Controlled direction reception filtering of P- and S-waves in \(\tau\)-p space. (English) Zbl 0692.73027
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.
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.
MSC:
74J25 | Inverse problems for waves in solid mechanics |
74J10 | Bulk waves in solid mechanics |
86A15 | Seismology (including tsunami modeling), earthquakes |
60G35 | Signal detection and filtering (aspects of stochastic processes) |
74J99 | Waves in solid mechanics |
74H50 | Random vibrations in dynamical problems in solid mechanics |
93E11 | Filtering in stochastic control theory |