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In this paper, we discuss several approaches for a joint inversion of controlled source radiomagnetotelluric (CSRMT) and electrical resistivity tomography (ERT) data observed over anisotropic media. We compare results of 2D isotropic joint inversion with results of a newly developed joint 1D anisotropic inversion algorithm. The developed algorithm involves the full controlled source high frequency forward and inversion formulations without the plane wave assumption. We demonstrate that for measurements on an anisotropic subsurface the isotropic joint inversion cannot fit both datasets properly due to a high anisotropy of shallow horizons of quaternary sands and loams. The joint anisotropic inversion helps to solve this problem and highlights the advantages of a joint inversion of CSRMT and ERT data. We also demonstrate application of the laterally constrain algorithm for the anisotropic inversion. Results of the joint 1D anisotropic inversion of CSRMT and ERT data were successfully compared with existing borehole data.

The measuring problem of calibrating the cosmological distance scale is considered from the perspective of applicability conditions for regression analysis. The rank inversion and statistical inhomogeneity of information on SN Ia supernovae, used in the works of 1998–1999 and 2004–2007 to detect the “accelerating expansion of the Universe” and as an “extraordinary evidence” of its existence, respectively, are demonstrated to be the reason for the discrepancy and inconsistency of the obtained parametric estimates of the Friedman–Robertson–Walker model. Although the use of lack-of-fit tests for cosmological distance scale models reduces the above negative effects, the fact remains that the cosmological distance scale based on the redshift has neither metric nor ordinal status.

A rather neglected family of heterocyclic compounds, the 3-pyrazolines or 2,3-dihydro-1H-pyrazoles, has been studied theoretically at the B3LYP/6–311++G(d,p) level to obtain geometries and energies and at the GIAO/B3LYP/6–311++G(d,p) level for NMR chemical shifts. The calculated barriers of inversion of the N-substituents reproduce adequately the scarce experimental data. The calculated H and C chemical shifts are consistent with those reported in the literature. A combination of both results, geometries, and C chemical shifts, shed light on the conformation of N-phenyl groups., This work was carried out with financial support from the Ministerio de Ciencia, Innovación y Universidades (PGC2018-094644-B-C22) and the Dirección General de Investigación en Innovación de la Comunidad Autónoma de Madrid (P2018/EMT-4329 AIRTEC-CM). Thanks are also given to the CTI (CSIC) for their continued computa- tional support.

Before performing the inversion process, the original measured data set is often transformed (corrected, smoothed, Fourier-transformed, interpolated etc.). These preliminary transformations may make the original (statistically independent) noisy measurement data correlated. The noise correlation on transformed data must be taken into account in the parameter fitting procedure (inversion) by proper derivation of likelihood function. The covariance matrix of transformed data system is no longer diagonal, so the likelihood based metrics, which determines the fitting process is also changed as well as the results of inversion. In the practice, these changes are often neglected using the “customary” estimation procedure (simple least square method) resulting wrong uncertainty estimation and sometimes biased results. In this article the consequence of neglected correlation is studied and discussed by decomposing the inversion functional to “customary” and additional part which represents the effect of correlation. The ratio of two components demonstrates the importance and justification of the inversion method modification.

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.

This paper proposes a non‐iterative procedure for flaw(s) characterization based on Pulsed Eddy Current Testing (PECT) signals analysis. The adopted inversion strategy is based on the use of supervised statistical learning algorithms. A numerical forward solver, based on the Finite Integration Technique (FIT), is used for the generation of the training data (the input‐targets couples of the learning algorithm). Predictions are then carried out in almost real‐time using a non‐linear kernel based regression method, known as kernel ridge regression. It turns out that the direct fit of the regression model to the raw PECT signals may lead to poor prediction accuracy due to the large cardinality of PECT signals. To remedy this problem, an adaptive sampling strategy has been adopted in this work. The performance of the proposed methodology is discussed and compared with solutions proposed in the literature.

–“From a bag containing red and blue balls, two are removed at random. The chances are 50-50 that they will differ in color. What were the possible numbers of balls initially in the bag?” T...

