Azimuthal PP and PS seismic amplitude variation with angle inversion for orthogonal fracture weaknesses
Huaizhen Chen, Kristopher A. H. Innanen
Characterization of fracture connectivity is an important task in detection of fractures in hydrocarbon reservoirs. The current reflection coefficients are mainly derived under the assumption of horizontal or tilted transversely isotropic (HTI or TTI) media for a rock containing a single set of aligned fractures. Driven by an effective model for the case of two sets of orthogonal fractures in an isotropic background, we first express and simplify stiffness parameters in terms of two sets of normal and tangential fracture weaknesses. In the case of a reflection interface separating an isotropic medium and a medium that contains two sets of orthogonal fractures, we present the approximate perturbations in stiffness parameters, which are utilized for the derivation of PP- and PS-wave linearized reflection coefficients. Using the derived PP- and PS-wave reflection coefficients, we establish an inversion approach of joint azimuthal PP- and PS-wave amplitudes variation with incidence angle (AVA) to estimate the normal and tangential fracture weaknesses. In the inversion approach, the least-squares algorithm and Bayesian Markov chain Monte Carlo (MCMC) method are combined, and initial models of fracture weaknesses are built using results of anisotropic AVA gradient. We apply the proposed inversion approach to synthetic seismic data of different signal-to-noise ratios (SNR), and the established inversion approach can provide more accurate normal and tangential fracture weaknesses than the conventional least-squares algorithm even in the case of SNR of 2. Applying the inversion approach to real datasets of PP and PS waves, we obtain reliable results of fracture weaknesses that can match well log curve of velocity and anisotropic AVA gradient, which may provide the possibility to characterize how fractures distribute and to estimate fracture connectivity in hydrocarbon reservoirs.