Accurate estimation of permeability (κ) and gas saturation (Sg) is critical for identifying productive intervals in volcanic reservoirs, yet severe heterogeneity in rock matrix and fluid distribution poses significant challenges to reliable prediction. This study presents a physics-based seismic petrophysical inversion framework that integrates log-scale rock physics modeling with seismic-scale stochastic nonlinear inversion to quantitatively estimate κ and Sg. A rock physics model is formulated with a parameter α that modulates the permeability-dependent effective fluid modulus (Kf), providing a physically interpretable mechanism that allows Kf to vary continuously between relaxed and unrelaxed fluid mixing regimes. The parameter α is estimated from well logs using a model-based approach, and its strong correlation with κ demonstrates its utility as a permeability proxy. Two seismic indicators, Iα and IG, are derived from rock physics relationships linking α and fluid properties to κ and Sg measurements. The calibrated rock physics regressions provide quantitative estimates of κ and Sg from Iα and IG. A PP-wave reflectivity formulation parameterized by Iα and IG is derived, benchmarked against conventional expressions, and incorporated into the stochastic nonlinear inversion scheme to retrieve Iα and IG from seismic data. Synthetic tests confirm the robustness and accuracy of the proposed approach. For field data applications, stratigraphic complexity is addressed through seismic waveform-constrained prior construction, enabling reliable inversion of Iα and IG, which are then converted into κ and Sg via calibrated regressions. This framework provides a physics-based strategy for quantitative characterization of permeability and gas saturation in complex volcanic formations.
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