ELECTRICAL RESISTIVITY PARAMETER ESTIMATION AND MODEL APPRAISAL USING BAYESIAN INFERENCE

Electrical resistivity data are often acquired to provide non-invasive information about subsurface structural and hydrogeologic properties. Interpretation of resistivity data is typically accomplished with traditional least-squares inversion techniques, which produce a single “best” resistivity model given the available data. In reality, however, there are many models that fit the measured data within acceptable error bounds due to the ill-posed and non-unique nature of the inverse problem. Without strong prior information to favor one model over another, all models that fit the data must be considered plausible. Additionally, the ultimate goal is typically not just a resistivity model, but rather the answer to a (hydro)geologic question such as: What is the depth to the bottom of an aquifer?, or How well do the measured data constrain estimates of near-surface properties?

To address these issues, a Bayesian Markov Chain Monte Carlo (MCMC) strategy is implemented to estimate the posterior distribution of models that fit the measured data. Analysis of this ensemble of acceptable models provides valuable information about likely parameter values, non-uniqueness, correlation, and uncertainty. Although computationally expensive, the algorithm is relatively straightforward in that it requires many evaluations of the forward problem (i.e., predicting data for a given model), and is therefore easily adapted to a wide variety of parameter estimation problems. This work is based primarily on the analysis of one-dimensional (1D) soundings that are stitched together in order to analyze two-dimensional (2D) datasets, although an approach for directly estimating 2D models is also proposed. A measure of model simplicity is incorporated by allowing the number of layers in the model to be a free parameter, but favoring models with fewer layers.