Generalized Force Approach to Point-to-Point Ionospheric Ray Tracing and Systematic Identification of High and Low Rays

Igor A Nosikov,Vera A Ivanova,Aleksey V Podlesnyi,Pavel F Bessarab,Gennady A Zhbankov,Maxim V Klimenko

doi:10.1109/tap.2019.2938817

Abstract

A variant of the direct optimization method for point-to-point ionospheric ray tracing is presented. The method is well suited for applications where the launch direction of the radio wave ray is unknown, but the position of the receiver is specified instead. Iterative transformation of a candidate path to the sought-for ray is guided by a generalized force, where the definition of the force depends on the ray type. For high rays, the negative gradient of the optical path functional is used. For low rays, the transformation of the gradient is applied, converting the neighborhood of a saddle point to that of a local minimum. Knowledge about the character of the rays is used to establish a scheme for systematic identification of all relevant rays between the given points, without the need to provide an accurate initial estimate for each solution. Various applications of the method to isotropic ionosphere demonstrate its ability to resolve complex ray configurations including 3-D propagation and multi-path propagation where rays are close in the launch direction. Results of the application of the method to ray tracing between Khabarovsk and Tory show good quantitative agreement with the measured oblique ionograms.

Highlights

H IGH-FREQUENCY (HF) radio waves are widely used in various applications, including far-distance communication and probing of the ionosphere
The operating frequency is close to the lowest usable frequency (LUF) of the F2 ionospheric layer which results in that two of the rays – high ray of the F1 layer and low ray of the F2 layer – almost merge
We have presented a variant of the direct optimization method for solving the point-to-point ionospheric ray tracing problem

Summary

Introduction

H IGH-FREQUENCY (HF) radio waves are widely used in various applications, including far-distance communication and probing of the ionosphere. The theory of ionospheric radio waves based on the eikonal approximation was mostly developed during the 1950s and 60s [1]–[5] providing a tool for numerous ray tracing models including those for magnetoactive ionosphere [6]–[13]. There, the problem of point-to-point ionospheric ray tracing arises, where relevant radio paths between the transmitter and receiver need to be found. A common approach to this boundary-value problem is the numerical integration of the dynamical equations for the rays combined with the shooting method, where the launch direction is systematically refined until the ray homes in on the specified landing point with the desired precision. Care must be taken to send out enough rays in various directions so as not to skip relevant raypaths which satisfy the boundary condition

Methods

Results

Conclusion