R in addition to om stress in addition to Omori’s law Yan Y. Kagan Department of Earth in addition to Space Sciences, University of Cali as long as nia Los Angeles
Fredericks, Dave, General Manager has reference to this Academic Journal, PHwiki organized this Journal R in addition to om stress in addition to Omori’s law Yan Y. Kagan Department of Earth in addition to Space Sciences, University of Cali as long as nia Los Angeles Abstract We consider two statistical regularities that were used to explain Omori’s law of the aftershock rate decay: Levy in addition to Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behavior under the influence of various r in addition to om factors, i.e., post-earthquake stress time history is described by a Brownian motion. Both distributions decay to zero as long as time intervals close to zero. This feature contradicts the high immediate aftershock level according to Omori’s law. We propose that these distributions are influenced by the power-law stress distribution in the neighborhood of the earthquake focal zone in addition to we derive new distributions as a mixture of power-law stress with the exponent psi in addition to Levy as well as IGD distributions. These new distributions describe the resulting inter-earthquake time intervals in addition to they closely resemble Omori’s law. The new Levy distribution has a pure power-law as long as m with the exponent -(1+psi/2) in addition to the mixed IGD has two exponents, same as Levy as long as small time intervals in addition to -(1+psi) as long as longer times. This power-law behavior should be replaced by even longer time intervals by a uni as long as m seismicity rate corresponding to the long-term tectonic de as long as mation. These background rates are computed based on our as long as mer analysis of the earthquake size distribution in addition to its connection to the plate tectonics. We analyze several earthquake catalogs to confirm in addition to illustrate our theoretical results. Finally we discuss how the parameters of r in addition to om stress dynamics can be determined either through a more detailed statistical analysis of earthquake occurrence or by new laboratory experiments. URL: http://eq.ess.ucla.edu/~kagan/igd-index.html References Bird, P., in addition to Y. Y. Kagan, 2004. Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, in addition to coupling in seven tectonic settings, Bull. Seismol. Soc. Amer., 94(6), 2380-2399 (plus electronic supplement). Bird, P., C. Kreemer, in addition to W. E. Holt, 2010. A long-term as long as ecast of shallow seismicity based on the Global Strain Rate Map, Seismol. Res. Lett., 81(2), 184-194 (plus electronic supplement). Enescu, B., J. Mori, M. Miyazawa, in addition to Y. Kano, 2009. Omori-Utsu law c-values associated with recent moderate earthquakes in Japan, Bull. Seismol. Soc. Amer., 99(2A), 884-891. Helmstetter, A., Y. Y. Kagan, in addition to D. D. Jackson, 2005. Importance of small earthquakes as long as stress transfers in addition to earthquake triggering, J. Geophys. Res., 110(5), B05S08, doi:10.1029/2004JB003286, pp. 1-13. Kagan, Y. Y., 1991. Likelihood analysis of earthquake catalogues, Geophys. J. Int., 106(1), 135-148. Kagan, Y. Y., 1994. Distribution of incremental static stress caused by earthquakes, Nonlinear Processes in Geophysics, 1, 172-181 Kagan, Y. Y., 2002a. Aftershock zone scaling, Bull. Seismol. Soc. Amer., 92, 641-655. Kagan, Y. Y., 2002b. Seismic moment distribution revisited: II. Moment conservation principle, Geophys. J. Int., 149, 731-754. Kagan, Y. Y., 2004. Short-term properties of earthquake catalogs in addition to models of earthquake source, Bull. Seismol. Soc. Amer., 94(4), 1207-1228. Kagan, Y. Y., P. Bird, in addition to D. D. Jackson, 2010. Earthquake Patterns in Diverse Tectonic Zones of the Globe, Pure Appl. Geoph., The Frank Evison Volume167(6/7), 721-741, doi: 10.1007/s00024-010-0075-3. Lavallee, D., 2008. On the r in addition to om nature of earthquake sources in addition to ground motions: a unified theory, Advances in Geophysics, 50, 427-461. Matthews, M. V., W. L. Ellsworth, in addition to P. A. Reasenberg, 2002. A Brownian model as long as recurrent earthquakes, Bull. Seismol. Soc. Amer., 92, 2233-2250. Powers, P. M., in addition to Jordan, T. H., 2010. Distribution of Seismicity Across Strike-Slip Faults in Cali as long as nia, J. Geophys. Res., 115(B05), Article Number: B05305. Vere-Jones, D., 2010. Foundations of Statistical Seismology, Pure Appl. Geophys., 167(6/7), 645-653, doi: 10.1007/s00024-010-0079-z . Bird et al., 2010 Distribution curves in Figs. 10-13 consist of two parts: as long as small time intervals they follow a power-law in addition to as long as larger intervals the distribution is parallel to the Poisson rate. The difference between regression parameters in Figs. 5 in addition to 6 is small, there as long as e the size of earthquake focal zone either does not change in various tectonic zones or modifies slightly.
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