Assessment of the completeness of earthquake catalogs

Abstract

Since earthquake catalogs are not complete over the magnitude range covered, one should check the completeness of catalogs before any use. To this end, I propose a new method based on the Chi-square test to assess the completeness of earthquake catalogs. The performance of the method was tested using simulated earthquake catalogs. The performance test revealed that the method slightly underestimates the magnitude of catalog completeness, mc at the significance level lower than about 20%. Even in this condition, however, the maximum earthquake, mmax and the Richter-b can still be estimated with acceptable accuracies unless the catalog size is not too small. It is not recommended to increase the significance level for a better estimation of mc because the estimation of mc itself is not an ultimate goal but just a preliminary step to the other studies such as estimation of Richter-b or mmax. The application of the method to the Korean earthquakes showed that an optimal significance level can be chosen from the investigation of the behavior of estimates over a range of the significance level. The performance of the method was also compared with those of the two existing methods using the sub-catalogs of the Japanese earthquakes and the Switzerland earthquakes: the present method gives the largest estimates of mc. The application to real catalogs suggests that an optimal significance level is specific to each catalog. Therefore, it is empathized that one should investigate the behaviors of estimates over a range of the significant level to confirm the stability of estimates.