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

Isostatic equilibrium is commonly understood to be the state of equilibrium–neglecting mantle dynamics and the slow relaxation of the crust–achieved when there are no lateral gradients in hydrostatic or lithostatic pressure, and thus no lateral flow, at depth within the lower viscosity mantle that underlies the outer crust of a planetary body. 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 leads to an overestimate of the compensation depth. The magnitude of the discrepancy depends on the density structure of the body and the wavelength of the relevant topography, and is most pronounced when the compensation depth is a substantial fraction of the body’s radius. Compared with the ‘equal pressures’ model, we show that analyses incorporating the ‘equal masses’ model may overestimate crustal thicknesses by as much as ~27% in the case of the lunar highlands, by ~10% in the case of the Martian highlands, and by nearly a factor of two in the case of Saturn’s small icy moon Enceladus.

Read this paper on arXiv…

D. Hemingway and I. Matsuyama
Wed, 1 Mar 17

Comments: 22 pages of text; 3 figures; prepared for submission to GRL