Method of Transverse Displacements Formulation for Calculating the HF Radio Wave Propagation Paths. Statement of the Problem and Preliminary Results

Application of the nudged elastic band method to the point-to-point radio wave ray tracing in IRI modeled ionosphere

“…In a previously proposed method of transverse displacements, only projected forces were used to find radio wave trajectories (Nosikov et al, 2016), which reduced i F^ computational costs but created a problem that control over the point distribution along the trajectory was lost. In the NEB method, defines position of the trajectory in space, while i spring F controls the distribution of the points along the trajectory.…”

Application of the optimization method to the point-to-point radio wave ray-tracing problem

“…In our investigations [22][23][24], the nudged elastic-band (NEB) method is applied to a point-to-point ionospheric ray-tracing problem. The method was originally developed to identify minimum-energy paths of chemical reactions [25], and it is widely used in various fi elds of science [26][27][28].…”

“…The minimum of the optical path can correspond to a highly nonuniform distribution of the points where there are several localization centers with very low density of points in between them. As a result, the information about the radio wave's trajectory in some critical regions may be lost (see, for example, [22]). The remedy to this problem lies in force projection and the inclusion of elastic forces, which is the basis of the nudged elastic-band (NEB) method.…”

“…is the parallel component of the artifi cial spring force acting between the points. We previously proposed a method of transverse displacements using only projected forces, i F  for the isotropic medium [22]. i F  defi nes the transverse displacement of the path, while the spring force controls the distribution of the points along the path.…”

Modeling the HF Ray Trajectories and Vertical and Oblique Ionograms in the Artificially Disturbed Ionosphere Based on Radiotomographic Data

“…To find the ray trajectories in the first case, a typical approach is to solve the eikonal equation by the method of characteristics [1]. In the second case, shooting methods, which are also based on solving the eikonal equation with a subsequent minimization of the deviation of the ray trajectory coordinates at the height of the receiver from the coordinates of the receiver [10], or the direct variational method based on the Fermat principle [11][12][13] can be applied. The shooting method requires more calculations compared to the variational method and is not always capable of reconstructing the upper rays adequately.…”