Controlled Direction Reception Filtering of P- and S-Waves In -P Space

Abstract

This paper presents a modified form of polarization position correlation (PPC) operator 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 τ-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 ω-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 ω-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 ω-p planes on a pixel-by-pixel basis (summing over a window dω × dp). The ratio of the eigenvalues yields the rectilinearity of polarization. A 2-D gain function based on rectilinearity may be used as a non-linear boost function in order to enhance strongly polarized P-wave pixels in the ω-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.