Coarse‐layer stripping of vertically variable azimuthal anisotropy from shear‐wave data

Abstract

Alford rotation analysis of 2C × 2C shear‐wave data (two source components, two receiver components) for azimuthal anisotropy is valid only when the orientation of that azimuthal anisotropy is invariant with depth. The Winterstein and Meadows method of layer stripping vertical seismic profiling (VSP) data relaxes this restriction for coarse‐layer variation of the orientation of the anisotropy. Here we present a tensor generalization of the conventional convolutional model of scalar wave propagation and use it to derive generalizations of Winterstein and Meadows layer stripping, valid for 2C × 2C data and for the restricted 2C-only case, in the VSP and reflection contexts. In the 2C × 2C VSP application, the result reduces to that of Winterstein and Meadows in the case where both fast and slow shear modes have the same attenuation and dispersion; otherwise, a balancing of mode spectra and amplitudes is required. The 2C × 2C reflection result differs from the 2C × 2C VSP result since two applications of the mode‐balancing and mode‐advance operations are required (since the waves travel up as well as down). Application to a synthetic data set confirms these results. The 2C × 2C reflection algorithm enables the exploration for sweet spots of high fracture intensity ahead of the bit without the restrictive assumption that the anisotropy orientation is depth invariant.