A New b Value Estimation Method in Rock Acoustic Emission Testing

The Gutenberg-Richter (G-R) relationship has been regarded as the fundamental description of the size distribution from large-scale-earthquake to small-scale-laboratory rock ruptures. However, because deviation from the G-R relationship has often been reported, especially when the amplitude distribution is used for b value estimation in rock acoustic emission testing, the effect of attenuation should be considered. Here, we perform a detailed analysis on the deviation of the size distribution from a G-R law and discuss modification of the attenuation on the doubly truncated size distribution from a more general perspective. We find that the attenuation will not modify the size distribution, and the b value is theoretically verified to be unchanged within an interval specified by the minimum and maximum amount of attenuation. Based on these discussions, we propose a new b value estimation procedure for rock acoustic emission testing and apply it to a dilation rupturing test; the results confirm that b value depends on material heterogeneity and stress.