EEPAS Statsei 4 Japan

Seismogenesis, scaling and the EEPAS model: 

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

Precursory Scale Increase (Ψ) – example: 

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

Ψ-phenomenon: Predictive relations: 

Ψ-phenomenon: Predictive relations

EEPAS Model - Formulation: 

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.

EEPAS model rate density: 

EEPAS model rate density where λ 0 is a baseline rate density, η is a normalising function and wi is a weighting factor and f, g, & h probability densities:

Slide7: 

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

Slide8: 

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.

Weighting strategies: 

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

EEPAS model – fitting & testing: 

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

Questions: 

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

Slide12: 

Regions of surveillance New Zealand California Japan Greece

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

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

Slide14: 

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

Observations: 

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.

Slide17: 

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

Modified magnitude distribution: 

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

Modified magnitude distribution (2): 

Modified magnitude distribution (2) 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 Let x denote magnitude of mainshock, and y that of an aftershock. Assume If we set γ = α σM2, and δ′ = δ - α σM2/2, then where Gi(y) is the survivor function of gi(y).

Modified magnitude distribution (3): 

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).

Slide21: 

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

Results: 

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.

Slide23: 

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

Slide24: 

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

Conclusions: 

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.