A Helmholtz iterative solver with semianalytical preconditioner for the frequency‐domain full‐waveform inversion

2010 ◽  
Author(s):  
Dmitry Neklyudov ◽  
Ilya Silvestrov ◽  
Vladimir Tcheverda
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Iterative Solver ◽  
Full Waveform

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

Three-dimensional frequency-domain full-waveform inversion with an iterative solver

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC149-WCC157 ◽  
Author(s):  
René-Édouard Plessix
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Three Dimensional ◽  
Iterative Solvers ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
Ocean Bottom Seismometer ◽  
Iterative Solver ◽  
Data Set ◽  
Full Waveform

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.

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.

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