Domes on Europa: The Role of Thermally Induced Compositional Diapirism

The Young's modulus E of ice is an important parameter in models of tidal deformation [1, e.g] and in converting flexural rigidities to ice shell thicknesses [2, e.g.]. There is a disagreement of an order of magnitude between measurements of E in the laboratory (9 GPa) and from field observations (≈1 GPa). Here I use a simple yielding model to address this discrepancy, and conclude that E = 9 GPa is consistent with the field observations. I also show that flexurally-derived shell thicknesses for icy satellites are insensitive to uncertainties in E. Lab Measurements Because ice may creep or fracture under an applied stress, it behaves elastically only if the loading frequency is high and stresses are small. Lower temperatures expand the parameter space in which elastic behaviour is expected. The most reliable way of determining E in the laboratory is to measure the sound velocity in ice and thus derive the elastic constants. The values of E found are consistently about 9 GPa [3; 4]. Field Measurements Field techniques rely on observing the response of ice shelves to tidal deformation [5]. In this case, loading frequencies are much lower (∼ 10 −5 Hz) and stresses much higher (∼1 MPa). Fractures are commonly observed, and creep is also likely to occur [6]; thus, not all of the shelf may respond in an elastic fashion. The length-scale of the response of an ice shelf to tidal deformation is determined by the parameter β [7], where: β 4 = 3ρg (1 − ν 2) ET 3 e. (1) Here ρ is the density of the sea, g is the acceleration due to gravity, ν is Poisson's ratio and Te is the effective elastic thickness of the ice shelf. The effective elastic thickness is defined as the thickness of a purely elastic plate which would produce the same response to loading as the actual ice shelf. Note that Te will be less than the total ice shelf thickness h if ductile creep or fracture are important [8]. Field measurements of ice shelf deformation allow β to be determined [7]. Inspection of equation 1 shows that in order to derive E, a value for Te must be assumed. One approach is to assume that the elastic thickness Te is the same as the total ice shelf thickness h, which may be measured directly. Doing so results in values for E which are significantly smaller …