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Num. Meth. Prog., 2015, Volume 16, Issue 4, Pages 586–594 (Mi vmp567)  

Calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known

K. G. Gadylshin, M. I. Protasov

A. A. Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A numerical method is proposed for the calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known. The properties of frequency-dependent rays are analyzed and compared with the classical ray theory and with the method of finite-difference modeling for the first time. In this paper we study the dependence of these rays on the frequency of probing signals and show the convergence of the exact rays to the classical rays with increasing frequency. A number of numerical experiments demonstrate the distinctive features of exact frequency-dependent rays, in particular, their ability to penetrate into shadow zones impenetrable for the classical rays.

Keywords: Helmholtz equation, exact frequency-dependent rays, ray theory, numerical methods.

Full text: PDF file (1322 kB)
UDC: 550.341
Received: 08.10.2015

Citation: K. G. Gadylshin, M. I. Protasov, “Calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known”, Num. Meth. Prog., 16:4 (2015), 586–594

Citation in format AMSBIB
\Bibitem{GadPro15}
\by K.~G.~Gadylshin, M.~I.~Protasov
\paper Calculation of exact frequency-dependent rays when the solution of the Helmholtz equation is known
\jour Num. Meth. Prog.
\yr 2015
\vol 16
\issue 4
\pages 586--594
\mathnet{http://mi.mathnet.ru/vmp567}


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