Inverse problems involving the one-way wave equation: medium function reconstruction

Inverse problems are considered for the linear one-way one-dimensional wave equation or transport equation. In particular the wave speed reconstruction problem for a medium is discussed. Inverse problems for non-stationary, but also non-dispersive, media are examined; this means problems for which the slab medium parameters are both spatially and temporally varying are considered. Both theoretical and numerical results are given for the methods presented. Theoretical results obtained for this equation can be generalised to second order equations.