Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000geoji.142..351v&link_type=abstract
Geophysical Journal International, Volume 142, Issue 2, pp. 351-360.
Astronomy and Astrophysics
Astronomy
9
Earth Models, Gravitational Stability
Scientific paper
The gravitational stability of spherical, self-gravitating, hydrostatically pre-stressed planetary models remains a subject of active interest. Love (1907, 1911) was the first to show that purely elastic models can become unstable when values of rigidity and bulk modulus are insufficient to counteract self-gravitational collapse. We revisit his calculations and extend his work to show that so-called dilatational (or `D') modes of a viscoelastic sphere can also become unstable to self-gravitation in a specific region of Lamé parameter space. As an example, we derive a marginal stability curve for the dilatational modes of a homogeneous planetary model at spherical harmonic degree two. We demonstrate that the stability conditions are independent of viscosity and that the instability will occur only when the homogeneous earth model is already unstable to the elastic instability described by Love (1907, 1911). Finally, we also consider a class of Rayleigh-Taylor (or `RT') instabilities related to unstable density stratification in planetary models. This convective instability is explored using both a homogeneous Maxwell viscoelastic sphere (which has an unstable layering at all depths) and a suite of Maxwell earth models that adopt the elastic and density structure of the seismic model PREM (which has regions of unstable density stratification within the upper mantle). We argue that previous studies have significantly overestimated the potential importance of these modes to Earth evolution. For example, suggestions that the timescale of the RT modes is short relative to the age of the Earth face the fundamental problem that the ensuing convective instability would have long ago destroyed the unstable layering and produced an adiabatic profile. We predict that at low degrees the RT instabilities for a PREM density profile and realistic viscosity stratification have timescales comparable to the age of the Earth. It is unclear, in any event, whether the unstable density layering in the PREM upper mantle is robust.
Mitrovica Jerry X.
Vermeersen L. A. L.
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