Inverse substructure method for model updating of structures
NASA Astrophysics Data System (ADS)
Weng, Shun; Xia, Yong; Zhou, Xiao-Qing; Xu, You-Lin; Zhu, Hong-Ping
2012-12-01
Traditional model updating of large-scale structures is usually time-consuming because the global structural model needs to be repeatedly re-analyzed as a whole to match global measurements. This paper proposes a new substructural model updating method. The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions. The method is extended to the case when the measurement is carried out at partial degrees-of-freedom of the structure. The extracted substructural flexibility matrices are then used as references for updating the corresponding substructural models. An orthogonal projector is employed on both the extracted substructural measurements and the substructural models to remove the rigid body modes of the free-free substructures. Compared with the traditional model updating at the global structure level, only the sub-models at the substructural level are re-analyzed in the proposed substructure-based model updating process, resulting in a rapid convergence of optimization. Moreover, only measurement on the local area corresponding to the concerned substructures is required, and those on other components can be avoided. The effectiveness and efficiency of the proposed substructuring method are verified through applications to a laboratory-tested frame structure and a large-scale 600 m tall Guangzhou New TV Tower. The present technique is referred to as the inverse substructuring model updating method as the measured global modal data are disassembled into the substructure level and then the updating is conducted on the substructures only. This differs from the substructuring model updating method previously proposed by the authors, in which the model updating is still conducted in the global level and the numerical global modal data are assembled from those of substructures. That can be referred to as the forward substructuring model
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.
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
2001-01-01
For interpreting observational data, and in particular for use in inverse methods, accurate and realistic chemical transport models are essential. Toward this end we have, in recent years, helped develop and utilize a number of three-dimensional models including the Model for Atmospheric Transport and Chemistry (MATCH).
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. PMID:21874959
Interpretation of Trace Gas Data Using Inverse Methods and Global Chemical Transport Models
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
1997-01-01
This is a theoretical research project aimed at: (1) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for long lived gases important in ozone depletion and climate forcing, (2) utilization of inverse methods to determine these source/sink strengths which use the NCAR/Boulder CCM2-T42 3-D model and a global 3-D Model for Atmospheric Transport and Chemistry (MATCH) which is based on analyzed observed wind fields (developed in collaboration by MIT and NCAR/Boulder), (3) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple titrating gases, and, (4) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3-D models. Important goals include determination of regional source strengths of methane, nitrous oxide, and other climatically and chemically important biogenic trace gases and also of halocarbons restricted by the Montreal Protocol and its follow-on agreements and hydrohalocarbons used as alternatives to the restricted halocarbons.
Studies of Trace Gas Chemical Cycles Using Inverse Methods and Global Chemical Transport Models
NASA Technical Reports Server (NTRS)
Prinn, Ronald G.
2003-01-01
We report progress in the first year, and summarize proposed work for the second year of the three-year dynamical-chemical modeling project devoted to: (a) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for long lived gases important in ozone depletion and climate forcing, (b) utilization of inverse methods to determine these source/sink strengths using either MATCH (Model for Atmospheric Transport and Chemistry) which is based on analyzed observed wind fields or back-trajectories computed from these wind fields, (c) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple titrating gases, and (d) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3D models. Important goals include determination of regional source strengths of methane, nitrous oxide, methyl bromide, and other climatically and chemically important biogenic/anthropogenic trace gases and also of halocarbons restricted by the Montreal protocol and its follow-on agreements and hydrohalocarbons now used as alternatives to the restricted halocarbons.
A comparison of three gravity inversion methods for crustal thickness modelling in Tibet plateau
NASA Astrophysics Data System (ADS)
Bagherbandi, Mohammad
2012-01-01
Crustal thickness can be determined by gravimetric methods based on different assumptions, e.g. by isostatic hypotheses. Here we compare three gravimetric inversion methods to estimate the Moho depth. Two Moho models based on the Vening Meinesz-Moritz hypothesis and one by using Parker-Oldenburg's algorithm, which are investigated in Tibet plateau. The results are compared with CRUST2.0, and it will be presented that the estimated Moho depths from the Vening Meinesz-Moritz model will be better than the Parker-Oldenburg's algorithm.
Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H
2016-05-01
The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel. PMID:27250181
Integration of Multiple Field Methods in Characterizing a Field Site with Bayesian Inverse Modeling
NASA Astrophysics Data System (ADS)
Savoy, H.; Dietrich, P.; Osorio-Murillo, C. A.; Kalbacher, T.; Kolditz, O.; Ames, D. P.; Rubin, Y.
2014-12-01
A hydraulic property of a field can be expressed as a space random function (SRF), and the parameters of that SRF can be constrained by the Method of Anchored Distributions (MAD). MAD is a general Bayesian inverse modeling technique that quantifies the uncertainty of SRF parameters by integrating various direct local data along with indirect non-local data. An example is given with a high-resolution 3D aquifer analog with known hydraulic conductivity (K) and porosity (n) at every location. MAD is applied using different combinations of simulated measurements of K, n, and different scales of hydraulic head that represent different field methods. The ln(K) and n SRF parameters are characterized with each of the method combinations to assess the influence of the methods on the SRFs and their implications. The forward modeling equations are solved by the numerical modeling software OpenGeoSys (opengeosys.org) and MAD is applied with the software MAD# (mad.codeplex.com). The inverse modeling results are compared to the aquifer analog for success evaluation. The goal of the study is to show how integrating combinations of multi-scale and multi-type measurements from the field via MAD can be used to reduce the uncertainty in field-scale SRFs, as well as point values, of hydraulic properties.
FEMSECT: An inverse section model based on the finite element method
NASA Astrophysics Data System (ADS)
Losch, M.; Sidorenko, D.; Beszczynska-MöLler, A.
2005-12-01
A new inverse model is presented for the analysis of hydrographic section data in conjunction with velocity measurements. The model offers advantages over commonly applied interpolation techniques because it combines data and physical assumptions such as geostrophic balance in the framework of a finite element discretization. Specifically, a quadratic objective function of model-data misfits is minimized to give estimates of transports together with formal error estimates. The finite element method allows the accurate representation of highly irregular bottom topography and ensures consistent interpolation of model variables to measurement points. The model is called Finite Element Method Section model (FEMSECT). FEMSECT also gives improved flexibility and performance over standard box models by allowing dynamic adjustment of the model variables temperature and salinity. Idealized test cases illustrate that the finite element methods solve the thermal wind equations far more accurately than standard finite difference methods, especially in the presence of steep topography. For a more realistic test, FEMSECT is applied to hydrographic conductivity-temperature-depth section data and moored instrument current meter measurements from an array in the Fram Strait. Transport estimates by FEMSECT prove to be more robust and less sensitive to the spatial data resolution than estimates by a conventional interpolation method that only uses information from moored instruments. FEMSECT is available as a highly portable Matlab code and can be run on an ordinary desktop computer.
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.
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. PMID:22559695
A novel model for diffusion based release kinetics using an inverse numerical method.
Mohammadi, Hadi; Herzog, Walter
2011-10-01
We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important. PMID:21382735
NASA Astrophysics Data System (ADS)
Revil, A.
2009-12-01
We will present new developments in the seismoelectric method in the case of porous media saturated by one Newtonian fluid, two immiscible Newtonian fluids, or one viscoelastic fluid like heavy oil. Rather than using the classical approach based on the zeta potential, our approach rely on a volumetric charge density of the pore volume, which is in turn related to the permeability. We will show how seismoelectric propoerties can be derived from an analysis of the complex conductivity in porous rocks and the analysis of self-potential signals of electrokientic nature. The connection between spectral induced polarization, streaming potential, and seismoelectric properties will be made in the case of a sand saturated by a simple supporting electrolyte. The seismoelectric field equations are solved with Comsol Multiphysics 3.5. We will present various applications of the seimoelectric methods to detect interface like the water table and to remotely determine the material properties of oil and gas reservoirs or DNAPL plumes. In each application, we will discss both the co-seismic signals and the seismoelectric conversions. In the case of a porous material saturated by a viscoelastic fluid, we will show that the resonance of the fluid can lead to a huge amplification of the seismoelectric response. Inverse modeling can be done with a variety of deterministic and stochastic algorithms. Several cases will be discussed regarding the inversion of material properties and boundaries.
NASA Astrophysics Data System (ADS)
Aldrin, John C.; Shell, Eric B.; Oneida, Erin K.; Sabbagh, Harold A.; Sabbagh, Elias; Murphy, R. Kim; Mazdiyasni, Siamack; Lindgren, Eric A.
2016-02-01
The objective of this work is to demonstrate and validate model-based inversion techniques to characterize length, depth, width and orientation of surface-breaking cracks using eddy current NDE under varying probe conditions. A series of parametric studies of probe characteristics are presented for a fixed set of well-characterized flaws with varying length, depth, opening width and orientation angle. Results show inversion performance differences between probes with the same design specifications. Inversion results were also evaluated for a probe that was selectively controlled for varying probe liftoff, varying tilt in two directions, and orientation. Certain levels of probe tilt and liftoff were found to degrade the performance of the inversion technique. By using a model calibration process that incorporates the matching probe calibration data, better inversion results can be achieved, to a limited degree. There is a need to more appropriately adapt the model through the calibration fit to compensate for varying probe tilt and liftoff. Results are presented for a model transform approach, evaluating scale and phase terms based on the best model fit with the calibration data. The results for certain severe cases of liftoff were improved using the transformed model; however, it does not address all probe conditions. Future work is proposed to use a full model-based transformation approach using more comprehensive meta-model representations.
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.
Identification of strain-rate and thermal sensitive material model with an inverse method
NASA Astrophysics Data System (ADS)
Peroni, L.; Scapin, M.; Peroni, M.
2010-06-01
This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strainrates and temperatures. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields) or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena). Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work. The method presented requires strong effort both from experimental and numerical point of view, anyway it allows to precisely identify the parameters of different material models. This could provide great advantages when high reliability of the material behaviour is necessary. Applicability of this method is particularly indicated for special applications in the field of aerospace engineering, ballistic, crashworthiness studies or particle accelerator technologies, where materials could be submitted to strong plastic deformations at high-strain rate in a wide range of temperature. Thermal softening effect has been investigated in a temperature range between 20°C and 1000°C.
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)
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 Technical Reports Server (NTRS)
Hartley, Dana; Prinn, Ronald
1993-01-01
The paper investigates the feasibility of using an inverse method based on a linear Kalman filter in a three-dimensional atmospheric transport model, for the determination of regional surface fluxes with rapid convergence, using data from a finite number of observation sites. It was found that the inverse method used was capable to accurately determine regional surface fluxes using the present ALE/GALE sites, and to converge to the correct solution within a year or two, using initial conditions very different from the final solution.
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
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.
NASA Astrophysics Data System (ADS)
Xu, Zhengwei
Modeling of induced polarization (IP) phenomena is important for developing effective methods for remote sensing of subsurface geology and is widely used in mineral exploration. However, the quantitative interpretation of IP data in a complex 3D environment is still a challenging problem of applied geophysics. In this dissertation I use the regularized conjugate gradient method to determine the 3D distribution of the four parameters of the Cole-Cole model based on surface induced polarization (IP) data. This method takes into account the nonlinear nature of both electromagnetic induction (EMI) and IP phenomena. The solution of the 3D IP inverse problem is based on the regularized smooth inversion only. The method was tested on synthetic models with DC conductivity, intrinsic chargeability, time constant, and relaxation parameters, and it was also applied to the practical 3D IP survey data. I demonstrate that the four parameters of the Cole-Cole model, DC electrical resistivity, rho 0 , chargeability, eta time constant, tau and the relaxation parameter, C, can be recovered from the observed IP data simultaneously. There are four Cole-Cole parameters involved in the inversion, in other words, within each cell, there are DC conductivity (sigma0 ), chargeability (eta), time parameters (tau), and relaxation parameters (C) compared to conductivity only, used in EM only inversion. In addition to more inversion parameters used in IP survey, dipole-dipole configuration which requires more sources and receivers. One the other hand, calculating Green tensor and Frechet matrix time consuming and storing them requires a lot of memory. So, I develop parallel computation using MATLAB parallel tool to speed up the calculation.
Estimating the Hydraulic Properties of Mountainous Podzol Soils Using Inverse Modeling Methods
NASA Astrophysics Data System (ADS)
Kuraz, Michal; Jacka, Lukas; Havlicek, Vojtech; Pavlasek, Jirka; Pech, Pavel
2016-04-01
The aim of this research is an evaluation of the soil hydraulic parameters (SHP) for a mountainous podzolic soil profile. The SHPs for the lower layers can be identified using standard approaches - a single ring (SR) infiltration experiment and a Guelph permeameter (GP) measurement. However, the thickness of the top soil layer is often much lower than the depth required to embed an SR or GP device, and the SHP for the top soil layer exhibits large temporal and spatial changes due to changes in vegetation activity during the seasons and a distinct alternation of wetting and drying cycles. SHPs for the top soil layer are therefore very difficult to measure directly. The SHPs for the top soil layer were therefore 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. We discuss issues in assigning the initial and boundary condition setup, and the influence of spatial and temporal discretization on the values of the identified SHPs. 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 Kuraz et al. (2013, 2014, 2015) 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.
NASA Astrophysics Data System (ADS)
Xue, Haile; Shen, Xueshun; Chou, Jifan
2015-10-01
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
Best Basis Methods for the Modelling and Inversion of Potential Fields
NASA Astrophysics Data System (ADS)
Michel, Volker; Telschow, Roger
2016-04-01
There are many trial functions (e.g. on the sphere) available which can be used for the modelling of a potential field. Among them are orthogonal polynomials such as spherical harmonics and radial basis functions such as spline or wavelet basis functions. We present an algorithm, the Regularized Functional Matching Pursuit (RFMP), and an enhancement (the ROFMP), which construct a kind of a best basis out of trial functions of different kinds. This basis is tailored for the particular problem and the given data set. The objective of the optimization is the minimization of the Tikhonov-regularized data misfit. One main advantage is that the constructed approximation inherits the advantages of the different basis systems. By including spherical harmonics, coarse global structures can be represented in a sparse way. However, the additional use of spline basis functions allows a stable handling of scattered data grids. Furthermore, the inclusion of wavelets and scaling functions yields a multiscale analysis of the potential. In addition, ill-posed inverse problems (like a downward continuation or the inverse gravimetric problem) can be regularized with the algorithm. We show some numerical examples to demonstrate the possibilities which the algorithms provide.
NASA Astrophysics Data System (ADS)
Murphy, R. Kim; Sabbagh, Harold A.; Sabbagh, Elias H.; Zhou, Liming; Bernacchi, William; Aldrin, John C.; Forsyth, David; Lindgren, Eric
2016-02-01
The use of coupled integral equations and anomalous currents allows us to efficiently remove `background effects' in either forward or inverse modeling. This is especially true when computing the change in impedance due to a small flaw in the presence of a larger background anomaly. It is more accurate than simply computing the response with and without the flaw and then subtracting the two nearly equal values to obtain the small difference due to the flaw. The problem that we address in this paper involves a 'SplitD' probe that includes complex, noncircular coils, as well as ferrite cores, inserted within a bolt hole, and exciting both the bolt hole and an adjacent flaw. This introduces three coupled anomalies, each with its on 'scale.' The largest, of course, is the bolt hole, followed (generally) by the probe, and then the flaw. The overall system is represented mathematically by three coupled volume-integral equations. We describe the development of the model and its code, which is a part of the general eddy-current modeling code, VIC-3D®. We present initial validation results, as well as a number of model computations with flaws located at various places within the bolt hole.
Bledsoe, Keith C.
2015-04-01
The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric. This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hirahara, K.; Hori, T.; Hyodo, M.; Hori, M.
2013-12-01
Many studies have focused on geodetic inversion analysis method of coseismic slip distribution with combination of observation data of coseismic crustal deformation on the ground and simplified crustal models such like analytical solution in elastic half-space (Okada, 1985). On the other hand, displacements on the seafloor or near trench axes due to actual earthquakes has been observed by seafloor observatories (e.g. the 2011 Tohoku-oki Earthquake (Tohoku Earthquake) (Sato et. al. 2011) (Kido et. al. 2011)). Also, some studies on tsunamis due to the Tohoku Earthquake indicate that large fault slips near the trench axis may have occurred. Those facts suggest that crustal models considering complex geometry and heterogeneity of the material property near the trench axis should be used for geodetic inversion analysis. Therefore, our group has developed a mesh generation method for finite element models of the Japanese Islands of higher fidelity and a fast crustal deformation analysis method for the models. Degree-of-freedom of the models generated by this method is about 150 million. In this research, the method is extended for inversion analyses of coseismic slip distribution. Since inversion analyses need computation of hundreds of slip response functions due to a unit fault slip assigned for respective divided cells on the fault, parallel computing environment is used. Plural crustal deformation analyses are simultaneously run in a Message Passing Interface (MPI) job. In the job, dynamic load balancing is implemented so that a better parallel efficiency is obtained. Submitting the necessary number of serial job of our previous method is also possible, but the proposed method needs less computation time, places less stress on file systems, and allows simpler job management. A method for considering the fault slip right near the trench axis is also developed. As the displacement distribution of unit fault slip for computing response function, 3rd order B
NASA Astrophysics Data System (ADS)
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.
