Statistical Modelling 2 (2002), 217234
Size distribution of geological faults: Model choice and parameter estimation
Hilde Grude Borgos,
Department of Mathematical Sciences, Norwegian University of Sciences
and Technology,
Trondheim,
Norway
Address for correspondence: Schlumberger Stavanger Research, P.O. Box
8013, N-4068 Stavanger
Henning Omre,
Department of Mathematical Sciences, Norwegian University of Sciences
and Technology,
Trondheim,
Norway
Chris Townsend,
Statoil R&D Centre,
Trondheim,
Norway
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 distribution 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.
Keywords:
Bayes factor; geological faults; MCMC sampling; pseudoprior
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