Inversion for the density‐depth profile of polar firn using a stepped‐frequency radar

Translating satellite measurements of ice sheet volume change into sea level contribution requires knowledge of the profile of density as a function of depth within the ice sheet and how this profile changes over time. This paper describes an interferometric method of inverting ground‐penetrating radar returns for the profile of firn density as a function of depth. The method is an interferometric implementation of the common‐midpoint approach, performed using a stepped‐frequency, phase‐sensitive ground‐penetrating radar. By recording the phase difference of returns with a range of antenna separations, the different path lengths through the firn allow recovery of a smoothed representation of the density profile. This density model is characterized by three parameters: surface density and two decay lengths for porosity, each operating over a different density range. Our results suggest that the stepped‐frequency radar used here can accurately recover differences in two‐way traveltime and produce useful estimates of the density profile. In a test of the method performed at Summit station in Greenland, the recovered density‐depth profile agreed with independent density measurements from an ice core and a neutron probe to within 6% root‐mean‐square error.