Multiblock SBP-SAT Methodology of Symmetric Matrix Form of Elastic Wave Equations on Curvilinear Grids

Abstract

A stable and accurate finite-difference discretization of first-order elastic wave equations is derived in this work. To simplify the origin and proof of the formulas, a symmetric matrix form (SMF) for elastic wave equations is presented. The curve domain is discretized using summation-by-parts (SBP) operators, and the boundary conditions are weakly enforced using the simultaneous-approximation-term (SAT) technique, which gave rise to a provably stable high-order SBP-SAT method via the energy method. In addition, SMF can be extended to wave equations of different types (SH wave and P-SV wave) and dimensions, which can simplify the boundary derivation process and improve its applicability. Application of this approximation can divide the domain into a multiblock context for calculation, and the interface boundary conditions of blocks can also be used to simulate cracks and other structures. Several numerical simulation examples, including actual elevation within the area of Lushan, China, are presented, which verifies the viability of the framework present in this paper. The applicability of simulating elastic wave propagation and the application potential in the seismic numerical simulation of this method are also revealed.