Analytic Solutions for Mantle Flow with Lateral Variations in Viscosity

Shijie Zhong

Seismological Laboratory, 252-21, California Institute of Technology, Pasadena, CA 91125

January 27, 1995

Submitted to Geophysical Journal International

Summary. Analytic solutions for two dimensional incompressible Stokes' flow with lateral variations in viscosity have been developed with a Green's function method and matrix propagator techniques. The analytic solutions are developed based on the observation that lateral variations in viscosity only result in mode coupling between viscosity and buoyancy in the horizontal dimension and not in the vertical dimension. The Green's function solution for flows with a viscosity that varies laterally with an exponential function indicates that if the lateral variation in viscosity is within one order of magnitude, the mode coupling between viscosity and buoyancy does not greatly influence the geoid at very long wavelength (e.g., degree 2) deduced from models ignoring the lateral variations in viscosity, but the relatively short wavelength geoid (degree 4 and higher modes) is seriously contaminated by mode coupling. The solutions for sharp lateral variation in viscosity with propagator matrix techniques show that topography varies rapidly across the viscosity boundaries. These analytic approaches for lateral variations in viscosity may have applications to other geodynamics problems.