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

Healy, David; Jupp, Peter

doi:https://doi.org/10.5194/se-9-1051-2018

Articles | Volume 9, issue 4

https://doi.org/10.5194/se-9-1051-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/se-9-1051-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 9, issue 4

Research article

|

22 Aug 2018

Research article |

| 22 Aug 2018

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

David Healy and Peter Jupp

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Final revised paper (published on 22 Aug 2018)
Preprint (discussion started on 02 May 2018)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'reviewer comments', Anonymous Referee #1, 11 Jun 2018
- AC1: 'Response to Referee #1', David Healy, 09 Jul 2018
RC2: 'Review of: “Bimodal or quadrimodal? ….” By Healy & Jupp', Anonymous Referee #2, 11 Jun 2018
- AC2: 'Response to Referee #2', David Healy, 09 Jul 2018

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by David Healy on behalf of the Authors (09 Jul 2018) Author's response

ED: Referee Nomination & Report Request started (10 Jul 2018) by Federico Rossetti

RR by Nigel Woodcock (16 Jul 2018)

Suggestions for revision or reasons for rejection

This is a short, straightforward paper addressing an important issue in structural geology. The statistical tests derived here should be of wide interest and applicability.
My maths is too rusty to follow all the details of the statistical treatment. What I can follow looks right and the results are qualitatively sensible.
My only comments on the paper concern nomenclature of the patterns of poles to faults. I realise that the nomenclature is the published one of Healy et al. (2016) but the comments still need consideration.
The issues arise in lines 43 to 72 and in Figure 1.
a) The term ‘bilateral’ is used without definition in line 72, presumably to mean a pattern that is bilaterally symmetrical about one or more of the principal planes of the distribution. The issue is that all the illustrated ideal patterns are bilaterally symmetric about all the three principal planes, so ‘bilateral’ doesn’t seem to discriminate any one pattern.
b) The term ‘polymodal’ is applied to a pattern that is actually bimodal, with each mode dispersed along a small circle about sigma1. Another term, like ‘dispersed bimodal’ seems more accurate.
c) The term ‘orthorhombic’ is being equated to the ‘polymodal’ pattern only? Actually all the illustrated ideal patterns have orthorhombic symmetry, as they must have if they have three orthogonal mirror planes.
I suppose the central point is that the number of modes in a distribution is unrelated to its symmetry. A distribution needs both descriptors to specify it. So distributions could be bimodal and monoclinic, or polymodal and triclinic, or many other variants. Your statistical method (I think) only applies to orthorhombic distributions and maybe this should be stated up front.
This lack of clarity might cause confusion in the future literature?

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RR by Atilla Aydin (01 Aug 2018)

ED: Publish subject to minor revisions (review by editor) (03 Aug 2018) by Federico Rossetti

AR by David Healy on behalf of the Authors (06 Aug 2018) Author's response Manuscript

ED: Publish as is (07 Aug 2018) by Federico Rossetti

ED: Publish as is (07 Aug 2018) by Federico Rossetti (Executive editor)

AR by David Healy on behalf of the Authors (08 Aug 2018) Manuscript

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.