the advantages of a Newton-Raphson model-inversion technique as a design basis for an automatic trajectory control system in an aircraft with highly nonlinear characteristics. The simulation employed a detailed mathematical model of the aerodynamic and propulsion system performance characteristics of a vertical-attitude takeoff and landing tactical aircraft. The results obtained confirm satisfactory control system performance over a large portion of the flight envelope. System response to wind gusts was satisfactory for various plausible combinations of wind magnitude and direction.
Developing seasonal ammonia emission estimates with an inverse modeling technique.
Gilliland, A B; Dennis, R L; Roselle, S J; Pierce, T E; Bender, L E
2001-11-21
Significant uncertainty exists in magnitude and variability of ammonia (NH3) emissions, which are needed for air quality modeling of aerosols and deposition of nitrogen compounds. Approximately 85% of NH3 emissions are estimated to come from agricultural nonpoint sources. We suspect a strong seasonal pattern in NH 3 emissions; however, current NH3 emission inventories lack intra-annual variability. Annually averaged NH 3 emissions could significantly affect model-predicted concentrations and wet and dry deposition of nitrogen-containing compounds. We apply a Kalman filter inverse modeling technique to deduce monthly NH3 emissions for the eastern U.S. Final products of this research will include monthly emissions estimates from each season. Results for January and June 1990 are currently available and are presented here. The U.S. Environmental Protection Agency (USEPA) Community Multiscale Air Quality (CMAQ) model and ammonium (NH4+) wet concentration data from the National Atmospheric Deposition Program (NADP) network are used. The inverse modeling technique estimates the emission adjustments that provide optimal modeled results with respect to wet NH4+ concentrations, observational data error, and emission uncertainty. Our results suggest that annual average NH 3 emissions estimates should be decreased by 64% for January 1990 and increased by 25% for June 1990. These results illustrate the strong differences that are anticipated for NH3 emissions.
Reconstruction of multiple gastric electrical wave fronts using potential based inverse methods
Kim, J HK; Pullan, A J; Cheng, L K
2012-01-01
One approach, 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 was 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. PMID:22842812
Reconstruction of multiple gastric electrical wave fronts using potential-based inverse methods.
Kim, J H K; Pullan, A J; Cheng, L K
2012-08-21
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.
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
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
Ray, J.; Lee, J.; Yadav, V.; ...
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
NASA Astrophysics Data System (ADS)
Wang, M. C.; Niu, X. F.; Chen, S. B.; Guo, P. J.; Yang, Q.; Wang, Z. J.
2014-03-01
Chlorophyll content, the most important pigment related to photosynthesis, is the key parameter for vegetation growth. The continuous spectrum characteristics of ground objects can be captured through hyperspectral remotely sensed data. In this study, based on the coniferous forest radiative transfer model, chlorophyll contents were inverted by use of hyperspectral CHRIS data in the coniferous forest coverage of Changbai Mountain Area. In addition, the sensitivity of LIBERTY model was analyzed. The experimental results validated that the reflectance simulation of different chlorophyll contents was coincided with that of the field measurement, and hyperspectral vegetation indices applied to the quantitative inversion of chlorophyll contents was feasible and accurate. This study presents a reasonable method of chlorophyll inversion for the coniferous forest, promotes the inversion precision, is of significance in coniferous forest monitoring.
Analysis of Inverse Modelling Procedures For The Estimation of Parameters Controlling Macropore Flow
NASA Astrophysics Data System (ADS)
Roulier, S.; Jarvis, N.
Because they are objective, reproducible, and unambiguous, inverse modelling pro- cedures are increasingly used to identify water flow and solute transport parameters. This study focused on the development and testing of inverse methods to estimate transfer parameters in simulation models which account for rapid non-equilibrium flow in soil macropores. The dual-porosity/dual-permeability model of water flow and solute transport MACRO was linked with the inverse modelling package SUFI. The Bayesian approach followed by SUFI is stable, converging, and is not affected by the usual issues of initial values and local minima. A theoretical study was carried out using the combined tool SUFI/MACRO to assess data requirements for robust param- eter estimation in macropore flow models. Generated "dummy" data were used for this purpose, representing transient state leaching experiments for tracers and pesticides in small soil columns (20 cm height). General issues related to inverse modelling, such as internal correlation and sensitivity, were investigated. Attention was also focused on the significance of experimental and model errors, the degree of macropore flow in the system, and the availability of resident and flux concentrations. The study showed reliable results, especially in the case of strong macropore flow, but both resident and flux concentrations were needed. Errors (up to 30% for the pesticide concentrations) did not affect the robustness of the tool. SUFI linked to MACRO appeared thus to be well suited for global optimisation of the system parameters in soils affected by macropore flow.
