Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA , Rules of the Western Pacific Natural Laboratory April 23,

Stochastic models of earthquake occurrence and forecasting Long-term models for earthquake occurrence, optimization of smoothing procedure and its testing (Kagan and Jackson, 1994, 2000). Empirical branching models (Kagan, 1973a,b; Kagan and Knopoff, 1987; Ogata, 1988, 1998; Kagan, 2006). Physical branching models – propagation of earthquake fault is simulated (Kagan and Knopoff, 1981; Kagan, 1982).

Literature Kagan, Y. Y., Statistical methods in the study of the seismic process (translated from Russian by D. Vere-Jones; with discussion: comments by M. S. Bartlett, A. G. Hawkes, and J. W. Tukey), Bull. Int. Statist. Inst., 45(3), Kagan, Y. Y., A probabilistic description of the seismic regime, Izv. Acad. Sci. USSR, Phys. Solid Earth, , (English translation). Kagan, Y., and Knopoff, L., Earthquake risk prediction as a stochastic process, Phys. Earth Planet. Inter., 14, Kagan, Y. Y., and Knopoff, L., Statistical short-term earthquake prediction, Science, 236, Molchan, G. M., and Y. Y. Kagan, Earthquake prediction and its optimization, J. Geophys. Res., 97,

Literature Kagan, Y. Y., and D. D. Jackson, Long-term probabilistic forecasting of earthquakes, J. Geophys. Res., 99, 13,685-13,700. Jackson, D. D., and Y. Y. Kagan, Testable earthquake forecasts for 1999, Seism. Res. Lett., 70, Kagan, Y. Y., and D. D. Jackson, Probabilistic forecasting of earthquakes, (Leon Knopoff's Festschrift), Geophys. J. Int., 143, Kagan, Y. Y., Y. F. Rong, and D. D. Jackson, Probabilistic forecasting of seismicity, Chapter 5.2 in "EARTHQUAKE SCIENCE AND SEISMIC RISK REDUCTION", eds. F. Mulargia and R. J. Geller, pp , Kluwer, Dordrecht. Kagan, Y. Y., and D. D. Jackson, Comment on `Testing earthquake prediction methods: "The West Pacific short-term forecast of earthquakes with magnitude MwHRV >= 5.8"' by V. G. Kossobokov, Tectonophysics, (TECTO), 413(1-2),

Kagan, Y. Y., Statistical methods in the study of the seismic process (translated from Russian by D. Vere-Jones; with discussion: comments by M. S. Bartlett, A. G. Hawkes, and J. W. Tukey), Bull. Int. Statist. Inst., 45(3),

Kagan, Y., and Knopoff, L., Earthquake risk prediction as a stochastic process, PEPI, 14,

(b) Point process: Branching along magnitude axis, introduced by Kagan (1973a;b), see also Kagan and Knopoff, 1977 (a) Earthquake catalog data (c) Point process: Branching along time axis (Hawkes, 1971; Kagan & Knopoff, 1987; Ogata, 1988)

Kagan, Y. Y., and Knopoff, L., Statistical short- term earthquake prediction, Science, 236,

CMT catalog: Shallow earthquakes,

Kagan, Y. Y., and D. D. Jackson, Long- term probabilistic forecasting of earthquakes, J. Geophys. Res., 99, 13, ,700.

Long-term forecast: 1977-today Spatial smoothing kernel is optimized by using the first part of a catalog to forecast its second part. Kagan, Y. Y., and D. D. Jackson, Probabilistic forecasting of earthquakes, Geophys. J. Int., 143,

Time history of long-term and hybrid (short-term plus 0.8 * long-term) forecast for a point at latitude N., E. northwest of Honshu Island, Japan. Blue line is the long- term forecast; red line is the hybrid forecast.

