Viscoelastic Membrane Tectonics on Europa

Abstract:

The surface of Europa is crisscrossed by tectonic features generally attributed to time-dependent tidal deformations. For a long time, the membrane theory of elastic shells (thin shell or flattening model) has been popular to predict tidal tectonic patterns because it provides simple analytical formulas for tidal stresses. More recently, the theory of viscoelastic-gravitational deformations (or thick shell model) was applied to tidal tectonics so as to include viscoelastic effects. This method, however, is not transparent to the user and relies on numerical algorithms that are not always publicly available or fully benchmarked. As an alternative, we propose here to extend membrane theory to viscoelastic shells with depth-dependent rheology. Viscoelasticity is taken into account by replacing elastic constants with effective viscoelastic parameters that are easily computed for a given rheology. The membrane approach thus leads to simple formulas for viscoelastic tidal stresses. Because of its formulation in terms of tidal Love numbers, the membrane approach has clear relationships with both thin and thick shell models. Benchmarking with the thick-shell software SatStress leads to the discovery of an error in that code that changes stress components by up to 40%. As an application, we show that different stress-free states account for the conflicting predictions of thin and thick shell models about the magnitude of tensile stresses due to nonsynchronous rotation.