Using Laboratory Constraints to Evaluate the Possibility of Subduction in the Ice Shell of Europa

Introduction. Reconstructions of offset features on the surface of Europa demonstrate that it has been modified by lateral motions along narrow boundaries,  and indicate the existence in the past of convergent plate boundaries that accommodated several kilometers – to several tens of kilometers – of motion [5, 2]. If convergent boundaries existed, then this suggests that subduction of icy plates may have occurred in Europa’s past. Here, we build on the work of previous  modeling studies to examine the constraints on icy plate subduction within the ice shell of Europa. We follow previous efforts by using a 1D “subduction model”  to simulate the thermal and density evolution of a subducting ice plate along a predefined path [4, 3]. We use the output of the subduction model to evaluate the forces resisting and driving subduction to determine if subduction is favorable for a given set of simulation parameters [3]. The new contribution of our work  is in our methods for evaluating the resisting forces. In particular, we use laboratory measurements of the frictional and failure properties of ice to  evaluate the force required to bend the subducting plate. This provides a more accurate estimate compared to assuming that the subducting slab has a  viscous rheology [3]. As a result, we find that subduction is much more favorable.

Model Geometry. Figure 1 shows the geometry of the subduction model [4, 3]. An essential assumption is that the ice shell (of total thickness H_shell) is divided  into an upper, cold conductive layer of thickness H and a lower, warmer convective layer of thickness H_shell −H. We  assume that a section of the  conductive layer ("the slab")  is subducting into the convective layer along a predefined path.  In this model the warm,  convective layer must be present for the possibility of subduction due to the force of slab pull to exist. We assume that the temperature of the surface of the  shell is T_s and that the entire convecting layer has a temperature T_b . Finally, we assume that the slab has a salt content f_salt (volume %) relative to the  surrounding ice, and assume ρ_salt = 1444 kg/m³ , appropriate for natron [4].

Figure 1. Europa subduction model geometry, after [4]. The dashed, black line shows the centerline of the slab. The dashed, red line indicates the plate  interface, where F_shear exists.

Methods. We simulate heat flow and porous compaction in the slab by considering a one-dimensional column of the slab. We assume that this column moves through the defined slab geometry at a rate v_plate along the s-axis (Figure 1). We terminate simulations when the bottom surface of the slab encounters the bottom edge of the ice shell. We use the same set of governing equations used by Refs. [3] and [4] to solve for temperature and porosity in the column.

To determine if subduction is favorable, we evaluate the same driving and resisting forces considered by [3]:                 

                                   F_drive = F_slab + F_ridge ,                          F_resist = F_shear + F_bend ,

where F_slab is the force due to density contrasts between the slab and the surrounding ice (i.e. buoyancy); F_ridge is the ridge push force; F_shear is due to the shear resistance along the subducting slab boundary (defined by the red, dashed line in Figure 1); and F_bend is the force needed to bend the slab into its subduction geometry. If F_drive > F_resist then subduction is favorable. We evaluate F_bend by assuming that stresses within the slab cannot exceed those determined by a  laboratory defined failure envelope, or yield surface. We determine the failure envelope using temperature dependent data on the frictional properties of ice  [6] and its ductile creep behavior [1]. This reduces F_bend by 1 – 2 orders of magnitude compared to assuming that the stresses in the slab are governed by a  viscous rheology [3]; thus F_shear is the primary force that resists subduction, and F_bend is of secondary importance. We use a similar method to evaluate F_shear . At low temperatures we assume that F_shear is dominated by the frictional resistance along the slab boundary, while at higher temperatures the shear  resistance in dominated by ductile processes.

Figure 2. Values of F_drive /F_resist for H_shell = 20 km, v_plate = 4 mm/yr and different slab thicknesses and salt contents. Each dot represents an individual  simulation. The black line shows the F_drive /F_resist = 1 boundary.

Results. We conducted a parameter analysis over a range of slab thicknesses and salt contents, and find that subduction can be favorable for plausible values  of these parameters. Figure 2 shows values of F_drive /F_resist for 180 individual simulations with H_shell = 20 km and different values of H and f_salt . As the slab thickness increases, the plate interface becomes longer, resulting in larger F_shear . Thus, very large salt content is needed to achieve F_drive > F_resist for thicker slabs. Figure 3 shows the F_drive = F_resist boundaries for five different values of H_shell . Larger values of H_shell are more favorable for subduction because  F_slab increases with the length of slab that is contained within the shell; longer slabs exert larger slab pull forces. Overall, our results indicate that subduction of icy plates is favored by: (1) a high salt contrast between the slab and surrounding ice; (2) a thin conductive layer; and (3) a thick convective layer.

Figure 3. Contours of F_drive /F_resist = 1 for different ice shell thickness (H_shell ) indicated by the red numbers, in kilometers. Subduction is favorable at pairs of (H, f_salt ) values above the black line for each value of H_shell . Each line was determined from a set of 180 simulations as shown in Figure 2.

References

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[6] Zaman et al. (2024), JGR, 129(3):e2023JE008,215, doi:https://doi.org/10.1029/2023JE008215.