The topography of ocean worlds is often used to infer ice shell
thicknesses by assuming topography is compensated by a basal root. We
systematically test the stability of isostatically compensated
topography in ice shells. At short horizontal wavelengths, lithospheric
strength can support surface topography, while at long wavelengths,
buoyancy forces can support topography at the surface and base of the
ice shell over geologic time scales. These behaviors are also seen for
Airy isostasy in terrestrial worlds. Contrastingly at intermediate
scales, the mechanically weak lower ice shell can inhibit the transfer
of buoyancy forces to the surface. Factors such as surface temperature
can alter the contribution of lithospheric strength, decreasing the
stability of a compensating root. This nuanced understanding of icy
shell lithospheres provides crucial insights for interpreting surface
features and inferring underlying ice shell thickness, with substantial
relevance for upcoming space missions to the Jovian system.