1. Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, ykagan@ucla.edu, http://eq.ess.ucla.edu/~kagan.htmlykagan@ucla.edu Statistical properties of earthquake occurrence http://moho.ess.ucla.edu/~kagan/stsei6.ppt

2. Gutenberg-Richter law (distribution of earthquake size)

3. Gutenberg-Richter law (cont.)

4. For the last 20 years a paper has been published every 10 days which substantially analyses b-values. The best measurements of beta-value yields 0.63 (Kagan, 2002; Bird and Kagan, 2004), i.e. about 25% higher than 0.5. Magnitude errors increase beta-value by 3-8% (Kagan, 2000, 2002, 2003), aftershocks increase it by 10-15%, focal mechanism incoherence by 2-5(?) %. Therefore, we conjecture that beta- (or b-) value variations are property of catalogs not of earthquakes.

5. Omori ’ s law (short-term time dependence)  C-value measurements yielded values ranging from seconds to days (Kagan, 2004). Its variation is believed to provide evidence of physical mechanism for the earthquake rupture process. However, Enescu et al. (2009) and other careful measurements suggest that C=0, therefore the non- zero C-value also is a property of catalogs, not of earthquakes.

6.  If the branching property of earthquake occurrence is taken into account, the P-value would increase from ~1.0 to ~1.5 (Kagan and Knopoff, 1981). P=1.5 is suggested by the Inverse Gaussian distribution (Brownian Passage Time) at the short time intervals (Levy distribution).  If we consider earthquakes as consisting of elementary infinitesimal events, then K=1 (Kagan and Knopoff, 1981; Kagan, 1982). Omori’s law (cont.)

7. Spatial distribution of earthquakes It is fractal with the value of the fractal dimension (delta) of 2.25 for shallow seismicity (Kagan, 2007). There is no known mechanism that would explain this value, the only limits are 3.0 > delta > 2.0.

8. Focal mechanism distribution It also seems to be controlled by a fractal type distribution, but because of high dimensionality and complex topological properties (non-commutative group of 3-D rotations) very little theoretical advance can be made. It seems possible that tectonic earthquakes are pure double-couples (Kagan, 2009).

9. END Thank you