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.
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.
NASA Astrophysics Data System (ADS)
Masson, Y.; Pierre, C.; Romanowicz, B. A.; French, S. W.; Yuan, H.
2014-12-01
Yuan et al. (2013) developed a 3D radially anisotropic shear wave model of North America (NA) upper mantle based on full waveform tomography, combining teleseismic and regional distance data sampling the NA. In this model, synthetic seismograms associated with regional events (i.e. events located inside in the region imaged NA) were computed exactly using the Spectral Element method (Cupillard et al., 2012), while, synthetic seismograms associated with teleseismic events were performed approximately using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). Both the regional and the teleseismic dataset have been inverted using approximate sensitivity kernels based upon normal mode theory. Our objective is to improve our current model and to build the next generation model of NA by introducing new methodological developments (Masson et al., 2014) that allow us to compute exact synthetic seismograms as well as adjoint sensitivity kernels associated with teleseismic events, using mostly regional computations of wave propagation. The principle of the method is to substitute a teleseismic source (i.e. an earthquake) by an "equivalent" set of seismic sources acting on the boundaries of the region to be imaged that is producing exactly the same wavefield. Computing the equivalent set of sources associated with each one of the teleseismic events requires a few global simulations of the seismic wavefield that can be done once for all, prior to the regional inversion. Then, the regional full waveform inversion can be preformed using regional simulations only. We present a 3D model of NA demonstrating the advantages of the proposed method.
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.
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
A Bayesian method for microseismic source inversion
NASA Astrophysics Data System (ADS)
Pugh, D. J.; White, R. S.; Christie, P. A. F.
2016-05-01
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)
Kneller, Erik A.; Johnson, Christopher A.; Karner, Garry D.; Einhorn, Jesse; Queffelec, Thomas A.
2012-12-01
Published plate reconstructions commonly show significant differences in initial plate configuration and syn-extensional opening directions. The variability of published models is primarily due to the difficulty associated with restoring crustal stretching history. Here we present an inverse non-rigid kinematic method that inverts plate motion and present day crustal thickness to approximate the history of bulk lateral strain and crustal thinning associated with lithospheric stretching. The kinematic link between plate motion and bulk crustal thickness that is used with this method is based on insights obtained from geodynamic models. We implement this approach in open source kinematic modeling software and apply it to test new Early Mesozoic plate kinematic models of the Central Atlantic. This application shows that the patterns of stretching inferred from the syn-rift basins of the Newark Supergroup can be explained if (1) syn-rift Euler pole flow lines were parallel to the Grand Banks transform margin and (2) initial formation of the East Coast Margin Igneous Province was coincident with the formation of the Central Atlantic Magmatic Province. These syn-rift to breakup models of the Central Atlantic lead to better constrained models of early seafloor spreading that show full spreading velocities in the ultraslow regime and within the transition from ultraslow to slow spreading regimes.
A generalized inversion method: Simultaneous source localization and environmental inversion
NASA Astrophysics Data System (ADS)
Neilsen, Tracianne B.; Knobles, David P.
2002-05-01
The problem of localizing and tracking a source in the shallow ocean is often complicated by uncertainty in the environmental parameters. Likewise, the estimates of environmental parameters in the shallow ocean obtained by inversion methods can be degraded by incorrect information about the source location. To overcome both these common obstacles-environmental mismatch in matched field processing and incorrect source location in geoacoustic inversions-a generalized inversion scheme is developed that includes both source and environmental parameters as unknowns in the inversion. The new technique called systematic decoupling using rotated coordinates (SDRC) expands the original idea of rotated coordinates [M. D. Collins and L. Fishman, J. Acoust. Soc. Am. 98, 1637-1644 (1995)] by using multiple sets of coherent broadband rotated coordinates, each corresponding to a different set of bounds, to systematically decouple the unknowns in a series of simulated annealing inversions. The results of applying the SDRC inversion method to data from the Area Characterization Test II experiment performed on the New Jersey continental shelf are presented. [Work supported by ONR.
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.
Inverse methods-based estimation of plate coupling in a plate motion model governed by mantle flow
NASA Astrophysics Data System (ADS)
Ratnaswamy, V.; Stadler, G.; Gurnis, M.
2013-12-01
Plate motion is primarily controlled by buoyancy (slab pull) which occurs at convergent plate margins where oceanic plates undergo deformation near the seismogenic zone. Yielding within subducting plates, lateral variations in viscosity, and the strength of seismic coupling between plate margins likely have an important control on plate motion. Here, we wish to infer the inter-plate coupling for different subduction zones, and develop a method for inferring it as a PDE-constrained optimization problem, where the cost functional is the misfit in plate velocities and is constrained by the nonlinear Stokes equation. The inverse models have well resolved slabs, plates, and plate margins in addition to a power law rheology with yielding in the upper mantle. Additionally, a Newton method is used to solve the nonlinear Stokes equation with viscosity bounds. We infer plate boundary strength using an inexact Gauss-Newton method with line search for backtracking. Each inverse model is applied to two simple 2-D scenarios (each with three subduction zones), one with back-arc spreading and one without. For each case we examine the sensitivity of the inversion to the amount of surface velocity used: 1) full surface velocity data and 2) surface velocity data simplified using a single scalar average (2-D equivalent to an Euler pole) for each plate. We can recover plate boundary strength in each case, even in the presence of highly nonlinear flow with extreme variations in viscosity. Additionally, we ascribe an uncertainty in each plate's velocity and perform an uncertainty quantification (UQ) through the Hessian of the misfit in plate velocities. We find that as plate boundaries become strongly coupled, the uncertainty in the inferred plate boundary strength decreases. For very weak, uncoupled subduction zones, the uncertainty of inferred plate margin strength increases since there is little sensitivity between plate margin strength and plate velocity. This result is significant
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.
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.
An inverse method for the design of bodies of revolution by boundary integral modelling
NASA Astrophysics Data System (ADS)
Lewis, R. I.
A surface vorticity boundary integral method is presented for the design of bodies of revolution in axisymmetric flow. The analysis finds the desired body shape to deliver a prescribed surface potential flow velocity or pressure distribution. To achieve this the body surface is simulated by a flexible vorticity sheet of prescribed strength. Starting from an arbitrary first guess for the body shape, normally an ellipsoid, the flexible vortex sheet is successively realigned with its own self-induced flow field during an iterative process which converges accurately onto the desired shape. A well-proven analysis method is also presented for back-checking the final design.
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.
An exact inverse method for subsonic flows
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1988-01-01
A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.
Application of the least-squares inversion method: Fourier series versus waveform inversion
NASA Astrophysics Data System (ADS)
Min, Dong-Joo; Shin, Jungkyun; Shin, Changsoo
2015-11-01
We describe an implicit link between waveform inversion and Fourier series based on inversion methods such as gradient, Gauss-Newton, and full Newton methods. Fourier series have been widely used as a basic concept in studies on seismic data interpretation, and their coefficients are obtained in the classical Fourier analysis. We show that Fourier coefficients can also be obtained by inversion algorithms, and compare the method to seismic waveform inversion algorithms. In that case, Fourier coefficients correspond to model parameters (velocities, density or elastic constants), whereas cosine and sine functions correspond to components of the Jacobian matrix, that is, partial derivative wavefields in seismic inversion. In the classical Fourier analysis, optimal coefficients are determined by the sensitivity of a given function to sine and cosine functions. In the inversion method for Fourier series, Fourier coefficients are obtained by measuring the sensitivity of residuals between given functions and test functions (defined as the sum of weighted cosine and sine functions) to cosine and sine functions. The orthogonal property of cosine and sine functions makes the full or approximate Hessian matrix become a diagonal matrix in the inversion for Fourier series. In seismic waveform inversion, the Hessian matrix may or may not be a diagonal matrix, because partial derivative wavefields correlate with each other to some extent, making them semi-orthogonal. At the high-frequency limits, however, the Hessian matrix can be approximated by either a diagonal matrix or a diagonally-dominant matrix. Since we usually deal with relatively low frequencies in seismic waveform inversion, it is not diagonally dominant and thus it is prohibitively expensive to compute the full or approximate Hessian matrix. By interpreting Fourier series with the inversion algorithms, we note that the Fourier series can be computed at an iteration step using any inversion algorithms such as the
NASA Astrophysics Data System (ADS)
Zidikheri, Meelis J.; Potts, Rodney J.
2015-09-01
A simple inversion scheme for optimizing volcanic emission dispersion model parameters with respect to satellite detections is presented in this paper. In this scheme, multiple dispersion model simulations, obtained by varying relevant model parameters, are created and compared against satellite detections using pattern correlation as a measure of model agreement with observations. It is shown that the scheme is successful in inferring emission source parameters such as those describing the vertical extent of the nascent sulfur dioxide emissions in the November 2010 Mount Merapi eruption in Java, Indonesia. These optimal parameter values then become a basis for improved forecasts of the transport of volcanic emissions.
Statistical versus nonstatistical temperature inversion methods
NASA Technical Reports Server (NTRS)
Smith, W. L.; Fleming, H. E.
1972-01-01
Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.
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
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
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
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
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
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
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.
Ocean reverberation: Modeling, measurements and inversions
NASA Astrophysics Data System (ADS)
Zhou, Ji-Xun; Zhang, Xue-Zhen; Peng, Zhaohui; Li, Zhenglin
2012-11-01
Research on ocean reverberation has practical and scientific significance. Much progress has been made in the past three decades to improve our understanding of reverberation. However, there remain important unanswered questions and a real scarcity of high-quality basic research data sets. New progress on the reverberation modeling and the low-frequency (LF) seabed scattering characterization in shallow water (SW) requires three essential conditions: 1). A reliable reverberation model using a physics-based seabed scattering function, 2). Carefully calibrated broadband reverberation data, and 3). A ground truth about the seabed geoacoustic model. Some related work on these topics is introduced in this paper. The energy flux method for SW reverberation is briefly introduced. Integration of this method with physics-based seabed scattering models directly and intuitively results in a general expression for SW reverberation. A simple relationship between the classic scattering cross-section and the modal scattering matrix is derived. Some basic research data sets, including the reverberation level/vertical coherence as a function of time, frequency, depth/hydrophone separation and sea state, are reported. Reverberation data and model predictions are in good agreement, which results in some inversion results. The HF seabed scattering models and the energy flux method-derived reverberation model are validated using LF reverberation broadband data.
Putz, Ana-Maria; Putz, Mihai V
2012-01-01
The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands' assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature. PMID:23443102
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M.; Tuma, M.
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Crosswell born inversion for heterogeneous velocity models
Hegge, R.F.; Herman, G.C.; Sevink, A.G.J.
1994-12-31
The application of high-frequency asymptotic Born inverse scattering methods to cross-well imaging is discussed and illustrated with a number of model studies for synthetic data. In particular, attention is given to imaging problems that are associated with typical cross-well geometries. A severe problem is the existence of multiple travel paths between sources and receivers that are particularly apparent if low-velocity layers are present. When this occurs, the high-frequency asymptotic imaging method is no longer valid and large artifacts in the images can result. However, it is concluded that, even in the case of multiple travel paths, good images can be obtained by omitting the singularities in the imaging formula and by combining the results for different source locations.
Inverse Modeling Via Linearized Functional Minimization
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Wohlberg, B.; Vesselinov, V. V.; Tartakovsky, D. M.
2014-12-01
We present a novel parameter estimation methodology for transient models of geophysical systems with uncertain, spatially distributed, heterogeneous and piece-wise continuous parameters.The methodology employs a bayesian approach to propose an inverse modeling problem for the spatial configuration of the model parameters.The likelihood of the configuration is formulated using sparse measurements of both model parameters and transient states.We propose using total variation regularization (TV) as the prior reflecting the heterogeneous, piece-wise continuity assumption on the parameter distribution.The maximum a posteriori (MAP) estimator of the parameter configuration is then computed by minimizing the negative bayesian log-posterior using a linearized functional minimization approach. The computation of the MAP estimator is a large-dimensional nonlinear minimization problem with two sources of nonlinearity: (1) the TV operator, and (2) the nonlinear relation between states and parameters provided by the model's governing equations.We propose a a hybrid linearized functional minimization (LFM) algorithm in two stages to efficiently treat both sources of nonlinearity.The relation between states and parameters is linearized, resulting in a linear minimization sub-problem equipped with the TV operator; this sub-problem is then minimized using the Alternating Direction Method of Multipliers (ADMM). The methodology is illustrated with a transient saturated groundwater flow application in a synthetic domain, stimulated by external point-wise loadings representing aquifer pumping, together with an array of discrete measurements of hydraulic conductivity and transient measurements of hydraulic head.We show that our inversion strategy is able to recover the overall large-scale features of the parameter configuration, and that the reconstruction is improved by the addition of transient information of the state variable.
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-31
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
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.
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)
Aldrin, John C.; Sabbagh, Harold A.; Zhao, Liming; Sabbagh, Elias; Murphy, R. Kim; Keiser, Mark; Flores-Lamb, Jennifer; Forsyth, David S.; Motes, Doyle; Lindgren, Eric A.; Mooers, Ryan
2016-02-01
A comprehensive approach is presented to perform model-based inversion of crack characteristics using bolt hole eddy current (BHEC) techniques. Data was acquired for a wide range of crack sizes and shapes, including mid-bore, corner and through-thickness crack types, and from both standard eddy current hardware and a prototype BHEC system with z-axis position encoding. Signal processing algorithms were developed to process and extract features from the 2D data sets, and inversion algorithms using VIC-3D generated surrogate models were used for inverting crack size. New model results are presented, which now address the effect of having a corner crack at an edge and a through crack adjacent to two edges. A two-step inversion process was implemented that first evaluates the material layer thickness, crack type and location, in order to select the most appropriate VIC-3D surrogate model for subsequent crack sizing inversion step. Inversion results for select mid-bore, through and corner crack specimens are presented where sizing performance was found to be satisfactory in general, but also depend on the size and location of the flaw.
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
Sensitivity Analysis of Inverse Methods in Eddy Current Pit Characterization
NASA Astrophysics Data System (ADS)
Aldrin, John C.; Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Knopp, Jeremy S.
2010-02-01
A sensitivity analysis was performed for a pit characterization problem to quantify the impact of potential sources for variation on the performance of inverse methods. Certain data processing steps, including careful feature extraction, background clutter removal and compensation for variation in the scan step size through the tubing, were found to be critical to achieve good estimates of the pit depth and diameter. Variance studied in model probe dimensions did not adversely affect performance.
NASA Astrophysics Data System (ADS)
Kerschberger, P.; Gehrer, A.
2010-08-01
In recent years an increased interest in pump-turbines has been recognized in the market. The rapid availability of pumped storage schemes and the benefits to the power system by peak lopping, providing reserve and rapid response for frequency control are becoming of growing advantage. In that context it is requested to develop pump-turbines that reliably stand dynamic operation modes, fast changes of the discharge rate by adjusting the variable diffuser vanes as well as fast changes from pump to turbine operation. Within the present study various flow patterns linked to the operation of a pump-turbine system are discussed. In that context pump and turbine mode are presented separately and different load cases at both operation modes are shown. In order to achieve modern, competitive pump-turbine designs it is further explained which design challenges should be considered during the geometry definition of a pump-turbine impeller. Within the present study a runner-blade profile for a low head pump-turbine has been developed. For the initial hydraulic runner-blade design, an inverse design method has been applied. Within this design procedure, a first blade geometry is generated by imposing the pressure loading-distribution and by means of an inverse 3D potential-flow-solution. The hydraulic behavior of both, pump-mode and turbine-mode is then evaluated by solving the full 3D Navier-Stokes equations in combination with a robust turbulence model. Based on this initial design the blade profile has been further optimized and redesigned considering various hydraulic pump-turbine requirements. Finally, the progress in hydraulic design is demonstrated by model test results which show a significant improvement in hydraulic performance compared to an existing reference design.
