第20回統計地震学セミナー

日時

2011年9月2日(金)， 16:00〜17:00

場所

統計数理研究所 D312B室

講演者

Yan Kagan (Department Earth and Space Sciences (ESS), UCLA)

講演題目

Statistical properties of earthquake occurrence and their application for earthquake forecasting

概要

Earthquake occurrence exhibits scale-invariant statistical properties:
(a) Earthquake size distribution is a power-law (the Gutenberg-Richter relation for magnitudes or the Pareto distribution for seismic moment). Preservation of energy principle requires that the distribution should be limited on the high side; thus we use the generalized gamma or tapered Pareto distribution. The observational value of the distribution index is about 0.65. However, it can be shown that empirical evaluation is upward biased, and the index of 1/2, predicted by theoretical arguments, is likely to be its proper value. The corner (maximum) moment has an universal value for shallow earthquakes occurring in subduction zones. We also determined the corner moment values for 8 other tectonic zones.
(b) Earthquake occurrence has a power-law temporal decay of the rate of the aftershock and foreshock occurrence (Omori's law), with the index 0.5 for shallow earthquakes. The short-term clustering of large earthquakes is followed by a transition to the Poisson occurrence rate. In the subduction zones this transition occurs (depending on the deformation rate) after 7-15 years, whereas in active continents or plate-interiors the transition occurs after decades or even centuries.
(c) The spatial distribution of earthquakes is fractal: the correlation dimension of earthquake hypocenters is equal to 2.2 for shallow earthquakes.
(d) The stochastic 3-D disorientation of earthquake focal mechanisms is approximated by the rotational Cauchy distribution.

On the basis of our statistical studies, since 1977 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. Our recent program forecasts earthquakes on a 0.1 degree grid for a global region 90N--90S latitude. For this purpose 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 the 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 the spatially or temporally uniform Poisson distribution. The other method uses the error diagram to display the forecasted point density and the point events.

As an illustration of our methods, we are trying to answer a question: was the Tohoku mega-earthquake of 2011/3/11 a surprise? We consider three issues related to the 2011 Tohoku earthquake:
(1) Why was the magnitude limit for the Tohoku region so badly underestimated, and how can we estimate realistic limits for subduction zones in general?
(2) How frequently can such large events occur off Tohoku?
(3) Could short-term forecasts have offered effective guidance for emergency preparation?

Two methods can be applied to estimate the maximum earthquake size in any region: statistical analysis of available earthquake records, and the moment conservation principle -- how earthquakes release tectonic deformation. We have developed both methods since 1991. For subduction zones, the seismic record is usually insufficient (in fact it failed badly for Tohoku), because the largest earthquakes are so rare. However, the moment conservation principle yields consistent estimates for all subduction zones. Various measurements imply maximum moment magnitudes of the order 9.0--9.7. A comparison of the inter-earthquake secular strain accumulation and its release by the coseismic slip implies a similar maximum earthquake size estimate. Beginning in 1999 we used our statistical short- and long-term earthquake forecasts, based on the GCMT catalog, for the western Pacific, including Japan. We have posted them on the web and included expected focal mechanisms as well. Long-term forecasts indicate that the average frequency for magnitude 9 earthquakes in the Tohoku area is about 1/400 years. We have archived several forecasts made before and after the Tohoku earthquake. As expected, the Tohoku mega-earthquake changed the forecasted long-term rate by just a few percent. However, the magnitude 7.5 foreshock increased the short term rate to about 100 times the long-term rate, and the magnitude 9 event increased it briefly to more than 1000 times the long-term rate. These results could well justify the development of an operational earthquake forecasting plan.