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Comparison of average stress drop measures for ruptures with heterogeneous stress change and implications for earthquake physics

Noda, Hiroyuki and Lapusta, Nadia and Kanamori, Hiroo (2013) Comparison of average stress drop measures for ruptures with heterogeneous stress change and implications for earthquake physics. Geophysical Journal International, 193 (3). pp. 1691-1712. ISSN 0956-540X. doi:10.1093/gji/ggt074.

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Stress drop, a measure of static stress change in earthquakes, is the subject of numerous investigations. Stress drop in an earthquake is likely to be spatially varying over the fault, creating a stress drop distribution. Representing this spatial distribution by a single number, as commonly done, implies averaging in space. In this study, we investigate similarities and differences between three different averages of the stress drop distribution used in earthquake studies. The first one, Δσ¯¯¯¯¯M, is the commonly estimated stress drop based on the seismic moment and fault geometry/dimensions. It is known that Δσ¯¯¯¯¯M corresponds to averaging the stress drop distribution with the slip distribution due to uniform stress drop as the weighting function. The second one, Δσ¯¯¯¯¯A, is the simplest (unweighted) average of the stress drop distribution over the fault, equal to the difference between the average stress levels on the fault before and after an earthquake. The third one, Δσ¯¯¯¯¯E, enters discussions of energy partitioning and radiation efficiency; we show that it corresponds to averaging the stress drop distribution with the actual final slip at each point as the weighting function. The three averages, Δσ¯¯¯¯¯M, Δσ¯¯¯¯¯A, and Δσ¯¯¯¯¯E, are often used interchangeably in earthquake studies and simply called ‘stress drop’. Yet they are equal to each other only for ruptures with spatially uniform stress drop, which results in an elliptical slip distribution for a circular rupture. Indeed, we find that other relatively simple slip shapes—such as triangular, trapezoidal or sinusoidal—already result in stress drop distributions with notable differences between Δσ¯¯¯¯¯M, Δσ¯¯¯¯¯A, and Δσ¯¯¯¯¯E. Introduction of spatial slip heterogeneity results in further systematic differences between them, with Δσ¯¯¯¯¯E always being larger than Δσ¯¯¯¯¯M, a fact that we have proven theoretically, and Δσ¯¯¯¯¯A almost always being the smallest. In particular, the value of the energy-related Δσ¯¯¯¯¯E significantly increases in comparison to the moment-based Δσ¯¯¯¯¯M with increasing roughness of the slip distribution over the fault. Previous studies used Δσ¯¯¯¯¯M in place of Δσ¯¯¯¯¯E in computing the radiation ratio ηR that compares the radiated energy in earthquakes to a characteristic part of their strain energy change. Typical values of ηR for large earthquakes were found to be from 0.25 to 1. Our finding that Δσ¯¯¯¯¯E≥Δσ¯¯¯¯¯M allows us to interpret the values of ηR as the upper bound. We determine the restrictions placed by such estimates on the evolution of stress with slip at the earthquake source. We also find that Δσ¯¯¯¯¯E can be approximated by Δσ¯¯¯¯¯M if the latter is computed based on a reduced rupture area.

Item Type:Article
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URLURL TypeDescription
Lapusta, Nadia0000-0001-6558-0323
Kanamori, Hiroo0000-0001-8219-9428
Additional Information:© Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society. Accepted 2013 February 19. Received 2012 February 14; in original form 2011 May 13. First published online: March 26, 2013. This study was supported by the National Science Foundation (grant EAR0548277), the Southern California Earthquake Center (SCEC), the Gordon and Betty Moore Foundation, and the Seismological Laboratory at Caltech. SCEC is funded by NSF Cooperative Agreement EAR-0106924 and USGS Cooperative Agreement 02HQAG0008. The SCEC contribution number for this paper is 1703. This is Caltech Tectonics Observatory contribution 225. We gratefully acknowledge the reviews by Drs. Massimo Cocco, Eiichi Fukuyama, Art McGarr, and an anonymous reviewer which helped us improve the manuscript.
Group:Caltech Tectonics Observatory, Seismological Laboratory
Funding AgencyGrant Number
Southern California Earthquake Center (SCEC)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Seismological LaboratoryUNSPECIFIED
Subject Keywords:Earthquake dynamics; Dynamics and mechanics of faulting; Fractures and faults
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Southern California Earthquake Center (SCEC)1703
Caltech Tectonics Observatory225
Issue or Number:3
Record Number:CaltechAUTHORS:20130718-112434964
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39448
Deposited On:19 Jul 2013 18:25
Last Modified:09 Nov 2021 23:44

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