RAYLEIGH-TAYLOR INSTABILITIES OF A SELF-GRAVITATING EARTH

In the upper mantle and crust, common Earth models derived from seismi c observations have density gradients greater than the adiabatic one, and the Brunt-Vaisala frequency indicates the gravitational instabilit y of these layers. Here we use the linear viscoelastic theory of a sel f-gravitating compressible planet to determine the characteristic time s and excitation amplitudes of the Rayleigh-Taylor (RT) instabilities of the preliminary reference earth model (PREM) augmented by reasonabl e viscosity-depth profiles. Four different viscosity profiles are cons idered, with one of them varying continuously with depth. The RT modes are determined for spherical harmonic degrees up to 100. For each sph erical degree, a discrete spectrum of modes is found, with the distrib ution 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 pos t-glacial rebound studies, the characteristic times are of the order o f 10(7) to 10(8) y, while for a profile with a very low viscosity in t he asthenosphere the characteristic times found here are as low as 6 x 10(3) y. Owing to the limitations of the linear viscoelastic theory, which is valid for small deformations only and neglects all dynamic th ermal effects, we can only describe the existence of these modes but n ot their relative importance compared to thermal instabilities. Nevert heless, the characteristic times determined with this theory are descr iptive 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 t he interaction between surface loads and internal planetary dynamics. In regions of low asthenospheric viscosity, RT instabilities may signi ficantly 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.