Mimetic Finite Difference Modeling Of 2D Elastic P-SV Wave Propagation

Recently, efforts have been made by Kristek et al.(2002) toward the implementation of a zero-traction boundary condition for an elastic medium by using high-order staggered-grid finite-difference modeling and avoiding symmetry conditions, vacuum formulations, or, other approaches that require grid points located beyond the physical boundary (ghost points). In this work, a new set of numerical differentiators known as “mimetic” finite differences have been used to explicitly solve the exact boundary conditions and fully compute the displacement vector along a planar free surface of a 2D half space. No ghost points are used in our schemes. Two classical grids, the rotated staggered grid (RSG) and the standard staggered grid (SSG), have been enhanced by the inclusion of Compound nodes along the free surface boundary to allow this discretization process and place the displacement vector. Thus, three new algorithms are proposed here, one that works over a RSG, and two implemented using a SSG. Accuracy of these solvers is measured in terms of the dispersion of the numerical Rayleigh wave, and comparisons against Kristek et al.’s algorithm are presented.