Abstract Reservoir properties inversion is essential for seismic characterization in shale reservoirs, facilitating the comprehensive evaluation of geological and engineering sweet spots. However, inversion methods assuming isotropic media are limited in accurately characterizing anisotropic shale reservoirs. Assuming the transversely isotropic with a horizontal symmetry axis (HTI) media, a reflectivity equation incorporating P-wave modulus and S-wave modulus, density, normal fracture weakness, and tangential fracture weakness is first introduced by integrating the linear-slip theory and Nur's critical porosity model. Due to the complex nature of the rock physics relationships between elastic parameters and reservoir properties, it is challenging to directly characterize reservoir properties. To address this, we apply a first-order Taylor approximation to linearize the rock physics relationships. By combining the linearized equations, a novel anisotropic reflection coefficient equation is derived, which accounts for porosity, clay content, water saturation, normal fracture weakness, and tangential fracture weakness. The accuracy comparison and contribution analysis confirm the validity and precision of equation simplification and derivation. To tackle the ill-posed nature of the proposal distribution in traditional Markov chain Monte Carlo (MCMC) algorithm and to assess inversion uncertainty, an innovative adaptive proposal differential evolution MCMC (APDE-MCMC) algorithm is proposed. The algorithm enhances sampling efficiency and uncertainty quantification by combining adaptive proposal (AP) and differential evolution (DE) strategies. The AP component adaptively updates the proposal covariance based on accepted samples, while the DE component generates new candidates using evolutionary operations. The integration of the novel reflectivity equation with the APDE-MCMC algorithm enables direct seismic inversion of reservoir properties for anisotropic media. Applications to both synthetic and field seismic data demonstrate the effectiveness of the proposed method in shale reservoir characterization.
Zuo et al. (Wed,) studied this question.