We evaluated the efficiency of various models in describing the time decay of aftershock rate of 47 simple sequences occurred in California (37) from 1933 to 2004 and in Italy (10) from 1976 to 2004. We compared the models by the corrected Akaike Information Criterion (AICc) and the Bayesian Information Criterion (BIC), both based on the log-likelihood function but also including a penalty term that takes into account the number of independent observations and of free parameters of each model. These criteria follow two different approaches (probabilistic and Bayesian respectively) well covering the wide spectra of current views on model comparison. To evaluate the role of catalog incompleteness in the first times after the main shock, we compared the performance of different models by varying the starting time T s and the minimum magnitude threshold M min for each sequence. We found that Omori-type models including parameter c are preferable to those not including it, only for short T s and low M min while the latters generally perform better than the formers for T s longer than a few hours and M min larger than the main shock magnitude M m minus 3 units. For T s >1 day or M min >M m -2.5, only about 15% of the sequences still give a preference to models including c. This clearly indicates that a value of parameter c different from zero does not represent a general property of aftershock sequences in California and Italy but it is very likely induced in most cases by catalog incompleteness in the first times after the main shock. We also considered other models of aftershock decay proposed in the literature: the Stretched Exponential Law in two forms (including and not including a time shift) and the band Limited Power Law (LPL). We found that such models perform worse than the Modified Omori Model (MOM) and other Omori-type models for the large majority of sequences, although for LPL, the relatively short duration of the analyzed sequences (one year) might also contribute to its poor performance. Our analysis demonstrates that the the MOM with c kept fixed to 0 represent the better choice for the modeling (and the forecasting) of simple sequence behavior in California and Italy.3
SUMMARY
With the goal of constructing a homogeneous data set of moment magnitudes (Mw) to be used for seismic hazard assessment, we compared Mw estimates from moment tensor catalogues available online. We found an apparent scaling disagreement between Mw estimates from the National Earthquake Information Center (NEIC) of the US Geological Survey and from the Global Centroid Moment Tensor (GCMT) project. We suspect that this is the effect of an underestimation of Mw > 7.0 (M0 > 4.0 × 1019 Nm) computed by NEIC owing to the limitations of their computational approach. We also found an apparent scaling disagreement between GCMT and two regional moment tensor catalogues provided by the ‘Eidgenössische Technische Hochschule Zürich’ (ETHZ) and by the European–Mediterranean Regional Centroid Moment Tensor (RCMT) project of the Italian ‘Istituto Nazionale di Geofisica e Vulcanologia’ (INGV). This is probably the effect of the overestimation of Mw < 5.5 (M0 < 2.2 × 1017 Nm), up to year 2002, and of Mw < 5.0 (M0 < 4.0 × 1016 Nm), since year 2003, owing to the physical limitations of the standard CMT inversion method used by GCMT for the earthquakes of relatively low magnitude. If the discrepant data are excluded from the comparisons, the scaling disagreements become insignificant in all cases. We observed instead small absolute offsets (≤0.1 units) for NEIC and ETHZ catalogues with respect to GCMT whereas there is an almost perfect correspondence between RCMT and GCMT. Finally, we found a clear underestimation of about 0.2 units of Mw magnitudes computed at the INGV using the time‐domain moment tensor (TDMT) method with respect to those reported by GCMT and RCMT. According to our results, we suggest appropriate offset corrections to be applied to Mw estimates from NEIC, ETHZ and TDMT catalogues before merging their data with GCMT and RCMT catalogues. We suggest as well to discard the probably discrepant data from NEIC and GCMT if other Mw estimates from different sources are available for the same earthquakes. We also estimate approximately the average uncertainty of individual Mw estimates to be about 0.07 magnitude units for the GCMT, NEIC, RCMT and ETHZ catalogues and about 0.13 for the TDMT catalogue.
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