I have developed an approximate inversion scheme for surface-borehole electromagnetic data. The method aims at reducing the computational burden arising by the fine discretization required to accurately solve for the field distribution in the full complexity of the borehole system together with the reservoir medium. I first analyze numerical simulations of the surface-borehole response performed for a 1D layered earth, also incorporating the realistic complexity of the borehole system. The analysis brings useful insight to the requirement of incorporating fluid and mud/cement electrical properties when implementing an inversion by numerically simulating the full complexity of the system. Subsequently, the synthetic data set was used to test an inversion method that uses the data dominated by the casing effect to approximately describe the casing secondary fields. A scaling factor is then introduced to account for the current induced in the well as the exciting source is placed further below the casing shoe. The method is found to fairly well recover the known 1D resistivity strata; still, some bias is expected for the resistivity close below the casing shoe, where the data are anticipated to be the most distorted by the casing effect.

Migration velocity analysis (MVA) has been widely used for large scale model construction. To make full use of the wavefield information and obtain stable inversion results, wave-equation-based met...

We present a three-dimensional (3D) general-measure inversion scheme of crosswell electromagnetic (EM) data in the frequency domain with a direct forward solver. In the forward problem, we discretised the EM Helmholtz equation by the staggered-grid finite difference (SGFD) scheme and solved it using the Intel MKL PARDISO direct solver. By applying a direct solver, we simultaneously solved the multisource forward problems at a given frequency. In the inversion, we integrated a general measure of data misfit and model constraints with linearised least-squares inversion. We reconstructed a model with blocky features by selecting the appropriate measure parameters and model constraints. We used the adjoint equation method to explicitly calculate the Jacobian matrix, which facilitated the determination of an appropriate initial value for the regularisation coefficient in the objective function. We illustrated the inversion scheme using synthetic crosswell EM data with a general measure, the L2 norm, and, specifically, two mixed norms.

The use of Rayleigh wave dispersion curve for estimating shear wave velocity (Vs) is a common task in the field of engineering geophysics. However, because of the nonlinear nature of Rayleigh wave dispersion curves, using a proper technique in the inversion procedure in order to find adequate model parameters is a challenging problem. In this study, a comparative study is performed between linear and nonlinear inversion methods. Between different techniques, a new nonlinear searching algorithm, i.e., the modified cuckoo search (MCS) algorithm was introduced to invert the Rayleigh wave dispersion curves. Also, the generalized inverse (GI) method was used as a linear searching algorithm applied to the construction of the Vs profile. The proposed algorithms were tested by different synthetic (noisy and noise free) datasets. The results show that the MCS algorithm has more exploration ability in comparison with the original cuckoo search. Then, an actual dataset was inverted by the introduced inversion methods. The results show that the performance of the MCS is better than that of the GI method. MCS is a fast, powerful and user-friendly technique in the field of dispersion curve inversion.

In the article, the author analyzes the features of comedy dell’arte, the laws of poetic techniques and stylistic synthesis. Attention is drawn to the style and genre of the play, a synthesis of the principles of postmodernism, modernism, neo-baroque. The main artistic means of comedy dell’arte are analyzed. The study showed that the basic aesthetic principles of commedia dell’arte are reduced to an aesthetic system that contains three essential elements: first, the theater is held by a professional actor who is fully committed to the theater; secondly, the influence of theater is stronger through the synthesis of arts: plastic, music, dance and words; third, the soul of the play is action.

SUMMARY The largest earthquake recorded in South Korea occurred in Gyeongju on 2016 September 12. Since then, understanding the geological structures near the Gyeongju earthquake's epicentre has been demanded. As a preliminary step to understand the geological structures around the epicentre, a 3-D audio-magnetotelluric (AMT) survey was conducted. These 3-D AMT data were imaged through data processing and inversion. However, because the AMT data acquired in Gyeongju were very noisy, conventional imaging procedures did not yield reliable results. To obtain a reliable model inverted from such noisy data, we propose various imaging strategies: an additional data processing technique using the Nyquist diagram after conventional data processing and several inversion strategies related to the selection of data, the weighting of the data, the constraints on the model parameter vector and the Lagrange multiplier used for the regularization. By applying the additional data processing step and several inversion strategies, we were able to successfully invert the noisy field data. The inversion results verify that the data-screening procedure applying the Nyquist diagram remarkably improves the results compared with those obtained using only conventional data processing. The imaging strategies proposed in this case study can be used to image noisy MT/AMT field data for other regions.

