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Graph theory and the analysis of fracture networks

Graph theory and the analysis of fracture networks
Graph theory and the analysis of fracture networks
Two-dimensional exposures of fracture networks can be represented as large planar graphs that comprise a series of branches (B) representing the fracture traces and nodes (N) representing their terminations and linkages. The nodes and branches may link to form connected components (K), which may contain fracture-bounded regions (R) or blocks. The proportions of node types provide a basis for characterizing the topology of the network. The average degree <d> relates the number of branches (|B|) and nodes (|N|) and Euler's formula establishes a link between all four elements of the graph with |N| - |B| + |R| - |K| = 0. Treating a set of fractures as a graph returns the focus of description to the underlying relationships between the fractures and, hence, to the network rather that its constitutive elements. Graph theory provides a wide range of applicable theorems and well-tested algorithms that can be used in the analysis of fault and fracture systems. We discuss a range of applications to two-dimensional fracture and fault networks, and briefly discuss application to three-dimensions.
0191-8141
Sanderson, David J.
5653bc11-b905-4985-8c16-c655b2170ba9
Peacock, David C.P.
6a9e5a6a-445c-4412-8afa-053bcb1cc9cb
Nixon, Casey W.
757fe329-f10f-4744-a28e-0ccc92217554
Rotevatn, Atle
a5811643-0e5c-4b86-9145-54f5810fbe4c
Sanderson, David J.
5653bc11-b905-4985-8c16-c655b2170ba9
Peacock, David C.P.
6a9e5a6a-445c-4412-8afa-053bcb1cc9cb
Nixon, Casey W.
757fe329-f10f-4744-a28e-0ccc92217554
Rotevatn, Atle
a5811643-0e5c-4b86-9145-54f5810fbe4c

Sanderson, David J., Peacock, David C.P., Nixon, Casey W. and Rotevatn, Atle (2018) Graph theory and the analysis of fracture networks. Journal of Structural Geology. (doi:10.1016/j.jsg.2018.04.011).

Record type: Article

Abstract

Two-dimensional exposures of fracture networks can be represented as large planar graphs that comprise a series of branches (B) representing the fracture traces and nodes (N) representing their terminations and linkages. The nodes and branches may link to form connected components (K), which may contain fracture-bounded regions (R) or blocks. The proportions of node types provide a basis for characterizing the topology of the network. The average degree <d> relates the number of branches (|B|) and nodes (|N|) and Euler's formula establishes a link between all four elements of the graph with |N| - |B| + |R| - |K| = 0. Treating a set of fractures as a graph returns the focus of description to the underlying relationships between the fractures and, hence, to the network rather that its constitutive elements. Graph theory provides a wide range of applicable theorems and well-tested algorithms that can be used in the analysis of fault and fracture systems. We discuss a range of applications to two-dimensional fracture and fault networks, and briefly discuss application to three-dimensions.

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Accepted/In Press date: 13 April 2018
e-pub ahead of print date: 14 April 2018

Identifiers

Local EPrints ID: 421917
URI: http://eprints.soton.ac.uk/id/eprint/421917
ISSN: 0191-8141
PURE UUID: 68d92eb9-4c95-4982-8826-b3c4b6c44c38
ORCID for David J. Sanderson: ORCID iD orcid.org/0000-0002-2144-3527

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Date deposited: 09 Jul 2018 16:30
Last modified: 28 Apr 2022 04:43

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Contributors

Author: David C.P. Peacock
Author: Casey W. Nixon
Author: Atle Rotevatn

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