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Inversion of large-scale time-domain transient electromagnetic (TEM) surveys is computationally expensive and time-consuming. The calculation of partial derivatives for the Jacobian matrix is by far the most computationally intensive task, as this requires calculation of a significant number of forward responses. We propose to accelerate the inversion process by predicting partial derivatives using an artificial neural network. Network training data for resistivity models for a broad range of geological settings are generated by computing partial derivatives as symmetric differences between two forward responses. Given that certain applications have larger tolerances for modeling inaccuracy and varying degrees of flexibility throughout the different phases of interpretation, we present four inversion schemes that provide a tunable balance between computational time and inversion accuracy when modeling TEM datasets. We improve speed and maintain accuracy with a hybrid framework, where the neural network derivatives are used initially and switched to full numerical derivatives in the final iterations. We also present a full neural network solution where neural network forward and derivatives are used throughout the inversion. In a least-squares inversion framework, a speedup factor exceeding 70 is obtained on the calculation of derivatives, and the inversion process is expedited ~36 times when the full neural network solution is used. Field examples show that the full nonlinear inversion and the hybrid approach gives identical results, whereas the full neural network inversion results in higher deviation but provides a reasonable indication about the overall subsurface geology.

The modified numerical inversion of the Laplace transform (dubbed NILT) has been recently proposed as a fast and provably stable numerical simulation for general circuits. Although it has enabled increasing the simulation time step, it highlighted the need for robust approach that can recover the full waveform in between the time points generated by NILT. This paper presents a new approach that addresses this challenge. The proposed approach leverages the NILT framework from a high-order approximation paradigm that computes points on the circuit waveforms to a methodology that computes high order derivatives of the waveforms at the same points. Using those derivatives, an interpolation approach based on Hermite interpolation is used to construct the circuit waveforms on dense points. Numerical experiments are presented to demonstrate the accuracy of both approaches.

The controlled-source electromagnetic (CSEM) method is a crucial tool for near-surface investigations and hydrocarbon exploration because of its economic benefits. Limited resolution is one of the inherent defects of the CSEM method, and to obtain high contrast results a multinary transform function was introduced to CSEM 3-D inversion. The multinary transform function was constituted by superposing several error functions, and the transform function transformed the model parameters from continuously distributed space into a semistep distributed multinary space. To deal with complex geometries, the edge-based finite element (FE) method with an irregular hexahedral grid was applied to the modeling and inverse problem. We used the Gauss-Newton optimization method to minimize the Tikhonov parametric function. The complex chessboard model and the marine CSEM model with complex geometry were used to validate the ability of the new method in improving the resolution of the CSEM method. By comparing the results of conventional, focusing, and multinary inversion methods, the effectiveness of the multinary inversion method in depicting sharp boundaries of different physical properties was proved. Additionally, the comparisons proved that multinary inversion method can, to some extent, overcome the insensitivity to low conductors of the CSEM method.

Two-dimensional (2D) nuclear magnetic resonance (NMR) inversion operates with massive echo train data and is an ill-posed problem. It is very important to select a suitable inversion method for the 2D NMR data processing. In this study, we propose a fast, robust, and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters. Firstly, a method that combines window averaging (WA) and singular value decomposition (SVD) is used to compress the echo train data and obtain the singular values of the kernel matrix. Subsequently, an optimum regularization parameter in a fast manner using the signal-to-noise ratio (SNR) of the echo train data and the maximum singular value of the kernel matrix are determined. Finally, we use the Butler-Reeds-Dawson (BRD) method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion. The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.

In this letter, we concern the acoustic impedance (AI) inversion from the known reflectivity based on the increasingly mature deconvolution techniques. For seismic data with the complicated geological structures, we first construct the regularization model for the AI inversion with the proposed regularizer consisting of the total variation (TV) seminorm and the Frobenius norm of the Hessian. Second, we develop the split Bregman (SB) iterative algorithm in the frequency domain for solving the proposed model. Finally, we verify the effectiveness of our proposed method via synthetic and field data. Experimental results demonstrate that our proposed method can not only preserve the lateral continuity and the impedance interfaces of the inverted AI section well, but also provide a higher resolution impedance section than the other related methods.

