Time evolution of the wave equation using rapid expansion method

Reynam C. Pestana, Paul L. Stoffa

Research output: Contribution to journalArticlepeer-review

124 Scopus citations

Abstract

Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Original languageEnglish (US)
Pages (from-to)T121-T131
Number of pages1
JournalGEOPHYSICS
Volume75
Issue number4
DOIs
StatePublished - Jul 2010
Externally publishedYes

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