Universal shape profiles of earthquake ruptures.pdf

1 Universal shape profiles of earthquake ruptures Amit P. Mehta, Karin A. Dahmen, and Yehuda Ben-Zion* Department of Physics, University of Illinois at Urbana -Champaign, 1110 West Green Street, Urbana, IL 61801-3080 *Department of Earth Sciences, University of Southern CA, Los Angeles, CA 90089- 0740 Universal shape profiles in a variety of systems contain crucial information on the underlying dynamics. We develop such shape profiles for earthquakes as a stronger test of theory against observations. The earthquake analysis shows good agreement between theory and observations, with a discrepancy in one universal profile, just as in magnets. The analysis provides a stronger support for the idea that earthquakes are associated with criticality rather than event statistics only. The results point to the existence of deep connections between the physics of avalanches in different systems. PACS number(s): 64.60.Ht, 68.35.Rh, 62.20.Mk, 91.30.Px Introduction: Earthquake phenomenology is characterized by several power law distributions. For example, the frequency-moment distribution n(M0) of regional and global earthquakes 1 has the form:2,3 β??1 00 ~)( MMn (1) where the seismic moment M0 ~ i i i Au ??∑ with iu? and iA? being the local slip and rupture area during an earthquake, respectively, and the sum extends over the entire 2 fault. In terms of the magnitude M with )log(3/2~ 0MM for large earthquakes 4, eqn. (1) is rewritten as: bMaMn ?=))(log( (2) where the constant a characterizes the overall rate of activity in a region and the “b - value” β5.1=b gives the relative rates of events in different magnitude ranges. Observed b -values of global earthquakes with depth 50≤ km and horizontal-shear (strike-slip), compressional and extensional mechanisms are about 0.75, 0.85, and 1.05, respectively5. Another observed power law is the modified Omori law for aftershock decay rates around large rupture zones2,3: / ( ) pN t K t c? ? +～ (3