We extend prestack parsimonious Kirchhoff depth migration (Hua and McMechan 2003) (which is a fast migration), to two-dimensional (2D), two-component (2C), reflected elastic seismic data, from a P-wave source. The P-to-P reflected (PP) waves and P-to-S converted (PS) waves in an elastic common-source gather recorded at the earth’s surface are first separated into PP- and PS-wave seismograms. Source and receiver apparent slownesses (p values) are estimated for the peaks and troughs in both separated PP and PS waves. For each PP and PS reflection, a source ray is traced, in the P- (or the S-) velocity model, in the direction of the emitted ray angle (determined by the source p value), and a receiver ray is traced, in the P- or S-velocity model, back in the direction of the emergent PP (or the PS) wave ray angle (determined by the PP or PS wave receiver p value), respectively. The image point is adjusted from the intersection of the source and receiver rays to the point where the sum of the source and receiver times equals the observed two-way reflection traveltime. The orientation of the reflector surface is determined to satisfy Snell’s law at the ray intersection point. The amplitude of a P-wave (or an S-wave) is distributed over the first Fresnel zone along the reflector surface in the P (or S) image. Stacking over all the single-source P- and S-images separately gives the stacked P- and S- images, respectively. The quality of prestack parsimonious elastic Kirchhoff migration is not as good as that of full prestack Kirchhoff, or reverse-time, migration, but the computing time is reduced by orders of magnitude because the amount of ray tracing is significantly reduced. Thus, parsimonious elastic migration is most useful, when reducing computing time is more important than migration quality, such as in migration velocity analysis, which iterates migration many times.


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