Multipass SAR Processing for Ice Sheet Vertical Velocity and Tomography Measurements

Abstract

Vertical velocity is the rate at which ice moves vertically within an ice sheet, usually measured in meters per year. This movement can occur due to various factors, including accumulation, ice deformation, basal sliding, and subglacial melting. The measurement of vertical velocities within the ice sheet can assist in determining the age of the ice and assessing the rheology of the ice, thereby mitigating uncertainties due to analytical approximations in ice flow models.We apply differential interferometric synthetic aperture radar (DInSAR) techniques to data from the Multichannel Coherent Radar Depth Sounder (MCoRDS) to measure the vertical displacement of englacial layers within an ice sheet. DInSAR’s accuracy is usually on the order of a fraction of the wavelength (e.g., millimeter to centimeter precision is typical) in monitoring displacement along the radar line of sight (LOS). Ground-based Autonomous phase-sensitive Radio-Echo Sounder (ApRES) units have demonstrated the ability to precisely measure the relative vertical velocity by taking multiple measurements over time from the same location on the ice. Airborne systems can make a similar measurement but can suffer from deleterious spatial baseline effects since it is generally impossible to fly over the same stretch of ice on each pass with enough precision to ignore the spatial baseline. In this work, we compensate for spatial baseline errors using precise trajectory information and estimates of the cross-track layer slope using direction of arrival estimation. The current DInSAR algorithm is applied to airborne radar depth sounder data to produce results for flights near Summit Camp and the EGIG (Expéditions Glaciologiques Internationales au Groenland) line in Greenland. The existing approach estimates the parameters in multiple separated steps. However, each step has dependencies on all the values being estimated. To overcome this drawback, we have implemented a maximum likelihood estimator that jointly estimates the vertical velocity, the cross-track internal layer slope, and the unknown baseline error due to GPS and INS (Inertial Navigation System) errors. We incorporate the Lliboutry parametric model for vertical velocity into the maximum likelihood estimator framework.To improve the direction of arrival estimation of the internal layer slope, we also explore the use of focusing matrices against other wideband direction of arrival methods, such as wideband MLE, wideband MUSIC, and wideband MVDR, by comparing the mean squared error of the DOA estimates.