Abstract: Hydrocarbon recovery or CO₂ geosequestration alters reservoir properties, e.g. fluid saturation, pore pressure, and porosity. These changes manifest as time-lapse seismic responses. By integrating rock physics inversion with seismic inversion, we can effectively resolve these reservoir parameters from seismic data. However, rock physics inversion is inherently nonlinear. Furthermore, the two-step approach, which first inverts for elastic parameters and then estimates reservoir properties, not only introduces intermediate variables but also leads to cascading errors. To address these issues, we linearize the rock physics model via a Taylor series expansion and then integrate it with seismic forward modeling. This integration yields an amplitude-variation-with-offset equation, parameterized by fluid saturation, pore pressure, and porosity, based on which a Cauchy-constrained reservoir inversion method is developed within the Bayesian framework. The validation against both synthetic and field data demonstrates that the proposed approach provides stable and accurate predictions of fluid saturation, porosity, and pore pressure.