Abstract

An outstanding question for predicting hazard from induced seismicity is what controls the size distribution of events. For injection‐induced seismicity, ruptures may be confined to the region of perturbed stress and pore pressure when the background ratio of shear to normal stress is low. We explore the distribution of earthquake magnitudes under the restrictive assumption that no events occur outside the stress‐perturbed region around the injector. We derive mathematical expressions for the instantaneous distribution of earthquake magnitudes given a volume‐averaged seismicity rate, growth rate of the perturbed region, and background fault‐size distribution, assuming the latter follows a truncated Gutenberg–Richter distribution (GRD). The distribution of magnitudes can be written as the sum of three terms: faults fully inside the region, partially inside, and faults fully covering the region. The predicted frequency–magnitude distribution shows time‐dependent changes relative to the GRD. These depend on the ratio of largest fault size to the (time‐dependent) radius of the perturbed region and the b‐value. The largest magnitude event is the smaller of either the perturbed region or largest fault size present, and in some simulations is observed post shut‐in due to the high rate of events just after shut‐in coupled with the continued growth of the perturbed region.

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