Seismogenesis, scaling and the EEPAS model

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Seismogenesis, scaling and the EEPAS model. David Rhoades GNS Science, Lower Hutt, New Zealand. 4 th International Workshop on Statistical Seismology, Shonan Village, Japan, 9-13 January 2006. Precursory Scale Increase (Ψ) – example. Dashed lines show: - PowerPoint PPT Presentation

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  • Seismogenesis, scaling and the EEPAS modelDavid RhoadesGNS Science, Lower Hutt, New Zealand4th International Workshop on Statistical Seismology, Shonan Village, Japan, 9-13 January 2006

  • Precursory Scale Increase () exampleDashed lines show:a. Seismogenic area b. Magnitude increase c. Rate increase

  • -phenomenon: Predictive relations

  • EEPAS Model - FormulationEvery Earthquake is a Precursor According to Scale; i.e., it is evidence of the occurrence of the -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 densitywhere 0 is a baseline rate density, is a normalising function and wi is a weighting factor and f, g, & h probability densities:

  • Contribution of an individual earthquake to the rate density under the EEPAS model

    mi=4

    mi=5

  • 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 strategies1. Equal weights

    2. Low weight to aftershockswhere is a rate density that includes aftershocksand is the proportion of earthquakes that are not aftershocks

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

  • QuestionsDoes the EEPAS model work equally well at all magnitude scales?

    Are the parameter values universal across different regions and magnitude thresholds?

  • Regions of surveillance

    New Zealand

    California

    Japan

    Greece

  • Evolution of performance factor = L(EEPAS)/L(PPE)(a-c),

    or L(EEPAS)/L(SVP)(d)

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

  • ObservationsFor 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.

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

  • Modified magnitude distributionPresent model appears to be compromising between forecasting mainshocks and aftershocks for low magnitude application in S. CaliforniaChange magnitude distribution to allow for aftershocks

  • 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. AssumeIf we set = M2, and = - M2/2, thenwhere Gi(y) is the survivor function of gi(y).

  • Modified magnitude distribution (3)Then the combined magnitude distribution (for mainshocks and their aftershocks) is If > , then gi(m) can be normalized so that the forecast magnitude distribution follows the G-R relation with slope parameter b=ln10.

    If bM = 1, then the normalising function reduces to a constant (i.e., is independent of m).

  • Individual earthquake contribution to rate densitya. Original magnitude distribution b. Modified magnitude distribution

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

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

  • Modified magnitude distributionApplied to S. California with T
  • ConclusionsEEPAS 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 M and T are constrained, the optimal time, magnitude and location distributions differ little between regions.