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.