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. Plain Language Summary The Gutenberg‐Richter relationship is an intrinsic characteristic of the frequency‐size distribution of earthquake and laboratory rock ruptures, indicating that the number of small‐scale ruptures is much greater than the number of large‐scale ones. Nevertheless, due to many reasons such as the statistical methods, inadequate data acquisition, and data truncation in cumulative frequency distribution, deviation from a Gutenberg‐Richter relationship of the frequency‐size distribution is inevitable in practice. In order to understand the deviation of the frequency‐size distribution in the laboratory rock fracture testing, we perform a detailed analysis of the statistical methods and the attenuation effect on the Gutenberg‐Richter relationship of the frequency‐size distribution and propose a new procedure for scaling parameter estimation of Gutenberg‐Richter relationship. This newly proposed procedure shows its reliability in a dilation rupturing test and can well ensure the robustness of the scaling parameter estimation. Key Points The inferred b value for acoustic emission apparent amplitude is equal to that at source irrespective of the form of attenuation law The finite size of the sample leads to a finite range of applicability of the Gutenberg‐Richter law A new method is used to determine the finite range, and its application confirms that b depends on material heterogeneity and stress