Large-scale finite-difference and finite-element frequency-domain seismic wave modelling with multi-level domain-decomposition preconditioner

TL;DR

This paper presents a scalable frequency-domain seismic wave modeling method using multi-level domain-decomposition preconditioners, suitable for large-scale problems with sparse data from ocean bottom node surveys.

Contribution

It introduces an efficient Krylov subspace solver with a two-level ORAS preconditioner for large sparse linear systems in seismic modeling, implemented with finite differences and finite elements.

Findings

Validated accuracy against analytical solutions.

Demonstrated scalability with models up to 2 billion parameters.

Compared cost efficiency of finite difference and finite element schemes.

Abstract

The emergence of long-offset sparse stationary-recording surveys carried out with ocean bottom nodes (OBN) makes frequency-domain full waveform inversion (FWI) attractive to manage compact volume of data and perform attenuation imaging. One challenge of frequency-domain FWI is the forward problem, which requires the solution of large and sparse linear systems with multiple right-hand sides. While direct methods are suitable for dense acquisitions and problems involving less than 100 million unknowns, iterative solver are more suitable for large computational domains covered by sparse OBN surveys. Here, we solve these linear systems with a Krylov subspace method preconditioned with the two-level Optimized Restricted Additive Schwarz (ORAS) domain decomposition preconditioner, the prefix optimized referring to the use of absorbing conditions at the subdomain interfaces. We implement this method with finite differences on uniform grid and finite elements on unstructured tetrahedral meshes. A simulation in a model where the velocity linearly increases with depth allows us to validate the accuracy of the two schemes against an analytical solution while highlighting how their relative cost varies with the band of propagated wavelengths. A simulation in the overthrust model involving up to 2 billions of parameters allows us to tune the method and highlights its scalability.