Three-dimensional (3-D) inversion technique has become an important and practical approach for magnetotelluric (MT) data interpretation. In this article, we developed a 3-D parallelized MT inversion scheme using the edge-based finite element method and applied the developed method to the newly collected MT data in the Xinjiang Luntai area. The distorted hexahedral element is adopted to incorporate topography into the forward modeling and inversion for complicated scenarios. We use the Gauss-Newton optimization method to minimize the objective functional for MT inversion. The developed algorithm is parallelized using MPI over frequencies and parallel direct solvers when solving the forward and adjoint problems for each frequency. We compare the performance of the least-square QR (LSQR) factorization and preconditioned conjugate gradient (PCG) solvers for the model update within each Gauss-Newton iteration and found that the LSQR solver is more stable. The developed inversion algorithm is validated using several synthetic models. Finally, we applied the inversion algorithm to the subsurface resistivity imaging in the Luntai area. The recovered geoelectric model from full 3-D inversion fits well with the known geological and geophysical information. The recovered model shows a low resistivity layer which may be caused by the salt strata. Besides, the inversion results reveal the movement tectonic in this survey area within a depth of 9 km.

Gravity and magnetic inversion are important methods for comprehensive quantitative interpretation of data obtained in, e.g., mineral, oil and gas, and geothermal exploration. At present, the 3-D joint inversion technology of gravity and magnetic data is facing challenges from large-scale data exploration applications. In this letter, a new algorithm for 3-D joint inversion of gravity and magnetic data with high accuracy and low computational cost is presented. We use the geometric trellis method to perform fast forward calculations and then introduce the sparse constraint and adaptive sensitivity matrix into the model constraint terms. The inexact structural resemblance method is then used to add the cross-gradient constraint penalty term to the objective function. Finally, an algorithm (DS-TGN) combining data-space (DS) and truncated Gauss-Newton (TGN) methods is used to solve the joint inversion objective function. Numerical experiments with synthetic data show that the proposed algorithm can significantly reduce the computational cost and obtain high accuracy density and magnetization models with structural resemblance and sharp boundaries. We also apply the DS-TGN algorithm to data obtained in the area of Greater Khingan in northwestern Heilongjiang, China. The underground density and magnetization distribution results provide a high-resolution geological model for the detection of skarn-type deposits.

We propose seismic elastic full-waveform inversion (EFWI) using both the multiparametric approximate Hessian and the discrete cosine transform (DCT). EFWI is a promising technology for obtaining physical parameters. EFWI using the multiparametric approximate Hessian can suppress crosstalk artifacts for each physical parameter, but the computational burden increases as the number of physical parameters considered increases. In this study, to reduce the computational burden, DCT was used to compress the model parameters and accelerate EFWI in the truncated DCT domain. EFWI using DCT is possible to increase the calculation efficiency by reducing the total number of unknown variables. We implemented EFWI using monoparametric Hessian and multiparametric Hessian, which reduced the computational burden using DCT and conducted tests through numerical experiments using each Hessian. In numerical result, despite using a small number of DCT coefficients, we confirmed that contamination due to crosstalk artifacts was suppressed when EFWI was performed using the multiparametric approximate Hessian.

We investigate an algorithm for the 3-D inversion of frequency-domain airborne electromagnetic (AEM) data based on the forward modeling and sensitivity calculation by footprint-guided compact finite element method (CFEM). Unlike the conventional approach, the modeling volume in our algorithm for each transmitter-receiver pair is a regular hexahedral that encloses the footprint, rather than a large mesh for the entire survey area or the local mesh with a number of grids extending from the footprint. After the electric fields in the modeling volume are solved by vector finite element method (FEM) with an integral equation boundary condition, the response and sensitivity are explicitly calculated by employing the product of the prepared Green's functions and the vector of electric fields. The accuracy of this footprint-guided CFEM is validated by comparing it against conventional CFEM, and different synthetic models are tested by our inversion algorithm. The inversion tests of synthetic models show the feasibility of the combination of footprint-guided CFEM and Gauss-Newton optimization in recovering models within an acceptable error level, and the inversion results show a good agreement with the true models on both the model geometry and recovered conductivity.

