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

Abstract

The Kirchhoff theory is applied for the target strength of a rough, circular surface whose roughness is characterized by a two-dimensional, isotropic power-law wave number spectrum, W2(κ) = η2κ−p2. The reflection coefficient for ice and three nondimensional parameters are found to govern the target strength. These parameters are ζ=κ0a, η≡η2ap2−4, and p1=p2−1, where κ0 is the acoustic wave number, a is the radius of the surface, and p1 is the spectral exponent of the one-dimensional power-law wave-number spectrum from which W2(κ) is derived. The general influence of ζ, p1, and η on the target strength is discussed. Calculations of average target strength of the ice/water interface of a submerged cylindrical block of ice are shown, which are then compared with individual realizations of measured target strengths of ice blocks for ζ between 25 and 100, corresponding to frequencies between 20 and 80 kHz for a=0.29 m. Data and theory show that the (smooth surface) form function for a finite surface does not describe the observed diffraction pattern. Instead, the lobes of the pattern diminish and the nulls fill in—i.e., the total backscatter becomes more incoherent—as frequency increases or as the large wave-number components of the roughness spectrum contribute more to the total acoustic return. These comparisons also allowed us to infer the rough surface statistics of the ice surface and the compressional sound-speed structure within the skeletal zone of the ice.