Inferring the Mean Effective Elastic Thickness of the Outer Ice Shell of Enceladus from Diurnal Crustal Deformation

Abstract

The thickness of the outer ice shell plays an important role in several geodynamical processes at ocean worlds. Here we show that observations of tidally-driven diurnal surface displacements can constrain the mean effective elastic thickness, ˜del, of the ice shell. 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 ˜del values in the presence of such structural heterogeneities. We find that the presence of variations in ice shell thickness can significantly amplify deformation in thinned regions. If major faults are 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 ˜del that assume spherical symmetry a priori can deviate from the true value by as much as ~ 20% when structural heterogeneities are present. Such uncertainty is smaller than that found with approaches that rely on static gravity and topography (~ 250%) or analyzing diurnal libration amplitudes (~ 25%) to infer ˜del at Enceladus. As such, despite the impact of structural heterogeneities, we find that analysis of diurnal tidal deformation is a relatively robust approach to inferring ˜del.

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

“…We find that our approach can correct for over‐ (under‐) predictions of strain due to excessively low (high) initial estimates of $$\tilde{D}$$ (for details, see Text S3 in Supporting Information ). A reduced G (e.g., due to pervasive crustal fracturing) may also result in a derived value of $$\tilde{D}$$ that is inconsistent with constraints set by the amplitude of the forced libration of the ice shell (Berne et al., 2023b; Beuthe, 2018; Hemingway & Mittal, 2019; Van Hoolst et al., 2016). In this case, repeating our analysis with a lowered input G (see Table S1 in Supporting Information ) should produce a derived $$\tilde{D}$$ that more closely matches the mean thickness expected for the satellite (Hemingway & Mittal, 2019).…”

“…However, fractures may reduce elastic shear modulus along fault zones (e.g., the Tiger Stripes) or highly damaged regions of the ice shell (Vaughan, 1995). Our modeling approach can readily account for localized reductions in shear modulus along fault zones if the surface and subsurface geometry (e.g., dip angle and penetration depth) of these structures is known a‐priori (for more information, see Berne et al., 2023b). However, resolving thickness over large‐scale damage zones may require invoking additional assumptions regarding the expected shape of the crust at Enceladus.…”

“…We first construct a spherically symmetric model geometry that is broadly consistent with the elastic structure of the crust of Enceladus. Building on the methodology discussed in Berne et al (2023aBerne et al ( , 2023b) (cf. Section 2.1), we start with a hollow shell with prescribed outer radius R and uniform thickness 𝐴𝐴 D𝐷 (see Table S1 in Supporting Information S1 for chosen values for parameters used throughout this work).…”

“…PyLith input files (including sample surface topography data), post-processing scripts, and selected output files for this work are available on (Berne et al, 2023a). A full version of the forward FEM code, a user manual, and the workflow for inferring thickness from strain described in the current work is also available on (Berne et al, 2023a). The mesh geometries utilized in this study were created using CUBIT (v15.2), a node-locked licensed software which is available through the developer Sandia National Laboratories (CoreForm, 2020;Skroch et al, 2019).…”

“…Existing analytic and semi‐analytic models of diurnal tides at Enceladus cannot easily predict deformation caused by short‐wavelength variations in crustal thickness (Beuthe, 2018; Qin et al., 2016; Rovira‐Navarro et al., 2023; Wahr et al., 2006). However, numerical Finite Element Models (FEMs) can accurately simulate deformation for ice shell geometries that incorporate variations in crustal thickness across a wide range of spatial scales (Behounkova et al., 2017; Berne et al., 2023b; Souček et al., 2016, 2019).…”