This article presents a novel hybrid electromagnetic inversion method. The traditional 3-D variational Born iterative method (VBIM) is combined with the unsupervised machine-learning expectation maximization (EM). In each iteration, VBIM first outputs the pseudo-randomly distributed model parameters in all discretized cells in the inversion domain. Then the EM algorithm is used to classify them and estimate the mean model parameter values of each homogeneous scatterer or subscatterer supposing that the reconstructed model parameters in all cells comply with the Gaussian mixture model (GMM). At last, partial cells in the inversion domain classified as ``background'' will be removed and the unknowns in the next VBIM iteration are reduced. This process is implemented iteratively until no ``background'' cell can be removed anymore and the data misfit between the measured scattered field and reconstructed field reaches the stop criterion. Finally, the mean value of the model parameter estimated by EM is mandatorily assigned for each homogeneous scatterer or subscatterer. Numerical examples show that the proposed hybrid method works efficiently for the reconstruction of isotropic, anisotropic, homogeneous, or inhomogeneous scatterers. It also has a certain antinoise ability.

Transient electromagnetic (TEM) method is widely used in regional mineral resources surveys, environmental engineering geological surveys and shallow surface geophysical exploration, and so on. However, interpretation and inversion of TEM data is a complicated process. The traditional algorithm of TEM inversion employs the ``smoke ring'' fast imaging method, which can only reflect the approximate morphology of the stratigraphic model, and the inversion accuracy is low. Therefore, this method cannot meet the requirements of high-precision inversion. In this article, we present the firefly algorithm (FA) technology for TEM inversion. First of all, the response of the rectangular loop source TEM based on electric dipole integration was calculated and compared with the analytical solution results of the rectangular loop source and the accuracy of the algorithm was verified. Then, a layered medium model was established. The FA technology and ``smoke ring'' fast imaging method were used to perform inversion calculation, and the influence of random noise on the accuracy of the FA algorithm was analyzed. The results show that the FA has a high degree of fitting to the model, good anti-noise property, and fast search speed. Next, to illustrate the application effect of the FA algorithm in pseudo 2-D inversion, the 2-D model was established. The results show that the FA algorithm can reflect the distribution of the anomalous body more accurately, especially for the low-resistance anomalous body. Finally, we examined the effectiveness of the FA for TEM data processing by inverting survey data and comparing the results with those from the ``smoke ring'' fast imaging and particle swarm optimization (PSO) algorithms. The research works provide new methods and techniques for TEM data processing.

Transient electromagnetic method (TEM) is one of the major tools to image the subsurface resistivity. The gradient-based inversion of TEM data only provides a unique solution using a subjectively defined regularization penalty, leaving the uncertainty of the solution unaddressed. The Bayesian method can be used to estimate the model parameters, as well as quantify their uncertainty. However, it requires far higher computational costs than gradient-based inversion, which limits the Bayesian inversion of TEM data to 1-D assumptions. We propose an accelerated Bayesian method based on Markov chain Monte Carlo (MCMC) subposteriors to perform full 2-D inversion of TEM data. A robust scheme is designed to divide the model space of a TEM profile into subspaces so that independent MCMC chains can be used to update the parameters in each subspace in parallel. The division is based on the coverage of the source loops using a cumulative sensitivity matrix. Then, the subposteriors obtained at each subspace are merged to approximate the full posterior of the model space using a weighting strategy. A numerical test of a 2-D valley model is used to validate the proposed method. The Bayesian inversion successfully obtained posterior that converges to the true model. The median model makes a good inference of the model parameters, while the probability density function gives their uncertainty estimates. The statistical model of interest can be further extracted from the model ensemble. The proposed method provides an effective framework for Bayesian inversion of TEM data with a multidimensional forward operator.

BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round. This paper presents FPGA implementations of BIKE with the best area-time performance reported in literature. We optimize two key arithmetic operations, which are the sparse polynomial multiplication and the polynomial inversion. Our sparse multiplier achieves time-constancy for sparse polynomials of indefinite Hamming weight used in BIKE’s encapsulation. The polynomial inversion is based on the extended Euclidean algorithm, which is unprecedented in current BIKE implementations. Our optimized design results in a 5.5 times faster key generation compared to previous implementations based on Fermat’s little theorem.Besides the arithmetic optimizations, we present a united hardware design of BIKE with shared resources and shared sub-modules among KEM functionalities. On Xilinx Artix-7 FPGAs, our light-weight implementation consumes only 3 777 slices and performs a key generation, encapsulation, and decapsulation in 3 797 μs, 443 μs, and 6 896 μs, respectively. Our high-speed design requires 7 332 slices and performs the three KEM operations in 1 672 μs, 132 μs, and 1 892 μs, respectively.

