Three-Dimensional Joint Bayesian Inversion of Hydrothermal Data Using Automatic Differentiation

Abstract

We have developed a Bayesian inverse modeling tool for the joint inversion of hydraulic and thermal data. It is based on a well-known and well-tested forward modeling code, which solves the coupled steady state equations for heat and mass transfer. Because of the heat and pressure dependence of most petrophysical properties, this is a nonlinear problem. Different nonlinearities of petrophysical properties and pore-space models can be employed. The forward code was automatically differentiated to obtain partial derivative information. This information was used in several optimization schemes (Gauss-Newton, Quasi-Newton, Nonlinear Conjugate Gradients) to find the minimum of the Bayesian objective function. In addi-tion to the optimum model, the Bayesian approach supplies linear estimates of posterior covariances and related measures of uncertainty. We will present several instructive synthetic investigation demon-strating the power of the approach. Additionally, sensitivites and their use for the optimization of ex-perimental design are discussed.