Hierarchical inversion of brittleness indicator and fracture parameters for shale gas reservoirs with tilted transverse isotropy

Subsurface formations with aligned dipping fractures can be equivalent to the media with tilted transverse isotropy (TTI). For TTI-type organic-rich shale gas reservoirs, the Young's modulus is not a sensitive brittleness indicator as a low value may emerge at a high degree of brittleness. Therefore, a hierarchical seismic inversion method is proposed to directly predict the brittleness and fracture parameters of TTI-type organic-rich shale gas reservoirs. We derive a linearized P-wave reflection coefficient equation for TTI media in terms of a new brittleness indicator formulated as the function of the Young's modulus and Lamé constant (λ), fracture density and fracture dip. The reflection coefficient equation is rewritten in the form of the Fourier series to separate fracture information from background matrix information. Based on the Bayesian framework, the hierarchical inversion method is established to predict brittleness indicator and fracture parameters. The process is composed of three steps. Firstly, we utilize the discrete Fourier series to decouple the isotropic (zero-order) and anisotropic (second-order) components of azimuthal seismic data. Secondly, we invert fracture density and fracture dip from the second-order component of azimuthal data. Thirdly, the brittleness indicator can be estimated using the zero-order component. The model test and practical application indicate the robustness of the method and credible prediction of high-quality brittle reservoirs.