International audience; A receiver-extension strategy is presented as an alternative to recently promoted source-extension strategies, in the framework of high resolution seismic imaging by full waveform inversion. This receiver-extension strategy is directly applicable in time-domain full waveform inversion, and unlike source-extension methods it incurs negligible extra computational cost. After connections between difference source-extension strategies are reviewed, the receiver-extension method is introduced and analyzed for single-arrival data. The method results in a misfit function convex with respect to the velocity model in this context. The method is then applied to three exploration scale synthetic case studies representative of different geological environment, based on: the Marmousi model, the BP 2004 salt model, and the Valhall model. In all three cases the receiver-extension strategy makes it possible to start full waveform inversion with crude initial models, and reconstruct meaningful subsurface velocity models. The good performance of the method even considering inaccurate amplitude prediction due to noise, imperfect modeling, and source wavelet estimation, bodes well for field data applications.

This study focuses on advancing the inversion of aerosol data measured by a cascade impactor. We aim to find and validate a comprehensive and robust mathematical model for reconstructing a particle...

In this paper, we develop a subsampling Newton’s method to efficiently approximate the maximum likelihood estimate in logistic regression, which is especially useful for large-sample problems. One distinct feature of our algorithm is that matrix inversion is not explicitly performed. We propose two algorithms which are used to construct iteratively a sequence of matrices which converge to the Hessian of the maximum likelihood function on the subsample. We provide numerical examples to show that the proposed method is efficient and robust.

We study the full-waveform inversion (FWI) problem for the recovery of velocity model/image in acoustic media. FWI is formulated as a typical nonlinear optimization problem, many regularization tec...

The inversion of nuclear magnetic resonance (NMR) relaxometry data based on the first kind of Fredholm equation is an ill-posed problem. The accurate transverse relaxation time (T2) distribution is of great significance to improve the application of NMR. The T2 distribution from the norm smoothing method for low signal-to-noise ratio (SNR) data is inaccurate owing to a large penalty term of the objective function. It is therefore important to improve the inaccuracy of the regularized solution. A two-step inversion method for NMR relaxometry data using norm smoothing and artificial fish swarm algorithm (AFSA) is proposed to improve the accuracy of inversion results. First, the raw NMR echo data are compressed using a simplified singular value decomposition method to reduce the inversion time. The regularized inversion solution from the norm smoothing method is taken as the initial values of the AFSA. Through the uncertainty analysis of the regularized inversion solution, the boundary of the fish swarm is determined. A more accurate solution is obtained by the iteration of the AFSA. The results show that the AFSA-optimized T2 distribution is closer to the T2 distribution of model than the regularized inversion solution in terms of the relaxation time and intensity of signal, and thus calculating the formation porosity more accurately. The proposed method shows good performance for processing NMR core data.

S-wave velocity and mass density, which are two essential parameters in distinguishing lithology and hydrocarbon detection, are very difficult to retrieve even when long-offset gather data are used. P-P and P-SV waves joint inversion has been verified as an effective tool to accurately extract such fluid related parameters. However, registering the travel-time of P-P and P-SV waves on the identical coordinate is a significant but knotty problem for the joint inversion. Therefore, an improved strategy of prestack seismic joint inversion is proposed for accurately transforming the recorded data to elastic-parameter-based interpretive information. First, to overcome the weaknesses of artificial strenching and the local cross correlation-based method, a nonstrenching and globally optimal registration algorithm, i.e., dynamic time warping (DTW), is exploited to match the P-P and P-SV waves. Then, a new method has been developed for the joint inversion method by combining the logarithmic absolute-criterion-based misfit function with $\ell _{1-2}$ norm-based penalty, which can significantly improve the vertical resolution and stability of inversion results. The numerical examples demonstrate that the DTW algorithm can obtain better registered results than the conventional method. Moreover, the proposed joint inversion method performs better than the conventional prestack inversion in both resolution and accuracy, especially for the S-wave velocity.

In this article, a hierarchical subspace-based optimization method (HSOM), which combines the subspace-based optimization method (SOM) and hierarchical strategy using multi-frequency data, is proposed to reconstruct 2-D uniaxial anisotropic scatterers. The hierarchical strategy utilizes the results obtained at lower frequencies to provide initial information for higher frequency inversion. The domain of scatterers is extracted from the domain of interest at lower frequencies according to the range-constrained Otsu thresholding method. Then, the inversion at higher a frequency only executes in the domain of scatterers. Compared with the frequency-hopping approach, this method can obtain higher quality reconstruction images with much lower computation loads. Numerical examples validate the efficacy of the proposed method.

