Tesselations Stable under Iteration

In nature, fracture patterns occur in a great variety, arising from the coupling of a multitude of physical processes: tectonic deformation, volume changes accompanying diagenesis, temperature and/or internal fluid pressure fluctuations during burial, uplift and exhumation of brittle rocks with spatially highly variable properties. Fracture pattern modeling is therefore an interdisciplinary effort requiring an understanding of geological fracture mechanics and stochastic generating processes. While to date a number of stochastic models exist, classical models such as the Poisson line process lack the ability to reproduce features that are commonly seen in natural fracture patterns. This contribution presents a novel stochastic model based on tessellations stable under iteration also referred to as STIT. Such models naturally incorporate important features like fracture truncation and the possibility to extend their definition to arbitrary orientation distributions. Using statistical analysis we compare these novel geometries arising from STIT tessellations with classical DFN models and evaluate their applicability as a proxy for geological fault and fracture patterns. We also extend the standard STIT model to Fisher type distributions commonly used in the evaluation of orientation distributions of fractures in outcrops and fracture traces recovered from FMI logs. This allows us to apply the models to real world data sets such as the Kilve and Arches fracture outcrop data set. Download paper here