Mathematics – Complex Variables
Scientific paper
Oct 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975rspta.280..111b&link_type=abstract
Royal Society (London), Philosophical Transactions, Series A, vol. 280, no. 1293, Oct. 23, 1975, p. 111-130.
Mathematics
Complex Variables
3
Atmospheric Stratification, Complex Variables, Ionospheric Propagation, Phase-Space Integral, Ray Tracing, Wentzel-Kramer-Brillouin Method, Anisotropic Media, Approximation, Error Analysis, Propagation Modes, Radio Echoes, Wave Reflection
Scientific paper
The phase integral method is a form of ray theory, extended to use complex values of the space coordinates. The method involves the evaluation of integrals along suitably chosen contours in complex space. It is approximate but often capable of high accuracy and often quicker to use than more exact methods. Its justification is based on the physical principles of analytic continuation and of uniform approximation. For reflexion and coupling problems in a horizontally stratified ionosphere, the contours used for the phase integrals are determined by those real or complex heights called 'reflexion' or 'coupling' points, where two roots of the Booker quartic equation are equal. The study of the behaviour of the governing equations near these points shows when failure of the phase integral method may be expected.
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