3D numerical simulation of elastic waves with a frequency-domain iterative solver

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. T333-T344 ◽  
Author(s):  
Mikhail Belonosov ◽  
Victor Kostin ◽  
Dmitry Neklyudov ◽  
Vladimir Tcheverda
Keyword(s):  
Wave Propagation ◽  
Frequency Domain ◽  
Krylov Subspace ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Forward Modeling ◽  
Inversion Method ◽  
Algebraic Equations ◽  
Iterative Solver ◽  
Linear Algebraic Equations

The efficiency of any inversion method for estimating the medium parameters from seismic data strongly depends on simulation of the wave propagation, i.e., forward modeling. The requirements are that it should be accurate, fast, and computationally efficient. When the inversion is carried out in the frequency domain (FD), e.g., FD full-waveform inversion, only a few monochromatic components are involved in the computations. In this situation, FD forward modeling is an appealing potential alternative to conventional time-domain solvers. Iterative FD solvers, based on a Krylov subspace iterative method, are of interest due to their moderate memory requirements compared with direct solvers. A huge issue preventing their successful use is a very slow convergence. We have developed an iterative solver for the elastic wave propagation in 3D isotropic heterogeneous land models. Its main ingredient is a novel preconditioner, which provides the convergence of the iteration. We have developed and justified a method to invert our preconditioner effectively on the base of the 2D fast Fourier transform and solving a system of linear algebraic equations with a banded matrix. In addition, we determine how to parallelize our solver using the conventional hybrid parallelization (MPI in conjunction with OpenMP) and demonstrate the good scalability for the widespread 3D SEG/EAGE overthrust model. We find that our method has a high potential for low-frequency simulations in land models with moderate lateral variations and arbitrary vertical variations.

A finite-difference iterative solver of the Helmholtz equation for frequency-domain seismic wave modeling and full waveform inversion

Geophysics ◽  
2020 ◽  
pp. 1-43
Author(s):  
Xingguo Huang ◽  
Stewart Greenhalgh
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Frequency Domain ◽  
Iteration Method ◽  
Krylov Subspace ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Iterative Solver ◽  
Subspace Iteration ◽  
Full Waveform

We present a finite difference iterative solver of the Helmholtz equation for seismic modeling and inversion in the frequency-domain. The iterative solver involves the shifted Laplacian operator and two-level pre-conditioners. It is based on the application of the pre-conditioners to the Krylov subspace stabilized biconjugate gradient method. A critical factor for the iterative solver is the introduction of a new pre-conditioner into the Krylov subspace iteration method to solve the linear system resulting from the discretization of the Helmholtz equation. This new pre-conditioner is based upon a reformulation of an integral equation-based convergent Born series for the Lippmann-Schwinger equation to an equivalent differential equation. We demonstrate that the proposed iterative solver combined with the novel pre-conditioner when incorporated with the finite difference method accelerates the convergence of the Krylov subspace iteration method for frequency-domain seismic wave modeling. A comparison of a direct solver, a one-level Krylov subspace iterative solver and the proposed two-level iterative solver verified the accuracy and accelerated convergence of the new scheme. Extensive tests in full waveform inversion demonstrate the solver applicability to full waveform inversion applications.

scholarly journals Multi-scale time-frequency domain full waveform inversion with a weighted local correlation-phase misfit function

2019 ◽  
Vol 16 (6) ◽  
pp. 1017-1031 ◽  
Author(s):  
Yong Hu ◽  
Liguo Han ◽  
Rushan Wu ◽  
Yongzhong Xu
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Local Correlation ◽  
Time Frequency ◽  
Model Dependence ◽  
Full Waveform ◽  
Frequency Components

Abstract Full Waveform Inversion (FWI) is based on the least squares algorithm to minimize the difference between the synthetic and observed data, which is a promising technique for high-resolution velocity inversion. However, the FWI method is characterized by strong model dependence, because the ultra-low-frequency components in the field seismic data are usually not available. In this work, to reduce the model dependence of the FWI method, we introduce a Weighted Local Correlation-phase based FWI method (WLCFWI), which emphasizes the correlation phase between the synthetic and observed data in the time-frequency domain. The local correlation-phase misfit function combines the advantages of phase and normalized correlation function, and has an enormous potential for reducing the model dependence and improving FWI results. Besides, in the correlation-phase misfit function, the amplitude information is treated as a weighting factor, which emphasizes the phase similarity between synthetic and observed data. Numerical examples and the analysis of the misfit function show that the WLCFWI method has a strong ability to reduce model dependence, even if the seismic data are devoid of low-frequency components and contain strong Gaussian noise.

