2D and 3D frequency-domain elastic wave modeling in complex media with a parallel iterative solver

Abstract

Full-waveform inversion and reverse time migration rely on an efficient forward-modeling approach. Current 3D large-scale frequency-domain implementations of these techniques mostly extract the desired frequency component from the time-domain wavefields through discrete Fourier transform. However, instead of conducting the time-marching steps for each seismic source, in which the time step is limited by the stability condition, performing the wave modeling directly in the frequency domain using an iterative linear solver may reduce the entire computational complexity. For 2D and 3D frequency-domain elastic wave modeling, a parallel iterative solver based on a conjugate gradient acceleration of the symmetric Kaczmarz row-projection method, named the conjugate-gradient-accelerated component-averaged row projections (CARP-CG) method, shows interesting convergence properties. The parallelization is realized through row-block division and component averaging operations. Convergence is achieved systematically even when different physical factors such as the space-dependent Poisson's ratio, free-surface condition, and seismic attenuation are incorporated in the wave modeling. We determined that the scalability of CARP-CG was satisfactory, especially for large-scale applications, using up to several hundred computational cores. We found a potential improvement in computational complexity compared to timedomain modeling through numerical experiments. Finally, we achieved a convergence at 5 Hz in a 3D heterogeneous model, involving fast-slow-fast layers resembling waveguide geometries, with up to several hundred million unknowns, in fewer than 10 h on fewer than 200 cores. All of these results make CARP-CG a potential candidate of the forward modeling engine for seismic imaging on challenging models.

Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

“…CARP-CG has previously been used on this specific model [37], and has found other uses in geophysics applications [38], including the frequency domain elastic wave equation [23,27]. The Salt model provides the speed of sound in a 3-dimensional volume of the earth, measuring 13,440 × 13,440 × 4160 meters 3 .…”

Frequency‐domain double‐plane‐wave least‐squares reverse time migration

“…Lacking a good wave-equation solver might hinder the direct implementation for the proposed method in 3D. Currently, some ongoing efforts aim at efficiently solving Helmholtz equation in 3D (Riyanti et al 2007;Operto et al 2007;Li et al 2015), and preliminary results suggest 3D frequency-domain solvers can be potential candidates for the forward modelling engine for various uses of seismic imaging and inversion methods.…”

The method of polarized traces for the 3D Helmholtz equation

“…Within the geophysical community, the analytic incomplete LU (AILU) method was explored by Plessix and Mulder (2003) and applied in the context of 3D seismic imaging, resulting in some large computations (Plessix, 2007). A variant of Kazmarc preconditioners (Gordon and Gordon, 2010) have been studied and applied to timeharmonic wave equations by Li et al (2015). Although these solvers have, in general, relatively low memory consumption they tend to require many iterations to converge, thus hindering practical run-times.…”