The Gutenberg–Richter Relation May Not Hold for the Anthropogenic Seismicity

The empirical Gutenberg–Richter (GR) relation corresponds to an exponential model of magnitude distribution, the most widely used in the probabilistic assessments of seismic hazard and related risk. However, due to the complexity of seismic processes induced by technological activities, this model may not be applicable to anthropogenic seismicity (AS). Applying statistical hypotheses testing procedures, we investigate 63 AS catalogs resulting from various anthropogenic activities such as reservoir impoundment, underground mining, conventional and unconventional hydrocarbon extraction, geothermal energy production, and underground gas storage. In 30 cases (47.6%) the exponential model for magnitude is rejected. Furthermore, in 16 out of these cases, the magnitude probability density functions are complex, having either modes or bumps or both. We discuss possible reasons for the discovered statistically significant deviations of the actual magnitude distributions from the exponential distribution and hence from the GR relation. We demonstrate that using the exponential distribution may lead to unacceptable inaccuracy of seismic hazard estimates in AS. As a remedy, we recommend the use of kernel nonparametric estimators of magnitude distribution.