Inversion of roughness parameters of self-affine surfaces from backscattered waves

We propose an inverse method to recover the roughness parameters (altitude range Delta h(0), and Hurst exponent H) of self-affine surfaces from the energy spectrum of backscattered waves. A stochastic forward modelling of the spectrum of the backscattered wavefield averaged along a profile of finite length is proposed in the near-nadir and far-field configuration. A Bayesian formulation of the inverse problem is used to account for the random nature of both the data and the forward problem. An acoustic backscattering experiment is performed with a natural rough self-affine surface for which Delta h(0) and H are determined through direct measurements of the topography. The inversion of the experimental spectrum of the backscattered acoustic waves shows that a good determination of H is possible, while Delta h(0) is an unresolved parameter.