Yan Y. Kagan, David D. Jackson

Dept. Earth and Space Sciences, UCLA, Los Angeles,

CA 90095-1567, ykagan@ucla.edu, djackson@ucla.edu

http://scec.ess.ucla.edu/ykagan.html

Regional and Global Earthquake Forecasts

http://moho.ess.ucla.edu/~kagan/Kagan_Jackson_Seismo.ppt

Earthquake forecasting in diverse tectonic zones of the Globe

Since 1999 we have been forecasting long- and short-term rate of M>=5.8 earthquakes in two western Pacific regions using the CMT catalog (Jackson and Kagan, SRL, 1999; Kagan and Jackson, GJI, 2000). These forecasts are now available for testing at the SCEC CSEP (Collaboratory for the Study of Earthquake Predictability). However, the present method based on the CMT catalog can be extended only for subduction zones. Moreover, the high magnitude threshold of the catalog makes it unsuitable for forecasts in the areas with a relatively low seismicity level. The PDE (USGS) catalog has a lower magnitude threshold (4.8 vs 5.8 for CMT) and higher location accuracy. With moderate modifications the present methodology can be used for global or regional forecasts. We carried out a likelihood analysis of the PDE global catalog as well as subcatalogs covering different tectonic zones to determine the values of parameters for the short-term earthquake forecast. As an illustration of the forecast capability we applied it to California/Nevada, Greece, and Italy with surrounding territories. We discuss how these forecasts can be tested both retrospectively and prospectively. In principle a program can be designed to issue long- and short-term forecasts within a few minutes with the PDE catalog at the arbitrary spatial window: all it needs is some human capital, and rapid provision of the PDE catalog.

Literature (available at WEB)• Kagan, Y. Y., and D. D. Jackson, 1994. Long-term probabilistic

forecasting of earthquakes, J. Geophys. Res., 99, 13,685-13,700.

• Jackson, D. D., and Y. Y. Kagan, 1999. Testable earthquake forecasts for 1999, Seism. Res. Lett., 70, 393-403.

• Kagan, Y. Y., and D. D. Jackson, 2000. Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438-453.

• Kagan, Y. Y., P. Bird, and D. D. Jackson, 2008. Earthquake Patterns in Diverse Tectonic Zones of the Globe, submitted to Evison PAGEOPH issue.

• Kagan, Y. Y. and D. D. Jackson, 2008. Earthquake forecasting in diverse tectonic zones of the Globe, submitted to Evison PAGEOPH issue.

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).

GOALS

• 1. Forecasts must be falsifiable (testable) within a reasonable time period -- all methods.

• 2. Forecasts should produce in principle a stochastic ensemble of seismograms to simulate shaking of an object (statistical scenarios) -- CMT.

• 3. Forecast should be extended to all global seismogenic areas – PDE.

• 4. Both global and regional earthquake catalogs should be used for the forecast – PDE, ANSS.

CMT catalog: Shallow earthquakes, 1976-2005

We used the CMT catalog because it employs relatively consistent methods and reports tensor focal mechanisms. The focal mechanisms allow us to estimate the fault plane orientation for past earthquakes, through which we can identify a preferred direction for future events. Using the forecasted tensor focal mechanism, it is possible in principle to calculate an ensemble of seismograms for each point of interest on the earth's surface.

CMT catalog

Long-term forecast: 1977-today, CMTSpatial smoothing kernel is optimized by using the first part of a catalog to forecast its second part.Kagan, Y. Y., and D. D. Jackson, 2000. Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438-453.

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, 2000. Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438-453.

Here we demonstrate forecast effectiveness:displayed earthquakesoccurred aftersmoothed seismicity forecasthad been calculated.

Color tones show the rate density of earthquake occurrencecalculated using the CMT 1977-2003 catalog; 1700 simulatedearthquakes for 2004-2006 are shown in white.

I_2 – the likelihood score for earthquakes.I_3 – the likelihood score for forecasts.

World seismicity: 1990 – 2000 (PDE)

The PDE catalog has significant advantages over the CMT one. The PDE has a longer observation period (the surface wave magnitude M_S was determined starting from the middle of 1968), and a lower magnitude threshold (m_t). Depending on time period and region, the threshold is of the order 4.5 to 4.7 (Kagan, 2003), i.e., much lower than the CMT catalog threshold (around 5.4 to 5.8). This means that the forecast estimates can be practically obtained for all global seismic areas. The PDE reports earthquake hypocenters, which can be estimated much more precisely than the moment centroid locations reported by the CMT catalog.

