Yan Y. Kagan

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

CA 90095-1567, ykagan@ucla.edu, http://eq.ess.ucla.edu/~kagan.html

Full Earth high-resolution earthquake forecasts and their testing (Leon Knopoff lecture)

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

Leon Knopoff (1925/7/1–2011/1/20)

L. Knopoff was one of founders of statistical seismology

Outline of the Talk

• Quantitative earthquake prediction -- Leon Knopoff’s efforts at early stages and their later developments.

• Current global earthquake forecasts and their testing.

• Maximum size estimates for subduction zones relevant for Tohoku (Japan) M9 earthquake as well as long- and short-term seismicity rate forecasts in its region.

NLLI /)/(log 02Information score:

Predictive ratio or Probability gain:

The first quantitative model for earthquake forecast and testing of its effectiveness:

IG 2

where L is

the likelihood function, 0L is the likelihood functionfor the Poisson process and N is events number.

Kagan and Knopoff, Science, 236, 1563-1567, 1987.

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

Kagan, Y. Y., and D. D. Jackson, 1994. Long-term probabilisticforecasting of earthquakes, J. Geophys. Res., 99, 13,685-13,700.

Kagan, Y. Y., and D. D. Jackson, 1995. New seismic gap hypothesis: Fiveyears after, J. Geophys. Res., 100, 3943-3959.

N test (events number) L test (events location likelihood)R test (likelihood comparison of models)

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

Combined long- and short-term forecast for north- and south-western Pacific area

Kagan, Y. Y., and D. D. Jackson, 2000. Probabilistic forecasting of earthquakes, (Leon Knopoff's Festschrift), Geophys. J. Int., 143, 438-453.

Forecast:Long-term

earthquake rate based on PDE catalog 1969-

present.0.1 x 0.1 degree,

Magnitude M>=5.0

Forecast:Short-term

earthquake rate based on PDE catalog 1969-

present.0.1 x 0.1 degree,

Magnitude M>=5.0

Power-law kernel

Fisher distribution kernel

Adaptive kernel smoothing

Adaptive kernel smoothing

improves ourforecast in seismically quiet areas.

Tohoku M9 earthquake and tsunami

http://eq.ess.ucla.edu/~kagan/japan_2011_eq_index.html

Advantages ofthis distribution:

Simple (only one more parameter than G-R);Has a finite integrated moment (unlike G-R) for < 1;

Fits global subcatalogs slightly better than the gamma distribution.

Kagan, Seismic moment-frequency relation for shallow earthquakes: Regional comparison, J. Geophys. Res., 102, 2835-2852 (1997).

In the GCMT catalog, the number of earthquakes with M>=5.8 in a spherical rectangle 35-40N, 140-146E, covering the rupture area of the Tohoku event, is 108 for years 1977-2010. If we assume that the corner magnitude is well above M9.0 (like M9.6 for subduction zones, see Bird and Kagan, BSSA, 94(6), 2380-2399, 2004), this would mean that the repeat time for the M9 and larger event in this rectangle is about 370 years.

Elementary computation for earthquake rate

• Plate convergence rate at northern Honshu island is about 9 cm/year (Kanamori, Nature, 2011).

• If we assume that M9.25 earthquake has an average slip 25 m, this means, that (presuming all slip is by M9.25 quakes) their recurrence time should be about 280 years (McCaffrey, 2008). If we assume that the largest event is only M8.25, then they should repeat every 28 years! Changing the coupling coefficient to 50% would not resolve the paradox of the moment conservation principle: how to explain earthquake rate with the maximum event size less than M8?

Table of earthquake

pairs, M>=7.5

END

Thank you

END

Thank you

Since 1987 (Kagan and Knopoff, Science, 1987) we have developed statistical short- and long-term earthquake forecasts to predict earthquake rate per unit area, time, and magnitude. The forecasts are based on smoothed maps of past seismicity and assume spatial and temporal clustering (Kagan and Jackson, 2000; 2011). Our new program forecasts earthquakes on a 0.1 degree grid for a global region 90N--90S latitude. We use the PDE catalog that reports many smaller quakes (M>=5.0). For the long-term forecast we test two types of smoothing kernels based on power-law and on the spherical Fisher distribution. We employ adaptive kernel smoothing which improves our forecast in seismically quiet areas. Our forecasts can be tested within a relatively short time period since smaller events occur with greater frequency. The forecast efficiency can be measured by likelihood scores expressed as the average probability gains per earthquake compared to spatially or temporally uniform Poisson distribution. The other method uses the error diagram to display the forecasted point density and the point events.

Abstract

As an illustration, we display several short-term forecasts, madebefore and after the M9.1 Japanese Tohoku earthquake of 2011/3/11. AM7.5 foreshock occurred two days before the mainshock. Due to this, theshort-term rate immediately preceding the Tohoku event was about 100times higher than the long-term rates. After the Tohoku earthquake therate increased by a factor of 1000. One month later, the rate remainedabout 100 times higher than the long-term rate. The major issue for thelong-term seismicity forecast in the Tohoku area was the maximumearthquake size (Nature 2011/3/31; Science 2011/4/1). Whereas 2009Japan's seismic hazard map predicted the maximum magnitude of 7.7(ibid.), the estimate based on seismic moment conservation principleanticipated the maximum magnitude of the order M8.6--9.6. Is the focalarea of the Tohoku earthquake "destressed", making the probability of anew large event lower in this area, though it can increase in nearbyzones? Our results suggest that this may not be the case. We find thatearthquakes as large as M>=7.5 often occur in practically the same areaas previous large events.

Abstract (cont.)

Stochastic models of earthquake occurrence and forecasting

• Empirical branching models (Kagan, 1973a,b; Kagan and Knopoff, 1987; Ogata, 1988, 1998; Kagan, 2006; 2010).

• Long-term models for earthquake occurrence, optimization and testing of smoothing procedure (Kagan and Jackson, 1994, 2000; 2010).

• Physical branching models – propagation of earthquake fault is simulated (Kagan and Knopoff, 1981; Kagan, 1982).

Earthquake rate forecasting• The fractal dimension of earthquake process is lower

than the embedding dimension: Space – 2.2 in 3D,Time – 0.5 in 1D.

• This allows us to forecast rate of earthquake occurrence – specify regions of high probability and use temporal clustering for short-term forecast -- evaluating possibility of new event.

• Long-term forecast: Spatial smoothing kernel is optimized by using first temporal part of a catalog to forecast its second part.

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

Earthquake forecast conclusions

• We present an earthquake forecast program which quantitatively predicts both long- and short-term earthquake probabilities.

• The program is numerically and rigorously testable both retrospectively and prospectively as done by CSEP worldwide, as well as in California, Italy, Japan, New Zealand, etc.

• It is ready to be implemented as a technological solution for earthquake hazard forecasting and early warning.

Tohoku M9 earthquake and tsunami

http://eq.ess.ucla.edu/~kagan/japan_2011_eq_index.html

Kagan, JGR, 102, 2835-2852 (1997). Plot #12 is Flinn-Engdahl’s #19, Japan-Kamchatka, Mmax = 8.62+/-0.28