Source-receiver two-way wave extrapolation for prestack exploding-reflector modelling and migration

Abstract
Most modern seismic imaging methods separate input data into parts (shot gathers). We develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield forward or backward in time. This approach has the potential for generating accurate images free of artiefacts associated with conventional approaches. We derive novel high-order partial differential equations in the source-receiver time domain. The fourth-order nature of the extrapolation in time leads to four solutions, two of which correspond to the incoming and outgoing P-waves and reduce to the zero-offset exploding-reflector solutions when the source coincides with the receiver. A challenge for implementing two-way time extrapolation is an essential singularity for horizontally travelling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral-based extrapolation. Using spectral methods based on the low-rank approximation of the propagation symbol, we extrapolate only the desired solutions in an accurate and efficient manner with reduced dispersion artiefacts. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach.

Citation
Alkhalifah, T., Fomel, S., & Wu, Z. (2014). Source-receiver two-way wave extrapolation for prestack exploding-reflector modelling and migration. Geophysical Prospecting, 63(1), 23–34. doi:10.1111/1365-2478.12162

Acknowledgements
We are grateful to Anton Duchkov, Maarten de Hoop, Lexing Ying and Yu Zhang for many stimulating discussions on the subject. We thank the associate editor and two anonymous reviewers for their helpful suggestions and comments. We thank KAUST and specifically the KAUST-UT AEA Round 2 project for its support.

Publisher
Wiley

Journal
Geophysical Prospecting

DOI
10.1111/1365-2478.12162

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