Geodynamics - Problem Set 8

Problem Set 8 1) We can deduce some interesting results about mantle viscosity and global return flow from some simple 1-D models. Assume that plates are 100 km thick. Below the plates a low viscosity layer extends to 600 km depth, below which the mantle is assumed rigid. Model I: Oceanic Plate Trench 100 km { L Ridge vp { η 500 km z An oceanic plate moves from ridge to trench with velocity v. The plate has length L, the asthenosphere viscosity is η . There are two components to the flow in the asthenosphere (assumed 1 dimensional). The first is the flow dragged by the plate vc (for Couette flow). Write an expression for vc as a function of z, the depth below the base of the plate. The second flow component vR (Poiselle flow) results from the return flow of material from trench to ridge, sufficient to transport a flux of 100km ⋅v P , plus any material dragged in, back to the ridge. Write an expression for vR as a function of z, and for V T ( z) = V R (z ) + Vc (z ) . What is the total pressure drop from trench to ridge? What topographic surface expression would it have? Using a reasonable upper bound to this topography of 1 km, find an upper bound for η . How does this compare to one estimate from postglacial rebound of 1021 Pas? Model II: The real world is more complicated. In particular, because of the 3-D nature of plate geometry, more than one path exists from any given trench back to a ridge. For example, material subducting in the Aleutian arc can return to the East Pacific Rise beneath the Pacific Plate (L = 8,000 km) or beneath the N. American plate (L = 12,000 km). The pressure drop is the same either way. An idealized geometry is: EPR v =0 Aleut 12,000 km vp 8,000 km PAleut PEPR N. America EPR PEPR Pacific Write an expression and make a plot for the total flow velocity vT(z) underneath the Pacific and N. American plates. (Remember, under the Pacific, VT = Vc + VR; under N. America, VT = VR; all material arriving at the trench must return to the ridge.) Compare the results of the flow under the Pacific for Model I and Model II (include a plot of V(z) for both cases).