  This paper is concerned with an inverse source problem for the stochastic
biharmonic operator wave equation. The driven source is assumed to be a
microlocally isotropic Gaussian random field with its covariance operator being
a classical pseudo-differential operator. The well-posedness of the direct
problem is examined in the distribution sense and the regularity of the
solution is discussed for the given rough source. For the inverse problem, the
strength of the random source, involved in the principal symbol of its
covariance operator, is shown to be uniquely determined by a single realization
of the magnitude of the wave field averaged over the frequency band with
probability one. Numerical experiments are presented to illustrate the validity
and effectiveness of the proposed method for the case that the random source is
the white noise.
