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SUMMARY The b value is a critical parameter that has been used to describe spatial and temporal size distribution characteristics in data from both natural seismicity and laboratory rock acoustic emission (AE) tests. However, unlike the magnitude used for b value estimation in earthquakes which corrects for hypocentral distance, the apparent amplitude of the AE, is most commonly used for b value estimation in the rock AE test. This ignores the effect of attenuation, which may modify the frequency–amplitude distribution and affect the b value results. Here, we investigate the attenuation effect on the estimate of b value from synthetic data generated by random sampling of a doubly truncated frequency–amplitude distribution and a known underlying b value from a statistical perspective. We generated AE source amplitudes that obey an exponential distribution with different theoretical b values and applied an attenuation operator to obtain apparent frequency–amplitude data for comparison with the true underlying distribution. The results show that the b value is unchanged within a specific interval of amplitude distribution after accounting for attenuation under the conditions examined here, and that data truncation is the primary cause of modification of the frequency–amplitude distribution in the presence of attenuation, rather than attenuation alone. In addition, we employed the same synthetic data simulation scheme to estimate the minimum data volume for accurate estimation of the underlying b value from the apparent amplitude distribution. We found that the determination of the minimum data volume is influenced by the theoretical b value of the underlying distribution: the higher the theoretical b value, the larger the minimum data volume required, varying from 200 events from b 1.5 to 300 for b 1.5.
Chen et al. (Wed,) studied this question.