Bayesian inversion of azimuthal seismic amplitude data for indicators of interconnected aligned cracks

Huaizhen Chen, Kristopher A. Innanen

Detection of natural fractures and identification of infilling fluids in fractures are important objectives in exploration and characterization of unconventional reservoirs (e.g. shale or tight sand reservoirs). In the case of rocks containing interconnected aligned fractures, both anisotropy and attenuation appears in reflected amplitudes of seismic wave. Starting with an effective model of interconnected aligned fractures in an elastic and isotropic background, we first present simplified complex stiffness parameters as a function of attenuation factor 1/Q in an attenuative anisotropic medium, and perturbations in stiffness parameters across an interface separating two attenuative anisotropic media. Using an approximate relationship between reflection coefficient and scattering potentials, we derive a linearized complex PP-wave reflection coefficient in terms of reflectivities of P- and S-wave moduli and density and changes in the tangential fracture weakness delta_mathrm{T} and attenuation factor 1/Q, which provides a possibility to estimate fracture weakness and attenuation factor from reflection amplitudes. Based on the derived reflection coefficient, we propose an inversion approach of employing real and imaginary parts of complex seismic data in frequency domain for estimating unknown parameters following a Bayesian framework. Applying the inversion approach to frequency-dependent synthetic seismic datasets of different incidence and azimuthal angles, we may obtain the inverted tangential fracture weakness that can match the true value, and the attenuation factor can be estimated reliably even though the estimation should be improved at the location of fractured reservoir. Future work should focus on the illustration of stability and robustness of the proposed inversion approach and the verification of reliability of the approach using real datasets.