Speaker: Francois Bonneau
Date: Thursday 3rd of December, 1:20 pm and Thursday 10th of December, 1:20 pm.
Abstract:
Fracture networks (FN) are systems of complex mechanical discontinuities that dramatically impact the physical behavior of rocks. Their statistical characterization is an important first step of stochastic modeling. It is, however, a big challenge because field data are sparse and incomplete. Field observations present several biases due to sampling (censoring, truncation, orientation). The present paper concentrates on the statistical analysis of outcrops, which often may be considered as planar sections through three-dimensional FN. For the corresponding planar FN there exist well-elaborated statistical methods that yield first-order characteristics such as fracture density or fracture length distributions. Using ideas from stochastic geometry, in particular the theory of fiber processes and marked point processes, we develop second-order characteristics called pair correlation function and mark correlation function, which describe the variability of planar FN and their inner spatial correlations. Surprisingly, one of these characteristics is closely related to characteristics used in statistics of fractals applied to FN. We demonstrate the application of our ideas by field outcrops already published in the literature.