Frequency-domain acoustic wave modeling using a hybrid direct-iterative solver based on a parallel domain decomposition method: a tool for 3D Full Waveform Inversion?

With the acquisition of wide-aperture seismic data sets, full-waveform inversion is an attractive method for deriving velocity models. Three-dimensional implementations require an efficient solver for the wave equation. Computing 3D time-harmonic responses with a frequency-domain solver is complicated because a large linear system with negative and positive eigenvalues must be solved. Time-domain schemes are an alternative. Nevertheless, existing frequency-domain iterative solvers with an efficient preconditioner are a viable option when full-waveform inversion is formulated in the frequency domain. An iterative solver with a multigrid preconditioner is competitive because of a high-order spatial discretization. Numerical examples illustrated the efficiency of the iterative solvers. Three dimensional full-waveform inversion was then studied in the context of deep-water ocean-bottom seismometer acquisition. Three dimensional synthetic data inversion results showed the behavior of full-waveform inversion with respect to the initial model and the minimum frequency available in the data set. Results on a 3D real ocean-bottom seismometer data set demonstrated the relevance of full-waveform inversion, especially to image the shallow part of the model.

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Frequency-domain full-waveform inversion with an efficient iterative solver approach

10.1190/segam2017-17627726.1 ◽

2017 ◽

Author(s):

Fei Xie ◽

Jianping Huang ◽

Zhenchun Li

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Iterative Solver ◽

Full Waveform

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

Geophysics ◽

10.1190/geo2020-0411.1 ◽

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.

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Performances of 3D Frequency-Domain Full-Waveform Inversion Based on Frequency-Domain Direct-Solver and Time-Domain Modeling: Application to 3D OBC Data from the Valhall Field

10.2523/16881-ms ◽

2013 ◽

Cited By ~ 1

Author(s):

Romain Brossier ◽

Vincent Etienne ◽

Guanghui Hu ◽

Stephane Operto ◽

Jean Virieux

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Domain Modeling ◽

Direct Solver ◽

Full Waveform ◽

Time Domain Modeling

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

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz062 ◽

2019 ◽

Vol 16 (6) ◽

pp. 1017-1031 ◽

Cited By ~ 5

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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