A rock physics model for geophysical inversion in critical zone studies

Abstract The estimation of petrophysical properties, such as porosity and water saturation, from geophysical data through rock physics–based inversion is crucial for understanding groundwater and weathering processes in the critical zone (CZ). A unified rock physics model is developed to map porosity and water saturation to P- and S-wave velocities obtained from seismic data. The rock physics model is based on an exponential function whose parameters control the velocity values at the minimum and maximum porosity, as well as the rate at which velocity decreases with increasing porosity. The model incorporates Gassmann’s equation to account for partial saturation conditions. Unlike traditional rock physics models that apply only to specific geological settings, the new formulation accurately captures velocity changes in the near surface as materials transition from disaggregated sediments to fractured zones and ultimately to more coherent bedrock with depth, under fully saturated, partially saturated, and unsaturated conditions. By introducing Archie’s equation, the framework also models resistivity, allowing the integration of elastic and electrical rock physics relationships for an improved petrophysical characterization of the critical zone. Based on the proposed rock physics model, a Bayesian inversion workflow is developed to estimate porosity and water saturation from seismic velocity and electrical resistivity data. The inversion method provides probabilistic estimates of the petrophysical properties, accounting for measurement uncertainty and prior information. The rock physics model and the Bayesian inversion are applied to a field dataset from the Laramie Range, predicting porosity and water saturation from geophysical measurements. The method provides accurate spatial models of petrophysical data to inform hydrological analysis in the CZ and it enables data-driven characterization of weathered and fractured near-surface rocks.