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

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.

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Laplace-Fourier-domain elastic full-waveform inversion using time-domain modeling

Geophysics ◽

10.1190/geo2013-0283.1 ◽

2014 ◽

Vol 79 (5) ◽

pp. R195-R208 ◽

Cited By ~ 10

Author(s):

Hyunggu Jun ◽

Youngseo Kim ◽

Jungkyun Shin ◽

Changsoo Shin ◽

Dong-Joo Min

Keyword(s):

Time Domain ◽

Waveform Inversion ◽

Fourier Domain ◽

Full Waveform Inversion ◽

Domain Modeling ◽

Full Waveform ◽

Time Domain Modeling

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Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data

Geophysics ◽

10.1190/1.2957948 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE101-VE117 ◽

Cited By ~ 93

Author(s):

Hafedh Ben-Hadj-Ali ◽

Stéphane Operto ◽

Jean Virieux

Keyword(s):

High Resolution ◽

Frequency Domain ◽

Distributed Memory ◽

Waveform Inversion ◽

Steepest Descent Method ◽

Frequency Domain Method ◽

Full Waveform Inversion ◽

Direct Solver ◽

Velocity Models ◽

Full Waveform

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of [Formula: see text] and [Formula: see text], respectively. The maximum inverted frequencies are 15 and [Formula: see text] for the two applications. A maximum of 30 dual-core biprocessor nodes with [Formula: see text] of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

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A Comparison between Time-Domain and Frequency-Domain Full Waveform Inversion

80th EAGE Conference and Exhibition 2018 ◽

10.3997/2214-4609.201801667 ◽

2018 ◽

Author(s):

S.M.A. Shoja ◽

S. Abolhassani ◽

N. Amini

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Full Waveform

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Extraction of the tomography mode with nonstationary smoothing for full-waveform inversion

Geophysics ◽

10.1190/geo2018-0586.1 ◽

2019 ◽

Vol 84 (4) ◽

pp. R527-R537 ◽

Cited By ~ 5

Author(s):

Gang Yao ◽

Nuno V. da Silva ◽

Vladimir Kazei ◽

Di Wu ◽

Chenhao Yang

Keyword(s):

Time Domain ◽

Waveform Inversion ◽

Opening Angle ◽

Full Waveform Inversion ◽

Domain Modeling ◽

Scattering Angle ◽

Numerical Tests ◽

Reflection Data ◽

Full Waveform ◽

Migration Component

Full-waveform inversion (FWI) includes migration and tomography modes. The tomographic component of the gradient from reflection data is usually much weaker than the migration component. To use the tomography mode to fix background velocity errors, it is necessary to extract the tomographic component from the gradient. Otherwise, the inversion will be dominated by the migration mode. We have developed a method based on nonstationary smoothing to extract the tomographic component from the raw gradient. By analyzing the characteristics of the scattering angle filtering, the wavenumber of the tomographic component at a given frequency is seen to be smaller than that of the migration component. Therefore, low-wavenumber-pass filtering can be applied to extract the tomographic component. The low-wavenumber-pass smoothing filters are designed with Gaussian filters that are determined by the frequency of inversion, the model velocity, and the minimum scattering angle. Thus, this filtering is nonstationary smoothing in the space domain. Because this filtering is carried out frequency by frequency, it works naturally and efficiently for FWI based on frequency-domain modeling. Furthermore, because the maximum opening angle of the reflections in a typical acquisition geometry is much smaller than the minimum scattering angle for the tomographic component, which is generally set at 160°, there is a relatively large gap between the wavenumbers of the tomographic and migration components. In other words, the nonstationary smoothing can be applied once to a group of frequencies for time-domain FWI without leaking the migration component into the tomographic component. Analyses and numerical tests indicate that two frequency groups are generally sufficient to extract the tomographic component for the typical frequency range of time-domain FWI. The numerical tests also demonstrate that the nonstationary smoothing method is effective and efficient at extracting the tomographic component for reflection waveform inversion.

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

Geophysics ◽

10.1190/1.2759835 ◽

2007 ◽

Vol 72 (5) ◽

pp. SM195-SM211 ◽

Cited By ~ 183

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.

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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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