  The transverse coherence functions (TCFs) of phase and amplitude fluctuations
of a seismic wave are powerful to estimate the spatial distribution, length
scales, and strength of random heterogeneities. However, TCFs have been
formulated for transmitted waves only, not for reflected waves. In this paper,
we derive reflection TCFs for Gaussian random media. Furthermore, we propose to
invert for Gaussian random media using the reflection TCFs based on the grid
search. We validate the new reflection TCF formulas using 2D finite-difference
numerical experiments. The numerical example also illustrates the feasibility
and efficiency of the inversion. The stochastic inversion using reflected waves
can be used in both exploration and global seismology.