Fu, Y B; Chui, C K; Teo, C L
2013-04-01
Biological soft tissue is highly inhomogeneous with scattered stress-strain curves. Assuming that the instantaneous strain at a specific stress varies according to a normal distribution, a nondeterministic approach is proposed to model the scattered stress-strain relationship of the tissue samples under compression. Material parameters of the liver tissue modeled using Mooney-Rivlin hyperelastic constitutive equation were represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters were determined using inverse finite element method and inverse mean-value first-order second-moment (IMVFOSM) method respectively. This method was verified using computer simulation based on direct Monte-Carlo (MC) method. The simulated cumulative distribution function (CDF) corresponded well with that of the experimental stress-strain data. The resultant nondeterministic material parameters were able to model the stress-strain curves from other separately conducted liver tissue compression tests. Stress-strain data from these new tests could be predicted using the nondeterministic material parameters. Copyright © 2013 Elsevier Ltd. All rights reserved.
Inverse modeling of unsaturated flow using clusters of soil texture and pedotransfer functions
NASA Astrophysics Data System (ADS)
Zhang, Yonggen; Schaap, Marcel G.; Guadagnini, Alberto; Neuman, Shlomo P.
2016-10-01
Characterization of heterogeneous soil hydraulic parameters of deep vadose zones is often difficult and expensive, making it necessary to rely on other sources of information. Pedotransfer functions (PTFs) based on soil texture data constitute a simple alternative to inverse hydraulic parameter estimation, but their accuracy is often modest. Inverse modeling entails a compromise between detailed description of subsurface heterogeneity and the need to restrict the number of parameters. We propose two methods of parameterizing vadose zone hydraulic properties using a combination of k-means clustering of kriged soil texture data, PTFs, and model inversion. One approach entails homogeneous and the other heterogeneous clusters. Clusters may include subdomains of the computational grid that need not be contiguous in space. The first approach homogenizes within-cluster variability into initial hydraulic parameter estimates that are subsequently optimized by inversion. The second approach maintains heterogeneity through multiplication of each spatially varying initial hydraulic parameter by a scale factor, estimated a posteriori through inversion. This allows preserving heterogeneity without introducing a large number of adjustable parameters. We use each approach to simulate a 95 day infiltration experiment in unsaturated layered sediments at a semiarid site near Phoenix, Arizona, over an area of 50 × 50 m2 down to a depth of 14.5 m. Results show that both clustering approaches improve simulated moisture contents considerably in comparison to those based solely on PTF estimates. Our calibrated models are validated against data from a subsequent 295 day infiltration experiment at the site.
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.
A time domain inverse dynamic method for the end point tracking control of a flexible manipulator
NASA Technical Reports Server (NTRS)
Kwon, Dong-Soo; Book, Wayne J.
1991-01-01
The inverse dynamic equation of a flexible manipulator was solved in the time domain. By dividing the inverse system equation into the causal part and the anticausal part, we calculated the torque and the trajectories of all state variables for a given end point trajectory. The interpretation of this method in the frequency domain was explained in detail using the two-sided Laplace transform and the convolution integral. The open loop control of the inverse dynamic method shows an excellent result in simulation. For real applications, a practical control strategy is proposed by adding a feedback tracking control loop to the inverse dynamic feedforward control, and its good experimental performance is presented.
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
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.
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.
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.
Improving rotorcraft survivability to RPG attack using inverse methods
NASA Astrophysics Data System (ADS)
Anderson, D.; Thomson, D. G.