Frequency-domain elastic full-waveform multiscale inversion method based on dual-level parallelism
NASA Astrophysics Data System (ADS)
Li, Yuan-Yuan; Li, Zhen-Chun; Zhang, Kai; Zhang, Xuan
2015-12-01
The complexity of an elastic wavefield increases the nonlinearity of inversion. To some extent, multiscale inversion decreases the nonlinearity of inversion and prevents it from falling into local extremes. A multiscale strategy based on the simultaneous use of frequency groups and layer stripping method based on damped wave field improves the stability of inversion. A dual-level parallel algorithm is then used to decrease the computational cost and improve practicability. The seismic wave modeling of a single frequency and inversion in a frequency group are computed in parallel by multiple nodes based on multifrontal massively parallel sparse direct solver and MPI. Numerical tests using an overthrust model show that the proposed inversion algorithm can effectively improve the stability and accuracy of inversion by selecting the appropriate inversion frequency and damping factor in lowfrequency seismic data.
Significant uncertainty exists in the magnitude and variability of ammonia (NH3) emissions. NH3 emissions are needed as input for air quality modeling of aerosols and deposition of nitrogen compounds. Approximately 85% of NH3 emissions are estimated to come from agricultural ...
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.
Hybrid optimization methods for Full Waveform Inversion
NASA Astrophysics Data System (ADS)
Datta, D.; Sen, M. K.
2014-12-01
FWI is slowly becoming the mainstream method to estimate velocity models of the subsurface from seismic data. Typically it makes use of a gradient descent approach in which a model update is computed by back propagating the residual seismograms and cross correlating with the forward propagating wavefields at each grid point in the subsurface model. FWI is a local optimization technique, which requires the starting model to be very close to the true model. Because the objective function is multimodal with many local minima, the requirement of good starting model becomes essential. A starting model is generated using travel time tomography. We propose two hybrid FWI algorithms one of which generates a very good starting model for a conventional FWI and the other, which works with a population of models uses gradient information from multiple starting locations in guiding the search. The first approach uses a sparse parameterization of model space using non-oscillatory splines, whose coeffiencts are estimated using an optimization algorithm like very fast simulated annealing (VFSA) by minimizing the misfit between the observed and synthetic data. The estimated velocity model is then used as a starting model for gradient-based FWI. This is done in the shot domain by converting the end-on marine geometry to a split spread geometry using the principle of reciprocity. The second approach is to uses an alternate global optimization algorithm called particle swarm optimization (PSO) where PSO update rules are applied. However, we employ a new gradient guided PSO that exploits the gradient information as well. This approach avoids the local minima and converges faster than a conventional PSO. We demonstrate our methods with application to 2D marine data sets from offshore India. Each line comprises over 1000 shots; our hybrid methods produce geologically meaningful velocity models fairly rapidly on a GPU cluster. We show that starting with the hybrid model gives a much
Inverse modeling of GPR signal for estimating soil water content
NASA Astrophysics Data System (ADS)
Lambot, S.; van den Bosch, I.; Slob, E. C.; Stockbroeckx, B.; Scheers, B.; Vanclooster, M.
2003-04-01
For a large variety of environmental and agricultural applications, the use of ground penetrating radar (GPR) for identifying soil water content is a matter of concern. However, the current state of technology still needs improvements and new developments. Research has focused on the development of an integrated inverse modeling approach including GPR design, GPR signal forward modeling, and GPR signal inversion to estimate simultaneously the depth dependent dielectric constant and electrical conductivity of the shallow subsurface. We propose to use as radar system a stepped frequency continuous wave radar with an ultrawide band dielectric filled TEM horn antenna used in monostatic mode. This configuration is appropriate for real time mapping and allows for a more realistic forward modeling of the radar-antenna-soil system. Forward modeling was based on the exact solution of Maxwell's equations and inversion was formulated by the classical least square problem. Given the inherent complex topography of the objective functions to optimize in electromagnetic inversion problems, we used for the inversion the recently developed global multilevel coordinate search algorithm that we combine sequentially with the local Nelder-Mead simplex algorithm. We applied the method in laboratory conditions on tank filled with sand subject to different water content levels considering a homogeneous water profile. The inverse estimation of the soil dielectric constant was remarkably well in accordance with each water content level and the corresponding theoretical values of the dielectric constant for the sand. Comparison of GPR measurements with estimations from time domain reflectometry (TDR) were also well in close agreement.
An inverse method for rheometry of power-law fluids
NASA Astrophysics Data System (ADS)
Hemaka Bandulasena, H. C.; Zimmerman, William B.; Rees, Julia M.
2011-12-01
This paper is concerned with the determination of the constitutive viscous parameters of dilute solutions of xanthan gum by means of an inverse method used in conjunction with finite element modeling of the governing system of partial differential equations. At low concentrations xanthan gum behaves as a shear-thinning, power-law non-Newtonian fluid. Finite element modeling is used to simulate the pressure-driven flow of xanthan gum solutions in a microchannel T-junction. As the flow is forced to turn the corner of the T-junction a range of shear rates, and hence viscosities, is produced. It is shown that the statistical properties of the velocity field are sensitive to the constitutive parameters of the power-law model. The inverse method is shown to be stable and accurate, with measurement error in the velocity field translating to small errors in the rheological parameter estimation. Due to the particular structure of the inverse map, the error propagation is substantially less than the estimate from the Hadamard criterion.
A variational Bayesian method to inverse problems with impulsive noise
NASA Astrophysics Data System (ADS)
Jin, Bangti
2012-01-01
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.
History and evolution of methods for solving the inverse problem.
van Oosterom, A
1991-10-01
This article serves as an introduction to the other articles in this issue devoted to the problem of the localization of neural generators. Elements of the theory of electric volume conduction are briefly introduced, as far as these apply to the interpretation of observed scalp potentials. First, some basic methods for display of the different aspects of the spatiotemporal information are described. Next, the most prominent source and volume conductor models that have been postulated for the involved forward problem are summarized. The problems of source identification and source localization, known as the inverse problem, are then formulated in terms of a parameter estimation procedure. The importance of introducing a priori information in the inverse problem, aimed at stabilizing (regularizing) the obtained solution, is emphasized. Methods for imposing such constraints are briefly outlined. PMID:1761703
Li, Ranran; Zou, Zhihong
2015-10-01
An integrated approach using the inverse method and Bayesian approach, combined with a lake eutrophication water quality model, was developed for parameter estimation and water environmental capacity (WEC) analysis. The model was used to support load reduction and effective water quality management in the Taihu Lake system in eastern China. Water quality was surveyed yearly from 1987 to 2010. Total nitrogen (TN) and total phosphorus (TP) were selected as water quality model variables. Decay rates of TN and TP were estimated using the proposed approach. WECs of TN and TP in 2011 were determined based on the estimated decay rates. Results showed that the historical loading was beyond the WEC, thus, reduction of nitrogen and phosphorus input is necessary to meet water quality goals. Then WEC and allowable discharge capacity (ADC) in 2015 and 2020 were predicted. The reduction ratios of ADC during these years were also provided. All of these enable decision makers to assess the influence of each loading and visualize potential load reductions under different water quality goals, and then to formulate a reasonable water quality management strategy. PMID:26426032
Inversion identities for inhomogeneous face models
NASA Astrophysics Data System (ADS)
Frahm, Holger; Karaiskos, Nikos
2014-10-01
We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions using the underlying integrable structure and crossing properties of the local Boltzmann weights. For the critical restricted solid-on-solid (RSOS) models these identities together with some information on the analytical properties of the transfer matrix determine the spectrum completely and allow to derive the Bethe equations for both periodic and general open boundary conditions.
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.
Determination of evaporation duct heights by an inverse method
NASA Astrophysics Data System (ADS)
Douvenot, R.; Fabbro, V.; Bourlier, C.; Saillard, J.; Fuchs, H.-H.; Essen, H.; Förster, J.
2007-10-01
The detection and tracking of naval targets, including low RCS objects like inflatable boats requires a thorough knowledge of the propagation properties of the maritime boundary layer. Models are in existence, which allow a prediction of the propagation factor using the parabolic equation algorithm. As a necessary input the refractive index of the atmosphere has to be known. This parameter, however, is strongly influenced by the actual atmospheric conditions, characterized mainly by air-sea temperature difference, humidity and air pressure. An approach was initiated to retrieve the vertical profile of the refractive index from sea clutter data. The method is based on the LS-SVM (Least-Squares Support Vector Machines) theory and has already been validated on simulated data. Here an inversion method to determine propagation factors is presented based upon data measured during the Vampira campaign conducted as a multinational approach over a transmission path across the Baltic Sea. As the propagation factor has been measured on two reference reflectors mounted onboard a naval vessel at different heights, the results can be combined in order to increase the accuracy of the inversion system. The paper discusses results achieved with the inversion method.
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.
Linear functional minimization for inverse modeling
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Wohlberg, B. E.; Vesselinov, V. V.; Tartakovsky, D. M.
2015-06-01
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. Addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Nonlinear inversion of pre-stack seismic data using variable metric method
NASA Astrophysics Data System (ADS)
Zhang, Fanchang; Dai, Ronghuo
2016-06-01
At present, the routine method to perform AVA (Amplitude Variation with incident Angle) inversion is based on the assumption that the ratio of S-wave velocity to P-wave velocity γ is a constant. However, this simplified assumption does not always hold, and it is necessary to use nonlinear inversion method to solve it. Based on Bayesian theory, the objective function for nonlinear AVA inversion is established and γ is considered as an unknown model parameter. Then, variable metric method with a strategy of periodically variational starting point is used to solve the nonlinear AVA inverse problem. The proposed method can keep the inverted reservoir parameters approach to the actual solution and has been performed on both synthetic and real data. The inversion results suggest that the proposed method can solve the nonlinear inverse problem and get accurate solutions even without the knowledge of γ.
A method for obtaining coefficients of compositional inverse generating functions
NASA Astrophysics Data System (ADS)
Kruchinin, Dmitry V.; Shablya, Yuriy V.; Kruchinin, Vladimir V.; Shelupanov, Alexander A.
2016-06-01
The aim of this paper is to show how to obtain expressions for coefficients of compositional inverse generating functions in explicit way. The method is based on the Lagrange inversion theorem and composita of generating functions. Also we give a method of obtaining expressions for coefficients of reciprocal generating functions and consider some examples.
NASA Astrophysics Data System (ADS)
Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E.; Sweeney, C.; Turner, A. J.
2015-11-01
Understanding methane emissions from the Arctic, a fast warming carbon reservoir, is important for projecting changes in the global methane cycle under future climate scenarios. Here we optimize Arctic methane emissions with a nested-grid high-resolution inverse model by assimilating both high-precision surface measurements and column-average SCIAMACHY satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes are integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated by six different biogeochemical models. We find that, the global methane emissions during July 2004-June 2005 ranged from 496.4 to 511.5 Tg yr-1, with wetland methane emissions ranging from 130.0 to 203.3 Tg yr-1. The Arctic methane emissions during July 2004-June 2005 were in the range of 14.6-30.4 Tg yr-1, with wetland and lake emissions ranging from 8.8 to 20.4 Tg yr-1 and from 5.4 to 7.9 Tg yr-1 respectively. Canadian and Siberian lakes contributed most of the estimated lake emissions. Due to insufficient measurements in the region, Arctic methane emissions are less constrained in northern Russia than in Alaska, northern Canada and Scandinavia. Comparison of different inversions indicates that the distribution of global and Arctic methane emissions is sensitive to prior wetland emissions. Evaluation with independent datasets shows that the global and Arctic inversions improve estimates of methane mixing ratios in boundary layer and free troposphere. The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic.
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
Spectrum reconstruction based on the constrained optimal linear inverse methods.
Ren, Wenyi; Zhang, Chunmin; Mu, Tingkui; Dai, Haishan
2012-07-01
The dispersion effect of birefringent material results in spectrally varying Nyquist frequency for the Fourier transform spectrometer based on birefringent prism. Correct spectral information cannot be retrieved from the observed interferogram if the dispersion effect is not appropriately compensated. Some methods, such as nonuniform fast Fourier transforms and compensation method, were proposed to reconstruct the spectrum. In this Letter, an alternative constrained spectrum reconstruction method is suggested for the stationary polarization interference imaging spectrometer (SPIIS) based on the Savart polariscope. In the theoretical model of the interferogram, the noise and the total measurement error are included, and the spectrum reconstruction is performed by using the constrained optimal linear inverse methods. From numerical simulation, it is found that the proposed method is much more effective and robust than the nonconstrained spectrum reconstruction method proposed by Jian, and provides a useful spectrum reconstruction approach for the SPIIS. PMID:22743461
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. PMID:26582359
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 scattering for a specific resonating group model nonlocality
Pantis, G.; Sofianos, S.A.
1996-10-01
An inverse scattering method of Lipperheide and Fiedeldey [Z. Phys. A {bold 286}, 45 (1978); {bold 301}, 81 (1981)] has been used to construct an energy-dependent potential from the elastic-scattering phase shifts of the recently developed {ital K} model of Kaneko, LeMere, and Tang [Phys. Rev. C {bold 44}, 1588 (1991); {bold 46}, 298 (1992)] for the {ital n}{minus}{alpha} and {ital n}{minus}{sup 40}Ca systems. The local momentum of the inversion potential is subsequently used to recover the Wigner transforms of the {ital K} model. The results obtained indicate that it is possible to find, via inversion, an {ital l}-independent Wigner transform, which, when calculated at all energies, can provide us with the full nonlocality. {copyright} {ital 1996 The American Physical Society.}
Inverse scattering for a specific resonating group model nonlocality
NASA Astrophysics Data System (ADS)
Pantis, G.; Sofianos, S. A.
1996-10-01
An inverse scattering method of Lipperheide and Fiedeldey [Z. Phys. A 286, 45 (1978); 301, 81 (1981)] has been used to construct an energy-dependent potential from the elastic-scattering phase shifts of the recently developed K model of Kaneko, LeMere, and Tang [Phys. Rev. C 44, 1588 (1991); 46, 298 (1992)] for the n-α and n-40Ca systems. The local momentum of the inversion potential is subsequently used to recover the Wigner transforms of the K model. The results obtained indicate that it is possible to find, via inversion, an l-independent Wigner transform, which, when calculated at all energies, can provide us with the full nonlocality.
Full-waveform modeling and inversion of physical model data
NASA Astrophysics Data System (ADS)
Cai, Jian; Zhang, Jie
2016-08-01
Because full elastic waveform inversion requires considerable computation time for forward modeling and inversion, acoustic waveform inversion is often applied to marine data for reducing the computational time. To understand the validity of the acoustic approximation, we study data collected from an ultrasonic laboratory with a known physical model by applying elastic and acoustic waveform modeling and acoustic waveform inversion. This study enables us to evaluate waveform differences quantitatively between synthetics and real data from the same physical model and to understand the effects of different objective functions in addressing the waveform differences for full-waveform inversion. Because the materials used in the physical experiment are viscoelastic, we find that both elastic and acoustic synthetics differ substantially from the physical data over offset in true amplitude. If attenuation is taken into consideration, the amplitude versus offset (AVO) of viscoelastic synthetics more closely approximates the physical data. To mitigate the effect of amplitude differences, we apply trace normalization to both synthetics and physical data in acoustic full-waveform inversion. The objective function is equivalent to minimizing the phase differences with indirect contributions from the amplitudes. We observe that trace normalization helps to stabilize the inversion and obtain more accurate model solutions for both synthetics and physical data.
Inverse method for estimating shear stress in machining
NASA Astrophysics Data System (ADS)
Burns, T. J.; Mates, S. P.; Rhorer, R. L.; Whitenton, E. P.; Basak, D.
2016-01-01
An inverse method is presented for estimating shear stress in the work material in the region of chip-tool contact along the rake face of the tool during orthogonal machining. The method is motivated by a model of heat generation in the chip, which is based on a two-zone contact model for friction along the rake face, and an estimate of the steady-state flow of heat into the cutting tool. Given an experimentally determined discrete set of steady-state temperature measurements along the rake face of the tool, it is shown how to estimate the corresponding shear stress distribution on the rake face, even when no friction model is specified.
An inverse design method for 2D airfoil
NASA Astrophysics Data System (ADS)
Liang, Zhi-Yong; Cui, Peng; Zhang, Gen-Bao
2010-03-01
The computational method for aerodynamic design of aircraft is applied more universally than before, in which the design of an airfoil is a hot problem. The forward problem is discussed by most relative papers, but inverse method is more useful in practical designs. In this paper, the inverse design of 2D airfoil was investigated. A finite element method based on the variational principle was used for carrying out. Through the simulation, it was shown that the method was fit for the design.
