Forming Ganymede’s Grooves: Producing Large-amplitude, Complex Deformation

We numerically simulate the extension of an ice lithosphere under conditions appropriate to the formation of Ganymede’s grooved terrain using a model that permits a decrease in the brittle strength of the ice as strain accumulates. The inclusion of such strain weakening results in increased localization of the surface deformation, producing large amplitude topography with complex deformation styles. These results mark the first time that truly groove-like morphologies have been produced by simulations of extensional tectonism in an ice shell. Background: Covering nearly two-thirds of the satellite, Ganymede’s grooved terrain consists of sets of roughly parallel ridges and troughs with peak-totrough amplitudes of 200 to 500 m and strongly periodic spacings of 3 to 10 km [1]. At high resolution ubiquitous small-scale (100 to 200 m amplitude and ~1 km spacing) deformation is also observed. This relatively young terrain may have formed via unstable extension of Ganymede’s ice lithosphere during which perturbations in the thickness of the lithosphere became amplified into periodically spaced pinches and swells that correspond to Ganymede’s large-scale ridges and troughs [2,3]. Applying an analytical model of unstable extension to Ganymede’s lithosphere, Dombard and McKinnon [4] found that the fastest growing modes of deformation had wavelengths and growth rates consistent with Ganymede’s grooved terrain. However, numerical modeling of groove formation at finite strains have struggled to produce sufficiently large amplitude deformation during extension of an ice lithosphere. Maximum amplitudes in these simulations were ~70 m [5]. The model: We use the finite element model Tekton (v2.3) to simulate the extension of an ice lithosphere. The model includes the elastic, viscous, and plastic deformation of ice. We assume a Young’s modulus of 10 10 Pa and an Poisson ratio of 0.25. The model utilizes a composite power-law rheology that accounts for dislocation creep (regimes A, B, and C), diffusion creep, and grain-size-sensitive creep (grain boundary sliding and basal slip) [6]. In general, dislocation creep mechanisms B, and C, and grain boundary sliding dominate the flow. Plasticity is modeled using a Drucker-Praeger yield criterion with a cohesion of 10 MPa and an angle of internal friction of 30 o . Model domains were initially 24 km deep and 40 km long with square elements 167 m on a side. Domains were extended by 31.5% over 10 5 years yielding a strain rate of 10 -13 s -1 . A small (10 m) sinusoidal perturbation was imposed at the surface of the domain to allow instabilities to initiate. In these simulations we assume a cold surface temperature of 70 K (appropriate for the polar region and a faint early Sun) and a thermal gradient of 10 K km -1 . Strain weakening. Plasticity is a continuum approach to modeling brittle behavior that assumes the lithosphere is pervasively fractured on a scale below the resolution of a single element, and that the cumulative behavior of these fractures can be treated as an addition to the viscous strain rate. Plastic behavior only occurs when the local stress (parameterized as the second invariant of the deviatoric stress) is greater than the yield strength of the material. Terrestrial models of tectonic deformation often assume that the yield strength of a material decreases as plastic strain accumulates. Thus a material “remembers” its strain history (i.e. material that has experienced more strain undergoes plastic failure more easily than material that has undergone less strain). Such strain weakening can lead to significant localization of strain and increased deformation amplitudes [e.g., 7]. In contrast to previous modeling [5] we have incorporated various strain weakening parameterizations into our models of groove formation (Fig. 1).