Correlations of Rock-Physics Model Parameters From Bayesian Analysis: Pressure- and Porosity-Dependent Models Applied to Unconsolidated Sands

Abstract

Correlations of rock-physics model inputs are important to know to help design informative prior models within integrated reservoir-characterization workflows. A Bayesian framework is optimal to determine such correlations. Within that framework, we use velocity and porosity measurements on unconsolidated, dry, and clean sands. Three pressure- and three porosity-dependent rock-physics models are applied to the data to examine relationships among the inputs. As with any Bayesian formulation, we define a prior model and calculate the likelihood in order to evaluate the posterior. With relatively few inputs to consider for each rock-physics model, we found that sampling the posterior exhaustively to be convenient. The results of the Bayesian analyses are multivariate histograms that indicate most likely values of the input parameters given the data to which the rock-physics model was fit. When the Bayesian procedure is repeated many times for the same data, but with different prior models, correlations emerged among the input parameters in a rock-physics model. These correlations were not known previously. Implications, for the pressure- and porosity-dependent models examined here, are that these correlations should be utilized when applying these models to other relevant data sets. Furthermore, additional rock-physics models should be examined similarly to determine any potential correlations in their inputs. These correlations can then be taken advantage of in forward and inverse problems posed in reservoir characterization.