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

Abstract

S U M M A R Y 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 t -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 w-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 w-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 w-p planes on a pixel-by-pixel basis (summing over a window dw x 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 w-p pass plane, prior to inverse RADON transformation.The success of this method in achieving wavefield skparation and background noise reduction is illustrated with synthetic and physical model seismic data.

Decoupled elastic prestack depth migration

“…(32)) can help to increase the quality of wavefield separation during PreSDM. Imaging via Alford rotation (Hou and Marfurt, 2002), extrapolation of scalar potentials (Zhe and Greenhalgh, 1997), and the controlled direction reception filtering in (s-p) space (Greenhalgh et al, 1990) may be regarded as alternative implementations of the projection E ( lm) (Eq. (32)).…”

Approximate separation of pure-mode and converted waves in 3-C reflection seismics by τ-p transform

“…Broadly speaking, techniques for wavefield separation fall into two categories: wave-theoretical methods (Dankbaar, 1985;Greenhalgh et al, 1990;Wapenaar et al, 1990;Amundsen and Reitan, 1995;Wang and Singh, 2002) and parametric methods (Esmersoy, 1990;Cho and Spencer, 1992). Exact wave-theoretical methods are directly based on the physics of wave propagation but require the specification of both P-and S-wave near-surface velocities for land data and additional density parameters for ocean-bottom cable (OBC) data.…”

Separation of P–P and P–SV wavefields by high resolution parabolic Radon transform

“…Wang et al (2002) proposed a τ − p domain scheme to separate P-and SV-wavefields by rotation of the horizontal and vertical components respectively. Al-anboori et al (2005) developed a simplified version of the separation scheme of Greenhalgh et al (1990), which has the advantage over exact wavefield separation schemes in that only a single parameter (the P-wave velocity for P-S wave enhancement or the S-wave velocity for P-P energy enhancement) needs to be specified. Liu et al (2012) presented a method of separation of up-going and down-going waves from three-component crosswell seismic data using the τ − p transform.…”

“…Tatham et al (1983) and Tatham and Goolsbee (1984) separated P-and SV-wavefields by limiting the range in p-values during the τ − p transform for either the horizontal or vertical component and the separation was applied to offshore data. Greenhalgh et al (1990) separated P-and SV-wavefields by forming a dot product between the signal vector and the slowness vector during projection of the seismic section into the τ − p space. Wang et al (2002) proposed a τ − p domain scheme to separate P-and SV-wavefields by rotation of the horizontal and vertical components respectively.…”