Estimating the ETAS model from an early aftershock sequence

Constraints on the Size of the Smallest Triggering Earthquake from the ETAS Model, B̊ath’s Law, and Observed Aftershock Sequences

The physics of earthquake triggering together with simple assumptions of self-similarity impose the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude md of completeness of seismic catalogs has no reason to be the same as the magnitude m0 of the smallest triggering earthquake, we use quantitative fits and maximum likelihood in...

Estimating stress heterogeneity from aftershock rate

We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich [1994]. We show than an exponential stress distribution P (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 dec...

Implications of an inverse branching aftershock sequence model.

The branching aftershock sequence (BASS) model is a self-similar statistical model for earthquake aftershock sequences. A prescribed parent earthquake generates a first generation of daughter aftershocks. The magnitudes and times of occurrence of the daughters are obtained from statistical distributions. The first generation daughter aftershocks then become parent earthquakes that generate seco...

Appendix S—Constraining Epidemic Type Aftershock Sequence (ETAS) Parameters from the Uniform California Earthquake Rupture Forecast, Version 3 Catalog and Validating the ETAS Model for Magnitude 6.5 or Greater Earthquakes

Operational earthquake forecasting in the Uniform California Earthquake Rupture Forecast, version 3 (UCERF3) model will be implemented using the Epidemic Type Aftershock Sequence (ETAS) model. Parameter values for the ETAS model are determined by fitting that model to the recent instrumental earthquake catalog. A grid search is done, and the loglikelihood is used as a measure of fit to estimate...

California aftershock model uncertainties.