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This paper presents a new approach to modelling wave propagation in random,linearly elastic materials, namely by means of Fourier integral operators(FIOs). The FIO representation of the solution to the equations of motion canbe used to identify the elastic parameters of the underlying media, as well astheir statistical hyperparameters in the randomly perturbed case. A stochasticversion of the FIO representation can be used for damage detection. Hypothesistests are proposed and validated, which are capable of distinguishing betweenan undamaged and a damaged material, even in the presence of random materialparameters.  The paper presents both the theoretical fundamentals as well as a numericalexperiment, in which the applicability of the proposed method is demonstrated.

Wave propagation in random media, parameter estimation and damage detection via stochastic Fourier integral operators