| Conventional Kirchoff migration can be made much faster by a priori calculation of ray incident directions, so rays are traced back only along the measured directions rather than in all possible directions. This implementation is known as parsimonious Kirchoff migration. For surface seismic data, the ray incident direction is measured by calculating the horizontal slowness components (or ray parameters) in the inline and crossline directions. However, this implementation does not work for vertical seismic profile (VSP) data, which has only a single vertical line of receivers, so the horizontal slownesses cannot be measured. We overcome this limitation for calculating incident directions from three-component VSP data by polarization analysis of the incident waves. Dip and azimuth angles of the waves are calculated at the receivers by estimating the data covariance matrix within a time window. For P-waves, the data covariance matrix defines the polarization ellipsoid which is then used to calculate the incident angles; for S-waves, an additional step is required because the polarization is orthogonal to the incident direction. For migration we perform ray tracing only along the measured incident directions, which eliminates the traveltime table calculation and reduces the total number of rays being traced. This enhances the efficiency of Kirchhoff migration of three-component VSP data. |
