Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion

A joint estimation of petrophysical properties is proposed that combines statistical rock physics and Bayesian seismic inversion. Because elastic attributes are correlated with petrophysical variables (effective porosity, clay content, and water saturation) and this physical link is associated with uncertainties, the petro-physical-properties estimation from seismic data can be seen as a Bayesian inversion problem. The purpose of this work was to develop a strategy for estimating the probability distributions of petrophysical parameters and litho-fluid classes from seismics. Estimation of reservoir properties and the associated uncertainty was performed in three steps: linearized seismic inversion to estimate the probabilities of elastic parameters, probabilistic upscaling to include the scale-changes effect, and petrophysical inversion to estimate the probabilities of petrophysical variables and litho-fluid classes. Rock-physics equations provide the linkbetween reservoir properties and velocities, and linearized seismic modeling connects velocities and density to seismic amplitude. A full Bayesian approach was adopted to propagate uncertainty from seismics to petrophysics in an integrated framework that takes into account different sources of uncertainty: heterogeneity of the real data, approximation of physical models, measurement errors, and scale changes. The method has been tested, as a feasibility step, on real well data and synthetic seismic data to show reliable propagation of the uncertainty through the three different steps and to compare two statistical approaches: parametric and nonparametric. Application to a real reservoir study (including data from two wells and partially stacked seismic volumes) has provided as a main result the probability densities of petrophysical properties and litho-fluid classes. It demonstrated the applicability of the proposed inversion method.