Direct petrophysical inversion of prestack seismic data using nonlinear Zoeppritz and rock-physics modeling via automatic differentiation

Abstract Rock-physics relations introduce strong nonlinearities into the mapping between reservoir properties and prestack seismic records. Conventional elastic-property-based twostep inversion workflows usually estimate elastic parameters first and then transform them into petrophysical parameters through rock-physics models. Such a sequential strategy is inherently susceptible to error propagation, especially when elastic inversion and rock-physics prediction are coupled through nonlinear relations. Although linearized direct inversion can partly reduce the error propagation associated with the two-step workflow, its accuracy remains limited by local linearizations of both seismic reflectivity and rock-physics relations, especially at large incidence angles or in strongly heterogeneous reservoirs. Moreover, explicit derivation of the resulting composite Jacobian is model-dependent and cumbersome. To address these limitations, this study develops a nonlinear direct petrophysical inversion framework based on automatic differentiation. The proposed method integrates the Zoeppritz equation with nonlinear rock-physics relations to construct a unified differentiable forward operator, which directly maps porosity, water saturation, and shale volume fraction to prestack seismic records. Automatic differentiation is used to calculate the gradients of the nested nonlinear forward operator, avoiding model-specific analytical Jacobian derivations and improving the flexibility of the inversion implementation. To improve the stability of multiparameter inversion, structure-guided regularization is further introduced to promote lateral continuity along geological structures while preserving sharp petrophysical contrasts across stratigraphic boundaries. Synthetic examples and a field application show that the proposed method improves the stability and geological consistency of petrophysical inversion, especially in terms of lateral continuity and preservation of major lithological and fluid-related boundaries.