Toroidal-Poloidal Partitioning of Lithospheric Plate Motions

Abstract

A spherical harmonic expansion of tectonic plate motions on the Earth requires both poloidal and toroidal harmonics. Each spectrum decays fairly uniformly as ℓ^-2 (ℓ is the spherical harmonic degree), and the toroidal-poloidal ratio of the degree power is between 0.5 and 1.0 for all degrees up to 128. Convection in a laterally homogeneous medium will excite only poloidal motions; hence the question of why the toroidal component of plate motion is so large. Numerical models of 3-D convection with surface plates show that the rheological heterogeneity represented by plate boundaries can account for the excitation of toroidal surface motions from an underlying poloidal convective flow. Plates also account for the ℓ^-2 decay of the spectra, which is a simple geometric consequence of the plate-like velocity field. Lateral viscosity variations can also account for the net rotation of the lithosphere in the hot spot reference frame; this requires order of magnitude lateral viscosity variations. The spectra of plate motions depends on the geometries of the plates as well as their relative motions. A Monte Carlo simulation of plate motions shows that the observed toroidal-poloidal ratio for all degrees is less than would be expected for most plate motions, given the existing geometry. Relatively simple numerical models of 3-D convection with surface plates evolve to a final steady state (when it exists) that minimizes the toroidal-poloidal ratio of plate motion. This suggests that the much more complex system of plates on the Earth may be similarly governed.