  We apply techniques of microlocal analysis to the study of the transverse
geometry of Riemannian foliations in order to analyze spectral invariants of
the basic Laplacian acting on functions on a Riemannian foliation with a
bundle-like metric. In particular, we consider the trace of the basic wave
operator when the mean curvature form is basic. We extend the concept of basic
functions to distributions and demonstrate the existence of the basic wave
kernel. The singularities of the trace of this basic wave kernel occur at the
lengths of certain geodesic arcs which are orthogonal to the closures of the
leaves of the foliation. In cases when the foliation has regular closure, a
complete representation of the trace of the basic wave kernel can be computed
for $t\not=0$. Otherwise, a partial trace formula over a certain set of lengths
of well-behaved geodesic arcs is obtained.
