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

Abstract

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.

Application of Acoustic Wave Propagation Analysis Methods for Monitoring a Miscible Mixing Zone in Porous Media

“…(1) (Dai, 1993;Dai et al, 1995;Vafidis, 1988;Vafidis et al, 1992), Biot's system of equations changes form into the following first-order system of differential equations:…”

Mapping the ancient port at the archaeological site of Itanos (Greece) using shallow seismic methods

“…Thus, taking into consideration the results of the P-wave refraction of seismic line S II , synthetic seismic data were created using a finite-difference method, which is based on the seismic wave equation (Vafidis et al, 1992). The first breaks on the field and synthetic seismograms were subsequently compared.…”

Seismic migration and absorbing boundaries with a one‐way wave system for heterogeneous media1

“…7 (Table 2), synthetic shot gathers with splitspread configuration were calculated using an independent finite-difference technique for P-SV wave propagation described by Vafidis et al (1992). The trace interval is 50m.…”

“…Instability of explicit schemes is not so severe for hyperbolic equations as it is for parabolic equations (Vafidis and Kanasewich 1991). A MacCormack finite-diflerence scheme of fourthorder accuracy in space and second-order accuracy in time and a dimensional splitting technique (Vafidis, Abramovici and Kanasewich 1992) form the basis of the numerical solution of the system (21) and are described in the Appendix. The MacCormack schemes consist of a predictor and a corrector and are very popular in solving first-order hyperbolic systems (Mitchell and Griffiths 1980).…”