Relations between Laplace’s spheroidal harmonics associated with different spheroidal coordinates are derived. The transition matrices for the functions of the 1st kind are lower triangular and are related by inversion. The matrices for the functions of the 2nd kind are the transposed ones for the functions of the 1st kind. The series for the functions of the 1st kind are finite, and those for the 2nd kind are infinite. In the latter case the region of convergence is considered. Using the derived relations, the rigid solution to the electrostatic problem for the multi-layered scatterers with nonconfocal spheroidal boundaries of the layers is obtained and the Rayleigh approximation is constructed, as well as an approximate approach to a similar light scattering problem, which provides reliable results far beyond the range of applicability of the Rayleigh approximation, is suggested.

SUMMARY The dynamic disturbance from explosion, earthquakes and stress impact may induce rock mass damage around the deep-buried tunnel. Here, we show the dynamic responses triggered by blasting load disturbance. In this paper, the theoretical formulae are first derived to evaluate the time-domain dynamic responses based on the wave function expansion method and the inversion of Laplace transform and then a self-developed numerical code, that is, elasto-plastic cellular automaton (EPCA), a module of CASRock, is subsequently employed to simulate the blasting induced elasto-plastic dynamic responses. It can be found from the analytical solutions that tensile stress concentration at two sidewalls occurs, while compressive counterpart at the roof and floor appears. Moreover, the radial velocity vibrations generate concentration at the two sidewalls, while the circumferential counterparts appear at the roof and floor. The numerical simulations indicate that compression-shear and tensile failure are the major mechanism for the rock mass damage around the rock tunnel. The analytical and numerical results help to understand the velocity vibrations and the major mechanism of rock mass damage and provide theoretical basis for the support of rock tunnel.

We present several global inverse mapping theorems in the general framework of metrically regular functions between Banach Spaces. From a characterization of global homeomorphisms with inverse locally Lipschitz continuous, several well-known and new theorems are deduced in more concrete contexts: e.g. Gâteaux derivatives, generalized Jacobians, coderivatives, strict prederivatives, pseudo-Jacobians. The relationships between them are also established.

We introduce, in this paper, the harmonic analysis associated with the Heckman-Opdam-Jacobi operator on $\mathbb {R}^{d+1}$ in the W -invariant case. Next, we study the generalized wavelets and the generalized wavelet transform associated with this operator and we establish their properties. In particular, we prove for the generalized wavelet transform Plancherel and inversion formulas.

The nearly analytic discrete (NAD) method is a kind of finite difference method with advantages of high accuracy and stability. Previous studies have investigated the NAD method for simulating wave propagation in the time-domain. This study applies the NAD method to solving three-dimensional (3D) acoustic wave equations in the frequency-domain. This forward modeling approach is then used as the “engine” for implementing 3D frequency-domain full waveform inversion (FWI). In the numerical modeling experiments, synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods. Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods. The inversion results show that the NAD method is more suitable than traditional methods, in terms of computational cost and stability, for 3D frequency-domain FWI, and represents an effective approach for inversion of subsurface model structures.

Based on the transmittance matrix ( T -matrix) approach, an efficient and stable rigorous coupled-wave analysis (RCWA) method for ultrathin multilayer gratings without solving eigenvalues is proposed in this letter. The numerical instability caused by the inversion of an ill-conditioned matrix in the traditional T -matrix approach is solved by implementing the proposed method. Besides, compared with the traditional RCWA method, the proposed method does not need to solve the eigenvalues and eigenvectors of the eigenmatrix, which avoids the numerical problems and time-consuming problems caused by this process. A numerical example shows that the results of CST simulations are consistent with the results obtained by the proposed method.

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.

In this work, we have proposed a scattering spectra-based method for inverting the surface materials and material proportions of space objects (SOs) from long distances. The results of this work shall improve efforts to characterize and predict the orbits of space debris. We first constructed a physical model for SO characterization based on scattering spectra and then provided a least-squares solution with minimum-norm (LSMN) algorithm for inverting the surface materials and material proportions of an SO. The optical reflectance of complex material surfaces was characterized using a bidirectional reflectance distribution function (BRDF)-based multimodal fusion model that uses the characteristics of the light source, the reflectance of the target’s surface materials, and structures, and the angle of incidence and reflection. The area of each material in the BRDF was then treated as the to-be-inverted parameter. The proposed method was then experimentally validated using four sets of materials. The materials and proportions of equiproportional and non-equiproportional combinations of materials were inverted by the proposed method, and the average inversion error was less than 10%. According to the relationship curve be-tween experimental data error and inversion error, and between theoretical error and inversion error, it can be concluded that the accuracy of inversion error has a linear relationship with the measurement data error. In summary, we have provided a new technical approach for the inversion and characterization of SO materials and material proportions from long distances.

