The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
|Original language||English (US)|
|Number of pages||1|
|State||Published - Sep 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: I thank Zedong Wu for generating the split-step Marmousi data set used here and for fruitful discussions. I thank KAUST for its support. I also thank the seismic wave analysis group for their support. I thank Jeff Shragge, Alexey Stovas, Bin Wang, and an anonymous reviewer for their helpful comments and suggestions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.