Model order reduction for seismic applications

TL;DR

This paper introduces a model order reduction method for seismic wave simulations that significantly accelerates computation by exploiting low-pass filtering in the Laplace domain, achieving high accuracy and stability.

Contribution

The authors develop a novel reduced order modeling approach for seismic wave equations using Laplace transform and POD-Greedy algorithms, ensuring exponential convergence and stability.

Findings

Achieves approximately 1000-fold reduction in unknowns.

Reduces computation time compared to implicit methods.

Ensures stable and accurate reduced models for wave problems.

Abstract

We propose a model order reduction approach to speed up the computation of seismograms, i.e. the solution of the seismic wave equation evaluated at a receiver location, for different model parameters. Our approach achieves a reduction of the unknowns by a factor of approximately 1000 for various numerical experiments for a 2D subsurface model of Groningen, the Netherlands, even if the wave speeds of the subsurface are relatively varied. Moreover, using parallel computing, the reduced model can approximate the (time domain) seismogram in a lower wall clock time than an implicit Newmark-beta method. To realize this reduction, we exploit the fact that seismograms are low-pass filtered for the observed seismic events by considering the Laplace-transformed problem in frequency domain. Therefore, we can avoid the high frequencies that would require many reduced basis functions to reach the desired accuracy and generally make the reduced order approximation of wave problems challenging. Instead, we can prove for our ansatz that for a fixed subsurface model the reduced order approximation converges exponentially fast in the frequency range of interest in the Laplace domain. We build the reduced model from solutions of the Laplace-transformed problem via a (Proper Orthogonal Decomposition-)Greedy algorithm targeting the construction of the reduced model to the time domain seismograms; the latter is achieved by using an a posteriori error estimator that does not require computing any time domain counterparts. Finally, we show that we obtain a stable reduced model thus overcoming the challenge that standard model reduction approaches do not necessarily yield a stable reduced model for wave problems.