The binned distribution densities of magnitudes in both the complete and the declustered catalogs of earthquakes in the Southern California region have two significantly different branches with crossover magnitude near M = 4.8. In the case of declustered earthquakes, the b-values on the two branches differ significantly from each other by a factor of about two. The absence of self-similarity across a broad range of magnitudes in the distribution of declustered earthquakes is an argument against the application of an assumption of scale-independence to models of main-shock earthquake occurrence, and in turn to the use of such models to justify the assertion that earthquakes are unpredictable. The presumption of scale-independence for complete local earthquake catalogs is attributable, not to a universal process of self-organization leading to future large earthquakes, but to the universality of the process that produces aftershocks, which dominate complete catalogs.
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