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

Douglas J. Hemingway, Isamu Matsuyama

Research output: Contribution to journalArticle

18 Scopus citations

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 2 in the case of Enceladus.

Original languageEnglish (US)
Pages (from-to)7695-7705
Number of pages11
JournalGeophysical Research Letters
Volume44
Issue number15
DOIs
StatePublished - Aug 16 2017

Keywords

  • admittance
  • crustal thickness
  • gravity
  • isostasy
  • isostatic equilibrium
  • topography

ASJC Scopus subject areas

  • Geophysics
  • Earth and Planetary Sciences(all)

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