Analytical Solutions For the Ray Perturbation In Depth‐Varying Media

SUMMARY In this paper, we present a simple closed‐form solution to the problem of ray propagation through media which have weak lateral inhomogeneities superimposed on an unperturbed velocity field which varies with depth only. We use a Lagrangian formulation of ray‐perturbation theory which incorporates corrections for differences in the arclength parameter in perturbed and unperturbed media at every instant a long the ray path. We show how it is possible to reduce the first‐order solution for the two‐point boundary‐value problem to the solution of a single initial‐value problem. In this way, the total Green's function for two‐point boundary‐value problems can be related to the propagator for initial‐value problems. Thus the analytical expressions derived for the propagators in this paper may be used to determine analytical expressions for the Green's function of the corresponding two‐point boundary‐value problem. the application of these results to tomographic reconstruction problems is discussed.