Is Airy Isostasy Applicable to Icy Moons?

Abstract

Airy isostasy is commonly used in planetary science to explain the relationship between crustal thickness variations and topography. Recently, several researchers have questioned the validity of this concept and proposed alternative approaches. Here we examine the accuracy of these approaches by comparing their results with those obtained from the numerical solution of the equations governing the flow in the crust of a small icy moon with a subsurface ocean. We find that the traditional approach based on application of Archimedes' principle with elevations referred to the geoid, provides a satisfactory estimate of crustal thickness for low harmonic degrees. The alternative approach, based on the deviatoric stress minimization, gives correct results for isoviscous model, but its accuracy deteriorates as the viscosity contrast increases. The other alternative approach, in which the deviatoric stress is neglected, is significantly less accurate than other methods, leading to biased results for models with a thick crust. Plain Language Summary Airy isostasy is a concept based on simple application ofArchimedes' principle, which is broadly used in solid Earth geophysics and planetary science to explain the relationship between crustal thickness variations and topography. However, the application of Airy isostasy to icy bodies is problematic due to large variations in ice viscosity and phase transitions occurring in the interior. Recently, several researchers have questioned the validity of the traditional approach to Airy isostasy and proposed alternative approaches. Here we examine the accuracy of these approaches by comparing their results with those obtained from the numerical solution of the equations governing the flow in the crust of a small icy moon with a subsurface ocean. The results of our modeling suggest that the traditional approach to Airy isostasy provides a satisfactory estimate of crustal thickness variations on large spatial scales. The alternative approach based on the deviatoric stress minimization gives correct results for isoviscous model, but its accuracy deteriorates as the viscosity contrast increases. The other alternative approach, in which the deviatoric stress is neglected, is significantly less accurate than the other methods, leading to biased results for models with a thick crust.The original concept of Airy isostasy (Airy, 1855) is based on the application of Archimedes' principle to Earth's crustal blocks. According to this concept, the crustal blocks, which are rigid and do not interact with each other, are floating on a fluid-like mantle of greater density than the crust (for a historical review,

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