Bilinear Magnitude‐Frequency Distributions and Characteristic Earthquakes During Hydraulic Fracturing

Previous studies show that a temporal drop in the b value (slope) of magnitude‐frequency distributions observed during hydraulic‐fracturing operations could signify the activation of a preexisting fault system. Based on a new data set from Alberta, Canada, we provide a case study wherein events induced during hydraulic fracturing are localized within spatial clusters with a range of b values from ∼1.0 to ∼2.5. The distribution in b values is related to the orientation and depth distribution of these clusters. As a consequence of the superposition of spatially varying clusters, the catalog for the entire data set yields a bilinear magnitude distribution with exceptionally low apparent b value at larger magnitude levels. Several clusters are compatible (at 95% confidence level) with the characteristic‐earthquake hypothesis, a controversial model for some fault systems wherein episodic large ruptures occur significantly above the maximum‐likelihood Gutenberg‐Richter relationship. Plain Language Summary The b value, or slope, of the semilogarithmic magnitude‐frequency distribution quantifies the relative distribution of large and small events. Variability in the b value over space and time provides insight into the changes of behavior within the subsurface. We show that there is significant variability in b values at both regional and local scales in Alberta, Canada. Using a new hydraulic‐fracturing data set, we show that there is an apparent bilinear magnitude distribution. By partitioning the seismic events into spatial and temporal clusters, we show they have varying b values and their superposition explains the bilinear behavior. Furthermore, we show that b value is strongly influenced by the orientation and depth expression of the faults. A number of moderate‐magnitude events fall above the 95% confidence bounds for maximum‐likelihood Gutenberg‐Richter distributions, which is consistent with the characteristic‐earthquake hypothesis. This hypothesis states that over long timescales, episodic rupture occurs over large fault segments such that magnitude‐frequency distributions observed during the interseismic period between characteristic events underestimate the probability of future large events. This could have important implications for quantifying hazard from injection‐induced earthquakes. Key Points Magnitude distributions for seismicity due to hydraulic fracturing exhibit strong spatial variability at local and regional scales Superposition of cluster