Inferring the Mean Thickness of the Outer Ice Shell of Enceladus From Diurnal Crustal Deformation

The thickness of the outer ice shell plays an importan t role in several geodynamical processes at ocean worlds. Here, we show that observations of tidally driven diurnal surface displacements can constrain the mean ice shell thickness, (d) over tilde (ice). Such estimates are sensitive to any significant structural features that break spherical symmetry such as faults and lateral variation in ice shell thickness and structure. We develop a finite-element model of Enceladus to calculate diurnal tidal displacements for a range of (d) over tilde (ice) values in the presence of such structural heterogeneities. Consistent with results from prior studies, we find that the presence of variations in ice shell thickness can significantly amplify deformation in thinned regions. If major faults ar e also activated by tidal forcing-such as Tiger Stripes on Enceladus-their characteristic surface displacement patterns could easily be measured using modern geodetic methods. Within the family of Enceladus models explored, estimates of (d) over tilde (ice) that assume spherical symmetry a priori can deviate from the true value by as much as similar to 41% when structural heterogeneities ar e present. Additionally, we show that crustal heterogeneities near the South Pole produce differences of up to 35% between Love number s evaluated at different spherical harmonic orders. A similar to 41% range in estimates of (d) over tilde (ice) from Love numbers is smaller than that found with approaches relying on static gravity and topography (similar to 250%) or analyzing diurnal libration amplitudes (similar to 85%) to infer (d) over tilde (ice) at Enceladus. As such, we find that analysis of diurnal tidal deformation is a relatively robust approach to inferring mean crustal thickness. Plain Language Summary For ocean worlds such as Enceladus, it is useful to determine the thicknesses of the outer ice crust-as it provides information about the depth of the ocean, the thermal evolution of the body, and the rate at which material at the surface can be recycled to the ocean by burial processes. By measuring the deformation of the surface in response to tidal forces, we can infer the mean ice shell thickness at Enceladus. Here, we show that the presence of large fault systems (such as the Tiger Stripes) or variations in the thickness of the ice shell (i.e., structural heterogeneities) affects Enceladus's response to tides. We find that estimates of ice shell thickness that ignore the potential impact of structural heterogeneities can deviate from true thickness values by up to 41%. This deviation is smaller than that found with other approaches that rely on analyzing gravity and topography (similar to 250%) or the periodic rigid rotation of the ice shell (similar to 85%) to infer Enceladus's mean ice shell thickness. As such, despite the presence of heterogeneities, measurements of tidal deformation at Enceladus would be a powerful probe of subsurface structure.