Stochastic and Centrifuge Modelling of Jointed Rock. Volume 3. Stochastic andTopological Fracture Geometry Model

摘要

A hierarchical model is developed to represent the geometry of fracture sets. Themost important characteristics of this model are the possibility to model sequential fracture genesis as it usually occurs in nature, and to model clustering. This model uses the inhomogeneous or the doubly stochastic (Cox) point process model to represent the midpoints of the primary set. In a second step, the fracture trace lengths of the primary set are modelled. This is done using Maximum Likelihood Estimates (MLE) of the observed data. In a third step, the secondary set is considered; in particular the independence/dependence of the two sets. The correlation of location with trace length is considered with the line-kernel function methods and the nearest neighbor fiber distance method. The hierarchical model has been applied to two cases in which detailed fracture patterns have been observed, one with a single set and one with two sets. The validity of the model was checked by visual comparison between model prediction and mapped patterns and most importantly, by statistical tests such as the second-moment analysis and the Monte Carlo test. A satisfactory fit of the predicted pattern was obtained in both cases.