Search

Point-to-point ray tracing is an important problem in many fields of science. While direct variational methods where some trajectory is transformed to an optimal one are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., this approach is not widely known in ionospheric point-to-point ray tracing. We apply the Nudged Elastic Band (NEB) method to a radio wave propagation problem. In the NEB method, a chain of points which gives a discrete representation of the radio wave ray is adjusted iteratively to an optimal configuration satisfying the Fermat’s principle, while the endpoints of the trajectory are kept fixed according to the boundary conditions. Transverse displacements define the radio ray trajectory, while springs between the points control their distribution along the ray. The method is applied to a study of point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model taking into account traveling ionospheric disturbances. A 2-dimensional representation of the optical path functional is developed and used to gain insight into the fundamental difference between high and low rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively., The authors thank F.S. Bessarab and V.V. Klimenko for fruitful discussions. This study was financially supported by Grants from the Russian Foundation for Basic Research (RFBR) Nos. 15-35-20364, 16-35-00590, Russian target Federal program 5-100 and the task of the Ministry of Education and Science, project No. 3.1127.2014/K.

A computationally efficient technique for the inversion of oblique ionograms into mid-point electron density profiles is described. The profile is given as the sum of quasi-parabolic functions suitable for ray tracing. The CPU time for a 486 desk top computer is 30 s.