Estimating the Trace Length Distribution of Fractures from Line Sampling Data

Abstract

This paper deals with the estimation of the length distribution of the set of traces induced by a fracture network along an outcrop. Because of field constraints (accessibility, visibility, censorship, etc…), all traces cannot be measured the same way. A measurement protocol is therefore introduced to systematize the sampling campaign. Of course, the estimation procedure must be based on this protocol so as to prevent any bias. Four parametric procedures are considered. Three of them (maximum likelihood, stochastic estimation-maximization and Bayesian estimation) are discussed and their performances are compared on 160 simulated data sets. They are finally applied to an actual data set of subvertical joints in limestone formations.