A Model Order Reduction Method for Seismic Applications Using the Laplace Transform

TL;DR

This paper introduces a Laplace transform-based model order reduction method for seismic wave problems, achieving exponential accuracy and providing explicit convergence bounds that are robust to wavelet parameters.

Contribution

It develops a novel MOR strategy in the Laplace domain for seismic applications, with proven convergence bounds and an intrinsic accuracy limit related to the wavelet shape.

Findings

Achieves exponential convergence in approximating seismic wave solutions.

Provides explicit, parameter-robust convergence bounds.

Identifies an intrinsic accuracy limit based on initial wavelet value.

Abstract

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave problems comprise the acoustic and elastic wave equations, with applications in seismic modeling. Motivated by recent Laplace-domain MOR methodologies, we construct reduced bases that approximate the time-domain solution with exponential accuracy. We prove convergence bounds that are explicit and robust with respect to the parameters controlling the Ricker wavelet's shape and width and identify an intrinsic accuracy limit dictated by the wavelet's value at the initial time. In particular, the resulting error bound is independent of the underlying Galerkin discretization space and yields computable criteria for the regime in which exponential convergence is observed.