Reduced Basis Method for 2nd Order Wave Equation: Application to One-Dimensional Seismic Problem

Abstract

We solve the 2nd order wave equation, hyperbolic and linear in nature, for the pressure distribution of one-dimensional seismic problem with smooth initial pressure and rate of pressure change. The reduced basis method, offline-online computational procedures and a posteriori error estimation are developed. We show that the reduced basis pressure distribution is an accurate approximation to the finite element pressure distribution and the offline-online computational procedures work well. The a posteriori error estimation developed shows that the ratio of the maximum error bound over the maximum norm of the reduced basis error has a constant magnitude of O(10²). The inverse problem works well, giving a “possibility region” of a set of system parameters where the actual system parameters may reside.