Nonlinear pre-stack inversion of anisotropy parameters and effective pressure driven by petrophysical modeling

Linear inversion techniques and simplified petrophysical models are commonly used to estimate pressure in shale reservoirs, but the complex petrophysics of fractured shale under deep pressure conditions remains poorly understood, particularly regarding the partial connectivity of pores and the influence of effective pressure on pore structures—factors often overlooked in conventional models. Additionally, achieving stable multi-parameter inversion in fractured shale reservoirs remains a significant challenge. To address these issues, this study presents a novel anisotropic petrophysical model to establish a quantitative relationship between effective pressure and elastic moduli of vertical transverse isotropy (VTI) properties of fractured reservoirs. Furthermore, an accurate PP-wave reflection coefficient equation for VTI media, incorporating effective pressure, is derived to enhance reflection coefficient accuracy while accommodating complex geological variations. Building on a convolutional neural network, a petrophysics- and seismic-driven pre-stack nonlinear inversion algorithm is developed to estimate effective pressure and fracture parameters. Synthetic and field data examples demonstrate that, compared with the Markov chain Monte Carlo (MCMC) nonlinear optimization algorithm, the proposed algorithm is stable and accurate, significantly improving effective pressure predictions in deep shale reservoirs. This study provides a novel theoretical framework and technical approach for deep shale gas exploration and development, paving the way for more precise reservoir parameter inversion and comprehensive hydrocarbon reservoir evaluation.