Inverse electromagnetic scattering models for sea ice

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 Manuscript received April 7, 1998; revised June 5, 1998. This work was supported by the Office of Naval Research, which provided funding for the Sea Ice Electromagnetics Accelerated Research Initiative. The work of K. M. Golden, S. A. Johnson, E. Cherkaeva, and D. Borup was supported by ONR Grants N00014-93-10 141 and N00014-94-10958, and NSF Grants DMS-9 622 367 and OPP-9 725 038. The work of M. Cheney and D. Isaacson was supported by ONR Grants N00014-93-1-0048 and N00014-96-1-0670, and an NSF Faculty Award for Women in Science and Engineering DMS9 023 630. The work of J. A. Kong and K.-H. Ding was supported by ONR Grants N00014-89-J-1107 and N00014-92-J-4098. The work of A. K. Fung and M. S. Dawson was supported by ONR Grant N00014-96-1-0517. The work of S. V. Nghiem and R. Kwok was supported by the Office of Naval Research through an agreement with the National Aeronautics and Space Administration. The work of J. Sylvester and D. P. Winebrenner was supported by ONR Grants N00014-89-J-3132, N00014-90-J-1369, N0001493-0295, and N00014-96-1-0266, and NSF Grant DMS-9 123 757. The work of R. G. Onstott was supported by ONR Contract N00014-93-C005. The work of I. H. H. Zabel was supported by ONR Grant N00014-92-J-1791. K. M. Golden and E. Cherkaeva are with the Department of Mathematics, University of Utah, Salt Lake City, UT 84112 USA (e-mail: [email protected]). D. Borup and S. A. Johnson are with the Department of Bioengineering, University of Utah, Salt Lake City, UT 84112 USA. M. Cheney and D. Isaacson are with the Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 USA. M. S. Dawson and A. K. Fung are with the Electrical Engineering Department, University of Texas, Arlington, TX 76019 USA. K.-H. Ding and J. A. Kong are with the Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. A. K. Jordan is with the Remote Sensing Division, Naval Research Laboratory, Washington, DC 20375 USA. R. Kwok and S. V. Nghiem are with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA. R. G. Onstott is with the Environmental Research Institute of Michigan, Ann Arbor, MI 48113-4001 USA. J. Sylvester is with the Department of Mathematics, University of Washington, Seattle, WA 98195 USA. D. P. Winebrenner is with the Applied Physics Laboratory, University of Washington, Seattle, WA 98195 USA. I. H. H. Zabel was with the Byrd Polar Research Center, Ohio State University, Columbus, OH 43210-1002 USA. She is now with Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 021739108 USA. Publisher Item Identifier S 0196-2892(98)06382-7. 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. Inversions for sea ice thickness have also been obtained through the application of neural networks to an analytic wave theory model, a reflectivity inversion scheme, and the use of proxy indicators. The role of neural networks in sea ice classification is also considered. It is anticipated that the broad-ranging advances in inverse scattering theory presented here may find application to closely related problems, such as medical imaging, geophysical exploration, and nondestructive testing of materials as well as generating new techniques for remotely reconstructing sea ice parameters.