28 October 1996 Seismic imaging with offset plane waves
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Migration is commonly used as a wavefield focussing tool in the study of the variation of reflection amplitude with offset (AVO), or with angle of incidence at reflectors. Migrations are typically applied to common offset or common incident angle sections. In many processing systems, common angle sections are formed by simple 1-d transformations from offset to angle of common midpoint (CMP) gathers based on ray tracing. In this paper, we provide a wave-equation framework for migrating common incidence angle sections that have been formed from Radon transforms over offset in CMP gathers. Radon transformation of the scalar wave equation results in an independent wave equation for each offset plane wave. The offset plane wave equation is nearly equivalent to the zero offset wave equation, except for an additional term related to dip in the mid-point direction, and to offset ray parameter (angle of incidence at the surface). Within this framework, finite difference, pseudo- spectral, and Kirchhoff migrations for common angle sections can be easily adapted from existing algorithms. The availability of a wave equation for common angle sections allows rigorous and efficient application of wave equation techniques for AVO studies and complex structural imaging problems.
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Charles C. Mosher, Charles C. Mosher, Douglas J. Foster, Douglas J. Foster, Siamak Hassanzadeh, Siamak Hassanzadeh, } "Seismic imaging with offset plane waves", Proc. SPIE 2822, Mathematical Methods in Geophysical Imaging IV, (28 October 1996); doi: 10.1117/12.255213; https://doi.org/10.1117/12.255213

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