Sampling uncertainties and source b likelihood for the Gutenberg-Richter b value from the Aki-Utsu method

The Aki-Utsu method of Gutenberg-Richter (G-R) b value estimation is often misapplied so that estimations not using the G-R histogram are often meaningless because they are not based on adequate samples. We propose a method to estimate the likelihood Pr( b ǀ b m , N , M 1 , M 2 ) that an observed b m estimate, based on a sample of N magnitudes within an [ M 1 − ≤ ΔM /2, M 2 + ΔM /2) range, where ΔM = 0.1 is the usual rounding applied to magnitudes, is due to a “true” source b value, b , and use these likelihoods to estimate source b ranges corresponding to various confidence levels. As an example of application of the method, we estimate the b values before and after the occurrence of a 7.4-magnitude earthquake in the Mexican subduction zone, and find a difference of 0.82 between them with 100% confidence that the b values are different.