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

Authors

  • K.G. Gadylshin Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
  • M.I. Protasov Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS https://orcid.org/0000-0003-0449-1639

DOI:

https://doi.org/10.26089/NumMet.v16r455

Keywords:

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

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.

Author Biographies

K.G. Gadylshin

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Junior Researcher

M.I. Protasov

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Senior Researcher

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Published

14-10-2015

How to Cite

Гадыльшин К., Протасов М. Calculation of Exact Frequency-Dependent Rays When the Solution of the Helmholtz Equation Is Known // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 586-594. doi 10.26089/NumMet.v16r455

Issue

Vol. 16 (2015): Issue 4.

Section

Section 1. Numerical methods and applications