A Novel Method for Improving the Robustness of Rock Acoustic Emission <i>b</i> Value Estimation through Data Volume Expansion

Abstract The slope b in Gutenberg–Richter (G–R) relationship is an essential parameter to describe the size distribution characteristics from small-scale acoustic emission (AE) to large-scale natural earthquake. Stable and accurate b value estimation is vital when analyzing rock damage and seismic hazards through the spatial and temporal variations of b values. Here, we perform a detailed analysis of the effect of data volume on b value estimation and proposed a new data volume expansion method to obtain accurate b value estimation based on maximum likelihood derivation. Then, the effectiveness of the newly proposed method is verified through synthetic AE data and found that the standard errors of b value estimation or log-linear characteristics of frequency–amplitude distributions after data volume expansion are smaller, and all differences between the theoretical and estimated b values are far less than 0.1. Meanwhile, we also adopt the newly proposed method for b value estimation in a specially designed laboratory rock AE test and discussed the applicability of the method through the relationship between internal structural characteristics of various rocks and their rupture source size distribution. The results indicate that the estimated b value after data volume expansion can better characterize the underlying source size distribution of rock samples under deformation.