Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

TL;DR

This paper extends the Love number framework to model isostasy as a viscoelastic relaxation process, showing how different loading histories influence Earth's crustal compensation and providing computational tools for analysis.

Contribution

It introduces a time-dependent viscoelastic model of Airy isostasy using Love numbers, linking static and dynamic approaches and offering computational codes.

Findings

Viscoelastic and viscous models are equivalent in isostasy.

Long-term models predict similar compensation for large-scale gravity.

Depth-dependent rheology affects long-wavelength compensation.

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 an elastic 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 examples of which are the constant load applied on the surface in the far past and the constant shape maintained by addition or removal of material at the compensation depth. The former model results in a shape decreasing exponentially with time and has no elastic analog, whereas the latter (stationary) model is equivalent to a form of elastic isostasy. Viscoelastic and viscous approaches are completely equivalent. If both load and shape vary slowly with time, isostatic ratios look like those of the stationary model. 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. Mathematica and Fortran codes are available for computing the isostatic ratios of an incompressible body with three homogeneous layers.