Decomposition of a seismic plane wave in three dimensional vertical seismic processing

摘要

A wavefield separation method and apparatus for 3D VSP data, which handles arbitrary 3D source and receiver geometries, and common shot 3C data oriented to North, East and Vertical geographical coordinates and makes use of anisotropic medium properties at the downhole receivers. When given a range of propagation angles, slowness and polarization vectors are computed for each plane wave and a linear system is solved at each frequency to yield the scalar plane-wave amplitudes. A novel regularization scheme is used that obviates the need for eigen analysis of the steering matrix. Sums within subsets of these scalar plane waves are constructed to provide up and down qP (P), qS (Sv) and Sh wavefields. Vector residuals can be computed for parameter testing, quality control and imaging purposes.