scholarly journals Parsimonious truncated Newton method for time-domain full waveform inversion based on Fourier-domain full-scattered-field approximation

Geophysics ◽  
2021 ◽  
pp. 1-147
Author(s):  
Peng Yong ◽  
Romain Brossier ◽  
Ludovic Métivier
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Cross Correlation ◽  
Waveform Inversion ◽  
Field Approximation ◽  
Second Order ◽  
Vector Product ◽  
First Order ◽  
Full Waveform ◽  
Truncated Newton

In order to exploit Hessian information in Full Waveform Inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag cross-correlation of the first-order/second-order incident wavefields and the second-order/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much more challenging as it is not affordable to store the entire time-dependent wavefields. The widely used wavefield recomputation strategy leads to computationally intensive tasks. We present an efficient alternative approach to computing the Hessian-vector product for time-domain FWI. In our method, discrete Fourier transform is applied to extract frequency-domain components of involved wavefields, which are used to compute wavefield cross-correlation in the frequency domain. This makes it possible to avoid reconstructing the first-order and second-order incident wavefields. In addition, a full-scattered-field approximation is proposed to efficiently simplify the second-order incident and adjoint wavefields computation, which enables us to refrain from repeatedly solving the first-order incident and adjoint equations for the second-order incident and adjoint wavefields (re)computation. With the proposed method, the computational time can be reduced by 70% and 80% in viscous media for Gauss-Newton and full-Newton Hessian-vector product construction, respectively. The effectiveness of our method is also verified in the frame of a 2D multi-parameter inversion, in which the proposed method almost reaches the same iterative convergence of the conventional time-domain implementation.

A Time-Domain Preconditioned Truncated Newton Approach to Visco-acoustic Multiparameter Full Waveform Inversion

2018 ◽  
Vol 40 (4) ◽  
pp. B1101-B1130 ◽  
Author(s):  
Pengliang Yang ◽  
Romain Brossier ◽  
Ludovic Métivier ◽  
Jean Virieux ◽  
Wei Zhou
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Truncated Newton

The SEISCOPE optimization toolbox: A large-scale nonlinear optimization library based on reverse communication

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. F1-F15 ◽  
Author(s):  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Waveform Inversion ◽  
Second Order ◽  
First Order ◽  
Truncated Newton ◽  
First Order Methods ◽  
Second Order Methods

The SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first-order methods (steepest-descent and nonlinear conjugate gradient) and second-order methods ([Formula: see text]-BFGS and truncated Newton), for the solution of large-scale nonlinear optimization problems. An efficient line-search strategy ensures the robustness of these implementations. The routines are proposed as black boxes easy to interface with any computational code, where such large-scale minimization problems have to be solved. Traveltime tomography, least-squares migration, or full-waveform inversion are examples of such problems in the context of geophysics. Integrating the toolbox for solving this class of problems presents two advantages. First, it helps to separate the routines depending on the physics of the problem from the ones related to the minimization itself, thanks to the reverse communication protocol. This enhances flexibility in code development and maintenance. Second, it allows us to switch easily between different optimization algorithms. In particular, it reduces the complexity related to the implementation of second-order methods. Because the latter benefit from faster convergence rates compared to first-order methods, significant improvements in terms of computational efforts can be expected.

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.

scholarly journals Time domain viscoelastic full waveform inversion

2017 ◽  
Vol 209 (3) ◽  
pp. 1718-1734 ◽  
Author(s):  
Gabriel Fabien-Ouellet ◽  
Erwan Gloaguen ◽  
Bernard Giroux
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform
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