Wave splitting and the reflection operator for the wave equation in R3

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Abstract
The problem of wave splitting in a nonhomogeneous medium in R3 is considered. Previous results for wave splitting in a planar stratified medium can be generalized to a general nonhomogeneous medium (with sufficiently smooth velocity). The wave equation is factorized into an up‐ and down‐going wave system using certain integral and integral‐differential operators. The equation for the reflection operator (which relates the up‐going wave to a down‐going wave) is then obtained, and certain properties of the reflection operator are deduced.