Waveform Inversion of Synthetic Ocean Models in the Laplace Domain
NASA Astrophysics Data System (ADS)
Rosado, H.; Blacic, T. M.; Jun, H.; Shin, C.
2014-12-01
In seismic oceanography, the processed images show where small temperature changes (as little as 0.03°C) occur, although they do not give absolute temperatures. To get a 2-D temperature map, the data must be inverted for sound speed, which is then converted to temperature using equations of state. Full waveform inversion requires a starting model that is iteratively updated until the residuals converge. Global search algorithms such as Genetic Algorithm do not require a starting model close to the true model, but are computationally exhausting. Local search inversion is less expensive, but requires a reasonably accurate starting model. Unfortunately, most marine seismic data has little associated hydrographic data and so it is difficult to create starting models close enough to the true model for convergence throughout the target area. In addition, the band-limited nature of seismic data makes it inherently challenging to extract the long wavelength sound speed trend directly from seismic data. Laplace domain inversion (LDI) developed by Changsoo Shin and colleagues requires only a rudimentary starting model to produce smooth background sound speed models without requiring prior information about the medium. It works by transforming input data to the Laplace domain, and then examining the zero frequency component of the damped wavefield to extract a smooth sound speed model - basically, removing higher frequency fluctuations to expose background trends. This ability to use frequencies below those effectively propagated by the seismic source is what enables LDI to produce the smooth background trend from the data. We applied LDI to five synthetic data sets based on simplified models of oceanographic features. Using LDI, we were able to recover smoothed versions of our synthetic models, showing the viability of the method for creating sound speed profiles suitable for use as starting models for other methods of inversion that output more detailed models.
Determination of transient fluid temperature using the inverse method
NASA Astrophysics Data System (ADS)
Jaremkiewicz, Magdalena
2014-03-01
This paper proposes an inverse method to obtain accurate measurements of the transient temperature of fluid. A method for unit step and linear rise of temperature is presented. For this purpose, the thermometer housing is modelled as a full cylindrical element (with no inner hole), divided into four control volumes. Using the control volume method, the heat balance equations can be written for each of the nodes for each of the control volumes. Thus, for a known temperature in the middle of the cylindrical element, the distribution of temperature in three nodes and heat flux at the outer surface were obtained. For a known value of the heat transfer coefficient the temperature of the fluid can be calculated using the boundary condition. Additionally, results of experimental research are presented. The research was carried out during the start-up of an experimental installation, which comprises: a steam generator unit, an installation for boiler feed water treatment, a tray-type deaerator, a blow down flashvessel for heat recovery, a steam pressure reduction station, a boiler control system and a steam header made of martensitic high alloy P91 steel. Based on temperature measurements made in the steam header using the inverse method, accurate measurements of the transient temperature of the steam were obtained. The results of the calculations are compared with the real temperature of the steam, which can be determined for a known pressure and enthalpy.
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.
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.
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.
Fast 3D inversion of airborne gravity-gradiometry data using Lanczos bidiagonalization method
NASA Astrophysics Data System (ADS)
Meng, Zhaohai; Li, Fengting; Zhang, Dailei; Xu, Xuechun; Huang, Danian
2016-09-01
We developed a new fast inversion method for to process and interpret airborne gravity gradiometry data, which was based on Lanczos bidiagonalization algorithm. Here, we describe the application of this new 3D gravity gradiometry inversion method to recover a subsurface density distribution model from the airborne measured gravity gradiometry anomalies. For this purpose, the survey area is divided into a large number of rectangular cells with each cell possessing a constant unknown density. It is well known that the solution of large linear gravity gradiometry is an ill-posed problem since using the smoothest inversion method is considerably time consuming. We demonstrate that the Lanczos bidiagonalization method can be an appropriate algorithm to solve a Tikhonov solver time cost function for resolving the large equations within a short time. Lanczos bidiagonalization is designed to make the very large gravity gradiometry forward modeling matrices to become low-rank, which will considerably reduce the running time of the inversion method. We also use a weighted generalized cross validation method to choose the appropriate Tikhonov parameter to improve inversion results. The inversion incorporates a model norm that allows us to attain the smoothing and depth of the solution; in addition, the model norm counteracts the natural decay of the kernels, which concentrate at shallow depths. The method is applied on noise-contaminated synthetic gravity gradiometry data to demonstrate its suitability for large 3D gravity gradiometry data inversion. The airborne gravity gradiometry data from the Vinton Salt Dome, USE, were considered as a case study. The validity of the new method on real data is discussed with reference to the Vinton Dome inversion result. The intermediate density values in the constructed model coincide well with previous results and geological information. This demonstrates the validity of the gravity gradiometry inversion method.
A Higher Order Iterative Method for Computing the Drazin Inverse
Soleymani, F.; Stanimirović, Predrag S.
2013-01-01
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747
The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method
NASA Astrophysics Data System (ADS)
Voronina, T. A.; Romanenko, A. A.
2016-04-01
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.
NASA Astrophysics Data System (ADS)
Jiang, Mingfeng; Xia, Ling; Shou, Guofa; Tang, Min
2007-03-01
Computing epicardial potentials from body surface potentials constitutes one form of ill-posed inverse problem of electrocardiography (ECG). To solve this ECG inverse problem, the Tikhonov regularization and truncated singular-value decomposition (TSVD) methods have been commonly used to overcome the ill-posed property by imposing constraints on the magnitudes or derivatives of the computed epicardial potentials. Such direct regularization methods, however, are impractical when the transfer matrix is large. The least-squares QR (LSQR) method, one of the iterative regularization methods based on Lanczos bidiagonalization and QR factorization, has been shown to be numerically more reliable in various circumstances than the other methods considered. This LSQR method, however, to our knowledge, has not been introduced and investigated for the ECG inverse problem. In this paper, the regularization properties of the Krylov subspace iterative method of LSQR for solving the ECG inverse problem were investigated. Due to the 'semi-convergence' property of the LSQR method, the L-curve method was used to determine the stopping iteration number. The performance of the LSQR method for solving the ECG inverse problem was also evaluated based on a realistic heart-torso model simulation protocol. The results show that the inverse solutions recovered by the LSQR method were more accurate than those recovered by the Tikhonov and TSVD methods. In addition, by combing the LSQR with genetic algorithms (GA), the performance can be improved further. It suggests that their combination may provide a good scheme for solving the ECG inverse problem.
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
Inverse problems of ultrasound tomography in models with attenuation
NASA Astrophysics Data System (ADS)
Goncharsky, Alexander V.; Romanov, Sergey Y.
2014-04-01
We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.
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 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.
Estimation of Trace Gas Fluxes by Inverse Modelling
NASA Astrophysics Data System (ADS)
Prinn, R. G.; Chen, Y.; Huang, J.; Golombek, A.
2003-12-01
A wide range of scientific questions regarding chemically and/or radiatively important trace gases necessitate determinations of their sources and sinks at local to global scales. A powerful method for such determinations involves solution of an inverse problem in which the observed concentrations are effectively Lagrangian line integrals and the unknown sources or sinks are contained in the integrands. The inverse problem consists of calculating optimal estimates of the unknowns in the Bayesian sense using an atmospheric transport model and trace gas measurements gathered over space and time. Great care is necessary to include the effects of both measurement and transport model errors in calculating the uncertainty in the optimal estimates. We review the results of recent studies which use three-dimensional Eulerian (specifically MATCH) or Lagrangian transport models and Kalman filter and other optimization methods to compute emissions of methane, nitrous oxide, and selected halocarbons. These studies use high frequency trace gas observations from global networks (AGAGE, CMDL) to calibrate a priori emission maps for particular processes and geographic regions. The methods allow estimation of time varying emissions. For the hydrogen-containing gases these emission estimates require accurate specification of the concentrations of the hydroxyl radical which constitute their major sink. Hydroxyl radical levels can be optimally estimated in a separate problem using measurements of methyl chloroform whose global emissions are already very well known. The results show that the inverse approach is a powerful complement to traditional surface flux aggregation methods. At the same time, the inverse approach has its own limitations associated especially with transport model errors and/or inadequate atmospheric measurements.
Updated Results for the Wake Vortex Inverse Model
NASA Technical Reports Server (NTRS)
Robins, Robert E.; Lai, David Y.; Delisi, Donald P.; Mellman, George R.
2008-01-01
NorthWest Research Associates (NWRA) has developed an Inverse Model for inverting aircraft wake vortex data. The objective of the inverse modeling is to obtain estimates of the vortex circulation decay and crosswind vertical profiles, using time history measurements of the lateral and vertical position of aircraft vortices. The Inverse Model performs iterative forward model runs using estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Iterations are performed until a user-defined criterion is satisfied. Outputs from an Inverse Model run are the best estimates of the time history of the vortex circulation derived from the observed data, the vertical crosswind profile, and several vortex parameters. The forward model, named SHRAPA, used in this inverse modeling is a modified version of the Shear-APA model, and it is described in Section 2 of this document. Details of the Inverse Model are presented in Section 3. The Inverse Model was applied to lidar-observed vortex data at three airports: FAA acquired data from San Francisco International Airport (SFO) and Denver International Airport (DEN), and NASA acquired data from Memphis International Airport (MEM). The results are compared with observed data. This Inverse Model validation is documented in Section 4. A summary is given in Section 5. A user's guide for the inverse wake vortex model is presented in a separate NorthWest Research Associates technical report (Lai and Delisi, 2007a).
Application of Carbonate Reservoir using waveform inversion and reverse-time migration methods
NASA Astrophysics Data System (ADS)
Kim, W.; Kim, H.; Min, D.; Keehm, Y.
2011-12-01
Recent exploration targets of oil and gas resources are deeper and more complicated subsurface structures, and carbonate reservoirs have become one of the attractive and challenging targets in seismic exploration. To increase the rate of success in oil and gas exploration, it is required to delineate detailed subsurface structures. Accordingly, migration method is more important factor in seismic data processing for the delineation. Seismic migration method has a long history, and there have been developed lots of migration techniques. Among them, reverse-time migration is promising, because it can provide reliable images for the complicated model even in the case of significant velocity contrasts in the model. The reliability of seismic migration images is dependent on the subsurface velocity models, which can be extracted in several ways. These days, geophysicists try to obtain velocity models through seismic full waveform inversion. Since Lailly (1983) and Tarantola (1984) proposed that the adjoint state of wave equations can be used in waveform inversion, the back-propagation techniques used in reverse-time migration have been used in waveform inversion, which accelerated the development of waveform inversion. In this study, we applied acoustic waveform inversion and reverse-time migration methods to carbonate reservoir models with various reservoir thicknesses to examine the feasibility of the methods in delineating carbonate reservoir models. We first extracted subsurface material properties from acoustic waveform inversion, and then applied reverse-time migration using the inverted velocities as a background model. The waveform inversion in this study used back-propagation technique, and conjugate gradient method was used in optimization. The inversion was performed using the frequency-selection strategy. Finally waveform inversion results showed that carbonate reservoir models are clearly inverted by waveform inversion and migration images based on the
Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan
2016-06-01
In this paper, we investigate the full-waveform inversion in the frequency domain. We first test the inversion ability of three numerical optimization methods, i.e., the steepest-descent method, the Newton-CG method and the Gauss- Newton method, for a simple model. The results show that the Gauss-Newton method performs well and efficiently. Then numerical computations for a benchmark model named Marmousi model by the Gauss-Newton method are implemented. Parallel algorithm based on message passing interface (MPI) is applied as the inversion is a typical large-scale computational problem. Numerical computations show that the Gauss-Newton method has good ability to reconstruct the complex model.
Estimating surface acoustic impedance with the inverse method.
Piechowicz, Janusz
2011-01-01
Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics. PMID:21939599
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).
Analysis and improvement for a linearized seafloor elastic parameter inversion method
NASA Astrophysics Data System (ADS)
Liu, Yangting; Liu, Xuewei; Ning, Hongxiao
2016-05-01
AVO inversion is an effective seismic exploration method to predict elastic parameters. In this paper, we review and analyze the linearized AVO inversion method previously published for seafloor elastic parameters, and present a modification strategy. Before the linearized inversion is performed, a proper near-angle range in which the relationship between the reflection coefficient and sine-squared incidence angle is linear needs to be provided. However, the near-angle range is determined by the elastic parameters which are to be estimated by inversion. Therefore, only an approximated value of the near-angle range can be provided for the linearized inversion. Model tests show that a too large near-angle range may cause inversion fault, and a too small near-angle range may cause unreliable estimation. Further analysis shows that the estimation stability can be further improved even though the linearized inversion is performed under an exact near-angle range. To mitigate the strong dependence on the near-angle range, we use the seafloor elastic parameters estimated from the linearized method as the initial model for an unconstrained optimization method. Compared with the previously published method, the modified method is more robust to noisy data and shows less dependence on the near-angle range.
Minimization search method for data inversion
NASA Technical Reports Server (NTRS)
Fymat, A. L.
1975-01-01
Technique has been developed for determining values of selected subsets of independent variables in mathematical formulations. Required computation time increases with first power of the number of variables. This is in contrast with classical minimization methods for which computational time increases with third power of the number of variables.
Homogenization method based on the inverse problem
Tota, A.; Makai, M.
2013-07-01
We present a method for deriving homogeneous multi-group cross sections to replace a heterogeneous region's multi-group cross sections; providing that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is developed using diffusion approximation to the neutron transport equation in a symmetrical slab geometry. Assuming that the boundary fluxes are given, two response matrices (RMs) can be defined. The first derives the boundary current from the boundary flux, the second derives the flux integral over the region from the boundary flux. Assuming that these RMs are known, we present a formula which reconstructs the multi-group cross-section matrix and the diffusion coefficients from the RMs of a homogeneous slab. Applying this formula to the RMs of a slab with multiple homogeneous regions yields a homogenization method; which produce such homogenized multi-group cross sections and homogenized diffusion coefficients, that the fluxes and the currents on the external boundary, and the region averaged fluxes are preserved. The method is based on the determination of the eigenvalues and the eigenvectors of the RMs. We reproduce the four-group cross section matrix and the diffusion constants from the RMs in numerical examples. We give conditions for replacing a heterogeneous region by a homogeneous one so that the boundary current and the region-averaged flux are preserved for a given boundary flux. (authors)
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.
Inverse Modeling of Groundwater Flow for a Fractured Confined Aquifer
NASA Astrophysics Data System (ADS)
Zhang, Y.; Wang, D.
2013-12-01
A two-dimensional inverse method is developed to simultaneously estimate steady-state hydraulic conductivities, state variables, and boundary conditions (BC) for a fractured confined aquifer. Computation experiments were performed with five fractured models where each model is driven by dominantly lateral flow (true BC) through both fractures (Kf) and matrix (Km). From each model, observation data including hydraulic heads and Darcy fluxes were sampled without imposing measurement errors. These data were provided to inversion to estimate Kf and the unknown model BC. For the first 4 models, the same sampling data density was used, while Kf/Km ratio is fixed at 10. The 1st model contains a single vertical fracture, and the error of the estimated Kf is almost 0. The 2nd model contains a single horizontal fracture, and the error of the estimated Kf is 4.6%. The 3rd model contains a vertical and a horizontal fracture, and the error is 5.3%. The 4th model is same as the third, except that the fracture volume is 25 times greater, and the error is 0.70%. In this model, the highest BC estimation error occurred at the domain corners, where the inversion extrapolation error is the greatest (reduction of this error will be investigated in the future with local grid refinement and increased data density). The 5th model contains a set of diagonal fractures, two of which run from the left bottom corner to the right top corner and the other one runs from the left top corner to the right bottom corner. For this model, under a given data density, increasing Kf/Km (10 to 1,000,000) was tested. Kf estimation is found not to be sensitive to this variability - the largest Kf error is only 5.27%. For the same model, at Kf/Km =10, local sensitivity analysis using 1 percent scaled sensitivity (1ss) suggests that observed heads at different locations are important for estimating different parameters. A global inverse sensitivity analysis was then performed by increasing the number of the
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.
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.
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.
A robust inverse inviscid method for airfoil design
NASA Astrophysics Data System (ADS)
Chaviaropoulos, P.; Dedoussis, V.; Papailiou, K. D.
