Inversion of wideband microwave reflectivity to estimate the thickness of Arctic lead-like sea ice

The inversion of coherent reflection data from lossy media in which waves are governed by the Helmholtz equation is problematic both mathematically and practically. Conventional layer stripping methods applied to this nonlinear inverse problem are unstable even in the lossless case, and instability is accentuated in the lossy case. The authors have stabilized layer stripping in the lossless case by enforcing causality with a nonlinear analog to the Hilbert transform. The analysis in this work has led to a nonlinear analog to the Payley-Wiener theorem in classical Fourier analysis. The classical theorem relates the width of the region of analyticity in the (complex) frequency (or wavenumber) domain to width in the (real) time (or spatial) domain. The nonlinear analog of this theorem, applied to reflection data, yields the thickness of the reflecting layer, albeit in a depth coordinate scaled by the travel time through the layer. The authors show by simulation that this method produces accurate thickness estimates even when applied to reflection from moderately lossy media. Application of this method to wideband, vertical incidence, microwave reflection data for sea ice, together with a "guess" for the average permittivity of the ice, yields an estimate of the sea ice thickness. They show via simulation that the thickness estimate is not very sensitive to the guess for average permittivity-the entire range of plausible values leads to a variation in thickness estimates of only about 10%.