A physical model for the motion of the Sierra Block relative to North America

We explain the motion of the Sierra Block with respect to North America by treating it as a rigid inclusion within a thin sheet of non-Newtonian fluid, representing the continental lithosphere of North America. Deformation within North America is driven by a constant velocity applied to its western boundary by the Pacific plate. The deforming lithosphere applies forces to the edges of the block, and the requirement that these forces sum to zero leads to an approximate analytical solution in which the speed of the block, normalized by the rate of plate relative motion, depends on the dimensions of the block, its distance from the boundary, and on the power-law index, n, in the constitutive relation for the non-Newtonian fluid. Numerical solutions to the thin viscous sheet equation confirm the validity of this approximation. The speed of the Sierra Block with respect to North America is consistent with that of a rigid body, of the same shape and position, embedded within a thin viscous sheet of non-Newtonian fluid having a power-law index, n, between 2 and 6. A tighter constraint on n is provided by profiles of velocity, taken in the direction perpendicular to plate relative motion; comparison between observed profiles and those from a thin sheet model support a value of n ∼ 3 for the index.