Stress drops and tidal modulation in a rate and state model with a velocity-weakening to -strengthening transition

We investigate the behavior of slow slip events in a rate and state model that is velocity-weakening at low slip rates and velocity-strengthening at high slip rates. We use a one-dimensional ``strip fault'' model, which treats the slow slip region as a rectangular zone where slip and stress vary along strike, but where stress is presumed to be uniform along dip. With this model, events propagate ``along strike'' with approximately steady state velocity and stress profiles. Stress decays gradually behind the front, reaching a minimum a distance between 10 and 100% of the updip-downdip length behind the front and then increasing slightly even farther from the front. The stress drops in major events in this model appear to be controlled by the ability of nucleated events to propagate along strike. We estimate the stress drop as a function of the model parameters by considering the strain energy released and the fracture energy dissipated at the tip during propagation. The stress drop decreases with increasing updip-downdip length and is smaller for the ``slip'' law formulation of the state evolution law than for the ``aging'' law. We apply tidal modulation to our models by including a sinusoidal forcing in shear stress. The dominant effect of this forcing is a gradual modulation of the propagating velocity profile, with maximum slip rates near or slightly after the maximum applied shear stress. In some cases we also observe small fronts that arise near the tidal maximum, beginning well behind the front and propagating farther back along strike. However, in our simulations these fronts propagate much too slowly to be good parallels for those observed in Cascadia. Using the aging law, we find that it is possible to reproduce both the stress drops and the tidal modulation observed in Cascadia with a reasonable range of parameters. On the other hand, using the slip law, the preferred state evolution law in this case, our models are able to reproduce both observations only for a very limited range of model parameters.