Prestack 2D parsimonious Kirchhoff depth migration of elastic seismic data

We have extended prestack parsimonious Kirchhoff depth migration for 2D, two-component, reflected elastic seismic data for a P-wave source recorded at the earth's surface. First, we separated the P-to-P reflected (PP-) waves and P-to-S converted (PS-) waves in an elastic common-source gather into P-wave and S-wave seismograms. Next, we estimated source-ray parameters (source p values) and receiver-ray parameters (receiver p values) for the peaks and troughs above a threshold amplitude in separated P- and S-wavefields. For each PP and PS reflection, we traced (1) a source ray in the P-velocity model in the direction of the emitted ray angle (determined by the source p value) and (2) a receiver ray in the P- or S-velocity model back in the direction of the emergent PP- or PS-wave ray angle (determined by the PP- or PS-wave receiver p value), respectively. The image-point position was adjusted from the intersection of the source and receiver rays to the point where the sum of the source time and receiver-ray time equaled the two-way traveltime. The orientation of the reflector surface was determined to satisfy Snell's law at the intersection point. The amplitude of a P-wave (or an S-wave) was distributed over the first Fresnel zone along the reflector surface in the P- (or S-) image. Stacking over all P-images of the PP-wave common-source gathers gave the stacked P-image, and stacking over all S-images of the PS-wave common-source gathers gave the stacked S-image. Synthetic examples showed acceptable migration quality; however, the images were less complete than those produced by scalar reverse-time migration (RTM). The computing time for the 2D examples used was about 1/30 of that for scalar RTM of the same data.