This paper presents an efficient implementation of the inversion algorithm based on the conjugate-gradient method (CGM) for solving inverse scattering problems. The original CGM provides good image...

Joint inversion is a widely used geophysical method that allows model parameters to be obtained from the observed data. Pareto inversion results are a set of solutions that include the Pareto front, which consists of non-dominated solutions. All solutions from the Pareto front are considered the most feasible models from which a particular one can be chosen as the final solution. In this paper, it is shown that models represented by points on the Pareto front do not reflect the shape of the real model. In this contribution, a collective approach is proposed to interpret the geometry of models retrieved in inversion. Instead of choosing single solutions from the Pareto front, all obtained solutions were combined in one “heat map”, which is a plot representing the frequency of points belonging to all returned objects from the solution set. The conducted experiment showed that this approach limits the problem of equivalence and is a promising way of representing the geometry of the model that was retrieved in the inversion process.

The work is devoted to the development of techniques and software for the quantitative interpretation of resistivity oil well logs. The article considers the results of applying the neural network approach to the processing of resistivity logging data measured at intervals composed of thin layers with contrasting electrical properties. The proposed algorithms combine the advantages of data interpretation based on a two-dimensional axisymmetric medium model and high performance, which allows them to be used at the primary processing stage, increasing the reliability of express interpretation.

Inversion of magnetic data has been an important tool for the interpretation of the data. The conventional inversion approaches cannot recover geologically acceptable models in the presence of remanence. Hence, some techniques have been developed for the inversion of magnetic amplitude data which is independent of magnetization direction. The conventional methods in the inversion of magnetic amplitude data give rise to blurred models with long tails. In this study, a new algorithm has been developed in favor of sparse inversion of the data that generates more focused models using the Cauchy norm. The algorithm applies a regularized conjugate gradient (RCG) method to acquire the inverse model. The new algorithm has been employed for the inversion of two data sets from synthetic examples and magnetic data sets over the Allahabad iron deposit in Iran and the Osborne copper–gold deposit in Australia. All data sets exhibit remanent magnetization. The results showed that the new algorithm generates robust solutions that are geologically acceptable.

This article presents a new algorithm for time-domain circuit simulation based on numerical inversion of Laplace transform (NILT). The proposed method, labeled NILT $n$ , shows that for the same computational cost of the conventional NILT, referred to as NILT0, the approximation error is reduced by a significant factor, permitting time-marching with much larger time steps and, consequently, saving significant computational cost per time step. Numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed approach.

The Gaver–Stehfest algorithm is widely used for numerical inversion of the Laplace transform. In this paper we provide the first rigorous study of the rate of convergence of the Gaver–Stehfest algorithm. We prove that Gaver–Stehfest approximations converge exponentially fast if the target function is analytic in a neighbourhood of a point and they converge at a rate $o(n^{-k})$ if the target function is $(2k+3)$-times differentiable at a point.

The magnetotelluric (MT) technique is an electromagnetic geophysical method, which is widely used as a complementary to seismic surveys for exploration of hydrocarbon reservoirs. In the inversion process, the method of matrix inverse calculation has a considerable effect on the speed of the inversion and the quality of obtained models. Lanczos Bidiagonalization (LB) method has been reported to be a fast and efficient approach for solving the inversion problems. In this study, we employ LB method for inverting large-scale 2D MT data. In LB algorithm, the full set of equations is replaced by a dimensionally reduced system of equations. As a result, the speed of the solution procedure is increased, while the original problem is solved with a high accuracy. In addition, we employ active constraint balancing approach for determining the optimum regularization parameter. The advantage of the method is that for highly resolvable parameters, a small value of the Lagrangian multiplier is assigned, and vice versa. The results of the synthetic data inversion show that both methods require equal computer memory but LB method is faster and more reliable than conjugate gradient method. The proposed approach is also applied to inverse real MT data collected from the Kashan area. The Kashan area is the most interesting area for oil and gas exploration of the Central Iran Basin. The inversion results obtained by LB are in a good agreement with the geological structure of the study area and the drilling data.

