Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States, and Japan

We mapped the minimum magnitude of complete reporting, M-c, for Alaska, the western United States, and for the JUNEC earthquake catalog of Japan. hi, was estimated based on its departure from the linear frequency-magnitude relation of the 250 closest earthquakes to grid nodes, spaced 10 km apart. In all catalogs studied, M-c was strongly heterogeneous. In offshore areas the M-c was typically one unit of magnitude higher than onshore. On land also, M-c can vary by one order of magnitude over distance less than 50 km. We recommend that seismicity studies that depend on complete sets of small earthquakes should be limited to areas with similar M-c, or the minimum magnitude for the analysis has to be raised to the highest common value of M-c. We believe that the data quality, as reflected by the M-c level, should be used to define the spatial extent of seismicity studies where M-c plays a role. The method we use calculates the goodness of fit between a power law fit to the data and the observed frequency-magnitude distribution as a function of a lower cutoff of the magnitude data. M-c is defined as the magnitude at which 90% of the data can be modeled by a power law fit. M-c in the 1990s is approximately 1.2 +/- 0.4 in most parts of California, 1.8 +/- 0.4 in most of Alaska (Aleutians and Panhandle excluded), and at a higher level in the JUNEC catalog for Japan. Various sources, such as explosions and earthquake families beneath volcanoes, can lead to distributions that cannot be fit well by power laws. For the Hokkaido region we demonstrate how neglecting the spatial variability of M-c can lead to erroneous assumptions about deviations from self-similarity of earthquake scaling.