Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA , EARTHQUAKE PATTERNS IN DIVERSE TECTONIC ZONES OF THE GLOBE

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).

Kagan, Y. Y., Likelihood analysis of earthquake catalogues, Geophys. J. Int., 106, Earthquake intensity function Time influence function (Omori’s law) Space influence function

Likelihood analysis of earthquake catalogues Y. Y. Kagan Geophys. J. Int. (1991) 106, CALNET -- Central California; PDE – global; Harvard – CMT global; DUDA – global M>7.0.

PARAMETER VALUES FOR VARIOUS SUBDIVISIONS OF CMT CATALOG, /03/31, Mw>= All Subd. Orog. Inter. Fast Slow N Mmax Inf/N Ind/N \mu b \delta \theta * * \sigma * \eps_r \eps_h * * 3.0* \sigma – focal size for M4 EQ; \eps_r – horizontal error; \eps_h – vertical error

Sumatra M 9.1 earthquake, t_m = 1.2 days

Landers, 1992, M=7.3; t_m=3.7 hours

PARAMETER VALUES FOR VARIOUS SUBDIVISIONS OF CMT CATALOG, /03/31, Mw>=5.6; close aftershocks removed (1.3%) All All/c N Mmax Inf/N Ind/N \mu b \delta \theta * 9. \sigma \eps_r \eps_h \sigma – focal size for M4 EQ; \eps_r – horizontal error; \eps_h – vertical error

World seismicity: 1990 – 2000 (PDE)

PARAMETER VALUES FOR VARIOUS SUBDIVISIONS OF PDE CATALOG, /01/01, M>= All Subd. Orog. Inter. Fast Slow N Mmax Inf/N Ind/N \mu b \delta \theta \sigma * \eps_r \eps_h 3.0* * 3.0* 3.0* \sigma – focal size for M4 EQ; \eps_r – horizontal error; \eps_h – vertical error

PARAMETER VALUES FOR VARIOUS SUBDIVISIONS OF PDE CATALOG, /01/01, M>=5.0; CLOSE AFTERSHOCKS REMOVED (5.5%) All Subd. Orog. Inter. Fast Slow N Mmax Inf/N Ind/N \mu b \delta * 0.0* 8. \theta * \sigma * 0.15* 0.15* 10. \eps_r \eps_h 3.0* * 3.0* 3.0* \sigma – focal size for M4 EQ; \eps_r – horizontal error; \eps_h – vertical error

Moment likelihood map

Moment Magnitude Distribution

Likelihood function iterations Red – Likelihood function; Blue – Ratio indepen./N; Green – branching coefficient (\mu)

Challenges We need to start by investigating how different branching models of seismicity approximate global earthquake catalogs. Global catalogs have an advantage of being considerably less inhomogeneous in time and space than local catalogs, and there are no spatial boundary effects which greatly complicate the analysis of local catalogs. Local seismicity is controlled by a few aftershock sequences of strong events. It is important, however, to analyze local catalogs as well to see that model parameter values are similar for worldwide and local catalogs. See

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Abstract We extend existing branching models for earthquake occurrences by incorporating potentially important estimates of tectonic deformation and by allowing the parameters in the models to vary across different tectonic zones. In particular we use the following short list of tectonic categories (similar to Bird & Kagan [2004]): (4) Trenches (including Subduction zones & Oceanic Convergent Boundaries, & earthquakes in outer rise or overriding plate); (3) Fast-spreading ridges (oceanic crust, spreading rate > 40 mm/a; includes transforms); (2) Slow-spreading ridges (oceanic crust, spreading rate < 40 mm/a, includes transforms); (1) Active continent (including continental parts of all orogens plus designated continental plate boundaries of Bird [2003]); (0) Plate-interior (the rest of the Earth's surface). We use these models to develop earthquake forecasts (i.e., maps of expected rate of occurrences of earthquakes above a given threshold magnitude) in several different categories: long-term (e.g., 5+ years, emphasizing spontaneous mainshocks) based on tectonic deformation and long-term clustering as recorded in catalogs; and short-term (e.g., daily, with emphasis on triggered seismicity). Each forecast is global to permit relatively rapid and conclusive testing.

Abstract (cont.) These forecasts differ in the weights they put on tectonic deformation versus instrumental seismicity, but all forecasts take account of the large differences in seismicity between different classes of plate boundary or different tectonic zones. See preliminary results at To test the long-term forecast efficiency numerically we calculate the concentration diagram. To make these diagrams we divide the region into small cells (0.5 by 0.5 degrees) and estimate the theoretical rate of earthquakes above the magnitude threshold for each cell; count the events that actually occurred in each cell; sort the cells in decreasing order of theoretical rate; and compute cumulative values of forecast and observed earthquake rates as shown for two western Pacific regions in (see FORECAST TEST FOR :). Similar plots have been used in several of our papers [Helmstetter et al., SRL, 2007; Shen et al., SRL, 2007]. In effect, these diagrams are equivalent to error diagrams proposed by Molchan [1990, 2003], and Molchan & Kagan [1992], but in this case instead of the temporal axis we use the spatial area as the horizontal axis. To make this concentration diagram look like an error diagram we flipped the plot along the horizontal line 0.5, so that, for example, for the NW Pacific region our model predicts that 75% of seismicity would be concentrated in 10% of the area.

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,

Conclusions We present an earthquake forecast program which quantitatively predicts both long- and short-term earthquake probabilities. The program is numerically and rigorously testable. It is ready to be implemented as a technological solution for earthquake hazard forecasting and early warning.

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