Mapping heterogeneities through avalanche statistics

Biswas, S. and Goehring, L. ORCID: 0000-0002-3858-7295, 2019. Mapping heterogeneities through avalanche statistics. Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, 377 (2136): 20180202. ISSN 1364-503X

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Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches, laboratory scale fracture and also in the outage statistics of power grids. In this work we model threshold-activated avalanche dynamics and investigate the time required to detect local variations in the ability of model elements to bear stress. We show that the detection time follows a scaling law where the scaling exponents depend on whether the feature that is sought is either weaker, or stronger, than its surroundings. We then look at earthquake data from Sumatra and California, demonstrate the trade-off between the spatial resolution of a map of earthquake exponents (i.e. the b-values of the Gutenberg-Richter law) and the accuracy of those exponents, and suggest a means to maximise both.

Item Type: Journal article
Publication Title: Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Creators: Biswas, S. and Goehring, L.
Publisher: The Royal Society Publishing
Date: January 2019
Volume: 377
Number: 2136
ISSN: 1364-503X
Divisions: Schools > School of Science and Technology
Record created by: Jill Tomkinson
Date Added: 25 Jun 2018 12:39
Last Modified: 17 Sep 2019 15:33

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