Frequency-dependent anistropy : effects of multiple fracture sets on shear-wave polarizations

From the analysis of a multi-component seismic data from vertical seismic profiling (VSP) for frequency-dependent anisotropy, we find that shear-wave anisotropy as inferred from measured time delays between split shear-waves decreases systematically as frequency increases. Whilst in general, the polarizations of the fast split shear-waves remain constant for deep receivers, we notice systematic rotation (up to 20°) of polarizations with frequency for shallow receivers. The variation of time delays with frequency has been successfully interpreted and modelled using a multi-scale rock physics model incorporating one aligned fracture set in a porous medium with randomly distributed micro-cracks. However, this model fails to explain the frequency-dependent shear-wave polarizations. It is speculated that if aligned micro-cracks and aligned fractures are in different directions (i.e. the conjugate angle is not zero), low frequency would indicate the direction of fractures and high frequency would give the orientation of micro-cracks. This speculation, however, has not been satisfactorily proven. In this study, we extend the previous model to allow multiple fracture sets inserted into background porous media. We then derive analytic expressions of polarization of shear-waves at normal incidence, and present a systematic study of shear-wave propagation in media with multi-sets of fractures. Our study demonstrates that the shear-wave polarizations will vary with frequency and the variation depends on the azimuths and angle of incidence relative to the orientations and crack densities of individual sets, and thus may help to explain the observed dependence of shear-wave polarization on frequency