As part of an effort to develop a systematic methodology for earthquake forecasts, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, well-known as the Epidemic-Type Aftershock Sequence model). The ETAS model is constructed on a (bare) Omori’s law, the Gutenberg-Richter law and the idea that large events trigger more numerous aftershocks....

[1] We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich. We show that an exponential stress distribution Pt(t) exp( t/t0) gives an Omori law decay of aftershocks with time 1/t, with an exponent p = 1 Asn/t0, where A is a parameter of the rate-and-state friction law and sn is the normal stress. Omori exponent p thus decrease...

We prove ergodicity of a point process earthquake model combining the classical stress release model for primary shocks with the Hawkes model for aftershocks.

The San Andreas fault is the longest fault in California and one of the longest strike-slip faults anywhere in the world, yet we know little about many aspects of its behavior before, during, and after large earthquakes. We conducted a study to locate and to estimate magnitudes for the largest foreshocks and aftershocks of the 1857 M 7.9 Fort Tejon earthquake on the central and southern segment...

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994]. We show that an exponential stress distribution Pτ (τ) ∼ exp(−τ/τ0) gives an Omori law decay of aftershocks with time ∼ 1/t, with an exponent p = 1− Aσn/τ0, where A is a parameter of the rate-and-state friction law, and σn the normal stress. Omori exponent p thus d...

in 2012 august 11 (12:23 utc) a moderate earthquake with mw=6.4 (usgs) occurred between ahar and varzaghan towns in azarbayjan province at northwest of iran. after eleven minutes another earthquake shook the area with mw=6.2 (usgs). these consecutive earthquakes followed by intensive sequences of aftershocks whereas the strongest one had mw=5.3 (usgs). in data processing including depth modific...

[1] A fundamental question in earthquake physics is whether aftershocks are predominantly triggered by static stress changes (permanent stress changes associated with fault displacement) or dynamic stresses (temporary stress changes associated with earthquake shaking). Both classes of models provide plausible explanations for earthquake triggering of aftershocks, but only the static stress mode...

In an earlier study (Van Lieshout and Stein in Math Gesoci 44(3):309–326, 2012) we postulated the existence of two major earthquakes in the 2005 Kashmir disaster instead of a single one, based upon the pattern of aftershocks. In this study, we explore this hypothesis further by fitting several spatial point pattern models. In particular, we discuss the Hawkes and the trigger process models for ...