Correlations of inclusion-based rock-physics model inputs from Bayesian analysis

Abstract

AbstractFor any given rock-physics model, knowledge of correlations among its inputs helps to define geologically and physically meaningful and informed models for a given problem. These informed models can, in turn, reduce the uncertainty in forward and inverse problems. We use a Bayesian framework to identify such correlations among inputs of two rock-physics models. That framework makes use of velocity and porosity measurements on both dry and brine-saturated carbonate samples. Two inclusion-based rock-physics models, the self-consistent approximation and the differential effective medium model, are analyzed along with these data to identify the underlying correlations. To do so, the posterior distribution must be evaluated, which is based on a prior model and the calculated likelihood function. Exhaustive sampling of the posterior is convenient in this case because relatively few input parameters to consider. Results are multi-variate histograms that indicate maximum a posteriori values of the inputs. Correlations among the inputs become evident when the Bayesian analysis is repeated many times with different prior models. These correlated values provide the inputs to optimized maximum a posteriori models. The correlations identified for the two rock-physics models under study should be used in relevant applications. Finally, all rock-physics models, along with an appropriate data set, should be examined in a similar Bayesian framework.