The problem of model recovering in the presence of impulse noise on the data is considered for the magnetotelluric (MT) inverse problem. The application of total variation regularization along with L1-norm penalized data fitting (TVL1) is the usual approach for the impulse noise treatment in image recovery. This combination works poorly when a high level of impulse noise is present on the data. A nonconvex operator named smoothly clipped absolute deviation (TVSCAD) was recently applied to the image recovery problem. This operator is solved using a sequence of TVL1 equivalent problems, providing a significant improvement over TVL1. In practice, TVSCAD requires the selection of several parameters, a task that can be very difficult to attain. A more simple approach to the presence of impulse noise in data is presented here. A nonconvex function is also considered in the data fitness operator, along with the total variation regularization operator. The nonconvex operator is solved by following a half-quadratic procedure of minimization. Results are presented for synthetic and also for field data, assessing the proposed algorithm’s capacity in model recovering under the influence of impulse noise on data for the MT problem.

In the context of holography, entanglement entropy can be studied either by i) extremal surfaces or ii) bit threads, i.e., divergenceless vector fields with a norm bound set by the Planck length. In this paper we develop a new method for metric reconstruction based on the latter approach and show the advantages over existing ones. We start by studying general linear perturbations around the vacuum state. Generic thread configurations turn out to encode the information about the metric in a highly nonlocal way, however, we show that for boundary regions with a local modular Hamiltonian there is always a canonical choice for the perturbed thread configurations that exploits bulk locality. To do so, we express the bit thread formalism in terms of differential forms so that it becomes manifestly background independent. We show that the Iyer-Wald formalism provides a natural candidate for a canonical local perturbation, which can be used to recast the problem of metric reconstruction in terms of the inversion of a particular linear differential operator. We examine in detail the inversion problem for the case of spherical regions and give explicit expressions for the inverse operator in this case. Going beyond linear order, we argue that the operator that must be inverted naturally increases in order. However, the inversion can be done recursively at different orders in the perturbation. Finally, we comment on an alternative way of reconstructing the metric non-perturbatively by phrasing the inversion problem as a particular optimization problem., Comment: 51 pages, 7 figures and 2 appendices. v2: Matches published version

The chiral exciton couplings within a Y-shaped amphiphilic glutamide-cyanostilbene (GCS) could be significantly biased by solvent polarity and hydration effects, which led to sign inversion of both the circular dichroism and circularly polarized luminescence of the GCS assemblies.

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.

In the type synthesis of kinematic chains, identification of distinct mechanisms of a kinematic chain is an important step. The links which are having same functional behavior are grouped as same inversion. In the present paper, an additive approach based on connectivities of the links is proposed. The functional behavior of any link as a part of k-chain can be found by means of topological analysis. In general, adjacency of a link with other links is a primary tool for the topological analysis. In the present paper, the extent of adjacency consideration is the main criteria by which similar functional behavior leading to same inversion is identified. A new parameter ‘Additive Adjacency’ is defined in the algorithm. A new computation table ‘Remote Adjacency Influence Table’ (RAIT) is introduced to control the progress of the adjacency calculations. The proposed method is tested on various linkages (8, 9, 10) with different Degree of Freedom (DoF).

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.

In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is described not only by the force applied at the contact point, but also by the additional rolling resistance torque. We show that the possibility or impossibility of tippe top inversion depends on the existence of specific integrals of the motion of the system. In this paper, we consider an example of the law of rolling resistance by which the area integral is preserved in the system. We examine in detail the case where the action of all dissipative forces reduces to the horizontal rolling resistance torque. This model describes fast rotations of the top between two horizontal smooth planes. For this case, we find permanent rotations of the system and analyze their linear stability. The stability analysis suggests that no tippe top inversion is possible under fast rotations between two planes.

Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate appro...