An irrotational inviscid compressible inverse design method for two-dimensional airfoil profiles is described. The method is based on the potential streamfunction formulation, where the physical space on which the boundaries of the airfoil are sought, is mapped onto the (phi, psi) space via a body-fitted coordinate transformation. A novel procedure based on differential geometry arguments is employed to derive the governing equations for the inverse problem, by requiring the curvature of the flat 2-D Euclidean space to be zero. An auxiliary coordinate transformation permits the definition of C-type computational grids on the (phi, psi) plane resulting to a more accurate description of the leading edge region. Geometry is determined by integrating Frenet equations along the grid lines. To validate the method inverse calculation results are compared to direct, `reproduction', calculation results. The design procedure of a new airfoil shape is also presented.
Point source moment tensor inversion through a Bayesian hierarchical model
NASA Astrophysics Data System (ADS)
Mustać, Marija; Tkalčić, Hrvoje
2016-01-01
Characterization of seismic sources is an important aspect of seismology. Parameter uncertainties in such inversions are essential for estimating solution robustness, but are rarely available. We have developed a non-linear moment tensor inversion method in a probabilistic Bayesian framework that also accounts for noise in the data. The method is designed for point source inversion using waveform data of moderate-size earthquakes and explosions at regional distances. This probabilistic approach results in an ensemble of models, whose density is proportional to parameter probability distribution and quantifies parameter uncertainties. Furthermore, we invert for noise in the data, allowing it to determine the model complexity. We implement an empirical noise covariance matrix that accounts for interdependence of observational errors present in waveform data. After we demonstrate the feasibility of the approach on synthetic data, we apply it to a Long Valley Caldera, CA, earthquake with a well-documented anomalous (non-double-couple) radiation from previous studies. We confirm a statistically significant isotropic component in the source without a trade-off with the compensated linear vector dipoles component.
Multiple paired forward and inverse models for motor control.
Wolpert, D M; Kawato, M
1998-10-01
Humans demonstrate a remarkable ability to generate accurate and appropriate motor behavior under many different and often uncertain environmental conditions. In this paper, we propose a modular approach to such motor learning and control. We review the behavioral evidence and benefits of modularity, and propose a new architecture based on multiple pairs of inverse (controller) and forward (predictor) models. Within each pair, the inverse and forward models are tightly coupled both during their acquisition, through motor learning, and use, during which the forward models determine the contribution of each inverse model's output to the final motor command. This architecture can simultaneously learn the multiple inverse models necessary for control as well as how to select the inverse models appropriate for a given environment. Finally, we describe specific predictions of the model, which can be tested experimentally. PMID:12662752
Bathymetric Sensitivity/Inversion in a River Model
NASA Astrophysics Data System (ADS)
Wilson, G.; Ozkan-Haller, H. T.
2010-12-01
In this study, we use ensemble-based methods to analyze riverine dynamics in the Regional Ocean Modeling System (ROMS). Our focus is on model sensitivity to bathymetric errors, with an aim towards the application of data assimilation techniques for bathymetric inversion. To that end, we investigate the bathymetric sensitivity with respect to various observable quantities (e.g. surface current, depth-averaged current, surface slope), and under different physical settings (e.g. river bank geometry, channel depth, flow rate) which may affect the underlying qualitative dynamics. Nominal conditions are chosen similar to those observed during the COHSTREX experiment (U. Washington, Stanford Univ.), conducted on the Snohomish River, WA, September 2009. The present results show that the hydrodynamic model is, in general, sensitive to bathymetric errors, and this is quantified statistically. However, we point out some basic challenges of exploiting this bathymetric sensitivity when assimilating data (i.e. for bathymetric inversion). Specifically, we evaluate the role of the prescribed bathymetric and observational error statistics, as well as the observation type and sampling scheme, in determining the quality of the bathymetric estimate. It is shown that although bathymetric inversion is feasible in an idealized setting, a detailed understanding of the bathymetric sensitivity (and its limitations) is essential when moving to real-world application.
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
NASA Astrophysics Data System (ADS)
Hu, Yongtao; Odman, M. Talat; Russell, Armistead G.
2009-12-01
A Community Multiscale Air Quality (CMAQ) model based inverse method is used for calibrating the 2004 elemental carbon (EC) emissions in the continental United States. We convert the Thermal Optical Transmittance (TOT) EC measurements to the Thermal Optical Reflectance (TOR) equivalents to fully utilize available observational networks. The reestimate of the total emissions is 0.40 Tg yr-1, about 13% higher than the a priori. The posterior CMAQ simulation driven by the adjusted emissions had an ˜10% reduction in annual average fractional error based on 24 h EC observations. Comparison of simulated EC concentrations to hourly aethalometer black carbon (BC) measurements improved as well. Also, using the EC scaling factors to adjust the primary particulate organic matter (OM) emissions improved performance for OM simulation. Results show that splitting sources further spatially and category-wise increases the flexibility of adjusting emissions according to the spatial variability of the emissions strength and hence makes a better reestimate of emissions.
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.
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…
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
Solving inverse problems of identification type by optimal control methods
Lenhart, S.; Protopopescu, V.; Yong, J.
1997-05-01
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 we present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), our 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. {copyright} {ital 1997 American Institute of Physics.}
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.
Kinematic Source Inversion Using Smoothly Curved Fault Model
NASA Astrophysics Data System (ADS)
Suzuki, W.; Aoi, S.; Sekiguchi, H.
2010-12-01
necessary to express the fault geometry as curved surface. In this study we develop an inversion method to derive a kinematic source rupture process using a curved fault model. The fault surface is mathematically presented by Non-Uniform Rational B-Spline (NURBS), which offers the flexible surface modeling. Multi-time-window linear waveform inversion scheme is implemented to the curved fault model. Points for calculating Green's function are generated at a shorter interval than subfaults for deriving slip history. This means that each subfault is also expressed by the curved surface, whereas the subfaults were based on the planar elements in most of previous studies that estimated source process on the curved fault. We apply the developed method to the 2008 Northern Iwate earthquake. Large slip areas are estimated at similar locations to the two-plane fault analysis. The synthetic waveforms agree with the observed ones comparably for both fault models. The total seismic moment is smaller for the curved fault than for the two-plane fault, which may indicate that inversion analysis using curved fault model could suppress artificial slip.
Indium oxide inverse opal films synthesized by structure replication method
NASA Astrophysics Data System (ADS)
Amrehn, Sabrina; Berghoff, Daniel; Nikitin, Andreas; Reichelt, Matthias; Wu, Xia; Meier, Torsten; Wagner, Thorsten
2016-04-01
We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.
Computational methods for inverse problems in geophysics: inversion of travel time observations
Pereyra, V.; Keller, H.B.; Lee, W.H.K.
1980-01-01
General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.
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
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.
Dispersion analysis with inverse dielectric function modelling.
Mayerhöfer, Thomas G; Ivanovski, Vladimir; Popp, Jürgen
2016-11-01
We investigate how dispersion analysis can profit from the use of a Lorentz-type description of the inverse dielectric function. In particular at higher angles of incidence, reflectance spectra using p-polarized light are dominated by bands from modes that have their transition moments perpendicular to the surface. Accordingly, the spectra increasingly resemble inverse dielectric functions. A corresponding description can therefore eliminate the complex dependencies of the dispersion parameters, allow their determination and facilitate a more accurate description of the optical properties of single crystals. PMID:27294550
Gaining insight into food webs reconstructed by the inverse method
NASA Astrophysics Data System (ADS)
Kones, Julius K.; Soetaert, Karline; van Oevelen, Dick; Owino, John O.; Mavuti, Kenneth
2006-04-01
The use of the inverse method to analyze flow patterns of organic components in ecological systems has had wide application in ecological modeling. Through this approach, an infinite number of food web flows describing the food web and satisfying biological constraints are generated, from which one (parsimonious) solution is drawn. Here we address two questions: (1) is there justification for the use of the parsimonious solution or is there a better alternative and (2) can we use the infinitely many solutions that describe the same food web to give more insight into the system? We reassess two published food webs, from the Gulf of Riga in the Baltic Sea and the Takapoto Atoll lagoon in the South Pacific. A finite number of random food web solutions is first generated using the Monte Carlo simulation technique. Using the Wilcoxon signed ranks test, we cannot find significant differences in the parsimonious solution and the average values of the finite random solutions generated. However, as the food web composed of the average flows has more attractive properties, the choice of the parsimonious solution to describe underdetermined food webs is challenged. We further demonstrate the use of the factor analysis technique to characterize flows that are closely related in the food web. Through this process sub-food webs are extracted within the plausible set of food webs, a property that can be utilized to gain insight into the sampling strategy for further constraining of the model.
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.
Balancing aggregation and smoothing errors in inverse models
Turner, A. J.; Jacob, D. J.
2015-01-13
Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less
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
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.
A finite-difference contrast source inversion method
NASA Astrophysics Data System (ADS)
Abubakar, A.; Hu, W.; van den Berg, P. M.; Habashy, T. M.
2008-12-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium.
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.
A fast inversion method for interpreting borehole electromagnetic data
NASA Astrophysics Data System (ADS)
Kim, H. J.; Lee, K. H.; Wilt, M.
2003-05-01
A fast and stable inversion scheme has been developed using the localized nonlinear (LN) approximation to analyze electromagnetic fields obtained in a borehole. The medium is assumed to be cylindrically symmetric about the borehole, and to maintain the symmetry a vertical magnetic dipole is used as a source. The efficiency and robustness of an inversion scheme is very much dependent on the proper use of Lagrange multiplier, which is often provided manually to achieve a desired convergence. We utilize an automatic Lagrange multiplier selection scheme, which enhances the utility of the inversion scheme in handling field data. In this selection scheme, the integral equation (IE) method is quite attractive in speed because Green's functions, the most time consuming part in IE methods, are repeatedly re-usable throughout the selection procedure. The inversion scheme using the LN approximation has been tested to show its stability and efficiency using synthetic and field data. The inverted result from the field data is successfully compared with induction logging data measured in the same borehole.
Propeller sheet cavitation noise source modeling and inversion
NASA Astrophysics Data System (ADS)
Lee, Keunhwa; Lee, Jaehyuk; Kim, Dongho; Kim, Kyungseop; Seong, Woojae
2014-02-01
Propeller sheet cavitation is the main contributor to high level of noise and vibration in the after body of a ship. Full measurement of the cavitation-induced hull pressure over the entire surface of the affected area is desired but not practical. Therefore, using a few measurements on the outer hull above the propeller in a cavitation tunnel, empirical or semi-empirical techniques based on physical model have been used to predict the hull-induced pressure (or hull-induced force). In this paper, with the analytic source model for sheet cavitation, a multi-parameter inversion scheme to find the positions of noise sources and their strengths is suggested. The inversion is posed as a nonlinear optimization problem, which is solved by the optimization algorithm based on the adaptive simplex simulated annealing algorithm. Then, the resulting hull pressure can be modeled with boundary element method from the inverted cavitation noise sources. The suggested approach is applied to the hull pressure data measured in a cavitation tunnel of the Samsung Heavy Industry. Two monopole sources are adequate to model the propeller sheet cavitation noise. The inverted source information is reasonable with the cavitation dynamics of the propeller and the modeled hull pressure shows good agreement with cavitation tunnel experimental data.
Inverse Problems in Complex Models and Applications to Earth Sciences
NASA Astrophysics Data System (ADS)
Bosch, M. E.
2015-12-01
The inference of the subsurface earth structure and properties requires the integration of different types of data, information and knowledge, by combined processes of analysis and synthesis. To support the process of integrating information, the regular concept of data inversion is evolving to expand its application to models with multiple inner components (properties, scales, structural parameters) that explain multiple data (geophysical survey data, well-logs, core data). The probabilistic inference methods provide the natural framework for the formulation of these problems, considering a posterior probability density function (PDF) that combines the information from a prior information PDF and the new sets of observations. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires modeling several properties and structural parameters, which relate to each other according to dependency and independency notions. Thus, conditional probabilities across model components also factorize. A common setting proceeds by structuring the model parameter space in hierarchical layers. A primary layer (e.g. lithology) conditions a secondary layer (e.g. physical medium properties), which conditions a third layer (e.g. geophysical data). In general, less structured relations within model components and data emerge from the analysis of other inverse problems. They can be described with flexibility via direct acyclic graphs, which are graphs that map dependency relations between the model components. Examples of inverse problems in complex models can be shown at various scales. At local scale, for example, the distribution of gas saturation is inferred from pre-stack seismic data and a calibrated rock-physics model. At regional scale, joint inversion of gravity and magnetic data is applied
A 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.
NASA Astrophysics Data System (ADS)
Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark
2005-09-01
Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.
A Geophysical Inversion Model Enhancement Technique Based on the Blind Deconvolution
NASA Astrophysics Data System (ADS)
Zuo, B.; Hu, X.; Li, H.
2011-12-01
A model-enhancement technique is proposed to enhance the geophysical inversion model edges and details without introducing any additional information. Firstly, the theoretic correctness of the proposed geophysical inversion model-enhancement technique is discussed. An inversion MRM (model resolution matrix) convolution approximating PSF (Point Spread Function) method is designed to demonstrate the correctness of the deconvolution model enhancement method. Then, a total-variation regularization blind deconvolution geophysical inversion model-enhancement algorithm is proposed. In previous research, Oldenburg et al. demonstrate the connection between the PSF and the geophysical inverse solution. Alumbaugh et al. propose that more information could be provided by the PSF if we return to the idea of it behaving as an averaging or low pass filter. We consider the PSF as a low pass filter to enhance the inversion model basis on the theory of the PSF convolution approximation. Both the 1D linear and the 2D magnetotelluric inversion examples are used to analyze the validity of the theory and the algorithm. To prove the proposed PSF convolution approximation theory, the 1D linear inversion problem is considered. It shows the ratio of convolution approximation error is only 0.15%. The 2D synthetic model enhancement experiment is presented. After the deconvolution enhancement, the edges of the conductive prism and the resistive host become sharper, and the enhancement result is closer to the actual model than the original inversion model according the numerical statistic analysis. Moreover, the artifacts in the inversion model are suppressed. The overall precision of model increases 75%. All of the experiments show that the structure details and the numerical precision of inversion model are significantly improved, especially in the anomalous region. The correlation coefficient between the enhanced inversion model and the actual model are shown in Fig. 1. The figure
A new inversion method for (T2, D) 2D NMR logging and fluid typing
NASA Astrophysics Data System (ADS)
Tan, Maojin; Zou, Youlong; Zhou, Cancan
2013-02-01
One-dimensional nuclear magnetic resonance (1D NMR) logging technology has some significant limitations in fluid typing. However, not only can two-dimensional nuclear magnetic resonance (2D NMR) provide some accurate porosity parameters, but it can also identify fluids more accurately than 1D NMR. In this paper, based on the relaxation mechanism of (T2, D) 2D NMR in a gradient magnetic field, a hybrid inversion method that combines least-squares-based QR decomposition (LSQR) and truncated singular value decomposition (TSVD) is examined in the 2D NMR inversion of various fluid models. The forward modeling and inversion tests are performed in detail with different acquisition parameters, such as magnetic field gradients (G) and echo spacing (TE) groups. The simulated results are discussed and described in detail, the influence of the above-mentioned observation parameters on the inversion accuracy is investigated and analyzed, and the observation parameters in multi-TE activation are optimized. Furthermore, the hybrid inversion can be applied to quantitatively determine the fluid saturation. To study the effects of noise level on the hybrid method and inversion results, the numerical simulation experiments are performed using different signal-to-noise-ratios (SNRs), and the effect of different SNRs on fluid typing using three fluid models are discussed and analyzed in detail.
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.
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.
Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.
2016-08-19
Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~101 to ~102 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less
Inverse modeling of flow tomography experiments in fractured media
NASA Astrophysics Data System (ADS)
Klepikova, Maria; Le Borgne, Tanguy; Bour, Olivier; de Dreuzy, Jean-Raynald
2014-05-01
Inverse modeling of fracture hydraulic properties and connectivity is a very challenging objective due to the strong heterogeneity of the medium at multiple scales and the scarcity of data. Cross-borehole flowmeter tests, which consist of measuring changes in vertical borehole flows when pumping a neighboring borehole, were shown to be an efficient technique to provide information on the properties of the flow zones that connect borehole pairs (Paillet, 1998, Le Borgne et al., 2007). The interpretation of such experiments may, however, be quite uncertain when multiple connections exist. We propose the flow tomography approach (i.e., sequential cross-borehole flowmeter tests) to characterize the connectivity and transmissivity of preferential permeable flow paths in fractured aquifers (Klepikova et al., 2013). An inverse model approach is developed to estimate log-transformed transmissivity values of hydraulically active fractures between the pumping and observation wells by inverting cross-borehole flow and water level data. Here a simplified discrete fracture network approach that highlights main connectivity structures is used. This conceptual model attempts to reproduce fracture network connectivity without taking fracture geometry (length, orientation, dip) into account. We demonstrate that successively exchanging the roles of pumping and observation boreholes improves the quality of available information and reduces the under-determination of the problem. The inverse method is validated for several synthetic flow scenarios. It is shown to provide a good estimation of connectivity patterns and transmissivities of main flow paths. It also allows the estimation of the transmissivity of fractures that connect the flow paths but do not cross the boreholes, although the associated uncertainty may be high for some geometries. The results of this investigation encourage the application of flow tomography to natural fractured aquifers.