2009-09-01
This paper presents the results of a preliminary investigation of optimal threat evasion strategies for improving the survivability of rotorcraft under attack by rocket propelled grenades (RPGs). The basis of this approach is the application of inverse simulation techniques pioneered for simulation of aggressive helicopter manoeuvres to the RPG engagement problem. In this research, improvements in survivability are achieved by computing effective evasive manoeuvres. The first step in this process uses the missile approach warning system camera (MAWS) on the aircraft to provide angular information of the threat. Estimates of the RPG trajectory and impact point are then estimated. For the current flight state an appropriate evasion response is selected then realised via inverse simulation of the platform dynamics. Results are presented for several representative engagements showing the efficacy of the approach.
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
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
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.
NASA Astrophysics Data System (ADS)
Kalscheuer, Thomas; Pedersen, Laust B.; Siripunvaraporn, Weerachai
2008-11-01
Electromagnetic surface measurements with the radiomagnetotelluric (RMT) method in the frequency range between 10 and 300kHz are typically interpreted in the quasi-static approximation, that is, assuming displacement currents are negligible. In this paper, the dielectric effect of displacement currents on RMT responses over resistive subsurface models is studied with a 2-D forward and inverse scheme that can operate both in the quasi-static approximation and including displacement currents. Forward computations of simple models exemplify how responses that allow for displacement currents deviate from responses computed in the quasi-static approximation. The differences become most obvious for highly resistive subsurface models of about 3000Ωm and more and at high frequencies. For such cases, the apparent resistivities and phases of the transverse magnetic (TM) and transverse electric (TE) modes are significantly smaller than in the quasi-static approximation. Along profiles traversing 2-D subsurface models, sign reversals in the real part of the vertical magnetic transfer function (VMT) are often more pronounced than in the quasi-static approximation. On both sides of such sign reversals, the responses computed including displacement currents are larger than typical measurement errors. The 2-D inversion of synthetic data computed including displacement currents demonstrates that serious misinterpretations in the form of artefacts in inverse models can be made if displacement currents are neglected during the inversion. Hence, the inclusion of the dielectric effect is a crucial improvement over existing quasi-static 2-D inverse schemes. Synthetic data from a 2-D model with constant dielectric permittivity and a conductive block buried in a highly resistive layer, which in turn is underlain by a conductive layer, are inverted. In the quasi-static inverse model, the depth to the conductive structures is overestimated, artefactual resistors appear on both sides of the
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.
Effects of geometric head model perturbations on the EEG forward and inverse problems.
von Ellenrieder, Nicolás; Muravchik, Carlos H; Nehorai, Arye
2006-03-01
We study the effect of geometric head model perturbations on the electroencephalography (EEG) forward and inverse problems. Small magnitude perturbations of the shape of the head could represent uncertainties in the head model due to errors on images or techniques used to construct the model. They could also represent small scale details of the shape of the surfaces not described in a deterministic model, such as the sulci and fissures of the cortical layer. We perform a first-order perturbation analysis, using a meshless method for computing the sensitivity of the solution of the forward problem to the geometry of the head model. The effect on the forward problem solution is treated as noise in the EEG measurements and the Cramér-Rao bound is computed to quantify the effect on the inverse problem performance. Our results show that, for a dipolar source, the effect of the perturbations on the inverse problem performance is under the level of the uncertainties due to the spontaneous brain activity. Thus, the results suggest that an extremely detailed model of the head may be unnecessary when solving the EEG inverse problem.
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)
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.
NASA Astrophysics Data System (ADS)
Alkharji, Mohammed N.
Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The
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.
NASA Astrophysics Data System (ADS)
Locatelli, R.; Bousquet, P.; Chevallier, F.; Fortems-Cheney, A.; Szopa, S.; Saunois, M.; Agusti-Panareda, A.; Bergmann, D.; Bian, H.; Cameron-Smith, P.; Chipperfield, M. P.; Gloor, E.; Houweling, S.; Kawa, S. R.; Krol, M.; Patra, P. K.; Prinn, R. G.; Rigby, M.; Saito, R.; Wilson, C.
