Scale dependence in earthquake phenomena and its relevance to earthquake prediction

The recent discovery of a low-velocity, low-e zone with a width of 50-200 m reaching to the top of the ductile part of the crust, by observations on seismic guided waves trapped in the fault zone of the Landers earthquake of 1992, and its identification with the shear zone inferred from the distribution of tension cracks observed on the surface support the existence of a characteristic scale length of the order of 100 m affecting various earthquake phenomena in southern California, as evidenced earlier by the kink in the magnitude frequency relation at about M3, the constant corner frequency for earthquakes with M below about 3, and the source controlled f(max) of 5-10 Hz for major earthquakes, The temporal correlation between coda Q(-1) and the fractional rate of occurrence of earthquakes in the magnitude range 3-3.5, the geographical similarity of coda Q(-1) and seismic velocity at a depth of 20 km, and the simultaneous change of coda Q(-1) and conductivity at the lower crust support the hypotheses that coda Q(-1) may represent the activity of creep fracture in the ductile part of the lithosphere occurring over cracks with a characteristic size of the order of 100 m. The existence of such a characteristic scale length cannot be consistent with the overall self-similarity of earthquakes unless we postulate a discrete hierarchy of such characteristic scale lengths. The discrete hierarchy of characteristic scale lengths is consistent with recently observed logarithmic periodicity in precursory seismicity.