Parsimonious migration of 3-C 3D VSP data

Abstract

Conventional Kirchhoff migration can be made much faster by a priori calculation of wave arrival directions, and tracing rays back only along the measured directions; this is known as parsimonious migration. For surface seismic data, where acquisition with 2D arrays is common, the wave arrival directions can be measured by using local slant stacking to calculate the two horizontal slowness components. The vertical slowness is then deduced by using the dispersion relation. For vertical seismic profile (VSP) data, where multiline acquisition is not possible, only the vertical component of the slowness vector can be measured, which is insufficient to constrain the wave arrival direction. We overcome this limitation for three-component VSP data by polarization analysis of the incident waves. Polar and azimuth anglesare calculated at the receivers by estimating the data covariance matrix and the vertical slowness, assuming isotropic media and linear polarization of both P- and S-waves. For P-waves, the data covariance matrix defines the polarization ellipsoid, which is then used to calculate the wave arrival direction. For S-waves, an additional step is required because the polarization is orthogonal to the propagation direction. Ray tracing along only the measured propagation directions eliminates the traditional traveltime table calculation, and enhances the efficiency of Kirchhoff migration of three-component VSP data. Distortions of the polarization caused by factors such as anisotropy are assumed to be corrected independently of the migration process described here. Synthetic examples for a flat reflector and for a salt flank model demonstrate the procedure and the image quality.