Short-pulse inversion of inhomogeneous media: a local spectral analysis in the time-domain

The relation between the time-domain scattering data and the scattering medium is established directly in the time domain. Two formulations are considered: A transient plane-wave spectrum and a local pulsed beam spectrum. They form the mathematical framework for two time-domain inverse scattering schemes for 3D inhomogeneous media. The transient plane-wave scheme is formulated in the Radon space where the transient plane-wave spectrum of the data is directly related to the Radon transform of the scattering medium. The pulsed beam scheme is formulated as a local Radon transform in the space-time domain, thereby leading to a local processing and inverse scattering schemes.