ERIC Educational Resources Information Center
Peretz, Dvora
2005-01-01
This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…
A new inverse regression model applied to radiation biodosimetry
Higueras, Manuel; Puig, Pedro; Ainsbury, Elizabeth A.; Rothkamm, Kai
2015-01-01
Biological dosimetry based on chromosome aberration scoring in peripheral blood lymphocytes enables timely assessment of the ionizing radiation dose absorbed by an individual. Here, new Bayesian-type count data inverse regression methods are introduced for situations where responses are Poisson or two-parameter compound Poisson distributed. Our Poisson models are calculated in a closed form, by means of Hermite and negative binomial (NB) distributions. For compound Poisson responses, complete and simplified models are provided. The simplified models are also expressible in a closed form and involve the use of compound Hermite and compound NB distributions. Three examples of applications are given that demonstrate the usefulness of these methodologies in cytogenetic radiation biodosimetry and in radiotherapy. We provide R and SAS codes which reproduce these examples. PMID:25663804
NASA Astrophysics Data System (ADS)
Camacho, A. G.; FernáNdez, J.; Gottsmann, J.
2011-02-01
We present a method for 3-D gravity inversion designed to obtain density contrast models described by subhorizontal layers limited by irregular discontinuity interfaces and models constituted by shallow basins with light infill. It is based on a previously published inversion method that provides, in a nearly automatic approach, the 3-D geometry of isolated anomalous bodies. The basic adjustment constraints are model fitness (fitting the anomaly data) and model smoothness (minimizing the total anomalous mass). For models corresponding to subhorizontal layers, we consider an additional minimization condition: the proximity to prescribed horizontal interfaces. This condition is arranged by including an additional weighting (inverse proportional to the distance to the interface) in the covariance matrix for model parameters. The approach works, according a growth process that increases, step by step, the volume of the adjusted anomalous bodies. Some advantages of the method are simultaneous adjustment of a (linear) regional gravity trend, possibility of including simultaneously positive and negative anomalous structures in the model, and unified inversion approach for isolated bodies, basins, and subhorizontal interface structures. We include several simulation examples and an application case (layered model for the volcanic island of Tenerife).
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. PMID:23759201
Inverse distributed hydrological modelling of Alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2006-06-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2 in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. Application of a 2-dimensional numerical
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.
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
An analytic method for the inverse problem of MREPT
NASA Astrophysics Data System (ADS)
Palamodov, V.
2016-03-01
Magnetic resonance electric properties tomography (MREPT) is a medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. This method consists of reconstructing the admittivity distribution from the positive rotating component of the magnetic field. In the newest paper of Ammari et al (2015 Inverse Problems 31 105001) an approximate method of reconstruction of variable admittivity was proposed. In this paper a method for exact reconstruction of the admittivity from data of the positive rotating component of the field is given.
Wavelets-regularization method for particle size inversion in photon correlation spectroscopy
NASA Astrophysics Data System (ADS)
Wang, Yajing; Shen, Jin; Zheng, Gang; Liu, Wei
2012-07-01
For ill-posed inversion problem of photon correlation spectroscopy (PCS), a wavelet-regularization inversion method (WRIM) which combines wavelet multiscale inversion strategy with classical regularization inversion method (CRIM) was proposed. By using this method, the original inversion problem is decomposed into several subproblems on different multiscale spaces. As a result, we can successively obtain solution of original inversion problem according to the particle sizes inverted from the coarsest scale to the finest scale. The simulation and experimental data was respectively inverted by two methods. The inversion results demonstrate that WRIM has better global convergence, higher accuracy and more strong noise immunity than CRIM.
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.
NASA Astrophysics Data System (ADS)
Brochart, David; Andréassian, Vazken
2015-04-01
Precipitation is known to exhibit a high spatial variability. For this reason, raingage measurements, which only provide a local information about rainfall, may not be appropriate to estimate areal rainfall. On the other hand, catchments have the ability to aggregate rainfall over their area and route it to a unique point - the outlet - where it can be easily measured. A catchment can thus be viewed as a large raingage, with the difference that what is measured at the outlet is a complex transformation of the rainfall. In this communication, we propose to use a model of this transformation (a so-called rainfall-runoff model) and to infer rainfall from an observed streamflow using a Monte Carlo method. We apply the method to 202 catchments in France and compare the inferred rainfall with the areal raingage-based rainfall measurements. We show that the inferred rainfall accuracy directly depends on the accuracy of the rainfall-runoff model. Potential applications of this method include rainfall estimation in poorly gaged areas, correction of uncertain rainfall estimates (e.g. satellite-based rainfall estimates), as well as historical reconstitution of rainfall based on streamflow measurements.
Inversion method based on stochastic optimization for particle sizing.
Sánchez-Escobar, Juan Jaime; Barbosa-Santillán, Liliana Ibeth; Vargas-Ubera, Javier; Aguilar-Valdés, Félix
2016-08-01
A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem. PMID:27505357
A broadband spectral inversion method for spatial heterodyne spectroscopy
NASA Astrophysics Data System (ADS)
Cai, Qisheng; Bin, Xiangli; Du, Shusong
2014-11-01
Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique with many advantages, such as high throughput, good robustness (no moving parts), and high resolving power. However, in the basic theory of SHS, the relationship between the wavenumber and the frequency of the interferogram is approximated to be linear. This approximation limits the spectral range of a spatial heterodyne spectrometer to a narrow band near the Littrow wavenumber. Several methods have been developed to extend the spectral range of the SHS. They use echelle gratings or tunable pilot mirrors to make a SHS instrument work at multiple narrow spectral bands near different Littrow wavenumbers. These solutions still utilize the linear relationship between the wavenumber and the frequency of the interferogram. But they need to separate different spectral bands, and this will increase the difficulty of post processing and the complexity of the SHS system. Here, we solve this problem from another perspective: making a SHS system work at one broad spectral band instead of multiple narrow spectral bands. As in a broad spectral range, the frequency of the interferogram will not be linear with respect to the wavenumber anymore. According to this non-linear relationship, we propose a broadband spectral inversion method based on the stationary phase theory. At first, we describe the principles and the basic characters of SHS. Then, the narrow band limitation is analyzed and the broadband spectral inversion method is elaborated. In the end, we present a parameter design example of the SHS system according to a given spectral range, and the effectiveness of this method is validated with a spectral simulation example. This broadband spectral inversion method can be applied to the existing SHS system without changing or inserting any moving components. This method retains the advantages of SHS and there is almost no increase in complexity for post processing.
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
Model validation and selection based on inverse fuzzy arithmetic
NASA Astrophysics Data System (ADS)
Haag, Thomas; Carvajal González, Sergio; Hanss, Michael
2012-10-01
In this work, a method for the validation of models in general, and the selection of the most appropriate model in particular, is presented. As an industrially relevant example, a Finite Element (FE) model of a brake pad is investigated and identified with particular respect to uncertainties. The identification is based on inverse fuzzy arithmetic and consists of two stages. In the first stage, the eigenfrequencies of the brake pad are considered, and for three different material models, a set of fuzzy-valued parameters is identified on the basis of measurement values. Based on these identified parameters and a resimulation of the system with these parameters, a model validation is performed which takes into account both the model uncertainties and the output uncertainties. In the second stage, the most appropriate material model is used in the FE model for the computation of frequency response functions between excitation point and three measurement points. Again, the parameters of the model are identified on the basis of three corresponding measurement signals and a resimulation is conducted.
Inverse distributed hydrological modelling of alpine catchments
NASA Astrophysics Data System (ADS)
Kunstmann, H.; Krause, J.; Mayr, S.
2005-12-01
Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2) in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. A detailed covariance analysis was performed
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-06-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least squares ℓ2 sense and of a model coefficient norm in a ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multi-resolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the non-linear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-08-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least-squares ℓ2 sense and of a model coefficient norm in an ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multiresolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the nonlinear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Compositing radar reflectivity observations with an inverse method
NASA Astrophysics Data System (ADS)
Roca-Sancho, Jordi; Berenguer, Marc; Sempere-Torres, Daniel
2013-04-01
Quantitative Precipitation Estimation (QPE) has been one of the main applications of weather radars since its early stages. Nowadays, many advances have improved such estimates and radar networks have been deployed in many countries. In parallel, uncertainty in radar QPE has become a subject of interest by itself because of its significant role in the quality of estimates. When several radars cover the same area, some sources of uncertainty (e.g. path attenuation by intense precipitation, beam blockage or beam broadening), can be dealt using information from the least-affected radars instead of only reproducing a single radar approach in each one. So far, composites of radar observations are carried out through simple criteria (by picking the closest observation, the maximum value…) or quality indices -that need a priori definition of quality descriptors. This study proposes an alternative methodology to retrieve the 3-dimensional reflectivity field most compatible with the measurements from the different radars of the network. With this aim, the methodology uses a model that simulates the radar sampling of the atmosphere. The model settings consider the specific features of each radar such as the location, hardware parameters (frequency, beam width, pulse length…) and scanning strategy. The methodology follows the concept of an inverse method based on the minimization of a cost function that penalizes discrepancies between the simulated and actual observations for each radar of the network. It is worth noting that for radar at attenuating wavelengths, the proposed methodology implicitly corrects the effect of attenuation due to intense rainfall. The methodology has been applied on the network of C-band radars in the vicinity of Barcelona, Spain. The retrievals have been obtained for a 12 hours of rainfall with reflectivity observations of two radars; observations from a third independent radar have been used for verification at different heights. Conventional
[A hyperspectral subpixel target detection method based on inverse least squares method].
Li, Qing-Bo; Nie, Xin; Zhang, Guang-Jun
2009-01-01
In the present paper, an inverse least square (ILS) method combined with the Mahalanobis distance outlier detection method is discussed to detect the subpixel target from the hyperspectral image. Firstly, the inverse model for the target spectrum and all the pixel spectra was established, in which the accurate target spectrum was obtained previously, and then the SNV algorithm was employed to preprocess each original pixel spectra separately. After the pretreatment, the regressive coefficient of ILS was calculated with partial least square (PLS) algorithm. Each point in the vector of regressive coefficient corresponds to a pixel in the image. The Mahalanobis distance was calculated with each point in the regressive coefficient vector. Because Mahalanobis distance stands for the extent to which samples deviate from the total population, the point with Mahalanobis distance larger than the 3sigma was regarded as the subpixel target. In this algorithm, no other prior information such as representative background spectrum or modeling of background is required, and only the target spectrum is needed. In addition, the result of the detection is insensitive to the complexity of background. This method was applied to AVIRIS remote sensing data. For this simulation experiment, AVIRIS remote sensing data was free downloaded from the NASA official websit, the spectrum of a ground object in the AVIRIS hyperspectral image was picked up as the target spectrum, and the subpixel target was simulated though a linear mixed method. The comparison of the subpixel detection result of the method mentioned above with that of orthogonal subspace projection method (OSP) was performed. The result shows that the performance of the ILS method is better than the traditional OSP method. The ROC (receive operating characteristic curve) and SNR were calculated, which indicates that the ILS method possesses higher detection accuracy and less computing time than the OSP algorithm. PMID:19385196
Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem
NASA Astrophysics Data System (ADS)
Burger, Martin; Løseth Elvetun, Ole; Schlottbom, Matthias
2015-12-01
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to perturbed or not well resolved domains, and which allow for efficient discretizations not resolving any fine detail of those geometries. For forward problems in partial differential equations methods based on diffuse interface representations have gained strong attention in the last years, but so far they have not been considered systematically for inverse problems. In this work we introduce a diffuse domain method as a tool for the solution of variational inverse problems. As a particular example we study ECG inversion in further detail. ECG inversion is a linear inverse source problem with boundary measurements governed by an anisotropic diffusion equation, which naturally cries for solutions under changing geometries, namely the beating heart. We formulate a regularization strategy using Tikhonov regularization and, using standard source conditions, we prove convergence rates. A special property of our approach is that not only operator perturbations are introduced by the diffuse domain method, but more important we have to deal with topologies which depend on a parameter \\varepsilon in the diffuse domain method, i.e. we have to deal with \\varepsilon -dependent forward operators and \\varepsilon -dependent norms. In particular the appropriate function spaces for the unknown and the data depend on \\varepsilon . This prevents the application of some standard convergence techniques for inverse problems, in particular interpreting the perturbations as data errors in the original problem does not yield suitable results. We consequently develop a novel approach based on saddle-point problems. The numerical solution of the problem is discussed as well and results for several computational experiments are reported. In
Ray, J.; Lee, J.; Yadav, V.; Lefantzi, S.; Michalak, A. M.; van Bloemen Waanders, B.
2015-04-29
Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting.more » Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also
Investigating the reliability of kinematic source inversion with dynamic rupture models
NASA Astrophysics Data System (ADS)
Zhang, Y.; Song, S.; Dalguer, L. A.; Clinton, J. F.
2011-12-01
An essential element of understanding the earthquake source processes is obtaining a reliable source model via geophysical data inversion. However, the epistemic uncertainties in the kinematic source inversion produce a variety of source model estimates for any given event. Thus, as done in the Source Inversion Validation (SIV) project, it is important to validate our inversion methods with synthetic data by testing forward Green's function calculation and comparing various inversion methods. Spontaneous dynamic rupture modeling, which incorporates the conservation laws of continuum mechanics and the constitutive behavior of rocks under frictional sliding, is capable of producing physically self-consistent kinematic description of the fault and its associated seismic wave propagation resulting in ground motions on the surface. Here we develop accurate dynamic rupture simulation of a vertical strike slip fault. Our source model is composed of well-defined asperities (patches of large stress drop) and we assume that fault rupture is governed by the linear slip weakening friction model. The resulting near-source ground motions dominated by low frequency (up to 1Hz) are used for testing our inversion method. We performed various inversion tests and compared estimated solutions with true solutions obtained by the forward dynamic rupture modeling. Our preliminary results show that estimated model spaces could be significantly perturbed, depending on data and modeling schemes used in the inversion, not only in terms of spatial distribution of model parameters, but also in terms of their auto- and cross-correlation structure. The Bayesian approach in source inversion is becoming increasingly popular because of the recent common availability of high performance computing capabilities. We adopted the Bayesian approach in our source inversion test, so that we can more effectively analyze the uncertainty of estimated models and also implement physically guided regularization
Demonstration of model-based inversion of electromagnetic signals for crack characterization
NASA Astrophysics Data System (ADS)
Shell, Eric B.; Aldrin, John C.; Sabbagh, Harold A.; Sabbagh, Elias; Murphy, R. Kim; Mazdiyasni, Siamack; Lindgren, Eric A.
2015-03-01
The objective of this work is to demonstrate model-based inversion techniques to characterize the length, depth, width, and orientation of surface-breaking cracks using eddy current (EC) NDE. The paper presents experimental testing to acquire high fidelity automated eddy current data, enhancements made in VIC-3D® to improve both speed and accuracy, benchmark studies demonstrating model accuracy, improved data registration and reduction methods, and surrogate models and model calibration schemes to ensure the fastest and highest quality models are used for inversion. Initial inversion results indicate the potential to accurately size cracks and EDM notches over a wide range of flaw characteristics and probe orientations. Insight into EC variability for POD crack sets is presented using inversion results for crack length and depth.
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.
Inverse estimation of parameters for an estuarine eutrophication model
Shen, J.; Kuo, A.Y.
1996-11-01
An inverse model of an estuarine eutrophication model with eight state variables is developed. It provides a framework to estimate parameter values of the eutrophication model by assimilation of concentration data of these state variables. The inverse model using the variational technique in conjunction with a vertical two-dimensional eutrophication model is general enough to be applicable to aid model calibration. The formulation is illustrated by conducting a series of numerical experiments for the tidal Rappahannock River, a western shore tributary of the Chesapeake Bay. The numerical experiments of short-period model simulations with different hypothetical data sets and long-period model simulations with limited hypothetical data sets demonstrated that the inverse model can be satisfactorily used to estimate parameter values of the eutrophication model. The experiments also showed that the inverse model is useful to address some important questions, such as uniqueness of the parameter estimation and data requirements for model calibration. Because of the complexity of the eutrophication system, degrading of speed of convergence may occur. Two major factors which cause degradation of speed of convergence are cross effects among parameters and the multiple scales involved in the parameter system.
