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The use of topology in fracture network characterization

The use of topology in fracture network characterization
The use of topology in fracture network characterization
In two-dimensions, a fracture network consist of a system of branches and nodes that can be used to define both geometrical features, such as length and orientation, and the relationship between elements of the network – topology. Branch lengths are preferred to trace lengths as they can be uniquely defined, have less censoring and are more clustered around a mean value. Many important properties of networks are more related to topology than geometry.

The proportions of isolated (I), abutting (Y) and crossing (X) nodes provide a basis for describing the topology that can be easily applied, even with limited access to the network as a whole. Node counting also provides an unbiased estimate of frequency and can be used in conjunction with fracture intensity to estimate the characteristic length and dimensionless intensity of the fractures. The nodes can be used to classify branches into three types – those with two I-nodes, one I-node and no I-nodes (or two connected nodes). The average number of connections per branch provides a measure of connectivity that is almost completely independent of the topology. We briefly discuss the extension of topological concepts to 3-dimensions.
Fracture, Network, Topology, Geometry
0191-8141
55-66
Sanderson, D.J.
5653bc11-b905-4985-8c16-c655b2170ba9
Nixon, C.W.
757fe329-f10f-4744-a28e-0ccc92217554
Sanderson, D.J.
5653bc11-b905-4985-8c16-c655b2170ba9
Nixon, C.W.
757fe329-f10f-4744-a28e-0ccc92217554

Sanderson, D.J. and Nixon, C.W. (2015) The use of topology in fracture network characterization. Journal of Structural Geology, 72, 55-66. (doi:10.1016/j.jsg.2015.01.005).

Record type: Article

Abstract

In two-dimensions, a fracture network consist of a system of branches and nodes that can be used to define both geometrical features, such as length and orientation, and the relationship between elements of the network – topology. Branch lengths are preferred to trace lengths as they can be uniquely defined, have less censoring and are more clustered around a mean value. Many important properties of networks are more related to topology than geometry.

The proportions of isolated (I), abutting (Y) and crossing (X) nodes provide a basis for describing the topology that can be easily applied, even with limited access to the network as a whole. Node counting also provides an unbiased estimate of frequency and can be used in conjunction with fracture intensity to estimate the characteristic length and dimensionless intensity of the fractures. The nodes can be used to classify branches into three types – those with two I-nodes, one I-node and no I-nodes (or two connected nodes). The average number of connections per branch provides a measure of connectivity that is almost completely independent of the topology. We briefly discuss the extension of topological concepts to 3-dimensions.

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More information

Published date: March 2015
Keywords: Fracture, Network, Topology, Geometry
Organisations: Geology & Geophysics, Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 375431
URI: http://eprints.soton.ac.uk/id/eprint/375431
ISSN: 0191-8141
PURE UUID: 67479eb4-4345-4a16-a6d1-ad41f56f1cb3
ORCID for D.J. Sanderson: ORCID iD orcid.org/0000-0002-2144-3527

Catalogue record

Date deposited: 24 Mar 2015 13:30
Last modified: 10 Dec 2019 01:41

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