Gutenberg–Richter b-value determination and large-magnitudes sampling

Aki’s maximum likelihood method of Gutenberg–Richter b-value estimation is based on the premise that magnitudes above a given threshold are distributed exponentially and presupposes that sampling is adequate for all these magnitudes; clearly, sampling will not be adequate for magnitudes having average recurrence times longer than the observation time. Thus, for any given sample, there is a higher-magnitude completeness threshold. The importance of considering this higher-magnitude threshold is discussed, the effect of incomplete large-magnitude sampling is evaluated, and a method is given for correcting the observations.

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