Probing a Random Medium with a Pulse

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Abstract
This paper studies the reflection of pulses from a randomly layered half space. It characterizes the statistical properties of the reflected signals at the surface in a suitable asymptotic limit in which the pulse width is large compared to the typical size of the inhomogeneous layers but small compared to the macroscopic variations of the medium properties. It is shown how this characterization can be used to get the macroscopic properties of the medium from the reflected signals with optimal removal of the effects of the random inhomogeneities within the general framework of the model.