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Solid Earth An interactive open-access journal of the European Geosciences Union
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Volume 9, issue 4
Solid Earth, 9, 1051–1060, 2018
https://doi.org/10.5194/se-9-1051-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Solid Earth, 9, 1051–1060, 2018
https://doi.org/10.5194/se-9-1051-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 22 Aug 2018

Research article | 22 Aug 2018

Bimodal or quadrimodal? Statistical tests for the shape of fault patterns

David Healy1 and Peter Jupp2 David Healy and Peter Jupp
  • 1School of Geosciences, King's College, University of Aberdeen, Aberdeen AB24 3UE Scotland, UK
  • 2School of Mathematics & Statistics, University of St Andrews, St Andrews KY16 9SS Scotland, UK

Abstract. Natural fault patterns formed in response to a single tectonic event often display significant variation in their orientation distribution. The cause of this variation is the subject of some debate: it could be noise on underlying conjugate (or bimodal) fault patterns or it could be intrinsic signal from an underlying polymodal (e.g. quadrimodal) pattern. In this contribution, we present new statistical tests to assess the probability of a fault pattern having two (bimodal, or conjugate) or four (quadrimodal) underlying modes and orthorhombic symmetry. We use the eigenvalues of the second- and fourth-rank orientation tensors, derived from the direction cosines of the poles to the fault planes, as the basis for our tests. Using a combination of the existing fabric eigenvalue (or modified Flinn) plot and our new tests, we can discriminate reliably between bimodal (conjugate) and quadrimodal fault patterns. We validate our tests using synthetic fault orientation datasets constructed from multimodal Watson distributions and then assess six natural fault datasets from outcrops and earthquake focal plane solutions. We show that five out of six of these natural datasets are probably quadrimodal and orthorhombic. The tests have been implemented in the R language and a link is given to the authors' source code.

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Short summary
Fault patterns formed in response to a single tectonic event often display significant variation in their orientations. This variation could be noise on underlying conjugate (or bimodal) fault patterns or it could be intrinsic signal from an underlying polymodal (e.g. quadrimodal) pattern. We present new statistical tests and open source R code to calculate the probability of a fault pattern having two (bimodal, or conjugate) or four (quadrimodal) clusters based on their orientations.
Fault patterns formed in response to a single tectonic event often display significant variation...
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