Near-normal incidence scattering from rough, finite surfaces: Kirchhoff theory and data comparison

Abstract

Kirchhoff theory is developed for the backscattering strength and bistatic scattering strength of a finite rough surface whose roughness is characterized by an isotropic power-law wavenumber spectrum W1(κ) = β1κ T. Two nondimensional parameters are found that govern these scattering strengths. These are ζ≡κa and β≡β1aγ − 4, where a is the radius of the block. First, the general influence of ζ and β on both the backscattering strength and the bistatic scattering strength is discussed. Then, the theoretical backscattering strengths are compared with individual realizations at 20, 40, and 80 kHz of target strengths of submerged ice blocks of different radii, cut from undeformed first-year ice in the Arctic. For this comparison, the particular strength and exponent of W1(κ) have been determined from field measurements of undeformed first-year ice. Data and theory show that the smooth surface form function for this finite surface does not describe the diffraction pattern observed and predicted at high frequencies. Instead, the lobes of the pattern reduce and the nulls fill in as frequency increases. This includes substantial decreases in the mainlobe of the pattern at normal incidence. The physics of these results is described in part in terms of the overlap of the active angular region of the surface with the actual surface area. [Work is supported by the ONT with technical management by NOARL.]