The table below and accompanying plots are calculated on 2007/ 4/19 at midnight Los Angeles time. The last earthquake with scalar seismic moment M>=10^17.7 Nm (Mw>=5.8) entered in the catalog occurred in the region 0.0 > LAT. > -60.0, > LONG. > on 2007/ 4/16 at latitude and longitude , Mw = 6.42 ____________________________________________________________________ LONG-TERM FORECAST | SHORT-TERM Probability Focal mechanism | Probability Probability M>5.8 T-axis P-axis M>5.8 ratio eq/day*km^2 Pl Az Pl Az eq/day*km^2 Time- Longitude | | | Rotation Time- dependent/ | Latitude | | | angle dependent independent v v v v degree ……………………………………………………………………………………………………… E E E E E E E E E E E E E E E E E E E E E E E E E E E E-02 ………………………………………………………………………………………………………

Short-term forecast uses Omori's law to extrapolate present seismicity. Forecast one day before the recent (2006/11/15) M8.3 Kuril Islands earthquake.

KURILE ISLANDS SEISMICITY 2005-PRESENT (2007/04/22) LATITUDE 40-50N, LONGITUDE E Thr Thr Thr Thr Thr Thr Thr Thr Thr Thr Nor Nor Thr Nor Nor Thr

Forecast one day after the recent (2006/11/15) M8.3 Kuril Islands earthquake.

Forecast one day before the recent (2007/01/13) M8.1 Kuril Islands earthquake.

Forecast one day after the recent (2007/01/13) M8.1 Kuril Islands earthquake.

Forecast one day before the recent (2007/4/1) M8.1 Solomon Islands earthquake.

Forecast one day after the recent (2007/4/1) M8.1 Solomon Islands earthquake

Long-term Forecast Efficiency Evaluation We simulate synthetic catalogs using smoothed seismicity map. Likelihood function for simulated catalogs and for real earthquakes in the time period of forecast is computed. If the `real earthquakes’ likelihood value is within 2.5— 97.5% of synthetic distribution, the forecast is considered successful. Kagan, Y. Y., and D. D. Jackson, Probabilistic forecasting of earthquakes, Geophys. J. Int., 143,

Here we demonstrate forecast effectiveness: displayed earthquakes occurred after smoothed seismicity forecast had been calculated.

Kossobokov, Testing earthquake prediction methods: ``The West Pacific short-term forecast of earthquakes with magnitude MwHRV \ge 5.8", Tectonophysics, 413(1-2), See also Kagan & Jackson, TECTO, 2006, pp

Likelihood ratio – information/eq We approximate earthquake occurrence by Poisson cluster process and calculate the earthquake rate. Likelihood function is

Likelihood ratio – information/eq Similarly we obtain likelihood function for the null hypothesis model (Poisson process in time). Information content of a catalog : characterizes uncertainty reduction by use of a particular model. Kagan and Knopoff, PEPI, 1977; Kagan, GJI, 1991; Kagan and Jackson, GJI, 2000; Helmstetter, Kagan and Jackson, BSSA, 2006 (bits/earthquake)

Likelihood ratio – information/eq Because of power-law dependence of earthquake rate on time (Omori ’ s law), the likelihood function (l) approaches infinity when the prediction horizon is close to zero (i.e., for real-time earthquake prediction). Similarly, when spatial resolution of earthquake data increases, (l) again goes to infinity. Molchan diagram also approaches the ideal state for the prediction horizon close to zero, or if the location accuracy significantly increases..

CSEP Questions -- Answers What kind of model do you have? Grid-based, fault-based, alarm-based? Grid-based, with focal mechanism predicted What is your testing area? West Pacific, potentially global What is your input data and who is producing it? CMT How is your input data preprocessed? FORTRAN What tests do you apply? Likelihood, Error diagrams, Spatial concentration diagrams Do you imagine many other models with the same specification? Need a catalog of focal mechanism solutions When could your model be up and running in CSEP? It is currently running at my Web site What are your software needs? FORTRAN, IDL, but other software would work as well

END Thank you