VARIATION OF REFLECTION AND TRANSMISSION COEFFICIENTS WITH CRACK STRIKE AND CRACK DENSITY IN ANISOTROPIC MEDIA

Recent observations show that the differential amplitudes between the faster and slower split shear-waves in reflection surveys contain information about lateral variations of crack density in cracked reservoirs. However, the variation of amplitude with crack geometry when the crack strike changes with depth has not been reported previously. In this paper, we derive expressions for reflection and transmission coefficients of plane split shear-waves at vertical incidence at an interface separating two cracked (anisotropic) media with different crack strikes. We examine the effects on these coefficients as crack strike and crack density vary. For interfaces with large velocity-contrasts, the reflection coefficients carry little information about crack geometry, and the effects of crack strike varying with depth are negligible. In such cases, the polarization and time-delay of the split shear-waves are the only features which reliably diagnose anisotropy and contain information about the variation of crack strike and density. However, for interfaces with small velocity-contrasts, the effects of any variation of crack strike with depth cannot be neglected. In such cases, in addition to the polarization and time-delays of split shear-waves, both the differential amplitude of faster and slower shear-waves and the amplitude ratio of the two off-diagonal elements in the reflected data matrix after separation of split shear-waves, contain information about the variation of crack strike and crack density. In contrast, effects of crack strike changing with depth on transmitted waves are more sensitive regardless of the velocity-contrast and the degree of anisotropy.