2013-04-01
A modelling experiment has been conceived to assess the impact of transport model errors on the methane emissions estimated by an atmospheric inversion system. Synthetic methane observations, given by 10 different model outputs from the international TransCom-CH4 model exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the PYVAR-LMDZ-SACS inverse system to produce 10 different methane emission estimates at the global scale for the year 2005. The same set-up has been used to produce the synthetic observations and to compute flux estimates by inverse modelling, which means that only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. In our framework, we show that transport model errors lead to a discrepancy of 27 Tg CH4 per year at the global scale, representing 5% of the total methane emissions. At continental and yearly scales, transport model errors have bigger impacts depending on the region, ranging from 36 Tg CH4 in north America to 7 Tg CH4 in Boreal Eurasian (from 23% to 48%). At the model gridbox scale, the spread of inverse estimates can even reach 150% of the prior flux. Thus, transport model errors contribute to significant uncertainties on the methane estimates by inverse modelling, especially when small spatial scales are invoked. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher resolution models. The analysis of methane estimated fluxes in these different configurations questions the consistency of transport model errors in current inverse systems. For future methane inversions, an improvement in the modelling of the atmospheric transport would make the estimations more accurate. Likewise, errors of the observation covariance matrix should be more consistently prescribed in future inversions in order to limit the impact of transport model errors on estimated methane fluxes.
Inverse magnetic catalysis in the linear sigma model
NASA Astrophysics Data System (ADS)
Ayala, A.; Loewe, M.; Zamora, R.
2016-05-01
We compute the critical temperature for the chiral transition in the background of a magnetic field in the linear sigma model, including the quark contribution and the thermo-magnetic effects induced on the coupling constants at one loop level. For the analysis, we go beyond mean field aproximation, by taking one loop thermo-magnetic corrections to the couplings as well as plasma screening effects for the boson's masses, expressed through the ring diagrams. We found inverse magnetic catalysis, i.e. a decreasing of the critical chiral temperature as function of the intensity of the magnetic field, which seems to be in agreement with recent results from the lattice community.
Inverse geothermal modelling applied to Danish sedimentary basins
NASA Astrophysics Data System (ADS)
Poulsen, Søren E.; Balling, Niels; Bording, Thue S.; Mathiesen, Anders; Nielsen, Søren B.
2017-10-01
This paper presents a numerical procedure for predicting subsurface temperatures and heat-flow distribution in 3-D using inverse calibration methodology. The procedure is based on a modified version of the groundwater code MODFLOW by taking advantage of the mathematical similarity between confined groundwater flow (Darcy's law) and heat conduction (Fourier's law). Thermal conductivity, heat production and exponential porosity-depth relations are specified separately for the individual geological units of the model domain. The steady-state temperature model includes a model-based transient correction for the long-term palaeoclimatic thermal disturbance of the subsurface temperature regime. Variable model parameters are estimated by inversion of measured borehole temperatures with uncertainties reflecting their quality. The procedure facilitates uncertainty estimation for temperature predictions. The modelling procedure is applied to Danish onshore areas containing deep sedimentary basins. A 3-D voxel-based model, with 14 lithological units from surface to 5000 m depth, was built from digital geological maps derived from combined analyses of reflection seismic lines and borehole information. Matrix thermal conductivity of model lithologies was estimated by inversion of all available deep borehole temperature data and applied together with prescribed background heat flow to derive the 3-D subsurface temperature distribution. Modelled temperatures are found to agree very well with observations. The numerical model was utilized for predicting and contouring temperatures at 2000 and 3000 m depths and for two main geothermal reservoir units, the Gassum (Lower Jurassic-Upper Triassic) and Bunter/Skagerrak (Triassic) reservoirs, both currently utilized for geothermal energy production. Temperature gradients to depths of 2000-3000 m are generally around 25-30 °C km-1, locally up to about 35 °C km-1. Large regions have geothermal reservoirs with characteristic temperatures
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.
Locatelli, R.; Bousquet, P.; Chevallier, F.; ...
