An Open-source Gui for Calculating Icy Moon Tidal Stresses Using Satstress

Introduction: We have modified the open-source program SatStress (http://code.google.com/p/satstress), developed at the University of Colorado-Boulder and JPL [1], used for calculating the tidal stresses on a satellite that is fully differentiated into a rocky core, a global subsurface ocean, and a decoupled, ice shell. Wahr et al. (2009) [1] used gravitational potential theory to determine the tidal stresses on a satellite. Like SatStress, SatStressGUI (currently in beta testing) is capable of calculating the combined effects of diurnal tides and nonsynchronous rotation (NSR) for both elastic and viscoelastic cases. We felt that the lack of simple learning-curve accessibility of the source code created a need for a user-friendly program that was capable of the same calculations, while maintaining the intent of the SatStress developers to provide an opensource program for planetary scientists. Accordingly, SatStressGUI will eventually be open-source. About SatStressGUI: SatStressGUI is broken into five parts: Satellite, Stresses, Tensor, Grid, and Plot. The first part or tab (Satellite) is where the satellite is built (Fig. 1). As an example of what would be included in these parameters we have included a table that features the satellite built for Europa (Table 1) based on data in [1]. Each layer of the satellite is assumed to have a density !, two elastic moduli (shear modulus μ and Lamé parameter "), a layer thickness, l, and a viscosity, #. There is also an option to enter the tensile strength of the upper ice layer. This is for determining where lineaments will form if the tensile strength of the ice is overcome. The second tab (Stresses) is for selecting the stress components to be calculated. For now, diurnal and NSR are the only available stresses that are included. These can be done independently of each other if the user is only interested in diurnal stresses or NSR stresses. In this tab there is also a location to save the Love numbers for the satellite. The third tab (Tensor) offers the user the option to calculate the stress tensor or principal stresses at any single point on the satellite (as opposed to a grid of points). The input parameters are latitude/longitude, orbital position (diurnal), and time for NSR stress build-up (if applicable). For single-point calculations, no further parts/tabs of the program are needed. The fourth tab (Grid) allows the user define a grid of points anywhere on the satellite surface to calculate stresses (Fig. 2). This grid is used the final tab for projecting the data on a map. The Grid tab is also used for determining the amount of NSR and orbital location(s) where calculations will be performed. For calculating diurnal tides, the user specifies the orbital starting position, orbital termination position, and the number of increments during the orbit. For calculating the magnitude of the NSR stresses, the user enters a period of NSR rotation (one complete rotation of the ice shell), degrees of accumulation or time of accumulation, and the number of increments. The increment option allows the user to step through several calculations to see how the stress components change from the minimum input value to the maximum input value. In the final tab (Plot) the user can preview the results on the defined grid and export the data into a geospatial analysis program (such as ArcGIS). It is possible to contour gradients in principal stresses, mean stresses, and differential stresses. Similar to [1], tick marks can also be used to represent the principal stresses (Figure 3). For plotting tick marks, the available options are the principal stresses, planes of maximum shear stresses, and both normal components of the stress tensor. Cauchy’s equations have not yet been incorporated into the program for calculating normal and shear stresses for any plane, but may be added later. We have also included multiple map projections for displaying the data (cylindrical equidistant, Miller Cylindrical, Mercator, orthographic, and polar projection).