Towards inverse modeling of intratumor heterogeneity
NASA Astrophysics Data System (ADS)
Brutovsky, Branislav; Horvath, Denis
2015-08-01
Development of resistance limits efficiency of present anticancer therapies and preventing it remains a big challenge in cancer research. It is accepted, at the intuitive level, that resistance emerges as a consequence of the heterogeneity of cancer cells at the molecular, genetic and cellular levels. Produced by many sources, tumor heterogeneity is extremely complex time dependent statistical characteristics which may be quantified by measures defined in many different ways, most of them coming from statistical mechanics. In this paper, we apply the Markovian framework to relate population heterogeneity to the statistics of the environment. As, from an evolutionary viewpoint, therapy corresponds to a purposeful modi- fication of the cells' fitness landscape, we assume that understanding general relationship between the spatiotemporal statistics of a tumor microenvironment and intratumor heterogeneity will allow to conceive the therapy as an inverse problem and to solve it by optimization techniques. To account for the inherent stochasticity of biological processes at cellular scale, the generalized distancebased concept was applied to express distances between probabilistically described cell states and environmental conditions, respectively.
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.
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?'
Full waveform inversion in the frequency domain using direct iterative T-matrix methods
NASA Astrophysics Data System (ADS)
Jakobsen, Morten; Ursin, Bjørn
2015-06-01
We present two direct iterative solutions to the nonlinear seismic waveform inversion problem that are based on volume integral equation methods for seismic forward modelling in the acoustic approximation. The solutions are presented in the frequency domain, where accurate inversion results can often be obtained using a relatively low number of frequency components. Our inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. Both these solutions update the wavefield within the scattering domain after each iteration. The main difference is that the background medium Green functions are kept fixed in the first solution, but updated after each iteration in the second solution. This means that our solutions are very similar to the Born iterative (BI) and the distorted Born iterative (DBI) methods that are commonly used in acoustic and electromagnetic inverse scattering. However, we have eliminated the need to perform a full forward simulation (or to invert a huge matrix) at each iteration via the use of an iterative T-matrix method for fixed background media for the BI method and a variational T-matrix method for dynamic background media for the DBI method. The T-matrix (variation) is linearly related with the seismic wavefield data (residuals), but related with the unknown scattering potential model parameter (updates) in a non-linear manner, which is independent of the source-receiver configuration. This mathematical structure, which allows one to peel off the effects of the source-receiver configuration, is very attractive when dealing with multiple (simultaneous) sources, and is also compatible with the (future) use of renormalization methods for dealing with local minima problems. To illustrate the performance and potential of the two direct iterative methods for FWI, we performed a series of numerical
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.
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
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.
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.
Inverse rendering of Lambertian surfaces using subspace methods.
Nguyen, Ha Q; Do, Minh N
2014-12-01
We propose a vector space approach for inverse rendering of a Lambertian convex object with distant light sources. In this problem, the texture of the object and arbitrary lightings are both to be recovered from multiple images of the object and its 3D model. Our work is motivated by the observation that all possible images of a Lambertian object lie around a low-dimensional linear subspace spanned by the first few spherical harmonics. The inverse rendering can therefore be formulated as a matrix factorization, in which the basis of the subspace is encoded in a spherical harmonic matrix S associated with the object’s geometry. A necessary and sufficient condition on S for unique factorization is derived with an introduction to a new notion of matrix rank called nonseparable full rank. A singular value decomposition-based algorithm for exact factorization in the noiseless case is introduced. In the presence of noise, two algorithms, namely, alternating and optimization based are proposed to deal with two different types of noise. A random sample consensus-based algorithm is introduced to reduce the size of the optimization problem, which is equal to the number of pixels in each image. Implementations of the proposed algorithms are done on a real data set. PMID:25373083
Estimates of tropical bromoform emissions using an inversion method
NASA Astrophysics Data System (ADS)
Ashfold, M. J.; Harris, N. R. P.; Manning, A. J.; Robinson, A. D.; Warwick, N. J.; Pyle, J. A.
2013-08-01
Bromine plays an important role in ozone chemistry in both the troposphere and stratosphere. When measured by mass, bromoform (CHBr3) is thought to be the largest organic source of bromine to the atmosphere. While seaweed and phytoplankton are known to be dominant sources, the size and the geographical distribution of CHBr3 emissions remains uncertain. Particularly little is known about emissions from the Maritime Continent, which have usually been assumed to be large, and which appear to be especially likely to reach the stratosphere. In this study we aim to use the first multi-annual set of CHBr3 measurements from this region, and an inversion method, to reduce this uncertainty. We find that local measurements of a short-lived gas like CHBr3 can only be used to constrain emissions from a relatively small, sub-regional domain. We then obtain detailed estimates of both the distribution and magnitude of CHBr3 emissions within this area. Our estimates appear to be relatively insensitive to the assumptions inherent in the inversion process. We extrapolate this information to produce estimated emissions for the entire tropics (defined as 20° S-20° N) of 225 GgCHBr3 y-1. This estimate is consistent with other recent studies, and suggests that CHBr3 emissions in the coastline-rich Maritime Continent may not be stronger than emissions in other parts of the tropics.
NASA Astrophysics Data System (ADS)
Carter-McAuslan, Angela; Lelievre, Peter; Farquharson, Colin
2013-04-01
Gravity methods have long been used in mineral exploration. However, gravity methods have difficulty resolving small details. Seismic methods provide high resolving potential for use in mineral exploration. However, complicated hard-rock geology can make seismic data processing and interpretation difficult. By jointly inverting seismic tomography data with gravity data these difficulty may be overcome. We investigated the viability of deterministic minimum-structure style joint inversion of seismic traveltime and gravity data for the delineation of magmatic massive sulphide type geological targets. These tests also assessed the potential of employing borehole gravity. A number of synthetic Earth models were created. These models were built on triangular unstructured meshes, allowing for efficient generation of complicated, realistic geological structures. 2D models were based on conceptualized models of the magmatic massive sulphide body similar to the Eastern Deeps of the Voisey's Bay, Labrador, Canada. Single property and joint inversions were performed with seismic traveltimes and both ground-based and borehole gravity. There is a known relationship between seismic velocity and density for both silicate rocks and sulphide minerals for the models constructed; this lithological relationship was used to design an appropriate coupling strategy in the joint inversions. Joint inversions were able to successfully locate a buried high contrast target with a variety of survey designs. 2D inversions results provided guidance to 3D inversion. Experimentation with noise levels, mesh design, and various inversion parameters has led to a better understanding of how to practically apply joint inversion of traveltimes and gravity data to this and similar exploration problems.
NASA Astrophysics Data System (ADS)
Illman, Walter A.; Berg, Steven J.; Zhao, Zhanfeng
2015-05-01
The robust performance of hydraulic tomography (HT) based on geostatistics has been demonstrated through numerous synthetic, laboratory, and field studies. While geostatistical inverse methods offer many advantages, one key disadvantage is its highly parameterized nature, which renders it computationally intensive for large-scale problems. Another issue is that geostatistics-based HT may produce overly smooth images of subsurface heterogeneity when there are few monitoring interval data. Therefore, some may question the utility of the geostatistical inversion approach in certain situations and seek alternative approaches. To investigate these issues, we simultaneously calibrated different groundwater models with varying subsurface conceptualizations and parameter resolutions using a laboratory sandbox aquifer. The compared models included: (1) isotropic and anisotropic effective parameter models; (2) a heterogeneous model that faithfully represents the geological features; and (3) a heterogeneous model based on geostatistical inverse modeling. The performance of these models was assessed by quantitatively examining the results from model calibration and validation. Calibration data consisted of steady state drawdown data from eight pumping tests and validation data consisted of data from 16 separate pumping tests not used in the calibration effort. Results revealed that the geostatistical inversion approach performed the best among the approaches compared, although the geological model that faithfully represented stratigraphy came a close second. In addition, when the number of pumping tests available for inverse modeling was small, the geological modeling approach yielded more robust validation results. This suggests that better knowledge of stratigraphy obtained via geophysics or other means may contribute to improved results for HT.
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.
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. PMID:26048619
Physical-Based Inversion for Subsurface Flow and Transport Modeling
NASA Astrophysics Data System (ADS)
Zhang, Y.; Jiao, J.; Wang, D.; Irsa, J.
2014-12-01
A new and computationally efficient fluid flow and transport inverse theory has been developed for characterizing, calibrating, and modeling aquifers. The theory is capable of simultaneous estimation of model boundary conditions (for simple transient problems, also the initial conditions) and fluid flow and transport parameters, i.e., spatially distributed permeabilities, source/sink rates, storativity, and dispersivity. The theory is robust to measurement errors and strong parameter variability. Effective parameters can be estimated to represent unresolved heterogeneity, e.g., sub-grid features and spatially variable recharge. The theory has been extended to new problems including parameter structure identification, unsaturated and variably saturated flows (e.g., directly estimating the soil retention functions), joint flow and transport inversion (e.g., containment source identification), uncertainty analysis (e.g., integrating subsurface static and dynamic data via geostatistical inversion), and high performance computing (e.g., solving large inversion systems with parallel computing). This presentation will summarize the body of the inversion research and discuss new directions for future work.
Inverse problem for the current loop model: Possibilities and restrictions
NASA Astrophysics Data System (ADS)
Demina, I. M.; Farafonova, Yu. G.
2016-07-01
The possibilities of determining arbitrary current loop parameters based on the spatial structures of the magnetic field components generated by this loop on a sphere with a specified radius have been considered with the use of models. The model parameters were selected such that anomalies created by current loops on a sphere with a radius of 6378 km would be comparable in value with the different-scale anomalies of the observed main geomagnetic field (MGF). The least squares method was used to solve the inverse problem. Estimates close to the specified values were obtained for all current loop parameters except the current strength and radius. The radius determination error can reach ±120 km; at the same time, the magnetic moment value is determined with an accuracy of ±1%. The resolvability of the current force and radius can to a certain degree be improved by decreasing the observation sphere radius such that the ratio of the source distance to the current loop radius would be at least smaller than eight, which can be difficult to reach when modeling MGF.
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.
Analytic Differentiation of Barlat's 2D Criteria for Inverse Modeling
Endelt, Benny; Nielsen, Karl Brian; Danckert, Joachim
2005-08-05
The demand for alternative identification schemes for identification of constitutive parameters is getting more pronounced as the complexity of the constitutive equations increases, i.e. the number of parameters subject to identification. A general framework for inverse identification of constitutive parameters associated with sheet metal forming is proposed in the article. The inverse problem is solved, through minimization of the least square error between an experimental punch force sampled from a deep drawing and a predicted punch force produced from a coherent finite element model.
Inversion of canopy reflectance models for estimation of vegetation parameters
NASA Technical Reports Server (NTRS)
Goel, Narendra S.
1987-01-01
One of the keys to successful remote sensing of vegetation is to be able to estimate important agronomic parameters like leaf area index (LAI) and biomass (BM) from the bidirectional canopy reflectance (CR) data obtained by a space-shuttle or satellite borne sensor. One approach for such an estimation is through inversion of CR models which relate these parameters to CR. The feasibility of this approach was shown. The overall objective of the research carried out was to address heretofore uninvestigated but important fundamental issues, develop the inversion technique further, and delineate its strengths and limitations.
An evolution equation modeling inversion of tulip flames
Dold, J.W.; Joulin, G.
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
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.
NASA Astrophysics Data System (ADS)
Ma, Xiang; Zabaras, Nicholas
2009-03-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media.
Modeling and inverse feedforward control for conducting polymer actuators with hysteresis
NASA Astrophysics Data System (ADS)
Wang, Xiangjiang; Alici, Gursel; Tan, Xiaobo
2014-02-01
Conducting polymer actuators are biocompatible with a small footprint, and operate in air or liquid media under low actuation voltages. This makes them excellent actuators for macro- and micro-manipulation devices, however, their positioning ability or accuracy is adversely affected by their hysteresis non-linearity under open-loop control strategies. In this paper, we establish a hysteresis model for conducting polymer actuators, based on a rate-independent hysteresis model known as the Duhem model. The hysteresis model is experimentally identified and integrated with the linear dynamics of the actuator. This combined model is inverted to control the displacement of the tri-layer actuators considered in this study, without using any external feedback. The inversion requires an inverse hysteresis model which was experimentally identified using an inverse neural network model. Experimental results show that the position tracking errors are reduced by more than 50% when the hysteresis inverse model is incorporated into an inversion-based feedforward controller, indicating the potential of the proposed method in enabling wider use of such smart actuators.
Inversion of Airborne Contaminants in a Regional Model
Akcelik, V.; Biros, G.; Draganescu, A.; Ghattas, O.; Hill, J.; van Bloemen Waanders, B.; /SLAC /Pennsylvania U. /Texas U. /Sandia
2007-01-10
We are interested in a DDDAS problem of localization of airborne contaminant releases in regional atmospheric transport models from sparse observations. Given measurements of the contaminant over an observation window at a small number of points in space, and a velocity field as predicted for example by a mesoscopic weather model, we seek an estimate of the state of the contaminant at the beginning of the observation interval that minimizes the least squares misfit between measured and predicted contaminant field, subject to the convection-diffusion equation for the contaminant. Once the ''initial'' conditions are estimated by solution of the inverse problem, we issue predictions of the evolution of the contaminant, the observation window is advanced in time, and the process repeated to issue a new prediction, in the style of 4D-Var. We design an appropriate numerical strategy that exploits the spectral structure of the inverse operator, and leads to efficient and accurate resolution of the inverse problem. Numerical experiments verify that high resolution inversion can be carried out rapidly for a well-resolved terrain model of the greater Los Angeles area.
Inverse modeling of FIB milling by dose profile optimization
NASA Astrophysics Data System (ADS)
Lindsey, S.; Waid, S.; Hobler, G.; Wanzenböck, H. D.; Bertagnolli, E.
2014-12-01
FIB technologies possess a unique ability to form topographies that are difficult or impossible to generate with binary etching through typical photo-lithography. The ability to arbitrarily vary the spatial dose distribution and therefore the amount of milling opens possibilities for the production of a wide range of functional structures with applications in biology, chemistry, and optics. However in practice, the realization of these goals is made difficult by the angular dependence of the sputtering yield and redeposition effects that vary as the topography evolves. An inverse modeling algorithm that optimizes dose profiles, defined as the superposition of time invariant pixel dose profiles (determined from the beam parameters and pixel dwell times), is presented. The response of the target to a set of pixel dwell times in modeled by numerical continuum simulations utilizing 1st and 2nd order sputtering and redeposition, the resulting surfaces are evaluated with respect to a target topography in an error minimization routine. Two algorithms for the parameterization of pixel dwell times are presented, a direct pixel dwell time method, and an abstracted method that uses a refineable piecewise linear cage function to generate pixel dwell times from a minimal number of parameters. The cage function method demonstrates great flexibility and efficiency as compared to the direct fitting method with performance enhancements exceeding ∼10× as compared to direct fitting for medium to large simulation sets. Furthermore, the refineable nature of the cage function enables solutions to adapt to the desired target function. The optimization algorithm, although working with stationary dose profiles, is demonstrated to be applicable also outside the quasi-static approximation. Experimental data confirms the viability of the solutions for 5 × 7 μm deep lens like structures defined by 90 pixel dwell times.
Inverse modeling of the global CO cycle, 1. Inversion of CO mixing ratios
NASA Astrophysics Data System (ADS)
Bergamaschi, Peter; Hein, Ralf; Heimann, Martin; Crutzen, Paul J.
