Direct seismic inversion of reservoir properties for anisotropic media with the APDE-MCMC algorithm

ABSTRACT Inversion of reservoir properties is essential for seismic characterization in shale reservoirs, facilitating the comprehensive evaluation of geologic and engineering sweet spots. However, inversion methods that assume isotropic media are limited in accurately characterizing anisotropic shale reservoirs. Assuming a transversely isotropic medium with a horizontal symmetry axis, a reflectivity equation incorporating P-wave modulus, S-wave modulus, density, normal fracture weakness, and tangential fracture weakness was 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 was challenging to directly characterize reservoir properties. To address this, a first-order Taylor approximation was applied to linearize the rock-physics relationships. By combining the linearized equations, a novel anisotropic reflection coefficient equation was derived, which accounts for porosity, clay content, water saturation, normal fracture weakness, and tangential fracture weakness. The accuracy comparison and contribution analysis confirmed 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 was proposed. The algorithm enhanced sampling efficiency and uncertainty quantification by combining adaptive proposal (AP) and differential evolution (DE) strategies. The AP component adaptively updated the proposal covariance based on accepted samples, whereas the DE component generated new candidates using evolutionary operations. The integration of the novel reflectivity equation with the APDE-MCMC algorithm enabled direct seismic inversion of reservoir properties for anisotropic media. Applications to synthetic and field seismic data demonstrated the effectiveness of the proposed method in shale reservoir characterization.