The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges
Introduction
Europa's outer layer of H2O and trace minerals, primarily unidentified hydrated materials McCord et al., 1998, McCord et al., 2004, Carlson et al., 1999, is estimated to be ∼120 km thick Anderson et al., 1998, Pappalardo et al., 1999, McKinnon, 2004 and is hypothesized to exist as a liquid ocean beneath an outer shell of ice (e.g., Pappalardo et al., 1999). The H2O layer is likely comprised of three sub-layers: an outer, brittle/elastic ice layer, an underlying ductile layer of potentially convecting ice, and a lower layer of liquid. The densities of these layers are expected to be greater for lower layers, although some low-density pockets (such as briny ice/water or temperature-driven density anomalies) may occur throughout Pappalardo et al., 1998, Rathbun et al., 1998, Pappalardo and Barr, 2004.
The thickness of the ice shell is important to our understanding of Europan geologic features and processes, including the development of chaos features (disaggregated regions of the ice shell which have no correlative elsewhere in the solar system); impact crater morphology; the formation of ridges, bands, and faults (structural lineaments in the ice shell); and convection and diapirism related to the formation of pits, spots, and domes (generally circular disruptions in the ice). An accurate estimate of the ice thickness is important to exobiology studies, considering that ocean–surface interactions, which provide opportunities for life-forming chemicals in water to develop and be sustained through radiation at the surface, are limited by ice thickness Chyba and Phillips, 2001, Figueredo et al., 2003. Access to the ocean during future exploration, either directly or through remote sensing such as radar sounding, will also be affected by ice thickness.
Regardless of the thickness of the ductile portion of the ice shell, it is nonetheless important to determine the thickness of the outermost elastic portion of the ice shell as deduced from deformation on geologically short timescales. This elastic layer, at most, may represent the total thickness of the ice at the time or location where such deformation features formed (if the entire shell was able to behave elastically at the strain rates involved) and, at least, provides a lower bound to the total thickness of the ice shell. The thickness of the elastic layer is also a factor in the geological processes that control the surface morphologies of the various features observed, including pits, spots, domes, chaos, ridges, smooth bands, and ridged plains, regardless of the underlying mechanisms by which they form. The thickness of the elastic layer places important constraints on geophysical processes, such as thermal processes (heat input by tidal flexing of the outer shell, and heat loss by conduction through the shell), the occurrence and degree of tidal deformation, and the role of tidal stresses in the formation of geological features. Finally, the amount of potential flexure of the ice shell varies with the thickness of the shell.
Various methods, summarized in Table 1 (expanded from Pappalardo et al., 1999), have been utilized to determine Europa's ice shell thickness, with results ranging from ∼0.1–32 km. The thickest estimates result from thermal analyses, including convection models (motivated by observations of chaos, pits, spots, and domes, which are interpreted as having formed above ascending diapirs of buoyant ice Pappalardo et al., 1998, Rathbun et al., 1998, McKinnon, 1999), and calculations of thermal equilibrium and temperature gradients through the ice shell Ojakangas and Stevenson, 1989, Hussmann et al., 2002, Nimmo et al., 2003, Sotin et al., 2004. These models infer a relatively thick ice layer, generally ranging from 10–30 km. Impact studies indicate the thickness at various locations to be 2.4–19 km Moore et al., 1998, Moore et al., 2001, Greeley et al., 1998, Kadel et al., 2000, Turtle and Pierazzo, 2001, Turtle and Ivanov, 2002, Schenk, 2002.
