Converting Magnitudes Based on the Temporal Stability of a- and b-Values in the Gutenberg-Richter Law

Abstract

The problem of converting from one magnitude scale to another is revisited in light of a method that preserves the b ‐value of the Gutenberg–Richter (GR) law of one of the two magnitude distributions. This methodology allows for the use of all reliable magnitude data rather than data of only those events for which paired magnitudes are available. Our method avoids resolving incompatible magnitude ranges. The temporal stability of a ‐ and b ‐values and of the resulting linear relation coefficients is considered as a basis for selecting an optimum set of parameters and time intervals for the regression. This analysis also provides additional insight into the basic reporting characteristics through time for a particular network. The conversion of body‐wave magnitude ( m b) to surface‐wave magnitude ( M s) is considered, in particular, since that is the case often faced in many geographical areas that deal with limited data for M s. M s to M w conversion is then straightforward with the exception of very large events. Three regional data sets, drawn from the same source (International Seismological Centre [ISC] catalog) in order to avoid bias due to magnitude estimate procedures, are analyzed separately as test cases in order to show the advantages and possible limitations of the method. The results provide time intervals best suited for further analysis on the basis of seismic record integrity, in addition to offering further insight about the variability of the b ‐value as a function of data recording.