Bayesian AVAZ inversion with model constraint for fracture weaknesses
Azimuthal elastic inversion (AVO/AVA analysis) has a large potential for fracture characterization in the productive fractured strata of the shale gas and oil reservoirs. «Looseness» of the geological medium, caused by fracturing, including normal and tangential looseness, in accordance with «theory of surfaces with a linear slip» is a bridge between the seismic data and fracture characteristics. However, stability of the azimuthal elastic inversion methods for assessment of the anisotropy parameters and/or fracturing parameters using seismic data is debatable. This study explores an amplitude variation with incident angle and azimuth (AVAZ) inversion approach with model constraint for fracture weaknesses in Bayesian inversion scheme. Based on perturbation theory and stable phase approximation, the fracture medium can be considered as the superimposition of background medium and perturbation medium, and then the seismic scattering coefficient of fracture media can be derived. This equation establishes the relationship between seismic data and fracture weakness together with elastic parameters like P-wave and S-wave moduli and weaknesses. With this equation, an inversion approach in Bayesian scheme is proposed. This method implements the estimation of P-wave modulus, S-wave modulus, density, normal weakness and tangential weakness simultaneously. And the constraint from initial model enhances the stability of this method. In this approach, Gaussian and Cauchy distributions are explored for the likelihood and a priori probability distributions, respectively.