RAYLEIGH-TAYLOR INSTABILITIES OF A SELF-GRAVITATING EARTH

Abstract

In the upper mantle and crust, common Earth models derived from seismic observations have density gradients greater than the adiabatic one, and the Brunt-Vaisala frequency indicates the gravitational instability of these layers. Here we use the linear viscoelastic theory of a self-gravitating compressible planet to determine the characteristic times and excitation amplitudes of the Rayleigh-Taylor (RT) instabilities of the preliminary reference earth model (PREM) augmented by reasonable viscosity-depth profiles. Four different viscosity profiles are considered, with one of them varying continuously with depth. The RT modes are determined for spherical harmonic degrees up to 100. For each spherical degree, a discrete spectrum of modes is found, with the distribution of the characteristic times strongly depending on the viscosity profile, while the amplitudes are less dependent on the viscosity. The excitation amplitudes of the modes are of the same order of magnitude as those for stable eigenmodes taken into account in the modelling of post-glacial rebound. For typical viscosity profiles derived from post-glacial rebound studies, the characteristic times are of the order of 107 to 108y, while for a profile with a very low viscosity in the asthenosphere the characteristic times found here are as low as 6 x 103y. Owing to the limitations of the linear viscoelastic theory, which is valid for small deformations only and neglects all dynamic thermal effects, we can only describe the existence of these modes but not their relative importance compared to thermal instabilities. Nevertheless, the characteristic times determined with this theory are descriptive of the time scales required for a gravitational overturning to result in significant deformations after being excited by surface mass loads. If excited, the RT modes introduce a non-linear element into the interaction between surface loads and internal planetary dynamics. In regions of low asthenospheric viscosity, RT instabilities may significantly change the crustal response to glacial loading and deloading and even introduce a feedback between loading and crustal response. In fact, depending on the planetary repertoire of surface mass transport processes, these modes could effect the evolution of a planet.