2013-10-08
A modelling experiment has been conceived to assess the impact of transport model errors on methane emissions estimated in an atmospheric inversion system. Synthetic methane observations, obtained from 10 different model outputs from the international TransCom-CH4 model inter-comparison exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the three-component PYVAR-LMDZ-SACS (PYthon VARiational-Laboratoire de Météorologie Dynamique model with Zooming capability-Simplified Atmospheric Chemistry System) inversion system to produce 10 different methane emission estimates at the global scale for the year 2005. The same methane sinks, emissions and initial conditions have been applied to produce the 10more » synthetic observation datasets. The same inversion set-up (statistical errors, prior emissions, inverse procedure) is then applied to derive flux estimates by inverse modelling. Consequently, only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. Here in our framework, we show that transport model errors lead to a discrepancy of 27 Tg yr-1 at the global scale, representing 5% of total methane emissions. At continental and annual scales, transport model errors are proportionally larger than at the global scale, with errors ranging from 36 Tg yr-1 in North America to 7 Tg yr-1 in Boreal Eurasia (from 23 to 48%, respectively). At the model grid-scale, the spread of inverse estimates can reach 150% of the prior flux. Therefore, transport model errors contribute significantly to overall uncertainties in emission estimates by inverse modelling, especially when small spatial scales are examined. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher horizontal resolution in transport models. The large differences found between methane flux estimates inferred in these different configurations highly question the
Locatelli, R.; Bousquet, P.; Chevallier, F.; Fortems-Cheney, A.; Szopa, S.; Saunois, M.; Agusti-Panareda, A.; Bergmann, D.; Bian, H.; Cameron-Smith, P.; Chipperfield, M. P.; Gloor, E.; Houweling, S.; Kawa, S. R.; Krol, M.; Patra, P. K.; Rigby, M.; Saito, R.
2013-10-08
A modelling experiment has been conceived to assess the impact of transport model errors on methane emissions estimated in an atmospheric inversion system. Synthetic methane observations, obtained from 10 different model outputs from the international TransCom-CH4 model inter-comparison exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the three-component PYVAR-LMDZ-SACS (PYthon VARiational-Laboratoire de Météorologie Dynamique model with Zooming capability-Simplified Atmospheric Chemistry System) inversion system to produce 10 different methane emission estimates at the global scale for the year 2005. The same methane sinks, emissions and initial conditions have been applied to produce the 10 synthetic observation datasets. The same inversion set-up (statistical errors, prior emissions, inverse procedure) is then applied to derive flux estimates by inverse modelling. Consequently, only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. Here in our framework, we show that transport model errors lead to a discrepancy of 27 Tg yr^{-1} at the global scale, representing 5% of total methane emissions. At continental and annual scales, transport model errors are proportionally larger than at the global scale, with errors ranging from 36 Tg yr^{-1} in North America to 7 Tg yr^{-1} in Boreal Eurasia (from 23 to 48%, respectively). At the model grid-scale, the spread of inverse estimates can reach 150% of the prior flux. Therefore, transport model errors contribute significantly to overall uncertainties in emission estimates by inverse modelling, especially when small spatial scales are examined. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher horizontal resolution in transport models. The large differences found between methane flux estimates inferred in these different
Inverse modeling of CO surface sources using the MOPITT data
NASA Astrophysics Data System (ADS)
Pétron, G.; Granier, C.; Khattatov, B.; Lamarque, J.-F.; Yudin, V.; Gille, J.
2003-04-01
Carbon monoxide CO is a key component of the troposphere. It is the principal sink of hydroxyl radicals OH in the free troposphere (CO global mean lifetime is 2 months) and thus it controls indirectly the lifetime of many other species, such as methane CH_4. In the presence of nitrogen oxides, NO_x (>10-15 pptv), and sunlight, CO is a precursor of tropospheric ozone O_3. The processes leading to the emission of CO are fairly well established. CO is a byproduct of fossil fuel use and incomplete biomass combustion. The incomplete oxidation of hydrocarbons both natural and anthropogenic also produces substantial amounts of CO. Uncertainties attached to CO global sources are still high and, as a result, the comparison of model results and observations can show large discrepancies. These discrepancies are used to optimize the monthly sources of CO over large regions. This approach is refered to as inverse modeling. We will present results of a Bayesian inversion, obtained with our 3D global tropospheric Chemistry Transport Model (MOZART) combined with CMDL surface observations and MOPITT satellite data.