Source-independent extended waveform inversion based on space-time source extension: Frequency-domain implementation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R449-R461 ◽  
Author(s):  
Guanghui Huang ◽  
Rami Nammour ◽  
William W. Symes
Keyword(s):  
Source Function ◽  
Random Noise ◽  
A Priori ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Target Velocity ◽  
Extended Source ◽  
Full Waveform ◽  
Time Variables

Source signature estimation from seismic data is a crucial ingredient for successful application of seismic migration and full-waveform inversion (FWI). If the starting velocity deviates from the target velocity, FWI method with on-the-fly source estimation may fail due to the cycle-skipping problem. We have developed a source-based extended waveform inversion method, by introducing additional parameters in the source function, to solve the FWI problem without the source signature as a priori. Specifically, we allow the point source function to be dependent on spatial and time variables. In this way, we can easily construct an extended source function to fit the recorded data by solving a source matching subproblem; hence, it is less prone to cycle skipping. A novel source focusing annihilator, defined as the distance function from the real source position, is used for penalizing the defocused energy in the extended source function. A close data fit avoiding the cycle-skipping problem effectively makes the new method less likely to suffer from local minima, which does not require extreme low-frequency signals in the data. Numerical experiments confirm that our method can mitigate cycle skipping in FWI and is robust against random noise.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

3D elastic frequency-domain iterative solver for full-waveform inversion

2016 ◽  
Author(s):  
Mikhail Belonosov ◽  
Vladimir Tcheverda ◽  
Dmitry Neklyudov ◽  
Victor Kostin ◽  
Maxim Dmitriev
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Iterative Solver ◽  
Full Waveform

Mixed time–frequency domain simulation of a hydraulic inductance pipe with a check valve

2011 ◽  
Vol 225 (10) ◽  
pp. 2413-2421 ◽  
Author(s):  
R Scheidl ◽  
B Manhartsgruber ◽  
H Kogler
Keyword(s):  
Frequency Domain ◽  
Check Valve ◽  
Buck Converter ◽  
Frequency Domain Method ◽  
Parameter Study ◽  
Algebraic Equations ◽  
Efficient Computation ◽  
Time Frequency ◽  
Linear Algebraic Equations ◽  
Domain Modelling

This paper deals with the efficient computation of hydraulic switching systems with a check valve by a mixed time–frequency domain method; frequency-domain modelling is performed on the wave propagation in a pipe and time-domain modelling is applied to the switching valve and the check valve. The dual property of the check valve makes the complete problem have variational inequality properties. A solution method is presented which replaces the pressure and the flowrate of the check valve as a function of one new variable. The resulting system of non-linear algebraic equations is solved using a Newton–Raphson method in combination with a smoothing of the non-smooth properties of the check valve. The method is applied to a parameter study of a hydraulic buck converter.

Comparison of source-independent methods of elastic waveform inversion

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. R91-R100 ◽  
Author(s):  
Kun Xu ◽  
Stewart A. Greenhalgh ◽  
MiaoYue Wang
Keyword(s):  
Elastic Wave ◽  
Frequency Domain ◽  
Numerical Experiments ◽  
Random Noise ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Practical Procedure ◽  
Wave Inversion ◽  
Full Waveform

In this paper, we investigate several source-independent methods of nonlinear full-waveform inversion of multicomponent elastic-wave data. This includes iterative estimation of source signature (IES), standard trace normalization (STN), and average trace normalization (ATN) inversion methods. All are based on the finite-element method in the frequency domain. One synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature (KSS) inversion method. The numerical experiments show that the IES method is superior to both STN and ATN methods in two-component, elastic-wave inversion in the frequency domain when the source signature is unknown. The STN and ATN methods have limitations associated with near-zero amplitudes (or polarity reversals) in traces from one of the components, which destroy the energy balance in the normalized traces and cause a loss of frequency information. But the ATN method is somewhat superior to the STN method in suppressing random noise and improving stability, as the developed formulas and the numerical experiments show. We suggest the IES method as a practical procedure for multicomponent seismic inversion.

Application of frequency-domain waveform inversion method in Marmousi shots data

2012 ◽  
Vol 17 (4) ◽  
pp. 326-330 ◽  
Author(s):  
Meng Wang ◽  
Dong Zhang ◽  
Di Yao ◽  
Qianqing Qin ◽  
Lin Xu
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Inversion Method

scholarly journals NUMERICAL WAVE FIELDS QUASISTATIC MODELING IN FLUID-FILLED POROELASTIC MEDIA

2021 ◽  
Vol 2 (2) ◽  
pp. 298-311
Author(s):  
Sergey A. Solovyev ◽  
Vadim V. Lisitsa
Keyword(s):  
Temporal Frequency ◽  
Low Frequency ◽  
Wide Frequency Range ◽  
Algebraic Equations ◽  
Static State ◽  
Frequency Space ◽  
Poroelastic Media ◽  
Poroelastic Materials ◽  
Linear Algebraic Equations ◽  
Dependent Strain

This paper presents a numerical algorithm to simulate low-frequency loading of fluid-filled poroelastic materials and estimate the effective frequency-dependent strain-stress relations for such media. The algorithm solves Biot equation in quasi-static state in the frequency space. As a result a system of linear algebraic equations have to be solved for each temporal frequency. We use the direct solver, based on the $LU$ decomposition to resolve the SLAE. According to the presented numerical examples the suggested algorithm allows reconstructing the stiffness tensor within a wide Frequency range.

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