Inverse Acoustic Scattering Problem In Half-Space With Anisotropic Random Impedance

We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function with a pseudodifferential operator describing the covariance. We measure the amplitude of the backscattered field averaged over the frequency band and assume that the data is generated by a single reatization of lambda. Our main result is to show that under certain conditions the principal symbol of the covariance operator of lambda is uniquely determined. Most importantly, no approximations are needed and we can solve the full non-linear inverse problem. We concentrate on anisotropic models for the principal symbol, which leads to the analysis of a novel anisotropic spherical Radon transform and its invertibility. (C) 2016 Elsevier Inc. All rights reserved.