A single-step Bayesian petrophysical inversion algorithm based on a petrophysical reformulation of the P-wave reflection coefficients

We implement a fast, single-step, Bayesian inversion algorithm that directly infers the relevant petrophysical properties from seismic data, and we demonstrate its applicability on 3D onshore seismic data for the characterization of a clastic, gas-depleted, reservoir. First, a linear rock-physics model (RPM) derived from well log data by means of a stepwise regression, is used to relate the petrophysical properties of interest to the elastic parameters. Then, the linear RPM is used to rewrite the time-continuous P-wave reflectivity equation as a function of the petrophysical contrasts instead of elastic constants. This reformulation allows us to derive, in a single-step inversion, the petrophysical properties of interest around the target zone from pre-stack seismic data. The inversion is casted in a Bayesian framework and the error in the seismic data, the uncertainties in the RPM and the uncertainties related to the different scale of well log data (used to derive the RPM) and seismic data (the input of the inversion) are propagated into the final estimated petrophysical properties. Results on 3D data from a gas-sand reservoir and blind tests prove the application and the reliability of the method.