A Study of the Fourth-Order Small Perturbation Method for Scattering From Two-Layer Rough Surfaces

Predictions of the fourth-order small perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fie...

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Bibliographic Details
Published in:IEEE transactions on geoscience and remote sensing 2012-09, Vol.50 (9), p.3374-3382
Main Authors: Demir, M. A., Johnson, Joel T., Zajdel, Tom J.
Format: Article
Language:English
Subjects:
Applied geophysics
Backscatter
Backscattering
Convergence
Earth sciences
Earth, ocean, space
Exact sciences and technology
Geometry
Interface roughness
Internal geophysics
Layered media
Mathematical models
Moment methods
Perturbation methods
Radar cross sections
remote sensing
rough surface scattering
Rough surfaces
Scattering
Series (mathematics)
Studies
Surface roughness
Surface waves
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Summary:Predictions of the fourth-order small perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fields and incoherent ensemble-averaged normalized radar cross sections (NRCSs) up to the third and the fourth order in surface rms heights, respectively, are reviewed. It is shown that the fourth-order NRCS includes distinct contributions from upper and lower interface roughnesses, as well as an "interaction" term that couples the upper and lower interface roughnesses. A comparison with NRCS values computed using the "numerically exact" method of moments in the full bistatic scattering pattern is shown for verification, and NRCS values at the second and the fourth order are compared in order to assess the convergence of the SPM series. Although the number of parameters inherent in the two-layer rough surface scattering problem makes an exhaustive study of scattering effects difficult, several illustrative examples are presented to capture a range of scattering behaviors. The results emphasize the importance of interactions between the rough surfaces in producing cross-polarized backscattering and also indicate an increased significance of fourth-order contributions in the two-layer geometry as compared to the single-layer case.
ISSN:0196-2892
1558-0644
DOI:10.1109/TGRS.2011.2182614