Collective properties of injection-induced earthquake sequences: 1. Model description and directivity bias

Induced seismicity is of increasing concern for oil and gas, geothermal, and carbon sequestration operations, with several M > 5 events triggered in recent years. Modeling plays an important role in understanding the causes of this seismicity and in constraining seismic hazard. Here we study the collective properties of induced earthquake sequences and the physics underpinning them. In this first paper of a two-part series, we focus on the directivity ratio, which quantifies whether fault rupture is dominated by one (unilateral) or two (bilateral) propagating fronts. In a second paper, we focus on the spatiotemporal and magnitude-frequency distributions of induced seismicity. We develop a model that couples a fracture mechanics description of 1-D fault rupture with fractal stress heterogeneity and the evolving pore pressure distribution around an injection well that triggers earthquakes. The extent of fault rupture is calculated from the equations of motion for two tips of an expanding crack centered at the earthquake hypocenter. Under tectonic loading conditions, our model exhibits a preference for unilateral rupture and a normal distribution of hypocenter locations, two features that are consistent with seismological observations. On the other hand, catalogs of induced events when injection occurs directly onto a fault exhibit a bias toward ruptures that propagate toward the injection well. This bias is due to relatively favorable conditions for rupture that exist within the high-pressure plume. The strength of the directivity bias depends on a number of factors including the style of pressure buildup, the proximity of the fault to failure and event magnitude. For injection off a fault that triggers earthquakes, the modeled directivity bias is small and may be too weak for practical detection. For two hypothetical injection scenarios, we estimate the number of earthquake observations required to detect directivity bias.