Three-dimensional solutions of equations of dynamic elasticity by a New Rapid Expansion Method (REM)

Mickey Edwards, Dan Kosloff, Moshe Reshef, Ekkehart Tessmer

Research output: Contribution to conferencePaperpeer-review

Abstract

This work represents a new scheme for time integration of direct solution methods such as finite-difference, finite-element, and Fourier methods. Forward nodellng with elastic wave propagation is investigated. The rapid expansion method (REM), which we have developed, is based on a modified Chebychev expansion of the formal solution to the governing equations. The REM implementation of the equations of dynamic elasticity using the Fourier method is similar to previous development featuring conventional time integration of second order differencing. A high degree of parallelism exists between the calculations in one time step with temporal differencing and REM calculations. Spatial partial derivatives are computed in the same manner. Compared to time integration of second order differencing, larger time steps or increments are permissible with the REM implementation. For output time sections, results at intermediate times are obtained by resubstituting intermediate times in the computational equations. This does not require recomputation of spatial partial derivatives. The REM can be used to increase accuracy or to obtain comparable accuracy with fewer computations. Conventional time integration and REM methods have been implemented on the CRAY X-MP computer system using parallel processing and the large memory of the Solid-state Storage Device (SSD). The REM can be applied to acoustic and elastic wave propagation using formulations other than the Fourier method.

Original languageEnglish
Pages536-538
Number of pages3
DOIs
StatePublished - 1987
Externally publishedYes
Event1987 Society of Exploration Geophysicists Annual Meeting, SEG 1987 - New Orleans, United States
Duration: 11 Oct 198715 Oct 1987

Conference

Conference1987 Society of Exploration Geophysicists Annual Meeting, SEG 1987
Country/TerritoryUnited States
CityNew Orleans
Period11/10/8715/10/87

Fingerprint

Dive into the research topics of 'Three-dimensional solutions of equations of dynamic elasticity by a New Rapid Expansion Method (REM)'. Together they form a unique fingerprint.

Cite this