Size distribution of geological faults: Model choice and parameter estimation

Abstract

Geological faults are important in reservoir characterization, since they influence fluid flow in the reservoir. Both the number of faults, or the fault intensity, and the fault sizes are of importance. Fault sizes are often represented by maximum displacements, which can be interpreted from seismic data. Owing to limitations in seismic resolution only faults of relatively large size can be observed, and the observations are biased. In order to make inference about the overall fault population, a proper model must be chosen for the fault size distribution. A fractal (Pareto) distribution is commonly used in geophysics literature, but the exponential distribution has also been suggested. In this work we compare the two models statistically. A Bayesian model is defined for the fault size distributions under the two competing models, where the prior distributions are given as the Pareto and the exponential pdfs, respectively, and the likelihood function describes the sampling errors associated with seismic fault observations. The Bayes factor is used as criterion for the model choice, and is estimated using MCMC sampling. The MCMC algorithm is constructed using pseudopriors to sample jointly the two models. The statistical procedure is applied to a fault size data set from the Gullfaks Field in the North Sea. For this data set we find that the fault sizes are best described by the exponential distribution.