Summary: This paper presents a modified form of polarization position correlation operator (PPC) which can be used to separate P- and S-waves in a multicomponent seismic profile. The essence of the method (in seeking S- wave extinction) is to form a dot product between the signal vector and the slowness vector during projection of the seismic section into \(\tau\)- p space, using the P-wave velocity profile measured along the array. The dot product (in effect) is a linear controlled direction reception filter (CDR type 1) which selectively passes only P arrivals.
The second step is to use the converse rotation operator, during the forward transform, to compute both the P-wave \(\omega\)-p ‘pass plane’ and the orthogonal P-wave ‘extinction plane’. The two together are needed in order to preserve a measure of the total energy falling within any \(\omega\)-p pixel in the original time sections. The extinction plane on its own gives a measure of the success achieved by the CDRI filter in isolating P-wave energy in a pixel on the pass plane. The best measure of this success is given by performing a cross-spectral matrix analysis of the two \(\omega\)-p planes on a pixel-by-pixel basis (summing over a window \(d\omega\) \(\times dp)\). The ratio of the eigenvalues yields the rectilinearity of polarization. A 2-D gain function based on rectilinearity may be used as a nonlinear boost function in order to enhance strongly polarized P-wave pixels in the \(\omega\)-p pass plane, prior to inverse RADON transformation. The success of this method in achieving wavefield separation and background noise reduction is illustrated with synthetic and physical model seismic data.