Bistatic Radar Tomography of Shear Margins: Simulated Temperature and Basal Material Inversions

Abstract

A significant portion of the sea level contributions of Antarctica and Greenland comes from ice streams, but the physical processes controlling ice stream width are poorly understood, especially when topographic controls are absent. Recent modeling studies have indicated that ice stream width may be controlled by elevated temperatures inside ice stream shear margins. While radio echo sounders can provide measurements of englacial water storage and subglacial conditions, existing radar-sounding techniques cannot measure temperature profiles at the scale required to test this hypothesis. We propose using a wide-angle radar survey and tomographic inversion to resolve temperature profiles, gradients, and anomalies at the scale required to study the thermophysical controls on shear margins. Recent work produced a bistatic radar system capable of obtaining the long offsets required for well-constrained inversions; however, shear-margin-specific temperature inversion techniques have not been developed for this system. In this article, we develop Newton’s method and alternating direction method of multipliers’ inversions for estimating temperature distribution and basal material across ice stream shear margins. We evaluate the performance of these inversion techniques on simulated bistatic radar-sounding data. Our results suggest that bistatic radar tomography experiments should be able to produce temperature maps on 50 m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times50$ </tex-math></inline-formula> m grids with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.83~^{\circ} \text{C}~\pm ~0.084~^{\circ} \text{C}$ </tex-math></inline-formula> mean temperature error, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.58~^{\circ} \text{C}~\pm ~0.20~^{\circ} \text{C}$ </tex-math></inline-formula> maximum temperature error, and an error in relative basal permittivity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.63~\pm ~0.08$ </tex-math></inline-formula> for a 4-km transect.