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Radar Scatter from Layered Media and Rough Surfaces

By Pradeep Bobby and Eric W. Gill
Progress In Electromagnetics Research C, Vol. 90, 79-93, 2019


The generalized function approach for modeling radio wave scattering has been used to develop expressions for the scatter from rough surfaces and for horizontally-stratified media. The scattered field from rough surfaces can be found in closed form if plane wave incidence is assumed, but the method is valid for any realizable source without resorting to using Hertz vectors. This approach was originally developed to model high frequency surface wave radar scattering from the ocean or across layers of ice covering the ocean using vertical polarization. This paper presents three extensions to the existing theory: the x component of the scattered field for rough surface scattering is developed, the assumption of a good conducting surface assumption is removed for a rough surface and the scatter from stratified media is simplified in terms of a scattering coefficient. The shape of the scattered field is not affected by the relative permittivity, but the intensity of the scattered field is weaker due to an increased transmission of energy through the surface. The goal for this research is to better understand how signatures from ice-penetrating radar can be used to distinguish hazardous ice ridges from other ice features. Here, ice ridges are modeled as layered media with a rough surface.


Pradeep Bobby and Eric W. Gill, "Radar Scatter from Layered Media and Rough Surfaces," Progress In Electromagnetics Research C, Vol. 90, 79-93, 2019.


    1. Rayleigh, J. W. S. B., The Theory of Sound, V.1, Macmillan, 1894.

    2. Rice, S. O., "Reflection of electromagnetic waves from slightly rough surfaces," Communications on Pure and Applied Mathematics, Vol. 4, No. 2–3, 351-378, 1951.

    3. Wait, J. R., "Perturbation analysis for reflection from two-dimensional periodic sea waves," Radio Science, Vol. 6, No. 3, 387-391, 1971.

    4. Barrick, D. E., "Theory of HF and VHF propagation across the rough sea, 1, the effective surface impedance for a slightly rough highly conducting medium at grazing incidence," Radio Science, Vol. 6, No. 5, 517-526, 1971.

    5. Barrick, D. E., "Theory of HF and VHF propagation across the rough sea, 2, application to HF and VHF propagation above the sea," Radio Science, Vol. 6, No. 5, 527-533, 1971.

    6. Rosich, R. K. and J. R. Wait, "A general perturbation solution for reflection from two-dimensional periodic surfaces," Radio Science, Vol. 12, No. 5, 719-729, 1977.

    7. Rodrıguez, E. and Y. Kim, "A unified perturbation expansion for surface scattering," Radio Science, Vol. 27, No. 1, 79-93, 1992.

    8. Ogilvy, J. A., "Wave scattering from rough surfaces," Reports on Progress in Physics, Vol. 50, No. 12, 1553, 1987.

    9. Winebrenner, D. P. and A. Ishimaru, "Application of the phase-perturbation technique to randomly rough surfaces," Journal of the Optical Society of America A, 1985.

    10. Rodrıguez, E., "Beyond the Kirchoff plane approximation," Radio Science, 1989.

    11. Wait, J. R., "Chapter II — Reflection of electromagnetic waves from horizontally stratified media," Electromagnetic Waves in Stratified Media (Revised Edition Including Supplemented Material), 8-63, J. R. Wait, ed., Pergamon, 1970.

    12. Tamir, T., H. C. Wang, and A. A. Oliner, "Wave propagation in sinusoidally stratified dielectric media," IEEE Transactions on Microwave Theory and Techniques, Vol. 12, 323-335, May 1964.

    13. Chen, Y. M., "Wave propagation in stratified random media," Radio Science, 1964.

    14. Bahar, E., "Radio wave propagation in stratified media with nonuniform boundaries and varying electromagnetic parameters: Full wave analysis," Canadian Journal of Physics, 1972.

    15. Walsh, J., "On the theory of electromagnetic propagation across a rough surface and calculations in the VHF region," Tech. Rep., Memorial University, 1980.

    16. Walsh, J. and S. K. Srivastava, "Rough surface propagation and scatter: 1. General formulation and solution for periodic surfaces," Radio Science, 1987.

    17. Walsh, J. and R. Donnelly, "A general theory of the interaction of electromagnetic waves with isotropic, horizontally layered media1 (summary)," Radio Science, 1987.

    18. Walsh, J. and R. Donnelly, "Consolidated approach to two-body electromagnetic scattering," Physical Review A, 1987.

    19. Pinel, N., C. Bourlier, and J. Saillard, "Degree of roughness of rough layers: Extensions of the rayleigh roughness criterion and some applications," Progress In Electromagnetic Research, 2010.

    20. Rice, S. O., "Mathematical analysis of random noise," The Bell System Technical Journal, Vol. 23, 282-332, July 1944.

    21. Strub-Klein, L. and D. Sudom, "A comprehensive analysis of the morphology of first-year sea ice ridges," Cold Regions Science and Technology, Vol. 82, No. Supplement C, 94-109, 2012.

    22. Kovacs, A., W. F. Weeks, S. Ackley, and W. D. Hibler, "Structure of a multi-year pressure ridge," ARCTIC, Vol. 26, No. 1, 1973.

    23. Parmerter, R. R. and M. D. Coon, "Model of pressure ridge formation in sea ice," Journal of Geophysical Research, Vol. 77, No. 33, 6565-6575, 1972.

    24. Kovacs, A. and D. Sodhi, "Ice pile-up and ride-up on arctic and subarctic beaches," Coastal Engineering, Vol. 5, No. Supplement C, 247-273, 1981.

    25. Tucker, III, W. B., D. S. Sodhi, and J. W. Govoni, "Structure of first-year pressure ridge sails in the Prudhoe bay region," The Alaskan Beaufort Sea, 115-135, P. W. Barnes, D. M. Schell, and E. Reimnitz, eds., Academic Press, 1984.

    26. Weeks, W. F., On Sea Ice, University of Alaska Press, 2010.

    27. Kubat, I., D. Fowler, and M. Sayed, "Chapter 18 — oating ice and ice pressure challenge to ships," Snow and Ice-related Hazards, Risks and Disasters, 647-676, J. F. Shroder, W. Haeberli, and C. Whiteman (eds.), Academic Press, Boston, 2015.

    28. Norton, K. A. and A. C. Omberg, "Maximum range of a radar set," Proceedings of the IRE, 1947.

    29. Kerr, D. E., "The propagation of short radio waves," Tech. Rep., MIT Radiation Lab. Series No. 13, 1951.

    30. Wadhams, P., "A comparison of sonar and laser profiles along corresponding tracks in the arctic ocean," Sea Ice Processes and Models, R. S. Pritchard, ed., 1980.

    31. Petty, A. A., M. C. Tsamados, N. T. Kurtz, S. L. Farrell, T. Newman, J. P. Harbeck, D. L. Feltham, and J. A. Richter-Menge, "Characterizing arctic sea ice topography using high-resolution icebridge data," The Cryosphere, 2016.

    32. Kovacs, A. and R. M. Morey, "Electromagnetic measurements of multi-year sea ice using impulse radar," Cold Regions Science and Technology, Vol. 12, No. 1, 67-93, 1986.

    33. Morey, R. M., A. Kovacs, and G. F. N. Cox, "Electromagnetic properties of sea ice," Cold Regions Science and Technology, Vol. 9, No. 1, 53-75, 1984.

    34. GeoScan Ground Penetrating Radar, .