The log-ratio model (LRM) with three model parameters (${\boldsymbol{n}}$, ${{\boldsymbol{m}}_1},$ and ${{\boldsymbol{m}}_0}$) has been widely used in shallow water bathymetry of multispectral images. At present, obtaining LRM model parameters by optimization algorithms depends on the setting of initial values [${\boldsymbol{n}}(0)$, ${{\boldsymbol{m}}_1}(0),$ and ${{\boldsymbol{m}}_0}(0)$] or initial value ranges. However, how to set the initial value can obtain model parameters more effectively and credibly, and the significance of each initial value in the optimization process is very important for LRM bathymetric retrieval method. In this article, remote sensing images and bathymetric data were used to determine the initial value ranges of credible model parameters, and then the sensitivity of each parameter was analyzed in the algorithm optimization process from the partial differential perspective, and the bathymetry was retrieved in the sea area near Ganquan Island. The results show that according to the partial differential analysis of model parameters, ${\boldsymbol{n}}$, with the smallest change rate in three LRM parameters and the rate of ${{\boldsymbol{m}}_1}$ and ${{\boldsymbol{m}}_0}$ is at least five times of it. So ${\boldsymbol{n}}(0)$ needs more iterations to achieve the optimal. Therefore, the initial value ${\boldsymbol{n}}(0)$ determines whether the optimization method can obtain credible LRM model parameters and the algorithm convergence speed. And when ${\boldsymbol{n}}(0) \in ({1/{{\boldsymbol{R}}_{{{\bf min}}}},\ 1000} ]$ (${{\boldsymbol{R}}_{{{\bf min}}}}$ is the minimum reflectance in blue and green bands), there must be a credible model parameter solution. The bathymetric retrieval results of the sea area with coral and sand substrates show the applicability of our initial value ranges in different substrate area.

In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theorem. By using the concept of q-delta sequences, we establish various axioms and set up q-spaces of generalized functions named q-Boehmian spaces. The new assigned spaces of q-generalized functions are acceptable and compatible with the classical spaces of the ordinary functions. Consequently, we extend the generalized q-Sumudu transform to the sets of q-Boehmian spaces. On top of that, we nominate the canonical q-embeddings between the q-integrable sets of functions and the q-integrable sets of q-Boehmians. Furthermore, we address the general properties of the generalized q-Sumudu transform and its inversion formula in some detail.

The classical finite continuous Radon transform is extended to generalized functions on certain spaces. The inversion formula by the kernel method is shown in a weak distributional sense. In the concluding section, its application in Mathematical Physics is discussed.

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.

Based on previous work and some related research [1]-[5], this author is able to develop a very interesting compact algorithm to compute the inverse of any nonsingular matrices, which could be real or complex. The mathematical formulation can be easily derived from the algorithm of the perturbed matrix inversion [1].

Geophysical Journal International, 225 (1), ISSN:0956-540X, ISSN:1365-246X

A cikkben a korábban már publikált egyszeres exponenciális kőzetfizikai modell továbbfejlesztését, az új többszörös exponenciális kőzetfizikai modellt mutatjuk be, amely leírja az akusztikus longitudinális hullámsebesség nyomásfüggését. Mivel a kőzetben a nyomás fokozásával egyidejűleg több relaxációs folyamat (pl. mikrorepedések vagy, pórustérfogat záródása, vagy szemcsehatárokon történő súrlódás, stb.) is okozhatja a terjedési sebesség növekedését, a modell egyszerre több mechanizmust képes kezelni. A korábban alkalmazott linerizált inverziós eljárás a lokális minimumban elakadhat, ezért az abszolút minimumot adó globális optimalizálás módszerét alkalmaztuk a laboratóriumban mért longitudinális sebesség-nyomás adatok feldolgozása során. A kifejlesztett modellegyenletet Simulated Annealing algoritmusban válaszegyenletként alkalmazva a modell kőzetfizikai paramétereit meg lehetett határozni. Az inverziós eredmények igazolták, hogy az új modellel és algoritmussal számított adatok pontosabban illeszkednek a kőzetmintán mért adatokhoz.

We introduce the directional short-time Fourier transform for which we prove a new inversion formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, Far...

The use of the method of seismic data acoustic inversion, in the presence of thick gas cap, can lead to difficulties when building background models of elastic parameters. In this regard, in the conditions of acoustically contrast thin environments within the perimeter of the Russkoye oil and gas condensate field, in addition to the standard version based on the well data, the authors considered a number of modified techniques ("block", "flat", and background models). The use of these background models provided the best results and made it possible to significantly improve the quality of predicting rock properties; based on the drilling results, effective penetration was ensured at 66 %, which was 102 % of the plan. Also, based on the inversion results, it became possible to predict reservoir properties using the Bayesian lithotype classification method.

