Inferring the Causal Structure Among Injection-Induced Seismicity with Linear Intensity Models

We present a method for earthquake causal attribution, which allows us to quantify the probability that an event is due to tectonic loading, a previous earthquake, or a fluid injection. The method is an extension of the stochastic declustering algorithm of Marsan and Lengliné (2008). Earthquake triggering is represented by nonparametric, mean-field kernels, which scale linearly with the seismic moment or hydraulic energy of the trigger. The kernels are estimated based on a linear intensity model via expectation–maximization, with uncertainties derived from Gaussian approximation of the incomplete-data likelihood. Some general implications of the resulting probabilistic causal structure, including an explicit algorithm to quantify the cascading effects, are illustrated. The estimators are validated using synthetic catalogs generated with an extended epidemic-type aftershock sequence model, which accounts for injection-induced earthquakes. Application to southern California seismicity and comparisons with the nearest-neighbor distance declustering method support the linearity assumption in the seismic moment. Application to seismicity related to CO ₂ injection in the Illinois Basin-Decatur Project (for the period 2011–2014) reveals that 11% of the earthquakes were directly triggered by injection, 89% were due to previous earthquakes, whereas the contribution from tectonic loading was negligible (< 1%). The earthquake interaction kernels in both cases show ∼1/t decay in time and indicate triggering by elastic static stress transfer; the injection kernels in the Decatur case suggest pore-pressure diffusion as a more likely mechanism than poroelasticity. The Gutenberg–Richter b-value is estimated to be larger for anthropogenic events (∼1.4) than natural ones (∼1.0). Deviations from the model suggest spatial anisotropy of earthquake interaction in both natural and induced settings.