Renormalized Omori Law, Conditional Foreshocks, Spatial Diffusion and Earthquake Prediction with the Etas Model

Tuesday, June 11, 2002 - 2:00pm - 3:00pm
Keller 3-180
Didier Sornette (University of California, Los Angeles)
The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay 1/t1+ of seismicity after an earthquake) and Gutenberg-Richter law (power law distribution of earthquake energies). We present new results and empirical tests on 1) new physically-based mechanisms for Omori's law with non-universal p-value, 2) the existence of renormalized or dressed Omori law with a p value which may be a function of the time scale of observation [1,2], 3) the exploration of new regimes of parameters, including a new mechanism for a finite-time singularity modeling for instance catastrophic failure [3], 4) the sub- and super-diffusion regimes of the ETAS model [4], 5) the demonstration that the p'-value for foreshock is smaller than the p-value for aftershock and the derivation of a deviatoric b-value for foreshocks [5], 6) the demonstration of an improved predictive skill at finite time horizons.

[1] A. Sornette and D. Sornette, Renormalization of earthquake aftershocks, Geophys. Res. Lett. 6, N13, 1981-1984 (1999) (

[2] A. Helmstetter and D. Sornette, Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks, in press in J. Geophys. Res. (

[3] D. Sornette and A. Helmstetter, New Mechanism for Finite-Time-Singularity in Epidemic Models of Rupture, Earthquakes and Starquakes, submitted to Phys. Rev. Lett. (

[4] A. Helmstetter and D. Sornette, Diffusion of Earthquake Aftershock Epicenters and Omori's Law: Exact Mapping to Generalized Continuous-Time Random Walk Models, submitted to Phys. Rev. E (

[5] A. Helmstetter, D. Sornette, J.-R. Grasso and G. Ouillon, Mainshocks are Aftershocks of Conditional Foreshocks: Theory and Numerical Tests of the Inverse and Direct Omori's law, submitted to J. Geophys. Res.