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Universal mean moment rate profiles of earthquake ruptures.pdf

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Universal mean moment rate profiles of earthquake ruptures

a r X i v : c o n d - m a t / 0 5 0 9 2 2 6 v 1 [ c o n d - m a t .d i s - n n ] 9 S e p 2 0 0 5 Universal mean moment rate profiles of earthquake ruptures Amit P. Mehta? and Karin A. Dahmen? Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080 Yehuda Ben-Zion? Department of Earth Sciences, University of Southern CA, Los Angeles, CA 90089-0740 Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg- Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on long spatio-temporal scales, we discuss results associated with a heterogeneous fault with long range stress-transfer interactions. To better understand earth- quake dynamics we focus on faults with Gutenberg-Richter like earthquake statistics and develop two universal scaling functions as a stronger test of the theory against observations than mere scal- ing exponents that have large error bars. Universal shape profiles contain crucial information on the underlying dynamics in a variety of systems. As in magnetic systems, we find that our analysis for earthquakes provides a good overall agreement between theory and observations, but with a potential discrepancy in one particular universal scaling function for moment-rates. The results point to the existence of deep connections between the physics of avalanches in different systems. PACS numbers: 64.60.Ht,68.35.Rh,62.20.Mk,91.30.Px INTRODUCTION Earthquake phenomenology is characterized by several power law distributions. The most famous of these are the frequency-size distributions (i.e. histograms) of re- gional and global earthquakes [1, 6], and the modified Omori law for the aftershock decay rate around large rupture zones [2, 3]. Using the seismic moment M0 for the earthquake size, the frequency-size distributions (or moment histogram) has the form (e.g., [4]) n(M0) ～ M?1