If the creep model is correct, the strongest correlation should be found between coda Q−1 and the rate of occurrence of earthquakes with Mc, and the correlation should always be positive. Indeed, Jin and Aki (11) found a remarkable positive correlation between coda Q−1 and the fraction of earthquakes in the magnitude range Mc< M < Mc+0.5 for both central and southern California. Fig. 5 shows the result for central California where the appropriate choice of Mc is 4.0. The correlation is highest (0.84) for the zero time lag and decays symmetrically with the time shift as shown in Fig. 6. A very similar result is obtained for southern California where the appropriate choice of Mc is 3.0. The correlation is again the highest (0.81) at the zero time lag.
Thus, my current working hypothesis is that the temporal change in coda Q−1 reflects the activity of creep fractures in the ductile part of the lithosphere. The ductile part of the lithosphere is larger than the brittle part. The deformation in the ductile part is the source of stress in the brittle part. Although it was found that the coda Q−1 precursor is not reliable, the study of spatial and temporal variation in coda Q−1 may still be promising for understanding the loading process that leads to earthquakes in the brittle part.
The characteristic magnitude Mc attributed to the characteristic scale length of creep fracture in southern California is 3.0, which corresponds to the fault length of a few hundred meters. The closeness of this length to the fault zone width estimated from trapped modes suggests a generic relation between them.
Our creep model may be relevant for understanding some of the intriguing precursory phenomena. For example, the decrease in b value coincident with the increase in coda Q−1 before the Tangshan earthquake of 1976 (53) may be attributed to the activated creep fracture in the ductile crust with scale length corresponding to a Mc value of 4–5, which increased the stress in the brittle part of the crust.
As mentioned earlier, the overall self-similarity governing earthquakes with source dimension from 10 cm to 100 km requires a discrete hierarchy of characteristic scale lengths. Recently, Sornette and Sammis (61) reported a logarithmic periodicity in the precursory seismicity before the Loma Prieta earthquake of 1989. The Renormalization Group equation which leads to the logarithmic periodicity is discrete. One jumps from one time to another by a finite amount, implying the existence of a discrete hierarchy of characteristic scales. We may be at a threshold of building a truly physical theory of earthquake prediction based on the well-defined structure of the seismogenic zone.
This work was supported by the Southern California Earthquake Center under National Science Foundation Cooperative Agreement EAR-8920136 and U.S. Geological Survey Cooperative Agreement –14–08–0001–A0899 and in part by Department of Energy Grant DE-FG03–87ER13807.
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