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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 using the mirror reflection principle. Furthermore, we propose to invert for Gaussian random media using the reflection TCFs based on a grid search. We validate the new reflection TCF formulas using 2‐D elastic finite‐difference numerically modeled seismic data. We also show the feasibility and efficiency of the inverse problem. The stochastic inversion using reflected waves can be used in both exploration and global seismology.

Stochastic Inversion of Gaussian Random Media Using Transverse Coherence Functions for Reflected Waves: Theory and Method