Using Tidally‐Driven Elastic Strains to Infer Regional Variations in Crustal Thickness at Enceladus

Abstract

Constraining the spatial variability of the thickness of the ice shell of Enceladus (i.e., the crust) is central to our understanding of the internal dynamics and evolution of this small Saturnian moon. In this study, we develop a new methodology to infer regional variations in crustal thickness using measurements of tidally‐driven elastic strain that could be made in the future. As proof of concept, we recover thickness variations from synthetic finite‐element crustal models subjected to diurnal eccentricity tides. We demonstrate recovery of crustal thickness to within ∼2 km of true values across the crust with ∼10% error in derived spherical harmonic coefficients at degrees l ≤ 12. Our computed uncertainty is significantly smaller than the inherent ∼10 km ambiguity associated with crustal thickness derived solely from gravity and topography measurements. Therefore, future measurements of elastic strain can provide a robust approach to probe crustal structure at Enceladus.

A Spectral Method to Compute the Tides of Laterally Heterogeneous Bodies

“…1. The new spectral method shows good agreement with results obtained with the spectral-perturbation approach of Qin et al (2014) and the FEM model of Berne et al (2023aBerne et al ( , 2023b. Differences between the results obtained with the new method and the perturbation method grow as the amplitude of lateral variations increases.…”

“…We compare the results obtained with the spectral method presented here with those obtained using the spectral-perturbation method of Qin et al (2014 and the FEM code of Berne et al (2023aBerne et al ( , 2023b.…”

“…We obtain the tidal response for the reference Enceladus model (Table 1) for various types of lateral variations using both spectral methods and the FEM code. For the FEM approach, we adapt the methodology outlined in Berne et al (2023a) and Berne et al (2023b) to develop an FEM capable of simulating tidal deformation on laterally heterogeneous ocean worlds. FEMs solve the equation of motion for quasi-static problems by formulating 3D displacements (i.e., in response to applied forces and boundary conditions) as a series of linear shape functions across a mesh domain.…”

“…If a body is spherically symmetric, the tidal response is proportional to the tidal forcing-the body responds with a mode of the same wavelength as that of the forcing. In contrast, when internal properties vary laterally, modes of different wavelength are coupled and the tidal response contains modes of wavelengths other than that of the forcing (e.g., Berne et al 2023b). The tidal response spectrum contains information about the amplitude and patterns of lateral variations; hence, it can be used to constrain such variations-a technique known as tidal tomography (e.g., Métivier et al 2007;Zhong et al 2012;Qin et al 2014Lau et al 2017).…”