  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 can
be used to identify the elastic parameters of the underlying media, as well as
their statistical hyperparameters in the randomly perturbed case. A stochastic
version of the FIO representation can be used for damage detection. Hypothesis
tests are proposed and validated, which are capable of distinguishing between
an undamaged and a damaged material, even in the presence of random material
parameters.
  The paper presents both the theoretical fundamentals as well as a numerical
experiment, in which the applicability of the proposed method is demonstrated.
