Frequency-Dependent Amplitude Versus Offset Variations in Porous Rocks with Aligned Fractures

The theory of frequency-dependent amplitude versus offset (AVO) was developed for patchy-saturated model. In this work, we consider this theory in the case of an anisotropic medium based on a fractured-sandstone model. Thus, building on viscoelastic theory, we introduce a method for the computation of frequency-dependent AVO that is suitable for use in the case of an anisotropic medium. We use both analytical methods and numerical simulations to study P-P and P-S reflection coefficients, and results suggest that dispersion and anisotropy should not be neglected in AVO analysis. Indeed, for class I AVO reservoirs, the reflection magnitude of P-wave increases with frequency, while the responses of class II AVO reservoirs suggest that phase reversal occurs as frequency increases positively. In the case of class III AVO reservoirs, reflection magnitude decreases as frequency increases positively, while in the offset domain, the presence of anisotropy can distort or even reverse AVO responses. Thus, when compared to reflection coefficients for P-wave, reflection magnitude features of S-wave are more complex. The frequency-dependent AVO responses reported in this study provide insights for the interpretation of seismic anomalies in vertical transverse isotropy (VTI) dispersive reservoirs.