Apparent breaks in scaling in the earthquake cumulative frequency-magnitude distribution: Fact or artifact?

摘要

It has been suggested that the finite width of the seismogenic lithosphere can have a strong effect on the frequency-moment relation for large earthquakes. Theories have been proposed in which large earthquakes have either a shallower or a steeper power-law slope in the incremental frequency-moment distribution, at characteristic seismic moments corresponding to earthquakes that rupture the entire seismogenic depth. However, many authors have applied the predicted double-slope distribution, which requires five independent parameters, to cumulative frequency data, and used the location of the break of slope to make inferences on characteristic size effects in the earthquake source in different seismotectonic regions. Here we examine the problem in a forward modeling mode by adding a realistic degree of statistical scatter to ideal incremental frequency-moment distributions of various commonly used forms. Adopting a priori the assumption of a piecewise linear distribution, we find in each case apparently statistically distinct breaks of slope that are not present in the parent distribution. These breaks of slope are artifacts produced by a combination of (a) high-frequency noise introduced by the random statistical scatter, (b) the more gradual natural roll-over in the cumulative frequency data near the maximum seismic moment, and (c) a systematic increase in the apparent regression coefficient due to the natural smoothing effect of the use of cumulative-frequency data. Therefore, if there is no apparent break of slope in the incremental distribution, it is unwise to interpret the cumulative-frequency data uniquely in terms of a break in slope. Until such breaks of slope can be distinguished in incremental-frequency data, we conclude that alternative methods (inversion of fault length and width from individual source mechanisms/aftershock sequences etc.) should be preferred for the examination of finite-depth effects, and that simpler solutions to the frequency-moment problem should be adopted for seismic-hazard applications. [References: 35]