3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM195-SM211 ◽  
Author(s):  
Stéphane Operto ◽  
Jean Virieux ◽  
Patrick Amestoy ◽  
Jean-Yves L’Excellent ◽  
Luc Giraud ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Frequency Domain ◽  
Waveform Inversion ◽  
Staggered Grid ◽  
Full Waveform Inversion ◽  
Domain Modeling ◽  
Acoustic Wave Propagation ◽  
Full Waveform ◽  
Grid Points

We present a finite-difference frequency-domain method for 3D visco-acoustic wave propagation modeling. In the frequency domain, the underlying numerical problem is the resolution of a large sparse system of linear equations whose right-hand side term is the source. This system is solved with a massively parallel direct solver. We first present an optimal 3D finite-difference stencil for frequency-domain modeling. The method is based on a parsimonious staggered-grid method. Differential operators are discretized with second-order accurate staggered-grid stencils on different rotated coordinate systems to mitigate numerical anisotropy. An antilumped mass strategy is implemented to minimize numerical dispersion. The stencil incorporates 27 grid points and spans two grid intervals. Dispersion analysis showsthat four grid points per wavelength provide accurate simulations in the 3D domain. To assess the feasibility of the method for frequency-domain full-waveform inversion, we computed simulations in the 3D SEG/EAGE overthrust model for frequencies 5, 7, and [Formula: see text]. Results confirm the huge memory requirement of the factorization (several hundred Figabytes) but also the CPU efficiency of the resolution phase (few seconds per shot). Heuristic scalability analysis suggests that the memory complexity of the factorization is [Formula: see text] for a [Formula: see text] grid. Our method may provide a suitable tool to perform frequency-domain full-waveform inversion using a large distributed-memory platform. Further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time- and frequency-domain modeling of wave propagation to perform 3D full-waveform inversion.

An optimal frequency-domain finite-difference operator with a flexible stencil and its application in discontinuous-grid modeling

Geophysics ◽  
2021 ◽  
pp. 1-41
Author(s):  
Na Fan ◽  
Xiao-Bi Xie ◽  
Lian-Feng Zhao ◽  
Xin-Gong Tang ◽  
Zhen-Xing Yao
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Waveform Inversion ◽  
Uniform Grid ◽  
Optimal Method ◽  
Velocity Models ◽  
Full Waveform ◽  
Rotationally Symmetric ◽  
Grid Points ◽  
Coarse To Fine

We develop an optimal method to determine expansion parameters for flexible stencils in 2D scalar wave finite-difference frequency-domain (FDFD) simulation. The proposed stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, where the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. The proposed method can work in FDFD discontinuous-grid with arbitrary integer coarse-to-fine gird spacing ratios. Numerical examples are presented to demonstrate how to apply this optimal method for the discontinuous-grid FDFD schemes with spacing ratios 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, while the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, the proposed discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging and full waveform inversion.

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.

2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R41-R53 ◽  
Author(s):  
Kun Xu ◽  
George A. McMechan
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Grid Point ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Domain Modeling ◽  
Full Waveform ◽  
Gradient Approach

To decouple the parameters in elastic full-waveform inversion (FWI), we evaluated a new multistep-length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction. To perform wavefield extrapolations for the inversion, we used parallelized high-precision finite-element (FE) modeling in the time domain. The inversion was implemented in the frequency domain; the data were obtained at every subsurface grid point using the discrete Fourier transform at each time-domain extrapolation step. We also used frequency selection to reduce cycle skipping, time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data, and source wavelet estimation at the receivers over the full frequency spectrum by using a fast Fourier transform. In the inversion, the velocity and density reconstructions behaved differently; as a low-wavenumber tomography (for velocities) and as a high-wavenumber migration (for density). Because velocities and density were coupled to some extent, variations were usually underestimated (smoothed) for [Formula: see text] and [Formula: see text] and correspondingly overestimated (sharpened) for [Formula: see text]. The impedances [Formula: see text] and [Formula: see text] from the products of the velocity and density results compensated for the under- or overestimations of their variations, so the recovered impedances were closer to the correct ones than [Formula: see text], [Formula: see text], and [Formula: see text] were separately. Simultaneous reconstruction of [Formula: see text], [Formula: see text], and [Formula: see text] was robust on the FE and finite-difference synthetic data (without surface waves) from the elastic Marmousi-2 model; satisfactory results are obtained for [Formula: see text], [Formula: see text], [Formula: see text], and the recovered [Formula: see text] and [Formula: see text] from their products. Convergence is fast, needing only a few tens of iterations, rather than a few hundreds of iterations that are typical in most other elastic FWI algorithms.

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.

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