Isostatic equilibrium in spherical coordinates and implications for crustal thickness on the Moon, Mars, Enceladus, and elsewhere

Abstract

Isostatic equilibrium is commonly defined as the state achieved when there are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at depth within the lower viscosity mantle that underlies a planetary body's outer crust. In a constant-gravity Cartesian framework, this definition is equivalent to the requirement that columns of equal width contain equal masses. Here we show, however, that this equivalence breaks down when the spherical geometry of the problem is taken into account. Imposing the "equal masses" requirement in a spherical geometry, as is commonly done in the literature, leads to significant lateral pressure gradients along internal equipotential surfaces, and thus corresponds to a state of disequilibrium. Compared with the "equal pressures" model we present here, the "equal masses" model always overestimates the compensation depth--by ~27% in the case of the lunar highlands and by nearly a factor of two in the case of Enceladus.

23 pages of text; 3 figures; accepted for publication in GRL

References in corpus (2)

• Enceladus's and Dione's floating ice shells supported by minimum stress isostasy
• Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

Cited by in corpus (5)

• The gravity field and interior structure of Dione
• Isostasy with Love: I Elastic equilibrium
• Tidal controls on the lithospheric thickness and topography of Io from magmatic segregation and volcanism modelling
• Isostasy with Love: II Airy compensation arising from viscoelastic relaxation
• Exploring the Interior Structure and Mode of Tidal Heating in Enceladus