Elastic wave propagation using fully vectorized high order finite-difference algorithms

Summarization: Two finite-difference schemes for solving the elastic wave equation in heterogeneous two-dimensional media are implemented on a vector computer. A modified Lax-Wendroff scheme that is second-order accurate both in time and space and is a version of the MacCormack scheme that is second-order accurate in time and fourth-order in space. The algorithms are based on the matrix times vector by diagonals technique that is fully vectorized and is described using a novel notation for vector supercomputer operations. The technique described can be implemented on a vector processor of modest dimensions and increase the applicability of finite differences. The two difference operators are compared and the programs are tested for a simple case of standing sinusoidal waves for which the exact solution is known and also for a two-layer model with a line source. A comparison of the results for an actual well-to-well experiment verifies the usefulness of the two-dimensional approach in modeling the results.Presented on: Geophysic