Polarization analysis can be achieved efficiently by treating a time window of a single-station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross-energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen-Lobve transform), all in one step.SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal-to-noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F-test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.

A high proportion of faces started in mechanized coal mines run into underground faults. The faults take many forms, from the splitting of a seam through a hidden stress pattern caused by subsidence or folding, to a washout or a vertical throw. All faults reduce face output. A throw of only 1.5 m can lead to a face being abandoned. Faults of this order cannot be mapped reliably from the surface. They may be mapped in an underground seismic survey. Roadways of a mine may give access to fast refracting horizons above and below a coal seam. Waveguiding in the plane of the seam, if it occurs, simplifies migration of wave trains reflected from discrete faults. The reduction problem involved in a fault mapping is only two‐dimensional. Given guiding, whether leaky or not, it is possible to map distributed faults of low reflectivity by shooting in transmission across a panel of coal. Algebraic reconstruction techniques are used here to reduce first break times‐of‐flight through a 425 × 950 m rectangular block of coal into the profile of a velocity inhomogeneity. Input data are derived by static correction from hand‐picked arrival times. The reduction itself is effected using an algorithm which accommodates underground site access restrictions. In back projecting first break velocities, a truncated cosine is used to weight the relative contributions of rays passing at different distances from any given mapping point. The reconstructed velocity field suggests that the coal panel is bisected by a ridge of higher velocity. The suspicion of a ridge is reinforced by results of an aberration test based on a standard Huygens‐Kirchhoff migration. The ridge is found to follow the general line of a system of pillars left in place during the mining of a lower horizon. It is concluded that channel waves may be used to map subsidence into old workings underground. Coal seams apparently share, with other sedimentary rocks, the property of a pressure‐sensitive seismic velocity.

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.