It is known from the potential theory that a continuous and planar layer of dipoles can exactly reproduce the total-field anomaly produced by arbitrary 3D sources. We have proven the existence of an equivalent layer having an all-positive magnetic-moment distribution for the case in which the magnetization direction of this layer is the same as that of the true sources, regardless of whether the magnetization of the true sources is purely induced or not. By using this generalized positivity constraint, we have developed a new iterative method for estimating the total magnetization direction of 3D magnetic sources based on the equivalent-layer technique. Our method does not impose a priori information about the shape or the depth of the sources, does not require regularly spaced data, and presumes that the sources have a uniform magnetization direction. At each iteration, our method performs two steps. The first step solves a constrained linear inverse problem to estimate a positive magnetic-moment distribution over a discrete equivalent layer of dipoles. We consider that the equivalent sources are located on a plane and have a uniform and fixed magnetization direction. In the second step, we use the estimated magnetic-moment distribution and solve a nonlinear inverse problem for estimating a new magnetization direction for the dipoles. The algorithm stops when the equivalent layer yields a total-field anomaly that fits the observed data. Tests with synthetic data simulating different geologic scenarios show that the final estimated magnetization direction is close to the true one. We apply our method to field data from the Goiás alkaline province, over the Montes Claros complex, in the center of Brazil. The results suggest the presence of intrusions with remarkable remanent magnetization, in agreement with the current literature for this region.

Horizontally and vertically aligned fractures (joints) permeated in an isotropic background can give rise to a long-wavelength equivalent orthorhombic medium, which is common for naturally fractured reservoirs. We have developed a feasible approach to characterize the horizontal and vertical fractures using observed azimuthal seismic reflection data. For weak anisotropy, we assume that the horizontal and vertical fractures are decoupled. Using a linear-slip orthorhombic model, we first obtain analytic expressions for the effective elastic stiffness matrix and the corresponding perturbed matrix of an effective orthorhombic anisotropic elastic medium. Combining the scattering function and the perturbed matrix of the orthorhombic medium, we then derive a linearized PP-wave reflection coefficient of effective orthorhombic medium in terms of compressional-wave (P-wave) and shear-wave (S-wave) moduli, density, and horizontal- and vertical-fracture-induced normal and tangential weaknesses. To handle the inverse problem for multiple model parameters in an orthorhombic medium, we reexpress the linearized PP-wave reflection coefficient as a Fourier series. According to the sensitivity analysis of Fourier coefficients (FCs) to isotropic background elastic parameters and four fracture weaknesses, we finally establish a three-step inversion approach to describe the orthorhombic model, which involves (1) estimation of the FCs at different incidence angles from observed azimuthal seismic data and determination of the symmetry axis azimuth, (2) an iterative Bayesian inversion for isotropic background elastic parameters and fracture weaknesses of horizontal fractures from the zeroth-order FC, and (3) an iterative Bayesian inversion for fracture weaknesses of vertical fractures from the second-order FC. The proposed approach is validated by tests on synthetic and field data sets, which demonstrates that the inversion results of P- and S-wave moduli, density, and four fracture weaknesses are robust and reasonable for gas-bearing fractured reservoir characterization with orthorhombic symmetry.

Numerical solutions of 3D isotropic elastodynamics form the key computational kernel for many isotropic elastic reverse time migration and full-waveform inversion applications. However, real-life scenarios often require computing solutions for computational domains characterized by non-Cartesian geometry (e.g., free-surface topography). One solution strategy is to compute the elastodynamic response on vertically deformed meshes designed to incorporate irregular topology. Using a tensorial formulation, we have developed and validated a novel system of semianalytic equations governing 3D elastodynamics in a stress-velocity formulation for a family of vertically deformed meshes defined by Bézier interpolation functions between two (or more) nonintersecting surfaces. The analytic coordinate definition also leads to a corresponding analytic free-surface boundary condition (FSBC) as well as expressions for wavefield injection and extraction. Theoretical examples illustrate the utility of the tensorial approach in generating analytic equations of 3D elastodynamics and the corresponding FSBCs for scenarios involving free-surface topography. Numerical examples developed using a fully staggered grid with a mimetic finite-difference formulation demonstrate the ability to model the expected full-wavefield behavior, including complex free-surface interactions.

Silicon has been investigated in recent years as an alloying anode material to enhance gravimetric energy density in lithium-ion batteries. While recent developments have suggested that silicon oxi...

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...