Beuthe, Mikael

published in Geophysical Journal International, 225, pp. 2157--2193

Abstract: Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. On Earth, it is used to subtract from gravity anomalies the contribution of nearly compensated surface topography. On icy moons and dwarf planets, it constrains the compensation depth which is identified with the thickness of the rigid layer above a soft layer or a global subsurface ocean. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. Isostasy should instead be defined either by minimizing deviatoric elastic stresses within the silicate crust or icy shell, or by studying the dynamic response of the body in the long-time limit. In this paper, I implement the first option by formulating Airy isostatic equilibrium as the combined response of an elastic shell to surface and internal loads. Isostatic ratios are defined in terms of deviatoric Love numbers which quantify deviations with respect to a fluid state. The Love number approach separates the physics of isostasy from the technicalities of elastic-gravitational spherical deformations, and provides a great flexibility in the choice of the interior structure. Since elastic isostasy is invariant under a global rescaling of the shell shear modulus, it can be defined in the fluid shell limit, which is simpler and reveals the deep connection with the asymptotic state of dynamic isostasy. Elastic isostasy is developed here in two versions, zero deflection isostasy and minimum stress isostasy, which are dual if the shell is homogeneous. Each isostatic model is combined with general boundary conditions applied at the surface and bottom of the shell, resulting in one-parameter isostatic families. In the thin shell limit, the influence of boundary conditions disappears as all isostatic family members yield the same isostatic ratios. At short wavelength, topography is supported by shallow stresses so that Airy isostasy becomes irrelevant. The isostatic ratios of incompressible bodies with three homogeneous layers are given in analytical form in the text and in complementary software.

Note: preprint arXiv:2011.15097
DOI: 10.1093/gji/ggab073
Links: link
Funding: PRODEX program managed by ESA and BELSPO/PRODEX program managed by ESA and BELSPO/PRODEX program managed by ESA and BELSPO