Geophysical research: article

E.N. Fedorov V.A. Pilipenko
Schmidt Institute of Physics of the Earth, Russian Academy of Sciences
Journal: Geophysical research
Tome: 24
Number: 1
Year: 2023
Pages: 85-92
UDK: 501
DOI: 10.21455/gr2023.1-6
Full text
Keywords: WKB approximation, geometrical optics, waves in geophysics.
Аnnotation: One of the main approximate methods for describing wave propagation in an inhomogeneous medium is the Wentzel–Kramers–Brillouin (WKB) approximation or the geometrical optics approximation. For its application, it is often assumed that the wavelength is small compared to the characteristic scale of the inhomogenei-ty. In this methodical note, attention is drawn to the fact that this condition is unnecessarily stringent, and for practical applications can be replaced by a softer condition for the smallness of the reciprocal wave number compared to the size of the inhomogeneity. A comparison of calculations using the WKB approximation and the exact analytical solution for the linear profile of the inhomogeneity clearly shows that under this condition, the WKB approximation gives good results.
Bibliography: Arfken G.D., Weber H.J., Harris F.E., Mathematical Methods for Physicists: A Comprehensive Guide, Boston, Oxford, Elsevier, 2013, 524 p.

Brekhovskikh L.M., Waves in layered media, New York, Academic Press, 1976, 520 p.

Vinogradova M.B., Rudenko O.V., Sukhorukov A.P., Teoriya voln (The wave theory), Moscow, Nauka, 1979, 384 p. [In Russian].

Ginzburg V.L., The propagation of electromagnetic waves in plasma, London, Pergamon Press, 1964, 535 p.

Davis K., Ionospheric Radio, London, Peter Peregrinus Ltd., 1990, 600 p.

Moiseev N.N., Asimptoticheskie metody nelineinoi mekhaniki (Asymptotic Methods of Nonlinear Mechanics), Moscow, Nauka, 1981, 400 p. [In Russian].

Savarenskii E.F., Seismic waves, Bangkok, ‎IPST, 1975, 288 p.

Pilipenko V.A., Mazur N.G., Fedorov E.N., Engebretson M.J., Interaction of propagating magnetosonic and Alfven waves in a longitudinally inhomogeneous plasma, J. Geophys. Res.: Space Physics, 2008, vol. 113, A08218, 12 p. doi: 10.1029/2007JA012651

Pilipenko V.A., Chugunova O.V., Engebretson M.J., Pc3-4 ULF waves at polar latitudes, J. Atmosph. Solar-Terr. Physics, 2008, vol. 70, pp. 2262-2274. doi: 10.1016/j.jastp.2008.09.006