Dynamic Controls on the Depth Sensitivity of Lower Crust Viscosity Inferences Over Tectonic Time Scales

It has been proposed that crustal deformation can result from flow in the lower crust over time scales of several million years (tectonic time scale). Pervious studies demonstrated that over these time scales, upper crustal deformation mainly depends on the flux of the lower crustal flow and not on the details of the flow at depth. As temperature increases with depth, the viscosity of the lower crust is expected to decrease. Thus a homogeneous Newtonian viscosity over an assumed homogenous viscous lower crustal channel is merely an apparent viscosity of the crust. We consider models of a lower crustal flow with depth-dependent viscosity in order to draw connections between this apparent viscosity and equivalent depth-dependent viscosity profiles. We find that there is a large range of depth-dependent viscosity profiles that are consistent with an inferred apparent viscosity. Also, the apparent viscosity is in general biased toward the lowest viscosities in the lower crust. Furthermore, if the lower crustal channel is underestimated, the apparent viscosity can be lower than the lowest actual viscosity in the lower crust. We also consider unidirectional flow in models with nonlinear, depth-dependent viscosity, and find that very low apparent viscosities are only consistent with either high temperatures or strong stresses driving lower crustal flow.