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Frequency-dependent anisotropy: Effects of multiple fracture sets on shear-wave polarisations

LIU En-Ru,YUE Jian-Hua,PAN Dong-MingDepartment of Geophysics,China University of Mining and Technology,Xuzhou 221008,China  
From the analysis of a multi-component VSP for frequency-dependent anisotropy,we find that shear-wave anisotropy as inferred from measured time delays between splitting shear-waves decreases systematically as frequency increases. Whilst in general the polarisations of the fast split shear-waves remain constant for deep receivers,we notice systematic rotation(up to 20°) of polarisations 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 polarisations.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 polarisation of shear-waves at normal incidence,and present a systematic study of shear-wave propagation in media.Our study demonstrates that the shear-wave polarisations 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 polarisation on frequency.
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