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Due to manufacturing defects or wear and tear, industrial components may haveuncertainties. In order to evaluate the performance of machined components, itis crucial to quantify the uncertainty of the scattering surface. This bringsup an important class of inverse scattering problems for random interfacereconstruction. In this paper, we present an efficient numerical algorithm forthe inverse scattering problem of acoustic-elastic interaction with randomperiodic interfaces. The proposed algorithm combines the Monte Carlo techniqueand the continuation method with respect to the wavenumber, which canaccurately reconstruct the key statistics of random periodic interfaces fromthe measured data of the acoustic scattered field. In the implementation of ouralgorithm, a key two-step strategy is employed: Firstly, the elasticdisplacement field below the interface is determined by Tikhonov regularizationbased on the dynamic interface condition; Secondly, the profile function isiteratively updated and optimised using the Landweber method according to thekinematic interface condition. Such a algorithm does not require a prioriinformation about the stochastic structures and performs well for bothstationary Gaussian and non-Gaussian stochastic processes. Numericalexperiments demonstrate the reliability and effectiveness of our proposedmethod.

Numerical method for the inverse scattering by random periodic structures