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The Geoid and Deep Earth Mass Anomaly Structure
Published in Petr Vaníček, Nikolaos T. Christou, GEOID and Its GEOPHYSICAL INTERPRETATIONS, 2020
An important result became evident from the results of the tapered disk models. The broader the disk, the steeper the rise in the geoid percentage CCC. However, even the disk with a 10,000 km diameter at 500 km depth does not have a steep enough rise for the geoid CCC to match that for a point mass at 2900 deep (Figure 4). Placing the disks at 100 km depth, or even the surface, increased that rise slightly. The earth has an equatorial circumference of close to 40,000 km, and harmonic degree 2 represents an equatorial wavelength of 1/2 that circumference by having four zero crossings, with two positive and two negative anomalies each having a width of 1/4 that circumference. The maximum width of a degree 2 or higher feature therefore is approximately 10,000 km. Thus, a thin tapered feature having a width (diameter) of greater than 10,000 km must therefore increase the coefficient value of spherical harmonic degree 1 and result in an offset of the center of mass relative to the center of figure. Thus, we can (must) conclude that a mass anomaly at 2900 km depth (core/mantle boundary region) cannot on earth be mimicked by a broad thin tapered mass anomaly at shallow or surface depth! The core/mantle boundary is not shallow enough. For the balanced deep point masses at 2900 km, there is a strong horizontal gradient along the equator at the divide between the positive and negative anomaly patterns. To replicate this pattern by a surficial mass distribution requires an abrupt substantial (thick) non-tapered mass anomaly contrast at the edges of a surficial mass anomaly distribution to make such strong horizontal gradients. And, a substantial mass anomaly (equal to the Earth’s greatest mass anomaly), if it existed at the Earth’s surface, would certainly be evidenced in an unobserved spectacularly different rock composition and structure for the topography of the New Guinea region in the southwestern Pacific. And, to imagine such great surface mass anomalies to be so distributed as to effect principally harmonic degrees 2 and 3, but not obscure the pattern contained in harmonic degrees 4 to 10 strains credence. Thus, a deep source for the major 2–3 degree field contribution deeper than the source for the elongate positive degree 4–10 geoid anomalies is indicated.
Magnetohydrodynamics of stably stratified regions in planets and stars
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
J. Philidet, C. Gissinger, F. Lignières, L. Petitdemange
In the present paper, we aim at modelling stably stratified layers in the geophysical and astrophysical contexts. In the planetary context, this corresponds to the 140 km thin shell located at the Core-Mantle Boundary (CMB), between the fluid, convective dynamo region and the solid mantle. In the stellar context, it corresponds to a radiative zone (more precisely a radiative envelope in the case of a massive or intermediate mass star). In both cases, the region that is being modelled is located between two spheres, and the aspect ratio in these two situations is drastically different (the planetary case is in the thin gap limit, whereas the stellar context is in the thick gap limit). It is important to stress that a 3D modelling of such a flow would be extremely time-consuming when it comes to use parameter values relevant to both regimes. In particular, the Ekman number E, which measures the ratio between the viscous force and the Coriolis force, is close to in both cases, whereas classical DNS can only reach (Schaeffer et al.2017). Furthermore, while classical models are essential to understand the evolution of magnetic fields on the magnetic dissipation time scale (about 10,000 years), they are less suitable to the study of much shorter timescales (less than a century), such as we are here. For these different reasons, we restrict ourselves to an axisymmetric study of the system. In performing an axisymmetric study, we implicitly preclude non-axisymmetric perturbations from triggering magnetic instabilities, and from inhibiting differential rotation. However, we only consider weak differential rotation in this paper, and these magnetic instabilities tend to be stabilised by rapid global rotation. Consequently, while this limitation must not be overlooked, the conclusions drawn from this study do not constitute unreasonable extrapolation.