Title: A new universal model explaining fracture-trace length distributions

Michael Krumbholz1, Christoph Hieronymus2, Jochen Kamm3

1Independent Researcher, Germany; 2Department of Earth Sciences, Uppsala University, Sweden; 3Geological Survey of Finland, Espoo, Finland

Event: GeoKarlsruhe 2021

Date: 2021

DOI: 10.48380/dggv-xxn5-7178

Fracture dimensions largely control rock properties like strength and permeability. Thus, knowing their statistical distributions is of great importance in many applied fields of the geosciences e.g., in geothermics, mineral exploration, and hydrology. They are also of academic interest since the statistical distribution of fracture dimensions (length, height, width) might provide inside in fracture formation mechanisms.

However, in the vast majority of cases this information is derived from observations in 2 dimensions, i.e., instead of a fractures length, not the true length, but a fractures-trace length (FTL) is measured. In conclusion information or even estimates about the length of an individual fracture and about the statistical distribution of fracture lengths of a fracture population are not possible.

We analyze the statistical distributions of FTLs mapped at 3 different scales under the application of different mapping schemes that are commonly used to account for the limitations that are unavoidable, when recording fracture lengths in 2 dimensions.

In our study we test how well powerlaw-, exponential-, Weibull-, lognormal-, and log-logistic distributions fit the FTL data. Our results show that FTLs are lognormal distributed independent of scale and mapping scheme and that the parameters of the lognormal distributions reflect outcrop quality and dimension.

In addition, we provide a comprehensive model that explains the observed lognormal distributions of FTLs. This model is based on random restrictions that control the observable FTLs and includes human error and bias in mapping.

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