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.

中文翻译：

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高斯随机介质随机反演的横向相干函数的反射波：理论和方法

地震波的相位和幅度波动的横向相干函数（TCF）强大，可以估算随机异质性的空间分布，长度尺度和强度。但是，TCF仅针对透射波而已制定，不适用于反射波。在本文中，我们使用镜像反射原理推导了高斯随机介质的反射TCF。此外，我们建议使用基于网格搜索的反射TCF来反转高斯随机介质。我们使用二维弹性有限差分数值模拟地震数据验证了新的反射TCF公式。我们还展示了反问题的可行性和效率。使用反射波的随机反演可用于勘探和全球地震学。