2000-01-01
A three-dimensional modeling study on atmospheric carbon monoxide is presented, based on the TM2 model. A Bayesian inverse technique is applied to optimize the agreement between model and observational data, including a priori source information as regularization term. Using the National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory data set for CO mixing ratios at 31 globally distributed sites, a posteriori CO budgets can be derived, which allow the model to reproduce the observations at most sites within two standard deviations of monthly mean values. Use of different spatiotemporal emission distributions for terpenes (Global Emissions Inventory Activity, ˜80% of emissions in the tropics; Hough [1991], ˜70% of emissions in the extratropical Northern Hemisphere) showed a large impact on calculated a posteriori source strengths and on the modeled partitioning among individual CO sources. In order to reproduce the interhemispheric gradient of observed CO mixing ratios, a ratio between total sources in the Northern Hemisphere and those in the Southern Hemisphere of ˜1.8 is required. While it is obvious that this asymmetry is mainly due to CO emissions from technological sources, the inversion results suggest that either (1) the global technological CO source strength is higher (˜800 Tg CO/yr) than present inventory based estimates or (2) CO from terpenes or vegetation (or additional sources with dominant emissions in the Northern Hemisphere) have a significant impact on the northern hemispheric mixing ratios. Further sensitivity studies showed that a posteriori results slightly depend on biomass burning seasonality (shifted by 1 month), but they are virtually identical for the two different OH fields (CH4-nonmethanehydrocarbons chemistry vs. CH4-Only chemistry). Inversion results, however, were sensitive to model wind fields used (based on meteorological observations of 1987 and 1986, respectively), mainly due to stations
FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2013-10-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational
FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
NASA Astrophysics Data System (ADS)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2012-09-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finance. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition
An inverse model for magnetorheological dampers based on a restructured phenomenological model
NASA Astrophysics Data System (ADS)
Qian, Li-Jun; Liu, Bo; Chen, Peng; Bai, Xian-Xu
2016-04-01
Magnetorheological dampers (MRDs), a semi-active actuator based on MR effect, have great potential in vibration/shock control systems. However, it is difficult to establish its inverse model due to its intrinsic strong nonlinear hysteresis behaviors, and sequentially the precise, fast and effective control could not be realized effectively. This paper presents an inverse model for MRDs based on a restructured phenomenological model with incorporation of the "normalization" concept. The proposed inverse model of MRDs is validated by the simulation of the force tracking. The research results indicate that the inverse model could be applied for the damping force control with consideration of the strong nonlinear hysteresis behaviors of the MRDs.
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
Research on inverse methods and optimization in Italy
NASA Technical Reports Server (NTRS)
Larocca, Francesco
1991-01-01
The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).
NASA Astrophysics Data System (ADS)
Biedermann, Eric; Jauriqui, Leanne; Aldrin, John C.; Goodlet, Brent; Pollock, Tresa; Torbet, Chris; Mazdiyasni, Siamack
2015-03-01
The objective of this paper is to investigate Resonance Ultrasound Spectroscopy (RUS) measurement models to more precisely connect changes in the resonance frequencies of nickel-based super-alloy material to the macro/microscopic state. RUS models using analytical solutions and the finite element method (FEM) were developed to address varying elastic properties, grain structures and creep. Experimental studies were performed investigating the effect of exposure to high temperatures and stress for varying part shape and three grain structure classes: single crystals, directionally-solidified and polycrystalline structures. Inversion using both traditional analytical models was enhanced in order to simultaneously estimate varying material properties and changes in part geometry due to creep. Inversion using surrogate models from FEM simulations was also developed, addressing varying crystal orientation and complex geometries. Results are presented comparing the forward model trends and inversion results with nickel alloy parts under various test conditions.
NASA Astrophysics Data System (ADS)
Zhang, Chengjiao; Li, Xiaojie; Yang, Chenchen
2016-07-01
This paper introduces a modified method of characteristics and its application in forward and inversion simulations of underwater explosion. Compared with standard method of characteristics which is appropriate to homoentripic flow problem, the modified method can be also used to deal with isentropic flow problem such as underwater explosion. Underwater explosion of spherical TNT and composition B explosives are simulated by using the modified method, respectively. Peak pressures and flow field pressures are obtained, and they are coincident with those from empirical formulas. The comparison demonstrates the modified is feasible and reliable in underwater explosion simulation. Based on the modified method, inverse difference schemes and inverse method are introduced. Combined with the modified, the inverse schemes can be used to deal with gas-water interface inversion of underwater explosion. Inversion simulations of underwater explosion of the explosives are performed in water, and equation of state (EOS) of detonation product is not needed. The peak pressures from the forward simulations are provided as boundary conditions in the inversion simulations. Inversion interfaces are obtained and they are mainly in good agreement with those from the forward simulations in near field. The comparison indicates the inverse method and the inverse difference schemes are reliable and reasonable in interface inversion simulation.
Two radiative inverse seesaw models, dark matter, and baryogenesis.
NASA Astrophysics Data System (ADS)
Baldes, Iason; Bell, Nicole F.; Petraki, Kalliopi; Volkas, Raymond R.
2013-07-01
The inverse seesaw mechanism allows the neutrino masses to be generated by new physics at an experimentally accessible scale, even with Script O(1) Yukawa couplings. In the inverse seesaw scenario, the smallness of neutrino masses is linked to the smallness of a lepton number violating parameter. This parameter may arise radiatively. In this paper, we study the cosmological implications of two contrasting radiative inverse seesaw models, one due to Ma and the other to Law and McDonald. The former features spontaneous, the latter explicit lepton number violation. First, we examine the effect of the lepton-number violating interactions introduced in these models on the baryon asymmetry of the universe. We investigate under what conditions a pre-existing baryon asymmetry does not get washed out. While both models allow a baryon asymmetry to survive only once the temperature has dropped below the mass of their heaviest fields, the Ma model can create the baryon asymmetry through resonant leptogenesis. Then we investigate the viability of the dark matter candidates arising within these models, and explore the prospects for direct detection. We find that the Law/McDonald model allows a simple dark matter scenario similar to the Higgs portal, while in the Ma model the simplest cold dark matter scenario would tend to overclose the universe.
Direct and inverse modeling of multiphase flow systems
Finsterle, S.
1995-10-01
A modeling study is presented which demonstrates how the combination of simulation and optimization techniques can be used to improve the design of a multi-component remediation system. A series of computer codes has been developed at the Lawrence Berkeley National Laboratory to solve forward and inverse problems in groundwater hydrology. Simulations of non-isothermal, three-phase flow of volatile organic compounds in three-dimensional heterogeneous media were performed. Inverse modeling capabilities have been developed which can be used for both automatic model calibration and optimization of remediation schemes. In this study, we discuss a sequence of simulations to demonstrate the potential use of numerical models to design and analyze cleanup of a contaminated aquifer.
Chang, Chia-Ling; Lo, Shang-Lien; Yu, Shaw-L
2006-06-01
The inverse distance method, one of the commonly used methods for analyzing spatial variation of rainfall, is flexible if the order of distances in the method is adjustable. By applying the genetic algorithm (GA), the optimal order of distances can be found to minimize the difference between estimated and measured precipitation data. A case study of the Feitsui reservoir watershed in Taiwan is described in the present paper. The results show that the variability of the order of distances is small when the topography of rainfall stations is uniform. Moreover, when rainfall characteristic is uniform, the horizontal distance between rainfall stations and interpolated locations is the major factor influencing the order of distances. The results also verify that the variable-order inverse distance method is more suitable than the arithmetic average method and the Thiessen Polygons method in describing the spatial variation of rainfall. The efficiency and reliability of hydrologic modeling and hence of general water resource management can be significantly improved by more accurate rainfall data interpolated by the variable-order inverse distance method. PMID:16917704
Advances in CBL Budgetting and Inverse Modelling by Applying an Off-the-shelf Mesoscale Model
NASA Astrophysics Data System (ADS)
van der Molen, M. K.; Dolman, H.; Ronda, R. J.
2005-12-01
Eddy flux towers measure carbon sinks/sources at a local scale (~0.1 km), with the CBL budget method fluxes may be determined at a landscape scale (~1 km), and inverse models may determine the source/sink distribution at a global/continental scale (~1000-10000 km). Although currently efforts are made to increase the resolution of inverse models to the regional scale (~100 km), the meso-scale (100-1000 km) is rather badly represented in this spectrum of approaches. Boundary layer profiles contain signatures of mesoscale processes, such as the effect of wind divergence, topography and forest breezes on the boundary layer height and the subsidence velocity. 3-D advection of resulting concentration gradients is one of the main reasons of failure of the CBL budget approach and the representation error in inverse models and may be addressed in mesoscale atmospheric models. This study shows that considerable improvement may be obtained in the interpretation of boundary layer profiles by running an off-the-shelf mesoscale model without detailed prior knowlegde of the surface flux distribution. The simulations were carried out in the region around Zotino, Central Siberia to aid the interpretation of profile observations collected as part of TCOS-Siberia.
NASA Astrophysics Data System (ADS)
Ganesan, A. L.; Rigby, M.; Zammit-Mangion, A.; Manning, A. J.; Prinn, R. G.; Fraser, P. J.; Harth, C. M.; Kim, K.-R.; Krummel, P. B.; Li, S.; Mühle, J.; O'Doherty, S. J.; Park, S.; Salameh, P. K.; Steele, L. P.; Weiss, R. F.
2014-04-01
We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDFs) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgment. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties than traditional methods.
NASA Astrophysics Data System (ADS)
Ganesan, A. L.; Rigby, M.; Zammit-Mangion, A.; Manning, A. J.; Prinn, R. G.; Fraser, P. J.; Harth, C. M.; Kim, K.-R.; Krummel, P. B.; Li, S.; Mühle, J.; O'Doherty, S. J.; Park, S.; Salameh, P. K.; Steele, L. P.; Weiss, R. F.
2013-12-01
We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDF) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgement. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties, than traditional methods.
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
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
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.
Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.
2005-01-01
. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.
Why does inverse modeling of drainage inventories work?
NASA Astrophysics Data System (ADS)
White, Nicky; Roberts, Gareth
2016-04-01
We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. This approach builds upon a more general, non-linear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. We have tested both algorithms by inverting thousands of river profiles from Africa, Eurasia, the Americas, and Australia. For each continent, the drainage network was constructed from a digital elevation model and the fidelity of river profiles extracted from this network was carefully checked using satellite imagery. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Inverse modeling of these substantial inventories of river profiles suggests that drainage networks contain coherent signals that record the regional growth of elevation. In the second part of this presentation, we use spectral analysis of river profiles to suggest why drainage networks behave in a coherent, albeit non-linear, fashion. Our analysis implies that large-scale topographic signals injected into landscapes generate spectral slopes that are usually red (i.e. Brownian). At wavelengths shorter than tens of km, spectral slopes whiten which suggests that coherent topographic signals cease to exist at these shorter length scales. Our results suggest that inverse modeling of drainage networks can reveal useful information about landscape growth through space and time.
2.5D complex resistivity modeling and inversion using unstructured grids
NASA Astrophysics Data System (ADS)
Xu, Kaijun; Sun, Jie
2016-04-01
The characteristic of complex resistivity on rock and ore has been recognized by people for a long time. Generally we have used the Cole-Cole Model(CCM) to describe complex resistivity. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by CCM parameters such as direct resistivity(ρ0), chargeability(m), time constant(τ) and frequency dependence(c). Thus it is very important to obtain the complex parameters of geologic body. It is difficult to approximate complex structures and terrain using traditional rectangular grid. In order to enhance the numerical accuracy and rationality of modeling and inversion, we use an adaptive finite-element algorithm for forward modeling of the frequency-domain 2.5D complex resistivity and implement the conjugate gradient algorithm in the inversion of 2.5D complex resistivity. An adaptive finite element method is applied for solving the 2.5D complex resistivity forward modeling of horizontal electric dipole source. First of all, the CCM is introduced into the Maxwell's equations to calculate the complex resistivity electromagnetic fields. Next, the pseudo delta function is used to distribute electric dipole source. Then the electromagnetic fields can be expressed in terms of the primary fields caused by layered structure and the secondary fields caused by inhomogeneities anomalous conductivity. At last, we calculated the electromagnetic fields response of complex geoelectric structures such as anticline, syncline, fault. The modeling results show that adaptive finite-element methods can automatically improve mesh generation and simulate complex geoelectric models using unstructured grids. The 2.5D complex resistivity invertion is implemented based the conjugate gradient algorithm.The conjugate gradient algorithm doesn't need to compute the sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying vector. In addition, the inversion target zones are
Inverse Modelling of Continental Margins and Sedimentary Basins
NASA Astrophysics Data System (ADS)
Edwards, G. R.; White, N.; Haines, J.
2004-12-01
The wealth of data available from the hydrocarbon industry provides us with detailed information about the subsidence histories of extensional sedimentary basins and passive margins. This resource is often exploited in forward models of basin and margin evolution although little attempt has been made to invert such data. We are interested in developing an inverse methodology in order to constrain the spatial and temporal variation of strain rate in these regions. Any inversion scheme which searches the possible movements of the lithosphere over geological time requires a fast forward model at its heart. We present a new kinematic model for use in such an inversion. Our finite-difference model is capable of simulating the thermal and subsidence effects of basins and margins that have undergone differential stretching with both depth and distance across the stretching area. Speed is achieved by a modular design and optimisation of the code for the architecture on which it is running. The model can simulate fifty million years of extension in around a second on a desktop computer. Currently there is much interest in cold continental margins such as the Newfoundland/Iberia system where crust has been thinned to zero but lithospheric mantle has been exhumed without extension. We believe this is not possible without differential thinning and will be testing this hypothesis with our new model. The inversion scheme is also being used to investigate flanks of actively rifting regions, such as those around Lake Baikal and the Albertine rift, and older extensional systems such as those in the Northern North sea.
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
Model Reduction of a Transient Groundwater-Flow Model for Bayesian Inverse Problems
NASA Astrophysics Data System (ADS)
Boyce, S. E.; Yeh, W. W.
2011-12-01
A Bayesian inverse problem requires many repeated model simulations to characterize an unknown parameter's posterior probability distribution. It is computationally infeasible to solve a Bayesian inverse problem of a discretized groundwater flow model with a high dimension parameter and state space. Model reduction has been shown to reduce the dimension of a groundwater model by several orders of magnitude and is well suited for Bayesian inverse problems. A projection-based model reduction approach is proposed to reduce the parameter and state dimensions of a groundwater model. Previous work has done this by using a greedy algorithm for the selection of parameter vectors that make up a basis and their corresponding steady-state solutions for a state basis. The proposed method extends this idea to include transient models by assembling sequentially though the greedy algorithm the parameter and state projection bases. The method begins with the parameter basis being a single vector that is equal to one or an accepted series of values. A set of state vectors that are solutions to the groundwater model using this parameter vector at appropriate times is called the parameter snapshot set. The appropriate times for the parameter snapshot set are determined by maximizing the set's minimum singular value. This optimization is a similar to those used in experimental design for maximizing information. The two bases are made orthonormal by a QR decomposition and applied to the full groundwater model to form a reduced model. The parameter basis is increased with a new parameter vector that maximizes the error between the full model and the reduced model at a set of observation times. The new parameter vector represents where the reduced model is least accurate in representing the original full model. The corresponding parameter snapshot set's appropriate times are found using a greedy algorithm. This sequentially chooses times that have maximum error between the full and
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.
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. PMID:22370094
Discovering Of GILD-TCCR Effects by GILD-TCCR Modeling and Inversion
NASA Astrophysics Data System (ADS)
Xie, G.; Xie, F.; Li, J.
2001-12-01
We had developed a successful 3D/2D seismic TCCR modeling and inversion algorithm from 1982 to 1989 Recent year, We discovered a new magnetic integral equation (Xie and Li, 1995, EM3DI) (SEG book, 1999), (Geophysics 2000) which has many advantages over the traditional electric integral equation (Hormand, 1975). The advantages of our magnetic integral equation are (1) the magnetic field is continuous when the magnetic permeability is continuous (which is usually a constant in underground), even through the electric resistivity and dielectric parameter are discontinuous. (2) the magnetic integral equation is second type integral equation with a weak and integrable kernel. (3) The relative parameter term is included. Since 1997, we have created a Global Integral and Local Differential decomposition method for forward modeling and backward inversion. The method named GILD modeling and inversion. (SEG book, Geophysics 2000, EM3D II 2001, Physica D, 1999) Currently, we discovered a very interesting phenomena in electromagnetic field, we call them GILD effects, when we calculated the 3D magnetic field excited by a vertical magnetic dipole source using our new GILD. It is a surprise discovering. This phenomena is occurred in the seismic scattering wave propagation in the fractures. Using the convention electromagnetic numerical method, the Hy was ignored because it is zero theoretically, its numerical value was very small and hiding in numerical noise. It was dropped before. There is gold in zero. l We used GILD method to calculate the scattering Hy accurately without any boundary error reflection. We discover that the imaging (in Fig. 2) of the Hy is very similar to imaging the electric resistivity of the coefficient model in (Fig. 1). This is very important in inversion. This is why our GILD inversion is high resolution. In the vertical magnetic dipole source case, by using convention method every one just calculate Hx and Hz. They ignored the Hy because the Hy is very
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.
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.