Robust estimators of palaeosecular variation


Suttie, Neil, Biggin, Andrew ORCID: 0000-0003-4164-5924 and Holme, Richard (2015) Robust estimators of palaeosecular variation. GEOPHYSICAL JOURNAL INTERNATIONAL, 200 (2). pp. 1044-1049.

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Abstract

The Fisher distribution is central to palaeomagnetism but presents several problems when used to characterize geomagnetic field directions as observed in sequences of volcanic rocks. First, it introduces a shallowing effect when used to define the mean of any group of directional unit vectors. This is problematic because it can suggest the presence of persistent non-axial dipole components when none are present. More importantly, it fails to capture the observed 'long tail' in distributions of both directions and associated virtual geomagnetic poles in terms of angular distance from a central direction. To achieve a good fit to data, it therefore requires the introduction of a second distribution (and therefore the estimation of additional parameters) or the arbitrary removal of data. Here we present a new distribution to describe palaeomagnetic directions and demonstrate that it overcomes both of these problems, generating robust indicators of both the central direction (or pole position) and the spread of palaeomagnetic data as defined by unit vectors. Starting from the assumption that poles (or directions) have an expected colatitude, rather than a mean location, we derive the spherical exponential distribution. We demonstrate that this new distribution provides a good fit to palaeomagnetic data sets from seven large igneous provinces between 15 and 65 Ma and also those produced by numerical dynamo models. We also use it to derive a new shape parameter which may be used as a diagnostic tool for testing goodness of fit of models to data and use this to argue for a shift in geomagnetic behaviour between 5 and 15 Ma. Furthermore, we point out that this new statistic can be used to determine the most appropriate distribution to be used when constructing confidence limits for poles. & copy; 2014 The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.

Item Type: Article
Additional Information: ## TULIP Type: Articles/Papers (Journal) ##
Uncontrolled Keywords: Probability distributions, Palaeomagnetic secular variation, Palaeomagnetism applied to geological processes
Depositing User: Symplectic Admin
Date Deposited: 03 Jun 2015 10:30
Last Modified: 15 Dec 2022 07:45
DOI: 10.1093/gji/ggu443
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/2012720

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