Stochastic optimization algorithm for inverse modeling of air pollution
NASA Astrophysics Data System (ADS)
Yeo, Kyongmin; Hwang, Youngdeok; Liu, Xiao; Kalagnanam, Jayant
2016-11-01
A stochastic optimization algorithm to estimate a smooth source function from a limited number of observations is proposed in the context of air pollution, where the source-receptor relation is given by an advection-diffusion equation. First, a smooth source function is approximated by a set of Gaussian kernels on a rectangular mesh system. Then, the generalized polynomial chaos (gPC) expansion is used to represent the model uncertainty due to the choice of the mesh system. It is shown that the convolution of gPC basis and the Gaussian kernel provides hierarchical basis functions for a spectral function estimation. The spectral inverse model is formulated as a stochastic optimization problem. We propose a regularization strategy based on the hierarchical nature of the basis polynomials. It is shown that the spectral inverse model is capable of providing a good estimate of the source function even when the number of unknown parameters (m) is much larger the number of data (n), m/n > 50.
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
Modeling direct and inverse problems in ferritic heat-exchanger tubes
NASA Astrophysics Data System (ADS)
Sabbagh, Harold A.; Aldrin, John C.; Murphy, R. Kim; Sabbagh, Elias H.
2012-05-01
We develop forward and inverse models, together with laboratory data, to characterize a SEACURE tube, with and without a drilled hole and/or tube-support plate (TSP). The measured data are impedances obtained using the HP4192A impedance analyzer, and model calculations are carred out using VIC-3D{copyright, serif}. We demonstrate conditions that are peculiar to ferritic tubes, and give insight into the optimum methods for characterizing the tubes and flaws within them.
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.
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
NASA Astrophysics Data System (ADS)
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
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.
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.
A direct-inverse method for transonic and separated flows about airfoils
NASA Technical Reports Server (NTRS)
Carlson, K. D.
1985-01-01
A direct-inverse technique and computer program called TAMSEP that can be sued for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicing the flowfield about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.
A direct-inverse method for transonic and separated flows about airfoils
NASA Technical Reports Server (NTRS)
Carlson, Leland A.
1990-01-01
A direct-inverse technique and computer program called TAMSEP that can be used for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicting the flow field about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.
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.
NASA Astrophysics Data System (ADS)
Kim, A.; Dreger, D. S.; Taira, T.
2009-12-01
In this study, we developed a finite-source inversion method using the waveforms of small earthquakes as empirical Green's functions (eGf) to study the rupture process of micro-earthquakes on the San Andreas fault. This method is different from the ordinarily eGf deconvolution method which deconvolves the seismogram of the smaller simpler-source event from the seismogram of the larger event recovering the moment rate function of the larger more complex-source event. In the eGf deconvolution method commonly spectral domain deconvolution is used where the small earthquake spectrum is divided from the larger target event spectrum, and low spectral values are replaced by a water-level value to damp the effect of division by small numbers (e.g. Clayton and Wiggins, 1976). The water-level is chosen by trial and error. Such a rough regularization of the spectral ratio can result in the solution having unrealistic negative values and short-period oscillations. Also the amplitude and duration of the moment rate functions can be influenced by the adopted water-level value. In this study we propose to use the eGf waveform directly in the inversion, rather than the moment rate function obtained from spectral division. In this approach the eGf is treated as the Green’s function from each subfault, and contrary to the deconvolution approach can make use multiple eGfs distributed over the fault plane. The method can therefore be applied to short source-receiver distance situations since the variation in radiation pattern due to source-receiver geometry is better accounted for. Numerical tests of the waveform eGf inversion method indicate that in the case where the large slip asperity is not located at the hypocenter, the eGf located near the asperity recovers the prescribed model better than that using an eGf co-located with the main shock hypocenter. Synthetic analyses also show that using multiple eGfs can better constrain the slip model than using only one eGf in the
NASA Astrophysics Data System (ADS)
Lehikoinen, A.; Huttunen, J. M.; Finsterle, S.; Kowalsky, M. B.; Kaipio, J. P.
