Testing the method of transverse displacements for calculating paths of the HF radio wave propagation in three dimensional inhomogeneous media

Propagation of the Russian Academy of Sciences (WD IZMIRAN), Kaliningrad, Russia There are two approaches for radio wave ray tracing when the endpoints of the ray are fixed. The standard approach is the shooting method where a ray is sent out in some direction and its landing point is used to modify the shooting direction and obtain the desired endpoint. However, there is no systematic, universal algorithm for refining the shooting direction. Another approach is based on direct utilization of the variational principle for the optical path (Fermat´s principle). The idea is to transform an arbitrary trajectory to an optimal one, while the endpoints of the trajectory are kept fixed according to the boundary conditions.