On inverse source problems for the one-way wave equation

Inverse problems are considered for the linear one-way wave equation or transport equation. The equation is one-dimensional and nonstationary, that is, it has spatial and time-dependent wave speed and dissipation. In particular a number of inverse source reconstruction problems are considered. Both theoretical and numerical results are given for the methods examined. In particular it is shown that the source reconstruction is unique, when the source function is separable as a function of time and space, for the inverse problems discussed. It is shown that the inverse source problems are ill-posed and regularisation is introduced to provide well-posed problems.