A stable implementation of the prestack exploding reflector modeling and migration

The double square-root DSR equation is known to image data by downward continuation using one-way depth extrapolation methods. A two-way time extrapolation of the DSR-derived phase operator suffers from an essential singularity for horizontally traveling waves. This singularity can be avoided by limiting the range of wavenumbers treated in a spectral-based extrapolation referred to as the low-rank method. However, the region around the singularity will still induce instability. We derive an approximation to the DSR formulation based on a high frequency approximation. The resulting equation is both highly accurate and free of singularities. Applications to synthetic data including imaging of the Marmousi dataset demonstrate the accuracy of the new prestack modeling and migration approach. © 2011 Society of Exploration Geophysicists.