A model for the distribution of aftershock waiting times

In this work the distribution of inter-occurrence times between earthquakes in aftershock sequences is analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of inter-occurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.Comment: 4 pages, 3 figure

Application of linked stress release model to historical earthquake data: comparison between two kinds of tectonic seismicity

The linked stress release model, incorporating a slow buildup of stress within a seismic region, its stochastic release through earthquakes and transfer between seismic regions, is applied to fit historical data from two typical kinds of seismicity: earthquakes occurring in intraplate (North China) and plate boundary (New Zealand) regions. The best model among different modifications of the basic model, which may reflect on a possible geophysical mechanism for earthquake occurrences, is obtained in terms of Akaike information criterion. For both tectonic regions studied, the linked stress release model fits the New Zealand data better than a collection of independent simple models, but is nearly indistinguishable from the simple stress release model in the case of North China. The seismicity in a plate boundary region due to subduction is more active and complex than that in an intraplate region due to collision between tectonic plates. The results highlight the major differences in tectonic seismicity, especially the heterogeneities of tectonic stress fields, and dynamic triggering mechanism with evidence that the crust may lie in a near-critical state

Bridging the gap between a stationary point process and its Palm distribution

In the context of stationary point processes measurements are usually made from a time point chosen at random or from an occurrence chosen at random. That is, either the stationary distribution P or its Palm distribution P° is the ruling probability measure. In this paper an approach is presented to bridge the gap between these distributions. We consider probability measures which give exactly the same events zero probability as P°, having simple relations with P. Relations between P and P° are derived with these intermediate measures as bridges. With the resulting Radon-Nikodym densities several well-known results can be proved easily. New results are derived. As a corollary of cross ergodic theorems a conditional version of the well-known inversion formula is proved. Several approximations of P° are considered, for instance the local characterization of Po as a limit of conditional probability measures P° N The total variation distance between P° and P1 can be expressed in terms of the P-distribution function of the forward recurrence time