The recurrence time (or probability of annual occurrence) of maximum credible earthquakes, Mmax, cannot be estimated directly from the mb frequency magnitude distribution because Mmax is estimated on the Ms scale. Converting Mmax to the mb scale is not an acceptable solution to this problem, primarily because the mb scale saturates for mb > 6. In addition, many large ruptures are multiple events, in which case mb is independent of Ms. Less than 16 per cent of the earthquakes included in the National Geophysical and Solar-Terrestrial Data Center Hypocenter Data File are assigned Ms values. Therefore, the frequency magnitude distribution is defined on the mb scale in most parts of the world. For the purpose of recurrence time estimates, we propose that the frequency magnitude distribution has to be defined by transforming mb values to Ms by the following equations
The bottom relation was obtained by straight line fits allowing for errors between 0.2 and 0.5 in both parameters. Where local networks furnish large numbers of ML values, these can be equated approximately to Ms values. Some of the procedures proposed in the literature for using the frequency-magnitude distribution for determining recurrence time of Mmax = 8 events lead to overestimates of an order of magnitude.