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Ionospheric ray-tracing equations and their solution
https://ieeexplore.ieee.org/document/7909582/
Ionospheric ray-tracing equations and their solution Abstract: The Haselgrove ray-tracing equations are derived directly from Maxwell's equations. Some …
Ionospheric Ray-Tracing Equations and their Solution
https://chuckrino.com/wp-content/uploads/2021/05/Coleman.pdf
From Equation (35), we obtain the ray-tracing equations d pi dt = V n2 /2 and d~/ dt = p, where dt = d<p/ l (i.e., t isthe group distance) and n2 ~ 1-X . These equations do not contain the background magnetic field, and hence can be solved far more efficiently than the original Haselgrove equations.
Ionospheric Ray Tracing - farside.ph.utexas.edu
https://farside.ph.utexas.edu/teaching/jk1/Electromagnetism/node95.html
Equation is essentially a contour integral in -space.The quantity is a relatively slowly varying function of , whereas the phase is a large and rapidly varying function of .As described in Section 7.12, the rapid oscillations of over most of the path of integration ensure that the integrand averages almost to zero. In fact, only those points on the path of integration where the phase is ...
Point‐to‐point ionospheric ray tracing by a direct ... - Wiley
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2011RS004748
Since their introduction more than 50 years ago, the equations of Haselgrove [Haselgrove, 1955, 1963; Haselgrove and Haselgrove, 1960] have provided the main tool for ray tracing. These equations are ideally suited to the situation where the initial point and launch direction of the ray are specified, but the final point is unknown.
An ionospheric ray-tracing technique and its application …
https://www.researchgate.net/publication/3444423_An_ionospheric_ray-tracing_technique_and_its_application_to_a_problem_in_a_long-distance_radio_propagation
A method is given for the determination of the equation of a ray path in a known ionosphere where there axe no horizontal gradients. It can partially take …
Variational methods in ionospheric ray tracing - IEEE …
https://ieeexplore.ieee.org/document/6050876/
This principle provides a variational equation for ray tracing and such equations are better suited to the solution of point to point ray tracing problems. The present paper will discuss the problems of directly solving Fermats principle and describe some recent work that has led to a successful variational approach to ionospheric ray tracing with magneto-ionic effects included. The figure …
(PDF) A general purpose ionospheric ray tracing procedure
https://www.researchgate.net/publication/27255800_A_general_purpose_ionospheric_ray_tracing_procedure
general purpose ionospheric ray tracing procedure is developed. The procedure is based on a numerical solution to the Haselgrove ray tracing equations and includes calculations of ionospherically...
DTIC ADA271058: A General Purpose Ionospheric Ray …
https://archive.org/details/DTIC_ADA271058
A general purpose ionospheric ray tracing procedure is developed. The procedure is based on a numerical solution to the Haselgrove ray tracing equations and... Skip to main content. Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted.
Ray tracing equations - home [Stanford Exploration Project]
http://sepwww.stanford.edu/public/docs/sep95/tariq1/paper_html/node13.html
Figure 9 shows sixteen rays originating from a source on the surface at the position x=0 for inhomogeneous models all of which have v v =v=1.5+0.5 z+0.2 x km/s and .These models differ in their shear wave velocities with rays given in the black curves corresponding to the ratio, r, of the vertical S-wave to P-wave velocities of 0.5, and rays given in the gray curves to r=0.
Fast Ionospheric Ray Tracing.
https://apps.dtic.mil/sti/citations/AD0786465
A hybrid computer was used to solve the equations governing the path of a radio wave thru the ionosphere. The simulation involves the solution of the ray tracing equations with the presence of a dipole magnetic field which requires generation of four functions of three variables, these functions being the electron density and its partial derivatives with respect to each of three …
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