Rapid expansion and pseudo spectral implementation for reverse time migration in VTI media


Pestana, Reynam C
Ursin, Bjørn
Stoffa, Paul L

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In isotropic media, we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media, P- and SV-waves are coupled, and the elastic wave equation should be used for RTM. For computational efficiency, a pseudo-acoustic wave equation is often used. This may be solved using a coupled system of second-order partial differential equations. We solve these using a pseudo spectral method and the rapid expansion method (REM) for the explicit time marching. This method generates a degenerate SV-wave in addition to the P-wave arrivals of interest. To avoid this problem, the elastic wave equation for vertical transversely isotropic (VTI) media can be split into separate wave equations for P- and SV-waves. These separate wave equations are stable, and they can be effectively used to model and migrate seismic data in VTI media where |ε- δ| is small. The artifact for the SV-wave has also been removed. The independent pseudo-differential wave equations can be solved one for each mode using the pseudo spectral method for the spatial derivatives and the REM for the explicit time advance of the wavefield. We show numerically stable and high-resolution modeling and RTM results for the pure P-wave mode in VTI media. © 2012 Sinopec Geophysical Research Institute.

Pestana RC, Ursin B, Stoffa PL (2012) Rapid expansion and pseudo spectral implementation for reverse time migration in VTI media. Journal of Geophysics and Engineering 9: 291–301. Available: http://dx.doi.org/10.1088/1742-2132/9/3/291.

RCP and PLS would like to acknowledge support received for this research from King Abdullah University of Science and Technology (KAUST). BU has received support from VISTA and the Norwegian Research Council through the ROSE project. The authors would like to thank Paul Fowler for a detailed review of an early version of the manuscript. Finally, the authors also thank Amerada Hess for making the synthetic data set available.

Oxford University Press (OUP)

Journal of Geophysics and Engineering


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