Deciding the number of processors that can efficiently speed-up solving a computationally intensive problem while perceiving efficient power consumption constitutes a major challenge to researcher in the HPC high performance computing realm. This paper exploits machine learning techniques to propose and implement a recommender system that recommends the optimal HPC architecture given the problem size. An approach for multi-objective function optimization based on neural network (neural network inversion) is employed. The neural network inversion approach is used for forward problem optimization. The objective functions in concern are maximizing the speedup and minimizing the power consumption. The recommendations of the proposed prediction systems achieved more than 89% accuracy for both validation and testing set. The experiments were conducted on 2500 CUDA core on Tesla K20 Kepler GPU Accelerator and Intel(R) Xeon(R) CPU E5-2695 v2.

Seismic high-resolution processing plays a critical role in reservoir target detection. As one of the most common approaches, regularization can achieve a high-resolution inversion result. However, the performance of regularization depends on the settings of the associated parameters and constraint functions. Further, it is difficult to solve an objective function with complex constraints, and it requires designing an optimization algorithm. In addition, existing algorithms have high computational complexity, which impedes the inversion of the large data volume. To address these problems, an optimization-inspired deep learning inversion solver is proposed to solve the blind high-resolution inverse (BHRI) problems of various seismic wavelets rapidly, called BHRI-Net. The method builds on ideas from classic regularization theory and recent advances in deep learning, and it makes full use of prior information encoded in the forward operator and noise model to learn an accurate mapping relationship. It unrolls the alternating iterative BHRI algorithm into a deep neural network, and it applies the convolutional neural network to learn proximal mappings, in which all parameters of the BHRI algorithm are learned from training data. Further, the proposed network can be split into two parts and incorporate the transfer learning strategy to invert field data, which increases the flexibility of the proposed network and reduces training time. Finally, the tests on synthetic and field data show that the proposed method can effectively invert the high-resolution data and seismic wavelet from observation data with improved accuracy and high computational efficiency.

Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement prestack LSRTM in a deep-learning framework and adopt strategies from the data science domain to accelerate convergence. Our hybrid framework leverages the existing physics-based models and machine-learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we find that minibatch gradients can reduce the computation cost by using a subset of total shots for each iteration. The minibatch approach not only reduces source crosstalk, but it is also less memory-intensive. Combining minibatch gradients with deep-learning optimizers and loss functions can improve the efficiency of LSRTM. Deep-learning optimizers such as adaptive moment estimation are generally well-suited for noisy and sparse data. We compare different optimizers and determine their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularized Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and find improvements over conventional LSRTM baselines. Our approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.

We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev duality products and to a new family of probing functions. The fractional order duality product proves to be able to greatly enhance the robustness of the reconstructions in some practically important but severely ill-posed inverse problems associated with the Radon transform. We present a detailed analysis to better understand the performance of the new probing and index functions, which are crucial to stable and effective numerical reconstructions. The DSM can be computed in a very fast and highly parallel manner. Numerical experiments are carried out to compare the DSM with a popular existing method, and to illustrate the efficiency, stability, and accuracy of the DSM.

The location estimation problem has been attracting a lot of research interest in recent years due to its significance for different areas of signal processing. This paper deals with a bistatic MIMO radar system where the targets are located in the near-field region. In this work, we derive the Cramer-Rao bound (CRB) for bistatic MIMO radar systems using the exact spherical wavefront model to evaluate the performance of target parameter estimation algorithms. The conditional and unconditional CRBs are derived for a system with one and multiple targets. For the one target system, we provide an analytical inversion of the Fisher Information Matrix (FIM) and obtain closed-form analytical non-matrix expressions of the CRB corresponding to the Cartesian and spherical coordinates of the targets. We compare the derived conditional and unconditional CRB with the performance of state-of-the-art localization algorithms and analyse the dependence of the CRB on various system parameters.

Two M-decomposed based identification algorithms are proposed for large-scale systems in this study. Since the least squares algorithms involve matrix inversion calculation, they can be inefficient for large-scale systems whose information matrices are ill-conditioned. To overcome this difficulty, the M-decomposed based least squares algorithm is developed, where the parameter vector is divided into M sub-vectors. Each sub-vector is estimated using the least squares algorithm, with the assumption that the other sub-vectors are known. The proposed algorithm has less computational efforts than those of the traditional least squares algorithm. To update the parameters with new arrived data, an M-decomposed based recursive least squares algorithm is also provided, this algorithm avoids matrix inversion calculation thus is more efficient. The simulation examples show the effectiveness of the proposed algorithms.

