Rock-physics stochastic inversion with the first-order difference approximation model

Reservoir petrophysical properties include porosity, clay content, water saturation that describe the physical properties of formations. However, rock-physics-based petrophysical inversion is challenged by the lack of reliable initial petrophysical properties model and the relatively complex overall expressions of rock-physics models. To address these limitations, we propose a rock-physics-driven stochastic inversion method for petrophysical properties estimation. First, a first-order difference approximation method is employed to simplify the rock-physics model. Using pre-stack seismic inverted elastic parameters (P-wave velocity, S-wave velocity, and density), the generalized inverse of the difference matrix is solved to construct high-quality initial petrophysical models, which enhances inversion stability and efficiency. Then, a stochastic inversion algorithm with variable sampling space is adopted to further improve the accuracy of petrophysical properties. Field application on a Southwest China gas reservoir demonstrates that the proposed method achieves efficient and robust petrophysical characterization. The core novelty lies in establishing initial models for rock-physics stochastic inversion through first-order difference rock-physics model simplification, which resolves the initial model deficiency of rock-physics inversion and effectively improves computational efficiency.