The AMR concept can be interpreted as a data-fitting exercise since there is no general relationship between the radius of the search, the magnitude range and the period of time before the mainshock according to its magnitude. However, based on the results of Bowman et al. (1998), the AMR circular search seems to be optimal between 150km and 250km around a magnitude 6.5-7.5 event. Figure 2.6 presents maps of c-values for a possible M7 event in southern California, using a 30-year period of time and three radii: 150km, 200km and 250km. The occurrence of large earthquakes during the tested period increases the c-value, meaning that there is no significant AMR at that time and location. Once the seismicity associated with this event is no longer included in the data set, the results are in better agreement with the seismicity. This is particularly the case for Loma Prieta in 1989 and for Hector Mine in 1999.
Figure 2.6 also presents a comparison between the AMR grid search results and models of stress change over southern California in order to evaluate if areas inferred to be highly stressed also exhibit significant evidence of accelerating seismicity. Rather than assuming a complete stress drop on all surrounding fault segments implied by the back-slip stress lobe (Bowman and King, 2001), we consider that stress evolves with time from contributions of coseismic, postseismic and interseismic processes, governed by the elastic and viscous properties of the lithosphere. This emphasizes the importance of postseismic relaxation processes in time-dependent stress transfer and resulting earthquake hazard. Except for the contributions from the largest earthquakes, there is no large variation in the stress pattern with time. The AMR and stress change maps do not look similar when there are many large earthquakes in the periods of the AMR calculations. However, they present similar features in 1985 and 1995.
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