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.

Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions

“…SBP FD methods may be used alone in moderately complex geometries, or as part of efficient hybrid solvers [25,17] when unstructured meshing capabilities are required in parts of the domain. Recent applications of SBP methods to elastic wave equations include [40], which applied a second-order accurate scheme to tilted transversely isotropic media, and [48], which solved the first-order form of the IEWE. Another noteworthy contribution [13] introduced dual first-derivative SBP operators to solve the AEWE.…”