| Abstract
The distribution of earthquake interevent times is a subject that has attracted
much attention in the statistical physics literature [1-3]. A recent paper proposes
that the distribution of earthquake interevent times follows from the the interplay of
the crustal strength distribution and the loading function (stress versus time) of the
Earth’s crust locally [4]. It was also shown that the Weibull distribution describes
earthquake interevent times provided that the crustal strength also follows the
Weibull distribution and that the loading function follows a power-law during the
loading cycle.
I will discuss the implications of this work and will present supporting evidence
based on the analysis of data from seismic catalogs. I will also discuss the
theoretical evidence in support of the Weibull distribution based on models of
statistical physics [5]. Since other-than-Weibull interevent times distributions are
not excluded in [4], I will illustrate the use of the Kolmogorov-Smirnov test in
order to determine which probability distributions are not rejected by the data.
Finally, we propose a modification of the Weibull distribution if the size of the
system under investigation (i.e., the area over which the earthquake activity occurs)
is finite with respect to a critical link size.
keywords: hypothesis testing, modified Weibull, hazard rate, finite size
References
[1]Â Â Â Corral, A., 2004. Long-term clustering, scaling, and universality in the
temporal occurrence of earthquakes, Phys. Rev. Lett., 9210) art. no. 108501.
[2]Â Â Â Saichev, A., Sornette, D. 2007. Theory of earthquake recurrence times, J.
Geophys. Res., Ser. B 112, B04313/1–26.
[3]Â Â Â Touati, S., Naylor, M., Main, I.G., 2009. Origin and nonuniversality of the
earthquake interevent time distribution Phys. Rev. Lett., 102 (16), art. no. 168501.
[4]Â Â Â Hristopulos, D.T., 2003. Spartan Gibbs random field models for geostatistical
applications, SIAM Jour. Sci. Comput., 24, 2125-2162.
[5]   I. Eliazar and J. Klafter, 2006. Growth-collapse and decay-surge evolutions,
and geometric Langevin equations, Physica A, 367, 106 – 128. |