Inferring Mass-Balance Patterns and Rates from Radar-Internal Layers in Martian Ice

Past and present accumulation and ablation rates are fundamental unknowns for the Martian Polar Layered Deposits (PLD), and this information is necessary if we are to decipher the connection between climate and PLD formation, evolution, and observable structure. Internal layers in ice masses can be detected with ice- penetrating radar, and these data are currently being collected across the PLD. These layers are the primary record of relative spatial patterns of accumulation and ablation (mass balance) available. Additional rate- controlling information, such as the layer age, the ice temperature, or the ice-grain sizes and ice-crystal fabric, can be used to infer the absolute rate of mass balance. Using synthetic data, we solve four different inverse problems that all attempt to infer the relative spatial pattern and the absolute rate of mass-balance in a flowing ice mass, by assuming that different combinations of information are available. In the first inverse problem, only the shape of an internal layer is available. This problem could potentially be solved with data currently available for Mars. In the second inverse problem, only the ice-surface topography is available. The shape of the ice surface only weakly reflects smaller-scale spatial variations in mass balance, and we can recover only an average of the actual values. In the third inverse problem, we know the shape of an internal layer, and the surface topography and ice temperature when the ice was flowing, and we can successfully recover both the spatial pattern and the rate of mass balance. In the fourth inverse problem, we know the shape of an internal layer, the ice-surface topography, and ice-rheological parameters involving at least two activation energies. We can also successfully infer the spatial pattern and rate of mass balance with this information, if conditions at the time of flow were in a regime where more than one deformation process was active. If past ice flow has affected the shapes of Martian internal layers, it is necessary to use an inverse approach to infer mass-balance patterns from internal-layer shapes. We demonstrate the feasibility of recovering this valuable information.