Inverse electromagnetic scattering models for sea ice
Golden, K.M.; Borup, D.; Cheney, M.; Cherkaeva, E.; Dawson, M.S.; Kung-Hau Ding; Fung, A.K.; Isaacson, D.; Johnson, S.A.; Jordan, A.K.; Jin An Kon; Kwok, R.; Nghiem, S.V.; Onstott, R.G.; Sylvester, J.; Winebrenner, D.P.; Zabel, I.H.H.
Geoscience and Remote Sensing, IEEE Transactions on
Volume 36, Issue 5, Sep 1998 Page(s):1675 - 1704
Digital Object Identifier 10.1109/36.718638
Summary:Inverse scattering algorithms for reconstructing the physical
properties of sea ice from scattered electromagnetic field data are
presented. The development of these algorithms has advanced the theory
of remote sensing, particularly in the microwave region, and has the
potential to form the basis for a new generation of techniques for
recovering sea ice properties, such as ice thickness, a parameter of
geophysical and climatological importance. Moreover, the analysis
underlying the algorithms has led to significant advances in the
mathematical theory of inverse problems. In particular, the principal
results include the following. (1) Inverse algorithms for reconstructing
the complex permittivity in the Helmholtz equation in one and higher
dimensions, based on layer stripping and nonlinear optimization, have
been obtained and successfully applied to a (lossless) laboratory
system. In one dimension, causality has been imposed to obtain stability
of the solution and layer thicknesses can be obtained from the recovered
dielectric profile, or directly from the reflection data through a
nonlinear generalization of the Paley-Wiener theorem in Fourier
analysis. (2) When the wavelength is much larger than the
microstructural scale, the above algorithms reconstruct a profile of the
effective complex permittivity of the sea ice, a composite of pure ice
with random brine and air inclusions. A theory of inverse homogenization
has been developed, which in this quasistatic regime, further inverts
the reconstructed permittivities for microstructural information beyond
the resolution of the wave. Rigorous bounds on brine volume and
inclusion separation for a given value of the effective complex
permittivity have been obtained as well as an accurate algorithm for
reconstructing the brine volume from a set of values. (3) Inverse
algorithms designed to recover sea ice thickness have been developed. A
coupled radiative transfer-thermodynamic sea ice inverse model has
accurately reconstructed the growth of a thin, artificial sea ice sheet
from time-series electromagnetic scattering data
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