Response of induced seismicity to injection rate reduction: models of delay, decay, quiescence, recovery and Oklahoma.

When injection-induced seismicity poses a risk to communities, the common approach to mitigation is either to dramatically injection rates, or to halt operations altogether. This strategy applies to both individual wells and well clusters, such as those within the Area of Interest for Triggered Seismicity in Western Oklahoma (WO), where in 2016 a 40% volume reduction mandate was imposed by the state regulator. Here, we quantify how induced seismicity responds to an injection reduction at the responsible well or wells. We introduce analytical and numerical models of pressure diffusion in idealized geometries, and couple these to steady-state pressurization and rate-state models of earthquake triggering. We find that the onset delay and post-reduction behavior - decay, sometimes quiescence, and recovery - depend on the critical triggering pressure, diffusion, and rate-state parameters. We then adapt our model to replicate, in an aggregate sense, wastewater injection and induced seismicity in Western Oklahoma. Using a four parameter model, we calibrate models that capture the timing of onset, peak seismicity, and recent pace of decline. Our models imply that diffusivity in the Arbuckle formation, into which high volume injection is occurring, is high (at least 6.8 m²s^-1). Furthermore, the critical triggering pressure is inferred to be between 0.01 and 0.15 MPa, and fluid overpressure at 4.5 km depth in the basement is estimated to have increased by as much as 0.55 MPa as of 2018. We simulate future seismicity in the region out to 2025 under three injection scenarios. Fixing the 2018 injection rate, which is already less than the maximum allowed by the state regulator, we suggest that there remains a high likelihood of further M>5 earthquakes. If the purpose of the volume reduction mandate in Western Oklahoma is to mitigate the risk of damaging earthquakes, then, at present levels, it is inadequate.