Seismogenesis and Scaling: EEPAS Model Explained in Statistical Seismology

1. Seismogenesis, scaling and the EEPAS model David Rhoades GNS Science, Lower Hutt, New Zealand 4th International Workshop on Statistical Seismology, Shonan Village, Japan, 9-13 January 2006

2. Precursory Scale Increase (Ψ) – example Dashed lines show: a. Seismogenic area b. Magnitude increase c. Rate increase

4. Ψ-phenomenon: Predictive relations

5. EEPAS Model - Formulation • “Every Earthquake is a Precursor According to Scale”; i.e., it is evidence of the occurrence of the Ψ-phenomenon on a particular scale . • Every earthquake initiates a transient increment of long-term hazard. The scale (of time, magnitude, location) depends on its magnitude. • The weight of its contribution may depend on other earthquakes around it. • The hazard at any given time, magnitude, and location depends on all previous earthquakes within a neighbourhood of appropriate scale.

6. EEPAS model rate density where λ0 is a baseline rate density, η is a normalising function and wi isa weighting factor and f, g, & h probability densities:

7. Contribution of an individual earthquake to the rate density under the EEPAS model • mi=4 • mi=5

8. Normalised rate density under the EEPAS model relative to a reference (RTR) rate density in which one earthquake per year, on average, exceeds any magnitude m in 10m km2. The fixed coordinates are those of the W. Tottori earthquake.

9. Weighting strategies 1. Equal weights 2. Low weight to aftershocks where is a rate density that includes aftershocks and ν is the proportion of earthquakes that are not aftershocks

10. EEPAS model – fitting & testing • Fitted to NZ earthquake catalogue 1965-2000, M>5.75 • Tested against PPE on CNSS catalogue of California, M > 5.75 • Tested against PPE on JMA catalogue of Japan, M > 6.75 • Optimised for JMA catalogue M > 6.25 • Fitted to NIED catalogue of central Japan M>4.75 • Tested against PPE on NZ catalogue 2001-2004 • Fitted to AUT catalogue of Greece, 1966-80, M>5.95, and tested against SVP 1981-2002 • Fitted to ANSS catalogue of southern California, M>4.95

11. Questions • Does the EEPAS model work equally well at all magnitude scales? • Are the parameter values universal across different regions and magnitude thresholds?

12. Regions of surveillance • New Zealand • California • Japan • Greece

13. Evolution of performance factor = L(EEPAS)/L(PPE)(a-c),or L(EEPAS)/L(SVP)(d)

14. Regions of surveillance Kanto: M > 4.75 S. California: M > 4.95

16. Observations For low magnitude applications in S. California and Kanto regions: • Spatially varying models are more informative with respect to SUP. • Equal weights version of EEPAS is better than version with aftershocks down-weighted. • Information rate of EEPAS with respect to spatially varying model is similar to applications at higher magnitude.

17. Fitted distributions for time, magnitude & location, given mi in applications of EEPAS model.

18. Modified magnitude distribution • Present model appears to be compromising between forecasting mainshocks and aftershocks for low magnitude application in S. California • Change magnitude distribution to allow for aftershocks

19. where H(s) = 1 if s > 0 and 0 otherwise. (Density integrates to expected number of aftershocks). Then magnitude distribution of aftershocks predicted by ith earthquake is Modified magnitude distribution (2) Let x denote magnitude of mainshock, and y that of an aftershock. Assume If we set γ= ασM2, and δ′ = δ- ασM2/2, then where Gi(y) is the survivor function of gi(y).

20. Modified magnitude distribution (3) Then the combined magnitude distribution (for mainshocks and their aftershocks) is • If α> β, then g′i(m) can be normalized so that the forecast magnitude distribution follows the G-R relation with slope parameter b=βln10. • If bM = 1, then the normalising function reduces to a constant (i.e., is independent of m).

21. Individual earthquake contribution to rate density a. Original magnitude distribution b. Modified magnitude distribution

22. Results • For S. California dataset, lnL of model is hardly improved. • Equal weight version of EEPAS still prevails. • Optimal value of δ′ ~1.3. • fi(t) parameters not changed much, but if σM and σT are constrained not to be small, then fi(t) is similar to other datasets, with only a small reduction of lnL.

23. Fitted distributions for time, magnitude & location, given mi in applications of EEPAS model.

24. Modified magnitude distribution Applied to S. California with σT<0.5 & σM<0.5.

25. Conclusions • EEPAS model works similarly well at higher and lower magnitudes, but with some parameter differences, that may indicate deviations from scaling in the long-term seismogenic process. • Superiority of equal-weights version at low magnitudes is unexplained. • Effect of aftershocks on the fitting and performance of the model needs further investigation. • When σM and σT are constrained, the optimal time, magnitude and location distributions differ little between regions.