PDE catalog

Drawbacks when compared to the CMT dataset: The PDE catalog lacks the focal mechanism solutions. Also, the PDE reports a somewhat inconsistent mix of different magnitudes (local-, body wave-, surface wave-, moment-, etc.) with less accuracy than the moment magnitude inferred from the CMT catalog. Moreover, the PDE magnitudes are influenced by strong systematic effects and biases. Another drawback is that the hypocenter, which the PDE catalog uses for representing location, could be at the edge of the rupture zone for a large earthquake. The moment centroid, reported by the CMT, more meaningfully describes the location even though the centroid is generally more uncertain than the hypocenter.

PDE catalog

Long-term forecast: 1977-today, CMT catalog, Mw>=5.8

Long-term forecast: 1977-today, PDE catalog, M>=5.8

Long-term forecast: 1969-today, PDE catalog, M>=5.0

http://bemlar.ism.ac.jp/wiki/index.php/Bird%27s_Zones

N -- is the earthquake number, M>=4.7,m_max maximummagnitude in a subcatalog,I/N -- information score per event in bits/eq,lambda T/N -- ratio of spontaneousevents to total, m -- branching ratiob -- b-value,a -- parent productivity exponenttheta -- temporal exponent,s_r -- focal size for M4 earthquake in km,epsilon_rho -- horizontal error in kmepsilon_h -- vertical error in km.

N -- is the earthquake number, M>=4.7,m_max maximummagnitude in a subcatalog,I/N -- information score per event in bits/eq,lambda T/N -- ratio of spontaneousevents to total, m -- branching ratiob -- b-value,a -- parent productivity exponenttheta -- temporal exponent,s_r -- focal size for M4 earthquake in km,epsilon_rho – horiz. error (km)epsilon_h -- vertical error (km).

Likelihood ratio – information/eq

Similarly we obtain likelihood function for the null hypothesis model (Poisson process in time)

0lInformation content of a catalog :

)2ln/()( 0 NllI characterizes uncertainty reduction by use of aparticular model.

Kagan and Knopoff, PEPI, 1977; Kagan, GJI, 1991;Kagan and Jackson, GJI, 2000; Helmstetter, Kagan and Jackson, BSSA, 2006

(bits/earthquake)

ETAS model parameterization

• Omori’s law: n = 1/(t + c)^p. c is not scaled with magnitude M, thus it is dependent on the magnitude threshold (Ogata, 1988, 1998).

• Spatial effects are not differentiated: location errors and dimension of aftershock zone need to be separated in parameterization.

• No determination of the likelihood score per event, thus the results are not comparable.

Kagan, Y. Y., and Knopoff, L., 1987. Statistical short-term earthquake prediction, Science, 236, 1563-1567.

Time history of long-term and hybrid (short-term plus 0.8 *long-term) forecast for a point at latitude 39.47 N., 143.54 E. northwest of Honshu Island, Japan. Blue line is the long-term forecast; red line is the hybrid forecast.

Short-term forecast: 1977-today, CMT catalog, M>=5.8

Omori’s law is used to extrapolate earthquake record.Parameters are determined by the maximum likelihood search.

The table below and accompanying plots are calculated on 2007/ 4/19at midnight Los Angeles time. The last earthquake with scalar seismic moment M>=10^17.7 Nm (Mw>=5.8) entered in the catalog occurred inthe region 0.0 > LAT. > -60.0, -170.0 > LONG. > 110.0 on2007/ 4/16 at latitude -57.89 and longitude 148.14, 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

……………………………………………………………………………………………………… 154.0 -7.5 1.49E-08 67 24 16 251 58.6 6.17E-11 4.13E-03 154.5 -7.5 2.02E-08 68 18 10 262 60.9 7.17E-11 3.54E-03 155.0 -7.5 2.60E-08 75 18 13 222 28.5 1.53E-09 5.88E-02 155.5 -7.5 3.51E-07 71 20 19 210 8.7 7.66E-07 2.2 156.0 -7.5 6.72E-08 76 20 14 216 20.0 8.49E-07 13. 156.5 -7.5 3.10E-08 76 28 13 231 41.4 5.12E-07 17. 157.0 -7.5 1.90E-08 1 327 16 236 44.7 1.37E-07 7.2 157.5 -7.5 8.92E-09 77 45 13 229 46.6 4.57E-09 0.51 158.0 -7.5 7.42E-09 79 60 11 228 45.3 9.06E-11 1.22E-02 158.5 -7.5 1.05E-08 49 147 4 52 54.2 1.66E-10 1.58E-02 159.0 -7.5 7.64E-09 47 147 4 242 58.8 1.07E-10 1.41E-02 ………………………………………………………………………………………………………

Short-term forecast uses Omori's law toextrapolate presentseismicity.

