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

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.