Inversion for subsurface anisotropy using estimates of shear-wave splitting

Abstract

SUMMARY Inversion of the parameters characterizing shear-wave splitting (polarizations, time delays, and differential attenuation) provides a way of obtaining a good starting model for full-wave anisotropic modelling, and improves the convergence to a final waveform match. This is necessary as the shear waves behave in a highly non-linear fashion with respect to anisotropy. Here we discuss the extent to which polarization and time-delay information, estimated from split shear waveforms, may supply details of this starting model. 3-D patterns of these parameters for different anisotropic models are considered, to investigate the potential of the inversion scheme. Guidelines are formed for the best arrangements of sources and geophones, to provide optimum resolution of an anisotropic model. The study indicates that in most cases different anisotropic models cannot be adequately distinguished using vertical seismic profiles (VSPs), reflection profiles, and cross-hole surveys in which separate polarization or time-delay measurements at one azimuth are made. Better results are obtained by combining polarization and time-delays estimates, preferably from more than one azimuth. The type of model parameters which can be resolved depends crucially upon the geometry of the acquisition system, and to a lesser extent on the background velocity structure. Individual model parameters are more difficult to extract, but some details appear (in principle) to be resolvable for certain types of survey. VSPs are most suitable to monitor crack strike and density of parallel, vertical, aligned cracks, and the dip of the fine layering contributing to layer-induced anisotropy. Cross-hole experiments are best for measuring the dip of the cracks. The resolution of the crack content and aspect ratio are determined principally by the position of line singularities, and either an offset VSP, or an adapted cross-hole survey may be adequate for resolving these properties if the line is shot at an appropriate azimuth with respect to the strike of the cracks. The ratio of crack-induced anisotropy to matrix anisotropy in sedimentary basins can be evaluated by measuring the positions of the point singularities in recordings of polarization and time-delay patterns using a near-offset VSP.