2007-05-01
We extend the previously presented methodology for imaging the evolution of electrically conductive fluids in porous media. In that method, the nonstationary inversion problem was solved using Bayesian filtering. The method was demonstrated using a synthetically generated test case where the monitored target is a time-varying water plume in an unsaturated porous medium, and the imaging modality was electrical resistance tomography (ERT). The inverse problem was formulated as a state estimation problem, which is based on observation- evolution models. As an observation model for ERT, the complete electrode model was used, and for time- varying unsaturated flow, the Richards equation was used as an evolution model. Although the "true" evolution of water flow was simulated using a heterogeneous permeability field, in the inversion step the permeability was assumed to be homogeneous. This assumption leads to approximation errors that have been taken into account by constructing a statistical model between the different realizations of the accurate and the approximate fluid flow models. This statistical model was constructed using an ensemble of samples from the evolution model in a way that the construction can be carried out prior to taking observations. However, the statistics of approximation errors actually depends on observations (through the state). In this work we extend the previously presented method so that the statistics of the approximation error are adjusted based on the observations. The basic idea of the extension is to gather those samples from the ensemble which at the current time best represents the observed state. We then determine the statistics of the approximation error based on these collated samples. The extension of the methodology provides improved estimates of water saturation distributions compared to the previously presented approaches. The proposed methodology may be extended for imaging and estimating parameters of dynamical processes
A field test of inverse modeling of seed dispersal.
Sánchez, Jose M Contreras; Greene, David F; Quesada, Mauricio
2011-04-01
Seed dispersal distance-a key process in plant population dynamics-remains poorly understood because of the difficulty of finding a source plant so well isolated from conspecifics that seeds or seedlings can be unambiguously attributed to it. Inverse modeling (IM) of seed dispersal, a simple statistical technique for parameterizing dispersal kernels, has been widely used since 1992; surprisingly, however, this approach has never been verified in the field. We released from 20 nearby trees the winged seeds of a liana species, Entada polystachya, near the coast in a tropical, dry forest in Jalisco, Mexico. With a two-parameter log-normal function, we found that IM predicted both the shape and scale parameters well as long as we used the entire data set. When, however, we subsampled (thus simulating the use of transects for seedlings or an array of seed traps), the estimates of the scale and shape parameters were often more than double the real values. The problem was due to the marked anisotropy (directional bias; in this case, in the direction of the diurnal sea breeze) of the individual dispersal curves. When we randomized the direction of dispersal of individual seeds from the trees (keeping dispersal distances unchanged), predictions of parameter values were excellent. Inverse modeling must include directional parameters when dealing with areas where strong anisotropy is to be expected, e.g., for wind dispersal of seeds near coasts or pollination by any vector where a plant species is limited to a strongly linear habitat such as river banks.
Distribution functions of magnetic nanoparticles determined by a numerical inversion method
NASA Astrophysics Data System (ADS)
Bender, P.; Balceris, C.; Ludwig, F.; Posth, O.; Bogart, L. K.; Szczerba, W.; Castro, A.; Nilsson, L.; Costo, R.; Gavilán, H.; González-Alonso, D.; de Pedro, I.; Fernández Barquín, L.; Johansson, C.
2017-07-01
In the present study, we applied a regularized inversion method to extract the particle size, magnetic moment and relaxation-time distribution of magnetic nanoparticles from small-angle x-ray scattering (SAXS), DC magnetization (DCM) and AC susceptibility (ACS) measurements. For the measurements the particles were colloidally dispersed in water. At first approximation the particles could be assumed to be spherically shaped and homogeneously magnetized single-domain particles. As model functions for the inversion, we used the particle form factor of a sphere (SAXS), the Langevin function (DCM) and the Debye model (ACS). The extracted distributions exhibited features/peaks that could be distinctly attributed to the individually dispersed and non-interacting nanoparticles. Further analysis of these peaks enabled, in combination with a prior characterization of the particle ensemble by electron microscopy and dynamic light scattering, a detailed structural and magnetic characterization of the particles. Additionally, all three extracted distributions featured peaks, which indicated deviations of the scattering (SAXS), magnetization (DCM) or relaxation (ACS) behavior from the one expected for individually dispersed, homogeneously magnetized nanoparticles. These deviations could be mainly attributed to partial agglomeration (SAXS, DCM, ACS), uncorrelated surface spins (DCM) and/or intra-well relaxation processes (ACS). The main advantage of the numerical inversion method is that no ad hoc assumptions regarding the line shape of the extracted distribution functions are required, which enabled the detection of these contributions. We highlighted this by comparing the results with the results obtained by standard model fits, where the functional form of the distributions was a priori assumed to be log-normal shaped.
