Bayesian linearized amplitude variation with offset and azimuth inversion and uncertainty analysis in horizontal transversely isotropic media

The stratum can be modelled as a horizontal transversely isotropic medium when a single set of vertically parallel fractures embedded in an isotropic background medium, which facilitates efficient study for fractured reservoirs. Elastic parameters and fracture weaknesses are important parameters to describe the characteristics of fractured reservoirs, and seismic inversion plays a significant role in parameters estimation. The commonly used deterministic inversion methods do not fully utilize the prior information and fails to present the uncertainty analysis of inversion results. To address these shortcomings, we propose a Bayesian linearized amplitude variation with offset and azimuth inversion method tailored for horizontal transversely isotropic media, enabling a more robust analysis of uncertainty. Within the framework of Bayesian inversion, the proposed method successfully derives analytical expressions for the posterior mean and covariance of both elastic parameters and fracture weaknesses. The response characteristics of the anisotropic reflection coefficient are analysed, and it is found that the perturbations of elastic parameters have a greater effect on reflection coefficient compared to fracture weaknesses. Synthetic data examples confirm that the accuracy of estimated P- and S-wave velocities and density surpasses that of fracture weaknesses, and the proposed method still performs well for the case of moderate noise. A field data example demonstrates that the inverted profiles agree well with the logging curve, and the estimated fracture weaknesses display significantly high values in the reservoir area. The estimated reservoir parameters not only contribute to a more accurate representation of the fractured gas-bearing reservoir but also provide insights into the target gas reservoir through its posterior distribution. Both synthetic and field data examples demonstrate the stability and reliability of the proposed method in characterizing fractured reservoirs. We determine that the proposed method provides an available tool for nuanced evaluation of uncertainty for the inversion results, and it is helpful for the fine description of fractured hydrocarbon-bearing reservoirs.