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AbstractForward 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.
CitationPestana, R. C., & Stoffa, P. L. (2010). Time evolution of the wave equation using rapid expansion method. GEOPHYSICS, 75(4), T121–T131. https://doi.org/10.1190/1.3449091
SponsorsThis work was made possible with funding from the King Abdullah University of Science and Technology (KAUST) and PETRO-BRAS/CENPES. We also thank CT-PETRO/CNPq-FINEP for providing funding and other support. Finally, we thank Bjorn Ursin for interesting and useful conversations.
PublisherSociety of Exploration Geophysicists