Application of Twersky’s boss scattering theory to laboratory measurements of sound scattered by a rough surface

Abstract

One of the many challenges in describing the scattering of sound by rough surfaces is to address the fact that most surfaces are three-dimensional. Furthermore, only their statistical properties may be known. Twersky’s model [V. Twersky, J. Acoust. Soc. Am. 29, 209–225 (1957)], by using a method of images and taking multiple scattering into account, established a general solution involving distributions of three-dimensional ‘‘bosses’’ (protuberances) on a base plane. A prominent advantage of the theory over others is that it can describe bosses of arbitrary orientation. In this present article the theory is compared with laboratory measurements of sound scattered by a continuously rough pressure-release surface. The mathematical surface in Twersky’s theory does not rigorously resemble the laboratory surface. Thus this study serves to assess the potential applicability of Twersky’s 3-D boss surface to continuously rough 3-D surfaces that may occur in nature. In the model, use is made of prolate hemispheroidal bosses oriented in a randomized range of directions and randomly packed to approximate the rough surface. These bosses and their distribution were chosen to resemble the general size, shape, orientation, and spacing of the major features of the rough surface. The data were taken from Horton et al. [C. W. Horton, S. K. Mitchell, and G. R. Barnard, J. Acoust. Soc. Am. 41, 635–643 (1967)] and Welton [P. J. Welton, report ARL-TR-75-30, University of Texas at Austin (1975)] and involve backscattered sound versus grazing angle for several frequencies. The comparisons of the numerical computations with Welton’s data show a reasonable agreement with respect to not only the boss orientation parameters but also the surface statistical parameters (rms roughness and correlation length). An interesting phenomenon is that the number of spheroidal modes required to fit the data increases as the frequency of the incident plane wave increases.