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

Abstract

International audienceWe 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 shows that 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 10 Hz. 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 O(35N(4)) for a N-3 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

Resolving the fine-scale velocity structure of continental hyperextension at the Deep Galicia Margin using full-waveform inversion

“…Forward modelling of synthetic wavefields through the starting model is achieved by solving the numerical wave equation (either acoustic or elastic) through a method of finite differences (Virieux 1986;Operto et al 2007).…”

Seismic Waves - Research and Analysis

“…This approach has been shown to be efficient for 2D forward problems (Hustedt et al, 2004;Jo et al, 1996;Stekl & Pratt, 1998). However, the time and memory complexities of the LU factorization, and its limited scalability on large-scale distributed memory platforms, prevents the use of the direct-solver approach for large-scale 3D problems (i.e., problems involving more than ten millions of unknowns) (Operto et al, 2007).…”

“…The sparse complex-valued matrix B has a symmetric pattern, although is not symmetric because of absorbing boundary conditions (Hustedt et al, 2004;Operto et al, 2007). The fourier transform is defined with the following convention…”

Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

“…The computational kernel is responsible for simulating seismic wavefields with the purpose of measuring data misfits, generating gradients and obtaining approximations to the Hessian. Some acceleration efforts focusing on the FWI computing kernels include porting these kernels to accelerator-based hardware [5,11,39], optimizing the kernels' performance in general purpose processors [23] for off-the-shelf hardware or parallelizing the kernels in many compute units [30,36,38]. Nevertheless, we wish to show here that there are workflow strategies that are orthogonal to kernel optimization and which result in notable computational savings, thus making elastic FWI a routinely applicable tool for 3D datasets.…”