Fracture Networks: Second-order Characterization from Oman and Hornelen outcrops

@inproceedings{BONNEAU_RM2021,
 abstract = { Fracture networks (FNs) are three-dimensional systems of complex mechanical discontinuities in rocks, which dramatically impact their physical behavior. Their statistical characterization is an important first step towards stochastic modeling and final understanding of FN. We concentrate on the statistical analysis of outcrops, which often may be considered as planar sections through three-dimensional FN. These outcrops offer two-dimensional information, and we speak also here about FN. For this planar case there exist established statistical methods which yield first-order or mean-value characteristics such as fracture density, fracture length distribution or rose of directions. We extend this situation by presenting a second-order theory, which aims to characterize the inner variability of planar FN. For this purpose we use ideas from the theory of marked point processes or object models, where the `points' are fracture or fracture branch centers and the marks lengths and strike azimuths. This leads to so-called pair correlation and mark correlation functions, which we recommend as new variability characteristics. In this context, we show that one of these characteristics is closely related to a classical characteristic used in statistics of fractals in the context of FN. The correlation functions are estimated for subsets of FN of similar orientation. We demonstrate the application of our ideas for the analysis of an artificial FN and two field outcrops already studied in the literature. It turns out that the orientation marks play a very important role. Structural differences are clearly characterized. },
 author = { Bonneau, Francois AND Stoyan, Dietrich },
 booktitle = { 2021 RING Meeting },
 publisher = { ASGA },
 title = { Fracture Networks: Second-order Characterization from Oman and Hornelen outcrops },
 year = { 2021 }
}