Scattering from a fractal surface: acoustical experiments and comparison with near-nadir models

A homogeneous resin print of the surface of a naturally-fractured granite block with an experimental Hurst exponent H≃0.7 is placed in a water tank. An acoustical source insonifies the surface in a near-nadir direction and the backscattered waves are recorded near the source. Such measurements are made at different positions along a profile above the surface in order to obtain the energy spectrum of the mean backscattered wavefield. The wavelength range considered is 0.58⩽λ⩽8.72 mm in water. A synthetic energy spectrum is obtained from a model [Shepard and Campbell, Icarus 141 (1999) 156] which represents the rough surface as an ensemble of point scatterers and assumes a single-scattering regime. This model reasonably fits with the experimental spectrum with the largest discrepancies observed for λ<2.5 mm. The fit is improved in the whole wavelength interval by accounting for the long-range topography variations occurring along the averaging profile.