A theory of wave scatter from an inhomogeneous medium with a slightly rough boundary and its application to sea ice

An analytical theory of electromagnetic wave scattering from an inhomogeneous medium with a slightly rough boundary surface is formulated. The inhomogeneity in the medium is assumed to vary continuously in the vertical direction. In addition, it is also assumed to have a small random variation in the horizontal direction. The medium is assumed to consist of two layers. Maxwell's equations are solved by using the small perturbation method together with Fourier transform technique. The resulting differential equations are solved by using WKB and variation of parameter methods. Field amplitudes in each medium are determined by taking boundary conditions into account. The expressions for first order polarized radar backscatter cross-section δ⁰ are obtained. An attempt is made to apply the developed theory to compute sea ice scatter. The complex permittivity of sea ice, which depends on both the temperature and salinity, varies with the depth of sea ice. In addition, there is certainly some variation in the horizontal direction. Thus, the developed model may be able to give useful estimates when applied to sea ice scattering. Numerical calculations are performed for polarized radar backscatter cross-section ($\text{σ}{}_{\mathrm{<mtext>vv</mtext>}}{}^{\mathrm{<mtext>0</mtext>}}\text{and}\text{σ}{}_{\mathrm{<mtext>HH</mtext>}}{}^{\mathrm{<mtext>O</mtext>}}$) at two frequencies, 13.3 GHz and 400 MHz. It can be shown that WKB method is applicable at both of these frequencies. These theoretical results are compared with the experimental results obtained from NASA Earth Resources Program mission 126. Theoretical results give the same absolute value of σ^O and the relative variation among the six ice types as is given by the experimental results.