Tectonic Processes on Europa:
Tidal Stresses, Mechanical Response, and Visible Features — (PART 5)
In this study we have considered Europa’s crust to be a uniform elastic sheet floating on a layer of liquid water. While this approximation is a useful, and perhaps the only, way to explore global stress patterns and effects, the real crust is much more complicated. In the lower portions of the crust, as the temperature approaches the melting point of water, the ice must be ductile on timescales that decrease with depth. For the diurnal elastic stress, we require that most of the crust be elastic over the diurnal timescale. For the component due to non-synchronous rotation, we require that elastic stress develop over about 1o of rotation, which is about 100 yr for the fastest possible rotation consistent with orientations viewed by Voyager and Galileo, or about 104 yr for the fastest rotation consistent with the apparent age of Cadmus Linea. Whether the bulk of the crust is elastic over 104 yr is problematic. For our model, it is not sufficient for only the upper portion of the crust to be elastic; the crust must stretch and crack through to liquid water.
A related concern is the role of lithostatic pressure. At depths greater than 100m, the weight of the ice above creates hydrostatic pressure comparable to the elastic stress that we have invoked to crack the ice. If such pre-stressing effectively strengthens the ice at depth, it might inhibit cracking through to a liquid layer.
On the other hand, even with the hydrostatic pressure, it may be possible for the extension to yield deep cracks. The cracking process is initiated by very rapid global strain over a few hours and the crack propagation is a rapid and dynamic process, which may not be constrained by equilibrium considerations. Moreover, as stress is relieved by cracking near the surface, it is concentrated at the bottom of the crack, driving material failure still deeper. Similarly, during propagation of linear cracks along the surface, stress is concentrated at the ends of the cracks, possibly far exceeding the level of stress computed for the intact ice shell. In addition, while hydrostatic preloading can limit horizontal tension at depth, the strain imposed by tides produces a differential between the vertical lithostatic compression and the horizontal component, such that the crack may continue to propagate downward, although not necessarily directly vertically. Finally, it is possible that cracks that initiate in the elastic upper portion of the crust are able to propagate further downward during subsequent diurnal working, as trapped debris ratchet the cracks open further. Our model of crack formation and evolution requires that some such processes do allow cracks to propagate completely through the crust.
Another assumption of our model is that the crust is uniform over the entire globe. Deviations from such uniformity must, in fact, produce regional heterogeneity and deviations from the global stress distributions that we have computed here. Cracking itself modifies the crust and the global stress. Such effects mean that we cannot expect to be able to fit all lineaments to this simple theoretical model. Even the most prominent, global-scale features (such as the ones we have highlighted in this paper) can at best be approximated by this model.
In this paper we have considered large-scale lineaments for which we have some geological evidence for evolution with time, and explored whether they can be correlated with global-scale sources of stress. A complete, systematic explanation of all cracking may be impossible for other reasons in addition to regional variations. For example, the complex, multiply overlying linear features on Europa suggest a long-term evolution reflecting great changes in the sources of stress themselves. They may represent the effects of non-synchronous rotation over several periods or of polar wandering, such that orderly monotonic time sequences would be obscured.
Indeed, there are major linear features that do not directly fit our global model. Most prominent are the globe-encircling lineaments that cross the equator at oblique orientations, generally near longitudes 90o and 270o. In all of the stress fields we have considered, tension at the equator is predominantly oriented north-south, a gross mismatch with the observed features. One such feature appears to be an extension of Asterius Linea along a great circle. Perhaps the large, obliquely equator-crossing lineaments were formed by a lengthening and joining of cracks like Minos with their symmetrical counterparts on the opposite side of the globe, with the propagation rapidly enhanced by the readjustment of the stress field as the cracking continues.