Ref: POSTER-2021-0011

Minimum stress isostasy with Love

Beuthe, Mikael

Poster presented at American Geophysical Union Fall Meeting, virtual meeting held online on 2020-12-01

Abstract: The outer shape and gravity field are not sufficient to constrain the interior of icy moons and dwarf planets unless they are supplemented by a mechanical model of the interior such as isostatic equilibrium. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. A more correct theory of isostasy can be defined instead by minimizing deviatoric elastic stresses within the crust, as proposed a long time ago by Harold Jeffreys. This idea is best implemented in the ‘Isostasy with Love’ framework, which formulates isostasy as the simultaneous response - fully described by Love numbers - of an elastic or viscoelastic shell to top and bottom loads. The minimum stress constraint can be combined with different boundary conditions resulting in a 1-parameter isostatic family. Minimum Stress Isostasy is dual to Zero-Deflection Isostasy (elastic isostasy with zero radial deforma- tion), in the sense that their isostatic family parameters are in one-to-one correspondence. Zero-Deflection Isostasy is in turn equivalent to viscous or viscoelastic isostasy with sta- tionary boundary conditions (Stokes-Rayleigh analogy). Thus, Minimum Stress Isostasy is identical to time-independent viscous isostasy, whereas time-dependent viscous isostasy results in slightly different predictions of geoid anomalies. The elastic-viscous equivalence shows that choosing the right boundary conditions matters more than choosing an elastic, viscoelastic, or viscous approach. Nevertheless, the influence of boundary conditions dis- appears in the thin shell limit as all approaches yield the same isostatic ratios. If the shell is homogeneous and incompressible, isostatic ratios (shape ratio, compensation factor, etc) can be obtained as analytical formulas in all isostatic models.

Note: Poster P081-0010
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
Conference Contributions & Seminars > Posters

 Record created 2021-01-25, last modified 2021-01-25