Abstract

The power-law relationship has been regarded as the fundamental description of the size distribution from large-scale-earthquake to small-scale-laboratory rock ruptures. However, deviation from the power-law relationship has often been reported, especially when the amplitude distribution is used for -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 power law and prove that the cumulative frequency distribution will inevitably result in deviation from the power law. We also discuss modification of the attenuation on the doubly truncated size distribution from a more general perspective. We find that in a certain interval, the attenuation will not modify the size distribution and the -value is theoretically verified to be unchanged. Based on these discussions, we propose a new -value estimation procedure for rock acoustic emission testing and apply it to a dilation rupturing test, the procedure exhibits good performance.