The significant advantage of the complex resistivity method is to reflect the abnormal body through multi-parameters, but its inversion parameters are more than the resistivity tomography method. Therefore, how to effectively invert these spectral parameters has become the focused area of the complex resistivity inversion. An optimized BP neural network (BPNN) approach based on Quantum Particle Swarm Optimization (QPSO) algorithm was presented, which was able to improve global search ability for complex resistivity multi-parameter nonlinear inversion. In the proposed method, the nonlinear weight adjustment strategy and mutation operator were used to enhance the optimization ability of QPSO algorithm. Implementation of proposed QPSO-BPNN was given, the network had 56 hidden neurons in two hidden layers (the first hidden layer has 46 neurons and the second hidden layer has 10 neurons) and it was trained on 48 datasets and tested on another 5 synthetic datasets. The training and test results show that BP neural network optimized by the QPSO algorithm performs better than the BP neural network without initial optimization on the inversion training and test models, and the mean square error distribution is better. At the same time, a double polarized anomalous bodies model was also used to verify the feasibility and effectiveness of the proposed method, the inversion results show that the QPSO-BP algorithm inversion clearly characterizes the anomalous boundaries and is closer to the values of the parameters.

Staggered-grid finite-difference (SFD) method has higher accuracy and stability than conventional method, so it is widely used in reverse time migration and full waveform inversion. However, due to...

We propose a new 3D inversion scheme to invert the near- and transition-zone data of CSAMT with topography accurately. In this new method, the earth was discretized into unstructured tetrahedra to fit the ragged topography and the vector finite-element method was adopted to obtain precise responses and good sensitivity. To simulate the attitude and shape of the transmitter, we divided a long-grounded transmitter into dipoles and integrated these dipoles to obtain good responses in the near- and transition-field zones. Next, we designed an L2 norm-based objective functional and applied a standard quasi-Newton method as the optimization method to solve the inverse problem and guarantee steady convergence. We tested our 3D inversion method first on synthetic data and then on a field dataset acquired from select sites near Changbai Mountain, China. In both tests, the new inversion algorithm achieved excellent fitting between the predicted and observed data, even in near- and transition-field zones, and the inversion results agreed well with the true model. These findings reveal that the proposed algorithm is effective for 3D inversion of CSAMT data.

Summary Efficient identification and characterization of fracture networks are crucial for the exploitation of fractured media such as naturally fractured reservoirs. Using the information obtained from borehole logs, core images, and outcrops, fracture geometries can be roughly estimated. However, this estimation always has uncertainty, which can be decreased using inverse modeling. Following the Bayes framework, a common practice for inverse modeling is to sample from the posterior distribution of uncertain parameters, given the observational data. However, a challenge for fractured reservoirs is that the fractures often occur on different scales, and these fractures form an irregular network structure that is difficult to model and predict. In this work, a multiscale-parameterization method is developed to model the fracture network. Based on this parameterization method, we present a novel history-matching approach using a data-driven evolutionary algorithm to explore the Bayesian posterior space and decrease the uncertainties of the model parameters. Empirical studies on hypothetical and outcrop-based cases demonstrate that the proposed method can model and estimate the complex multiscale-fracture network on a limited computational budget.

Aiming at the problem of high complexity and poor real-time performance of the traditional minimum variance (MV) algorithm, a low-complexity minimum variance algorithm combined with power method is proposed. Firstly, the echo data is transformed into beam domain by discrete cosine transform and the dimension reduction parameter is determined according to the data of scanning lines. Secondly, the maximum eigenvalue and corresponding eigenvector of sample covariance matrix are obtained by the power method to reduce the complexity of eigenvalue decomposition. Finally, by ignoring low-energy echo signal, the inversion of covariance matrix can be simplified to construct a new weighted vector, which can reduce the complexity of MV. The Field II simulation results show that the proposed algorithm has better resolution, contrast ratio and efficiency than the traditional MV algorithm, and outperforms the minimum variance algorithm based on eigenvalue decomposition (ESBMV) in resolution and efficiency.

We have developed the high-performance software and algorithmic software for solving the direct and inverse problems of modeling and inversion of spatially distributed magnetic, taking into account the relief. We show the results of solving the inverse problem of magnetic survey taking into account the relief for synthetic noisy data.

