Ref: SCART-2021-0034

Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

Beuthe, Mikael

published in Geophysical Journal International, 227, pp. 693-716

Abstract: In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper~I gave a general formulation of Airy isostasy as a loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two flavours of which are the constant load applied at a specific time and the constant shape maintained by addition or removal of material at the compensation depth. Whereas the former model has no elastic analog, the latter is equivalent to elastic isostasy with zero deflection at the surface, which was shown in Paper~I to be dual to minimum stress isostasy. Viscoelastic and viscous approaches are completely equivalent. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Analytical formulas for the isostatic ratios of an incompressible body with three homogeneous layers are given in complementary software.

Note: preprint arXiv:2012.15226
DOI: 10.1093/gji/ggab241
Links: link
Funding: PRODEX program managed by ESA and BELSPO/PRODEX program managed by ESA and BELSPO/PRODEX program managed by ESA and BELSPO

The record appears in these collections:
Royal Observatory of Belgium > Reference Systems & Planetology
Science Articles > Peer Reviewed Articles

 Record created 2021-01-25, last modified 2022-09-15