Kinematic waves in polar firn stratigraphy

Radar studies of firn on the ice sheets have revealed complex folds on its internal layering that form from the interplay of snow accumulation and ice flow. A mathematical theory for these fold structures is presented, for the case where the radar cross-section lies along the ice-flow direction and where the accumulation rate and ice-flow velocity are time-invariant. Our model, which accounts for firn densification, shows how ‘information’ (the depth and slope of isochrones) propagates on the radargram to govern its layer undulations. This leads us to discover universal rules behind the pattern of layer slopes on a distance-age domain, and understand why the loci of layer-fold hinges curve, emerge and combine on the radargram to form closed loops that delineate areas of rising and plunging isochrones. We also develop a way of retrieving the accumulation-rate distribution and layer ages from steady isochrone patterns. Analysis of a radargram from the onset zone of Bindschadler Ice Stream indicates that ice flow and accumulation rates have been steady there for the past ~400 years, and that spatial anomalies in the latter are coupled to surface topography induced by ice flow over the undulating ice-stream bed. The theory provides new concepts for the morphological interpretation of radargrams.