ALGEBRAIC PROCESSING TECHNIQUES FOR ESTIMATING SHEAR‐WAVE SPLITTING IN NEAR‐OFFSET VSP DATA: THEORY1

Abstract

AbstractA 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 least‐squares eigenanalysis or singular value decomposition. Although the methodology for shear‐wave 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.