Testing the completeness of earthquake catalogues and the hypothesis of self-similarity

Abstract

Self-similarity of the earthquake process is consistent with the observed linear b-value relation log (N) = a – bM, where N is the number of earthquakes with magnitude M. Deviations from linearity are believed to be due to statistical fluctuations because of the scarcity of events at large M, or from incompleteness because of a detection threshold at small M. Above some magnitude level, all local events are detected, because they exceed the noise background on the seismogram. As magnitude decreases, however, events go undetected as the seismic signal approaches the noise background. Thus more of the smallest events should be logged at night than during the day, because the cultural noise sources and winds are diminished at night, resulting in presumably quieter seismograms. Here we use this day-to-night noise modulation to develop a completeness test for earthquake catalogues; catalogues that indicate no significant modulation are considered complete. We test three catalogues and show that the completeness magnitude can be different from the magnitude at which the b-value departs from linearity. In particular, catalogues that show significant deviations in linearity at small M but are otherwise complete, are at odds with the hypothesis of earthquake self-similarity.