Inverse problem of the wave equation and the Schwinger approximation

A new method of profile inversion for acoustic waves propagating in a medium with spherical inhomogeneity based on the Schwinger variational method is presented. The wave equation of interest is transformed into a Schrodinger equation, so that the Born approximation and the new method could also be applied at high frequencies. It is shown that the new method is stable and is more accurate than the Born approximation. To illustrate the method, an exactly solvable analytical example is presented. Also numerical examples using synthetic data, with and without additive noise, are given and the corresponding inversion results and the stability of the method are studied.