Inversion of heterogeneous parabolic-type equations using the pilot points method
NASA Astrophysics Data System (ADS)
Alcolea, Andrés; Carrera, Jesús; Medina, Agustín
2006-07-01
The inverse problem (also referred to as parameter estimation) consists of evaluating the medium properties ruling the behaviour of a given equation from direct measurements of those properties and of the dependent state variables. The problem becomes ill-posed when the properties vary spatially in an unknown manner, which is often the case when modelling natural processes. A possibility to fight this problem consists of performing stochastic conditional simulations. That is, instead of seeking a single solution (conditional estimation), one obtains an ensemble of fields, all of which honour the small scale variability (high frequency fluctuations) and direct measurements. The high frequency component of the field is different from one simulation to another, but a fixed component for all of them. Measurements of the dependent state variables are honoured by framing simulation as an inverse problem, where both model fit and parameter plausibility are maximized with respect to the coefficients of the basis functions (pilot point values). These coefficients (model parameters) are used for parameterizing the large scale variability patterns. The pilot points method, which is often used in hydrogeology, uses the kriging weights as basis functions. The performance of the method (both its variants of conditional estimation/simulation) is tested on a synthetic example using a parabolic-type equation. Results show that including the plausibility term improves the identification of the spatial variability of the unknown field function and that the weight assigned to the plausibility term does lead to optimal results both for conditional estimation and for stochastic simulations.
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.
Video-based Nearshore Depth Inversion using WDM Method
NASA Astrophysics Data System (ADS)
Hampson, R. W.; Kirby, J. T.
2008-12-01
A new remote sensing method for estimating nearshore water depths from video imagery has been developed and applied as part of an ongoing field study at Bethany Beach, Delaware. The new method applies Donelan et al's Wavelet Direction Method (WDM) to compact arrays of pixel intensity time series extracted from video images. The WDM generates a non-stationary time series of the wavenumber and wave direction at different frequencies that can be used to create frequency-wavenumber and directional spectrums. The water depth is estimated at the center of each compact array by fitting the linear dispersion relation to the frequency-wavenumber spectrum. Directional spectral results show good correlation to directional spectral results obtained from a slope array located just offshore of Bethany Beach. Additionally, depth estimations from the WDM are compared to depth measurements taken with a kayak survey system at Bethany Beach. Continuous measurements of the bathymetry at Bethany Beach are needed for inputs to fluid dynamics and sediment transport models to study the morphodynamics in the nearshore zone and can be used to monitor the success of the recent beach replenishment project along the Delaware coast.
Attribution of recent trends in atmospheric methane using inverse modelling
NASA Astrophysics Data System (ADS)
McNorton, Joe; Wilson, Chris; Gloor, Manuel; Chipperfield, Martyn
2017-04-01
Atmospheric methane (CH4) accounts for approximately 20% of the total direct anthropogenic radiative forcing by long-lived greenhouse gases (0.48±0.05 Wm-2), the second largest contributor after CO2. Atmospheric observations highlight two notable changes in CH4 since 2007. Firstly, the growth rate of methane increased to ˜7ppb/yr. Secondly, the CH4 13C/12C-ratio (δ13C) has become increasingly 13C-depleted. One possible explanation for both of these, is an increase in 13C-depleted CH4 emissions. This could be through increases in natural biogenic sources (e.g. wetlands), anthropogenic biogenic sources (e.g. agriculture) or a combination of both. A decrease in 13C-enriched non-biogenic emissions (e.g. biomass burning) could be an explanation for the 13C-depletion, but does not explain the CH4 increase. A reduction in the atmospheric concentration of OH, the main oxidant for atmospheric methane, could also explain both 13C-depletion and CH4 increase. We have performed a synthesis inversion using a 3-D atmospheric global chemical transport model, TOMCAT, for both CH4 and δ13C from 2005-2014. The inversion uses surface observations of both CH4 and δ13C to spatially constrain source types and possible changes to OH concentration. We will use results from this synthesis inversion to attribute the upturn in CH4 growth to specific source and sinks, and to discuss the uncertainties in this attribution.
Piovesan, Davide; Pierobon, Alberto; Dizio, Paul; Lackner, James R
2011-03-01
A common problem in the analyses of upper limb unfettered reaching movements is the estimation of