Fundamentals of the method of transverse displacements for calculating the HF radio-wave propagation paths are presented. The method is based on the direct variational principle for the optical path functional, but is not reduced to solving the Euler—Lagrange equations. Instead, the initial guess given by an ordered set of points is transformed successively into a ray path, while its endpoints corresponding to the positions of the transmitter and the receiver are kept fixed throughout the entire iteration process. The results of calculation by the method of transverse displacements are compared with known analytical solutions. The importance of using only transverse displacements of the ray path in the optimization procedure is also demonstrated.
Similar content being viewed by others
References
V. I. Kurkin and V. N. Popov, Normal Wave Method in the High-Frequency Radio Communication Problem [in Russian], Nauka, Mosocw (1981).
S. N. Ponomarchuk, N. V. Il’in, and M. S. Penzin, Soln.-Zemn. Fiz., No. 25, 33 (2014).
D. S. Lukin and E. A. Palkin, Numerical Canonical Method in the Problems of Diffraction and Propagation of Electromagnetic Wvaes in Ionospheric Media [in Russian], Moscow Physical and Technical Institute, Moscow (1982).
Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics in Inhomogeneous Media, Springer-Verlag, Berlin (1990).
J. Haselgrove, J. Atmospher. Solar-Terr. Phys., 25, 397 (1963).
R. M. Jones and J. J. Stephenson, OT Report, 75–76, U.S. Department of Commerce, Office of Telecommunication, U.S. Government Printing Office, Washington, USA (1975).
M. Lockwood, Radio Sci., 16, No. 3, 385 (1981).
M. L. Evlashina, V. S. Mingalev, and G. A. Alad’ev, Geomagn. Aéron., 26, 82 (1986).
V. E. Zakharov and A. A. Chernyak, Vestn. RGU, No. 3, 36 (2007).
D. V. Blagoveshschensky, T. D. Borisov, and D. D. Rogov, Radiophys. Quantum Electron., 53, No. 3, 147 (2010).
D. S. Kotova, M. V. Klimenko, V. V. Klimenko, and V. E. Zakharova, Radiophys. Quantum Electron., 57, No. 7, 467 (2014).
G. G. Vertogradov, V. P. Uryadov, and V. G. Vertogradov, Radiophys. Quantum Electron., 48, No. 6, 405 (2005).
N. Y. Zaalov, E. M. Warrington, and A. J. Stocker, Radio Sci., 38, No. 3, 1052 (2003).
M. Yu. Andreev, D. V. Blagoveshchensky, V. M. Vystavnoi, et al., Geomagn. Aeron., 47, No. 4, 502 (2007).
D. V. Blagoveshchensky, M. Yu. Andreyev, V. S. Mingalev, et al., Adv. Space Res., 43, No. 12, 1974 (2009).
G. A. Zhbankov, A. T. Karpachev, V. A. Telegin, and K. G. Tsybulya, Geomagn. Aeron., 50, No. 1, 119 (2010).
A. Azzarone, C. Bianchi, M. Pezzopane, et al., Comp. Geosci., 42, 57 (2012).
A. T. Karpachev, G. A. Zhbankov, and V. A. Telegin, Geomagn. Aeron., 53, No. 6, 761 (2013).
A. Settimi, M. Pezzopane, M. Pietrella, et al., Radio Sci., 48, 167 (2013).
N. N. Kalitkin, Numerical Methods [in Russian], Nauka, Mosocw (1978), p. 266.
J. Um and C. Thurber, Bull. Seismolog. Soc. Amer., 77, No. 3, 972 (1987).
T. J. Moser, G. Nolet, and R. Snieder, Bull. Seismolog. Soc. Amer., 82, No. 1, 259 (1992).
G. Mills and H. Jonsson, Phys. Rev. Lett., 72, 1124 (1994).
L. Xu, G. Henkelman, C. T. Campbell, and H. Jonsson, Phys. Rev. Lett., 95, No. 14, 146103 (2005).
G. Henkelman and H. Jonsson, Phys. Rev. Lett., 90, No. 11, 116101 (2003).
R. F. Bessarab, V. M. Uzdin, and H. Jonsson, Phys. Rev. B, 88, No. 21, 214407 (2013).
C. J. Coleman, Radio Sci., 46, No. 5, RS5016 (2011).
H. Jonsson, G. Mills, and K. W. Jacobsen, Classical and Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore (1998).
D. Sheppard, R. Terrell, and G. Henkelman, J. Chem. Phys., 128, No. 13, 134106 (2008).
O. I. Yakovlev, V. P. Yakubov, V. P. Uryadov, and A. G. Pavel’ev, Propagation of Radio Waves [in Russian], Lenand, Moscow (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 59, No. 1, pp. 1–14, January 2016.
Rights and permissions
About this article
Cite this article
Nosikov, I.A., Bessarab, P.F. & Klimenko, M.V. Method of Transverse Displacements Formulation for Calculating the HF Radio Wave Propagation Paths. Statement of the Problem and Preliminary Results. Radiophys Quantum El 59, 1–12 (2016). https://doi.org/10.1007/s11141-016-9670-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-016-9670-1