Modeling Injection Induced Seismicity with Poro-Elasticity and Time-Dependent Earthquake Nucleation

Abstract:

The standard approach to modeling injection-induced seismicity (IIS) considers Coulomb failure stress changes accounting only for pore-pressure changes, which are solved by the diffusion equation. However, this “diffusion” triggering mechanism is not comprehensive. Lab experiments indicate earthquake nucleation also depends on stress history. Here we add two effects in modeling IIS: 1) poro-elastic coupling between solid stresses and pore-pressure, and 2) time dependent earthquake nucleation under applied stresses.

In this model, we compute stress and pore-pressure changes due to a point source injecting in a homogeneous, poro-elastic full space (Rudnicki, 1986). The Coulomb stress history is used to compute seismicity rate changes based on the time-dependent nucleation model of Dieterich (1994). Our new model reveals: 1) poro-elastic coupling breaks the radial symmetry in seismicity, 2) nucleation introduces a characteristic nucleation time ta, which affects the temporal evolution of seismicity rates, and 3) for some fault geometries, the seismicity rate may increase following shut in.

For constant injection flux, the log of seismicity rate scales with the change in Coulomb stress at short time, consistent with diffusion profiles. At longer time, the model predicts seismicity rates decaying with time, consistent with some observations. The contour shape and decay time are characterized by ta. For finite injection with box-car flux history, seismicity rates plummet near the injector, but may continue for some time at greater distance. Depending on fault orientations, seismicity rates may increase after shut-in due to coupling effects. It has been observed in some cases that the maximum magnitude of induced quakes occurs after shut-in. This may be understood by the fact that the volume of perturbed crust increases with injection time, which influences probability of triggering an event of a given magnitude. Whether coupling effects are important in post shut-in behavior is unknown, however we show that gradually decreasing injection flux can eliminate the post shut-in seismicity increase.