Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique

A variational method is used to select the specific, smooth decomposition of the total surface height spectral density function into surface height spectral density functions for the larger- and smaller-scale surfaces. Using this decomposition, the total like and cross-polarized scatter cross sections are expressed as weighted sums of physical optics scatter cross sections associated with the larger-scale surfaces and the tilt-modulated scatter cross sections for the smaller-scale surfaces. This variational technique has been shown to be stationary over a wide range of the variational parameter. Since only the slopes of the larger-scale surfaces tilt modulate the cross sections of the smaller-scale surfaces, it is necessary to select surface height spectral density functions for the larger-scale surfaces that do not require the introduction of artificial spatial cutoff wave numbers for the spectral density functions. The methods used to smoothly decompose the surface height spectral density functions result in no artificial rapid fluctuations in the corresponding surface height autocorrelation functions for the smaller- and larger-scale surfaces. This method can be applied to the remote sensing of rough sea or land surfaces.