Topography and Geoid Undulations Caused By Small-Scale Convection Beneath Continental Lithosphere of Variable Elastic Thickness

Abstract

Summary The effect of subcontinental upper mantle convection on topography, gravity and geoid undulation is studied with special regard to the effective elastic thickness of the continental lithosphere (hel). We designed a numerical model of the upper mantle-lithosphere system consisting of a constant viscosity fluid overlayed by a partly elastic plate. the boundary tractions (stresses) at the top of the convecting mantle model were applied to the lithosphere model for which we used the thin plate approximation. the total thickness of the lithosphere was kept constant to 150 km while the elastic thickness was varied between 0 and 150 km. the aspect ratio of the convecting mantle was varied between 0.7 and 3 and the Rayleigh number between 104 and 106. Our calculations demonstrate the effect of a thick elastic lithosphere on the surface observables: peak to peak averaged amplitude of topography, geoid undulation and gravity are strongly reduced and their spectra are low pass filtered. For an aspect ratio less than 1 and a very thick elastic lithosphere topography tends to zero and while geoid undulation and gravity may even become negative above the up welling plume. the spectral relation of geoid or gravity to topography (admittance) is nearly unaffected for hie, <70km. For Aie 70km admittance values for all wavelengths generally decrease with increasing elastic thickness of the plate and may become negative. Geoid admittance for the basic mode increases with larger aspect ratio, while gravity admittance for hie <100 km slightly decreases. Associating higher Rayleigh numbers of the convecting fluid with lower viscosity, an increase in Rayleigh number leads to considerable decrease of the surface observables. However, admittance values are only slightly affected and decrease approximately linearly with increasing Rayleigh number. Comparison of our results with observations of the topography spectrum and the free air gravity admittance for North America suggests that large aspect ratio cells beneath continents are unlikely. However, convection cells of aspect ratio 1 or less underlying an elastic lithosphere of at least 100 km thickness is in agreement with data. the Rayleigh number should be as high as 106.