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 150-160E

1 2005 8 1 4 40 47.09 154.22 15.0 5.70 0.4 68 286 5 29 Thr 2 2005 10 15 10 6 46.85 154.33 46.0 6.17 1.8 64 289 1 22 Thr 3 2006 8 20 3 1 49.58 156.87 35.6 6.05 1.2 72 350 10 229 Thr 4 2006 9 28 1 36 46.45 153.66 12.0 6.00 1.0 71 278 18 122 Thr 5 2006 9 30 17 50 46.36 153.50 12.0 6.65 9.3 69 296 21 130 Thr 6 2006 9 30 17 56 46.19 153.35 16.4 6.03 1.1 72 291 18 122 Thr 7 2006 10 1 9 6 46.44 153.68 12.0 6.63 8.8 70 297 20 127 Thr 8 2006 10 13 13 47 46.15 153.73 12.0 5.90 0.7 70 287 19 129 Thr 9 2006 11 12 21 27 48.21 154.77 48.6 6.00 1.0 80 299 10 120 Thr 10 2006 11 15 11 15 46.75 154.32 13.4 8.35 3400.0 60 302 30 123 Thr 11 2006 11 16 6 20 46.41 154.68 12.0 6.00 1.0 4 314 82 190 Nor 12 2006 12 7 19 10 46.23 154.44 13.8 6.40 4.0 2 322 86 83 Nor 13 2006 12 26 15 19 48.18 155.20 38.0 6.00 1.0 77 340 11 133 Thr 14 2007 1 13 4 23 46.18 154.80 12.0 8.14 1650.0 10 150 67 264 Nor 15 2007 1 13 17 37 47.04 156.44 26.6 6.02 1.1 5 176 48 272 Nor 16 2007 4 9 10 18 48.21 155.17 33.0 5.83 0.6 73 318 16 124 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.

Short-term forecast: 1969-today, PDE catalog, M>=5.0Omori’s law is used to extrapolate earthquake record.Parameters are determined by the maximum likelihood search.

Kossobokov, 2006. Testing earthquake prediction methods: ``The West Pacific short-term forecast of earthquakes with magnitude MwHRV \ge 5.8", Tectonophysics, 413(1-2), 25-31.

See also Kagan & Jackson, TECTO, 2006, pp. 33-38.

California and Nevada and its surrounding long-term seismicity forecast.Color tones show the rates of shallow earthquake occurrencecalculated using the PDE 1969-2008 catalog.

California and Nevada and its surrounding long-term seismicity forecast.Color tones show the rates of shallow earthquake occurrencecalculated using the ANSS 1932-2008 catalog.

California and Nevada and its surrounding long-term seismicity forecast.Color tones show the rates of shallow earthquake occurrencecalculated using the PDE 1969-2008 catalog.

California and Nevada and its surrounding short-termseismicity forecast.Color tones show the rates of shallow earthquake occurrencecalculated using the ANSS 1932-2008 catalog.

Forecast for the area surrounding the recent Chino Hills, CA earthquake (2008/07/29 m5.4).

The long-term forecasts (columns 3 and 6) are similar, taking into account different magnitude thresholds (m_t=4.7 for the PDE and m_t=4.0 for the ANSS catalog) and slightly different epicentral coordinates.

The ratio of two long-term earthquake rate sums for both catalogs 4.3.The expected ratio according to the Gutenberg-Richter relation with the b-value of 0.9: 10^0.63 = 4.27. Similarly, if we compare the short-term rates (columns 4 and 7) the rates ratio is 4.51.

Color tones show the rates of shallow earthquake occurrencecalculated using the PDE 1969-2008 catalog.

Short-term forecast: 1969-today, PDE catalog, M>=4.7

Here we demonstrate forecast effectiveness:displayed earthquakesoccurred aftersmoothed seismicity forecasthad been calculated.

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.

END

Thank you

Bird, P., Y. Y. Kagan, D. D. Jackson, F. P. Schoenberg,and M. J. Werner, 2008.Linear and Nonlinear Relations Between Relative Plate Velocityand Seismicity

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