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.

中文翻译：

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点对点电离层射线追踪和高低射线系统识别的广义力法

提出了一种用于点对点电离层射线追踪的直接优化方法的变体。该方法非常适合无线电波射线的发射方向未知但接收器的位置已被指定的应用。候选路径到所寻找射线的迭代变换由广义力引导，其中力的定义取决于射线类型。对于高光线，使用光路泛函的负梯度。对于低光线，应用梯度变换，将鞍点的邻域转换为局部最小值的邻域。关于射线特性的知识用于建立系统识别给定点之间所有相关射线的方案，而无需为每个解决方案提供准确的初始估计。该方法对各向同性电离层的各种应用证明了它能够解析复杂的射线配置，包括 3-D 传播和多径传播，其中射线在发射方向上很近。将该方法应用于 Khabarovsk 和 Tory 之间的射线追踪的结果表明，与测量的斜电离图具有良好的定量一致性。