Cognitive disorders especially epilepsy are closely linked with synchronization/desynchronization of neurons in the brain. In this paper, the dynamical modeling and behavior analysis of a FitzHugh–Nagumo neuron and also synchronization control of a network of FitzHugh–Nagumo neurons which promise the understanding of cognitive processing, are studied. To numerically simulate these models and in order to overcome their difficulties such as computational complexity, multi-dimensionality, non-linearity, having large spatial and temporal domains and also having a discrete initial data, we propose the use of a strongly meshless technique based on Wendland compactly supported radial basis function in conjunction with an operator splitting algorithm. The main advantage of the proposed algorithm is its computational complexity (for example O ( N x 1 3 + N x 2 3 ) of the inversion of all matrices) which is much lower than the complexity of pure radial basis functions method ( O ( N x 1 3 N x 2 3 ) of the inversion of matrices). Numerical experiments are presented showing that the proposed approaches are extremely accurate and fast.

Signal channelization enables efficient frequency domain processing and is a mainstay of astronomical signal processing, but applications that require high time resolution necessitate reconstruction of the original wide band signal. In a previous paper, a near-perfect method of reconstructing a time-limited input signal from the output of an oversampled polyphase filterbank (PFB) was described. Here, we consider the case where continuous signals are processed. We show that the most simplistic approach, which utilizes non-overlapping windows and a fast Fourier transform (FFT) channelizer, introduces large errors whose magnitude can equal the signal. The ringing introduced by truncation at the end of a block, combined with the cyclic nature of FFTs, leads to errors that are concentrated at block boundaries. These localized errors can be heavily suppressed by utilizing overlapping windows and nearly completely eliminated by apodizing the data blocks with a Tukey window. After these improvements, the much smaller residual error is concentrated at the PFB channel boundaries and is due to adjacent channels having different gain slopes at the channel boundary. Increasing the channel passband equalizes the gain slope at the channel boundary, and the error is reduced further. With these changes, errors as low as −100[Formula: see text]dB are achieved, and the method of reconstructing the channelized data meets the stringent signal purity requirement for astronomical applications such as radio pulsar timing.

The multi-scale discrete Radon transform (DRT) calculates, with linearithmic complexity, the summation of pixels, through a set of discrete lines, covering all possible slopes and intercepts in an image, exclusively with integer arithmetic operations. An inversion algorithm exists and is exact and fast, in spite of being iterative. In this work, the DRT forward and backward pair is evolved to propose two faster algorithms: central DRT, which computes only the central portion of intercepts, and periodic DRT, which computes the line integrals on the periodic extension of the input. Both have an output of size N×4N, instead of 3N×4N, as in the original algorithm. Periodic DRT is proven to have a fast inversion, whereas central DRT does not. An interesting application of periodic DRT is its use as building a block of discrete curvelet transform. Central DRT can provide almost a 2× speedup over conventional DRT, probably becoming the faster Radon transform algorithm available, at the cost of ignoring 15% of the summations in the corners.

Anchor graphs are a popular tool used in label prediction of sparsely labeled data. In anchor graphs, labels of labeled data are propagated to unlabeled data via anchor points; anchor points are the centers of k-means clusters. Anchor graph-based label prediction determines local weights between data points and anchor points by exploiting Nesterov's method to obtain the graph's adjacency matrix, and it inverts a matrix obtained from the adjacency matrix to predict labels., however, incurs high computation cost since (1) Nesterov's method is applied to all closest anchor points to compute local weights, and (2) the computation cost of the inversion matrix is cubic in the number of anchor points. We propose an approach that can efficiently perform anchor graph-based label prediction because of its two key advances: (1) it prunes unnecessary anchor points so they are not passed to Nesterov's method, and (2) it applies the conjugate gradient method in computing labels of data points to avoid matrix inversion. In addition, we propose to exploit basis vectors computed by SVD as anchor points to improve label prediction accuracy. Experiments show that our approach outperforms the previous approaches in terms of efficiency and accuracy.

To explore creep parameters and creep characteristics of salt rock, an Ansys numerical model of salt rock sample was established by using fractional creep constitutive model of salt rock, and an orthogonal test scheme was designed based on uniaxial compression test of salt rock samples. A large number of training data were obtained by combining the numerical model with the experimental scheme, and the model parameters were inverted by using the BP neural network. The model parameters are used for forwarding calculation, and the results are in good agreement with the measured strain data. This shows that the model parameter inversion method proposed in this paper can obtain reasonable parameter values and then accurately predict the creep behaviour of salt rock, which provides a good technical basis for related engineering practice and scientific research in the future.