Bimodal or quadrimodal? Statistical tests for the shape of fault patterns
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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.
Healy , D & Jupp , P 2018 , ' Bimodal or quadrimodal? Statistical tests for the shape of fault patterns ' , Solid Earth , vol. 9 , no. 4 , pp. 1051-1060 . https://doi.org/10.5194/se-9-1051-2018
© Author(s) 2018. This work is distributed under the Creative Commons Attribution 4.0 License.
DescriptionDavid Healy gratefully acknowledges receipt of NERC grant NE/N003063/1 and thanks the School of Geosciences at the University of Aberdeen for accommodating a period of research study leave, during which time this paper was written.
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