Wave Splitting and the Reflection Operator for the Wave Equation
The problem of wave splitting in a non-homogeneous medium (with sufficiently smooth velocity) is R 3 is considered. 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 obtained, and certain properties of the reflection operator are deduced, including the ideal set of measurements needed to determine the kernel of the reflection operator. The possible application to inverse problems is considered.
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