Power Law Rheology of Ice and the Relaxation Style and Retention of Craters on Ganymede
Authors: Thomas Paul J. , Schubert Gerald 
Published: February 2008

Numerical models of viscous relaxation of craters in ice, using rheological laws determined from laboratory data, previously indicated excessively short relaxation times (te, the time required for crater depth to become 1/e of its initial value) for craters on the icy satellites. A typical value of te was ∼104 years for a 100‐km‐diameter crater. These time scales are totally incompatible with the large regions of heavily cratered terrain on the icy satellites. We discuss the application of a numerical unite element model incorporating the most recent rheological data for ice at temperatures and pressures appropriate to the near‐surface regions of Ganymede. The model permits a full representation of a temperature and stress dependent (power law) viscosity for ice. For temperature gradients in reasonable agreement with those obtained from thermal and structural models of Ganymede we obtain relaxation times te ≳ 10 years for craters with diameters less than 100 km. For all craters with diameters greater than 10 km, the strong dependence of viscosity on stress was found to significantly shorten the relaxation time. An attempt was also made to determine whether Newtonian or non‐Newtonian rheological laws dominated relaxation for craters of various sizes. Newtonian rheologies appear to dominate crater relaxation only for situations where the effective temperature is several tens of degrees warmer than the surface is observed to be (perhaps because of the effect of an insulating regolith) and where temperature gradients are small. In this case, viscous relaxation of craters with diameters smaller than ≈25 km is expected to be dominated by Newtonian flow laws, provided that the currently accepted parameters (gross extrapolations from near‐melting temperature measurements) are valid for the low temperatures of the icy satellites. On the other hand, larger diameter craters undergo (at least initially) viscous relaxation determined by a strongly non‐Newtonian rheological law and have geologically short relaxation times (te ∼107 years, for a 300‐km crater), although these times may be extended by silicate suspensions and by dispersion hardening. This presumably accounts for the absence of such craters, in unmodified form, on Ganymede. Finally, the large stress exponent (n = 4.7) of the current rheological data for ice indicates a strong role for non‐Newtonian flow in determining the topography of viscously relaxing craterforms of this size. In principle, a threshold crater diameter (and hence stress) for the onset of non‐Newtonian viscous behavior could be obtained from Galileo images, allowing estimates to be made of near‐surface temperatures and thermal gradients in Ganymede's past. In practice, however, any morphological variability is almost certainly too subtle to be detected from imagery. The calculated relaxation times from this work are still much shorter than those indicated by the topographic relief of Ganymede's surface. This remains an unresolved problem. Possible ways in which the observations can be resolved with current laboratory data on ice deformation are discussed.