Fracture Networks: Second-order Characterization from Outcrops.

Francois Bonneau and Dietrich Stoyan. ( 2020 )
in: 2020 RING Meeting, ASGA

Abstract

Fracture networks (FN) are systems of complex mechanical discontinuities that dramaticallyimpact the physical behaviour of rocks. Their statistical characterization is an important first stepof stochastic modelling. 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 beconsidered as planar sections through three-dimensional FN. For the corresponding planar FNthere exist well elaborated statistical methods that yield first-order characteristics such as fracturedensity or fracture length distributions. Using ideas from stochastic geometry, in particular thetheory of fibre processes and marked point processes, we develop second-order characteristics calledpair correlation function and mark correlation function, which describe the variability of planar FNand their inner spatial correlations. Surprisingly, one of these characteristics is closely related tocharacteristics used in statistics of fractals applied to FN. We demonstrate the application of our ideas by field outcrops already published in the literature.

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BibTeX Reference

@INPROCEEDINGS{BONNEAU_STOYAN_RM2020,
    author = { Bonneau, Francois and Stoyan, Dietrich },
     title = { Fracture Networks: Second-order Characterization from Outcrops. },
 booktitle = { 2020 RING Meeting },
      year = { 2020 },
 publisher = { ASGA },
  abstract = { Fracture networks (FN) are systems of complex mechanical discontinuities that dramaticallyimpact the physical behaviour of rocks. Their statistical characterization is an important first stepof stochastic modelling. 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 beconsidered as planar sections through three-dimensional FN. For the corresponding planar FNthere exist well elaborated statistical methods that yield first-order characteristics such as fracturedensity or fracture length distributions. Using ideas from stochastic geometry, in particular thetheory of fibre processes and marked point processes, we develop second-order characteristics calledpair correlation function and mark correlation function, which describe the variability of planar FNand their inner spatial correlations. Surprisingly, one of these characteristics is closely related tocharacteristics used in statistics of fractals applied to FN. We demonstrate the application of our ideas by field outcrops already published in the literature. }
}