ZENG, X. and MACBETH, C. 1993. Algebraic processing techniques for estimating shear-wave splitting in near-offset VSP data: theory. Geophysical Prospecting 41, 1033-1066. A vector convolutional model for multicomponent data acquired in an anisotropic earth is used as a basis for developing algebraic solutions to interpret near-offset VSP data. This interpretation of the cumulative or interval medium response (Green's tensor) for shear waves, determines a polarization azimuth for the leading shear wave and the time-delay between the fast and slow split waves. The algebraic solutions effectively implement leastsquares eigenanalysis or singular value decomposition. Although the methodology for shearwave analysis is strictly relevant to a transmission response, it can be adapted to surface data for a uniform anisotropic overburden. The techniques perform well when calibrated and tested using synthetic seismograms from various anisotropic models. Noise tests demonstrate the sensitivity of the interval measurements to local interferences, particularly if the shear waves are generated by one source. Although the algorithms are faster than numerical search routines, this is not seen as their major advantage. The solutions may have potential in near real-time interpretation of shear-wave data in well logging, where they may be coded on a microchip to provide a direct stream of separated shear waves, or polarization and birefringence information. There may also be some benefit for large prestack multicomponent surface data sets, where the solutions provide a direct transformation to the split-shear-wave components, reducing the storage space for further processing.
Poor experimental control in shear-wave VSPs may contribute to unreliable estimates of shear-wave splitting and possible misinterpretation of the medium anisotropy. To avoid this, the acquisition and processing of multicomponent shear-wave data needs special care and attention. Measurement of asymmetry in the recorded data matrix using singular-value decomposition (SVD) provides a useful way of examining possible acquisition inaccuracies and may help guide data conditioning and interpretation to ensure more reliable estimates of shear-wave polarization azimuth. Three examples demonstrate how variations in shear-wave polarization and acquisition inaccuracies affect the SVD results in different ways. In the first example, analysis of synthetic seismograms with known depth changes in the polarization azimuth show how these may be detected. In the second example, a known source reorientation and polarity reversal is detected by applying SVD to near-offset, shear-wave VSP data, recorded in the Romashkino field, Tatar Republic. Additional information on a polarization change in the overburden is also obtained by comparing the SVD results with those for full-wave synthetic seismograms. The polarization azimuth changes from N160°E in the overburden to N117°E within the VSP depth range. Most of the shear-wave splitting is built up over the VSP depth range. The final example is a near-offset, shear-wave VSP data set from Lost Hills, California. Here, most of the shear-wave splitting is in the shallow layers before the VSP depth range. SVD revealed a known correction for horizontal reorientation of the sources, but also exhibited results with a distinct oscillatory behavior. Stripping the overburden effects reduces but does not eliminate these oscillations. There appears to be a polarization change from N45°E in the overburden to N125°E in the VSP section. The details in these examples would be difficult to detect by visual inspection of the seismograms or polarization diagrams. Results from these preliminary analyses are encouraging and suggest that it may be possible to routinely use this, or a similar technique, to resolve changes in the subsurface anisotropy from multicomponent experiments where acquisition has not been carefully controlled.
Frequency-modulated pulse trains can be applied in active sonar systems to improve the performance of conventional transmitted waveforms. Recently, two pulse trains have been widely researched as the transmitted waveforms for active sonars. The LFM-Costas pulse train was formed by modulating the linear frequency-modulated (LFM) waveform via the Costas sequence to remove the Doppler ambiguity of LFM pulses. The generalized sinusoidal frequency-modulated (GSFM) waveform, another frequency-modulated pulse train, achieved an ideal ambiguity function shape with thumbtack mainlobe. In this paper, we focus on constructing an optimization model to optimize the LFM-Costas and GSFM pulse trains with the genetic algorithm. The pulse trains can be improved on properties of both ambiguity function and correlations between sub-pulses. The optimized pulse trains are proven to have better detection performance than those of the initial pulse trains, including the lower sidelobe levels of ambiguity function, as well as lower cross-correlation property. Moreover, it is affirmed that the reverberation suppression performance of pulse trains has also been improved through the optimization model.
Multicomponent seismic data collected using directional sources are degraded by the wave excitation process due to inaccurate control of the ground motion. unequal activation strengths or ground couplings between differently oriented sources, and misalignment of the pad. These acquisition uncertainties are exacerbated by the complicated near‐surface scattering present in most seismic areas. Neither group of effects should be neglected in multicomponent analyses that make use of relative wavefield attributes derived from compressional and shear waves. These effects prevent analysis of the direct and reflected waves using procedures based on standard scalar techniques or a prima facia interpretation of the vector wavefield properties, even for the seemingly straightforward case of a near‐offset vertical seismic profile (VSP). Near‐surface correction, using a simple matrix operator designed from the shallowest recordings, alleviates many of these interpretational difficulties in near‐offset VSP data. Results from application of this technique to direct waves from a nine‐component VSP shot at the Conoco test‐site facility, Oklahoma, are encouraging. The technique corrects for unexpected compressional‐wave energy from shear‐wave vibrators and collapses near‐surface multiples, thus facilitating further processing for the upgoing wavefield. The method provides a simple and effective processing step for routine application to near‐offset VSP analyses.
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