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

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.