Deterministic and Statistical Reconstruction of Rough Surfaces from Acoustic Scattering

This work proposes a model inversion framework for the reconstruction of the elevation profile of a rough surface from acoustic scattering. The latter is measured at a microphone array while the surface is insonified with a broadband source. The forward model makes use of the Kirchhoff approximation, which provides reasonable accuracy at high frequencies or in the far field, while enabling an efficient exploration of the design space. A particular challenge in the inversion is the detailed reconstruction of an arbitrary surface of relatively large size from a limited set of microphones, leading to an under-determined problem. An initial estimate of the surface roughness profile is obtained in a deterministic manner by solving the inverse problem using a gradient-based optimiser. The inverse problem is then formulated in a statistical sense and solved using Bayesian inference. The sequential use of deterministic and statistical inversion yields a feasible solution and an uncertainty envelope. The procedure is demonstrated for a surface with a one-dimensional roughness profile.