Potential inversion from transmission data for the one-dimensional, wave equation

摘要

Consider an inhomogeneous medium on the half line with nonconstant potential which is zero beyond depth X. This medium is probed by an impulsive source generated on the boundary and the transmitted signal is measured at depth X over the time period X ≤ t≤3X. The interaction between the medium and the signal is governed by the one-dimensional wave equation with the potential being the conefficient of the zeroth order term.