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.

The split‐step Fourier method is used to prestack migrate two synthetic borehole‐to‐surface shot gathers. Model structures in the zone of specular illumination beneath the shot are reconstructed by using the split‐step Fourier method both to back‐propagate the recorded wavefield and to forward propagate the source wavelet. The overburden is vertically and laterally inhomogeneous. Each depth interval is treated as a homogeneous strip with the mean velocity plus an inhomogeneity correction term. The inhomogeneity correction term is split and spatially multiplied with each spectral component of the wavefield on its entry to and upon its exit from each strip. Propagation through each strip is effected by multiplication in the spatial frequency domain. The split‐step Fourier method offers a valuable alternative to finite‐difference migration for machines with limited memory. Three imaging methods are compared for two signal‐to‐noise ratios. They are: image extraction by traveltime, crosscorrelation with source wavelet, and deconvolution with source wavelet. At high signal‐to‐noise level, the image formed by deconvolution offers better spatial resolution than images formed by crosscorrelation with the source wavelet or by extraction using traveltime. If the signal‐to‐noise level is low, traveltime imaging deteriorates rapidly, while deconvolution images degrade towards those created by crosscorrelation imaging.

One fifth of the United Kingdom’s energy is derived from the gas fields of the southern North Sea. The area is divided into large fault blocks, which are laced with minor faults. Surface reflection seismic fault maps of the main producing horizon are distorted by salt rollers or pillows in the overlying high velocity Zechstein evaporites. We have developed an inexpensive method of confirming the presence of minor faults in the relatively flat base of the Zechstein around a well that would simplify production planning. Deep well sonic logs indicate that seismic velocity drops abruptly beneath the base Zechstein and then rises gradually with depth. This profile is characteristic of a whispering gallery, or a buried, variable‐index beam waveguide. If base Zechstein faults scatter energy efficiently into the waveguide, then the faults might be mapped by moving a seismic source over the surface and recording the mode converted arrivals at a geophone within the guide. To test this possibility, over 3000 shots were fired at 27-m intervals in thirteen lines spaced by ≈500 m from a 4436-cu in. (0.075-cu m) marine air gun array into a 3 km deep triaxial VSP geophone, stationed beneath the Rotliegendes. Secondary arrivals were found to move out across the raw field geophone gathers in the manner expected of down‐going compressional to both guided compressional and guided shear vertical mode conversions [P-P and P-SV] at the base of the Zechstein. Prestack migration yielded a map of mode conversion activity at the edges of known faults with throws of 30 + m over an area of [Formula: see text]. We conclude that there is an extensive seismic waveguide beneath the Zechstein in the southern North Sea. Faults scatter down‐going P waves efficiently into the guide; noise levels are low at the bottom of a borehole. Vertical reverberation follows a surface source as it moves away from the wellhead. Horizontal waveguiding reduces geometric spreading loss. These factors make it possible to map small reservoir faults with high‐resolution at long ranges from an exploration well.