A relatively thin ice layer, 0.1–10 km, is predicted by mechanical methods, which include: (1) modeling the flexure of the ice shell due to loading at the surface Tufts, 1998, Williams and Greeley, 1998, Chuang et al., 2001, Billings and Kattenhorn, 2002, Billings and Kattenhorn, 2003, Figueredo et al., 2002, Nimmo et al., 2003, Hurford et al., 2004; (2) buoyancy of “floating” ice rafts Carr et al., 1998, Williams and Greeley, 1998, Kadel and Greeley, 2000, Kadel et al., 2000; and (3) applications of fracture mechanics, including calculations of the depth to which a tidally induced, shell-penetrating fracture would have been able to penetrate in the given lithostatic stress field and analyses of fracture-bounded rafts in chaos regions Lucchitta and Soderblom, 1982, Schenk and McKinnon, 1989, Golombek and Banerdt, 1990, Carr et al., 1998, Greeley et al., 1998, Hoppa et al., 1999a, Greenberg et al., 2000.
An important feature of these analyses is that the thinner estimates typically result from mechanical methods, which can generally only estimate the thickness of the brittle or elastic portion of the ice shell near the surface at the time of load emplacement, whether or not it is underlain by a ductile layer. In contrast, thermal and impact models consider the entire ice shell and commonly assume the existence of a layer of ductile “warm” ice below the brittle layer. Regardless of the model used, it is clear that estimates of the thickness of the ice shell are somewhat variable. However, it has not been determined whether this variability is a function of the model itself or a reflection of some degree of spatial and/or temporal variability in the thickness of the ice shell.
In this study, we present calculations of elastic ice thickness based on the flexural response to loading at three locations on Europa and compare the results to previous estimates of the elastic thickness in order to ascertain potential reasons for variable estimates. Then we compare the published results from other flexural studies on Europa, noting models used, assumptions made, and locations of study so that we can differentiate thickness variability due to model uncertainties from real variations. In so doing, we will demonstrate that despite the difficulty and potential pitfalls of comparing ice thickness estimates based on disparate modeling approaches, there is sufficient evidence to indicate that the thickness of the Europan ice shell is not everywhere the same, indicating either a spatial or a temporal variability in ice shell thickness, or possibly both.
Section snippets
Plate bending theory and applications
The response of a planetary lithosphere to an applied surface load is regularly modeled as an elastic plate deflecting under a mathematically defined load (e.g., Walcott, 1970, Turcotte and Schubert, 1982, Comer, 1983, Schultz and Zuber, 1994). The deflection, w, caused by the load depends on the rigidity of the plate, which is defined by its elastic parameters and by its thickness. Two-dimensional models of line-loads have been used to study flexure caused by loading at terrestrial island
Thickness estimates along Europan ridges
To demonstrate the utility of our method for estimating elastic thickness, we measured the distance from three ridges on Europa to the associated flanking cracks and calculated plate thickness using Eq. (12). The development of flexure-related cracks requires stresses to be sufficiently high to break the ice shell; therefore, only large ridges tend to develop flanking cracks for the plate thicknesses and elastic properties that exist (Eq. (10)). Hence, examples of flanking cracks are not
Discussion
Although many methods have been employed to estimate the thickness of Europa's ice shell (Table 1), flexure analysis in particular has been utilized by several researchers to determine the elastic ice thickness at multiple locations (see Table 1, Mechanical methods: flexure). Estimates of elastic thickness based on this technique range from 100 m to 6 km. Any comparison of the results must consider the models used, the values of the various parameters, and the potential inaccuracies of the
Conclusions
We have calculated estimates of elastic ice thickness on Europa in three locations using flanking cracks as indications of maximum stress due to flexure caused by ridge loads. Our results are consistent with previous flexure analyses, which rely on locating the distance to the maximum upward deflection (forebulge) of the ice rather than the distance to the maximum stress and associated cracks. Because flanking cracks are more precisely located than is a slight forebulge, we conclude that the
Acknowledgements
This material is based upon work supported by a fellowship to Billings from the NASA–Idaho Space Grant Consortium under Grant no. NGT5-40108 and by NASA under Grant no. NAG5-11495 issued through the Office of Space Science to Kattenhorn. We thank Louise Prockter and Jay Melosh for valuable discussions, and reviewers Francis Nimmo and Patricio Figueredo for their helpful suggestions.
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