A bayesian approach to inclusion based rock physics modeling with multiple statistical ensembles

A statistics-based approach to rock physics often includes the calculation of a series of simulations to fit data along with probability associated with the modeling to characterize uncertainty. We present a Bayesian approach to determine the most probable rock-physics model (e.g., inclusion- based models). Our results also feature combinations of highly probable model inputs from posterior distributions; these combinations result from using many different sets of input values from a prior distribution where each set corresponds to an ensemble. Exhaustive sampling allows for the calculation of the full posterior distribution for each ensemble. We demonstrate this method using two inclusion-based rock-physics models, the self-consistent and differential effective medium models, along with measurements from a carbonate rock data set. Results indicate that the latter of the two models is the most probable. Analyses of the underlying model inputs indicate multiple but distinct clusters among those inputs. The problem is computationally demanding and requires parallel computation for tractability. Results from this work are applicable to data sets with similar velocity-porosity trends. More generally, the method is applicable to any other data set and relevant models of interest.