Bayesian Analysis to Determine Relative Significance of Inputs of a Rock-Physics Model

Rock-physics models relate rock properties to elastic properties through non-unique relationships and often in the presence of seismic data that contain significant noise. A set of inputs define the rock-physics model, and any errors in that model map directly into uncertainty in target seismic-scale amplitudes, velocities, or inverted impedances. An important aspect of using rock-physics models in this manner is to determine and understand the significance of the inputs into a rock-physics model under consideration. Such analysis enables the design of prior distributions that are informative within a reservoir-characterization formulation. We use the framework of Bayesian analysis to find internal dependencies and correlations among the inputs. This process requires the assignments of prior distributions, calculation of the likelihood function, whose product is the posterior distribution. The data are well-log data that come from a hydrocarbon-bearing set of sands from the Gulf of Mexico. The rock-physics model selected is the soft-sand model, which is applicable to the data from the reservoir sands. Results from the Bayesian algorithm are multivariate histograms that demonstrate the most frequent values of the inputs given the data. Four analyses are applied to different subsets of the reservoir sands, and each reveals some correlations among certain model inputs. This quantitative approach points out the significance of a singular or joint set of rock-physics model parameters.