Asymptotic Approximation for the Normal Modes in Sound Channel Wave Propagation

  1. Ari Ben-Menahem
  1. N.A. Haskell

Published Online: 21 MAR 2013

DOI: 10.1029/SP030p0074

Vincit Veritas: A Portrait of the Life and Work of Norman Abraham Haskell, 1905-1970

Vincit Veritas: A Portrait of the Life and Work of Norman Abraham Haskell, 1905-1970

How to Cite

Haskell, N.A. (1990) Asymptotic Approximation for the Normal Modes in Sound Channel Wave Propagation, in Vincit Veritas: A Portrait of the Life and Work of Norman Abraham Haskell, 1905-1970 (ed A. Ben-Menahem), American Geophysical Union, Washington, D. C.. doi: 10.1029/SP030p0074

Author Information

  1. Base Directorate for Geophysical Research, Air Force Cambridge Research Laboratories, Cambridge, Massachusetts

Publication History

  1. Published Online: 21 MAR 2013
  2. Published Print: 1 JAN 1990

ISBN Information

Print ISBN: 9780875907628

Online ISBN: 9781118667712

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Keywords:

  • Haskell, Norman Abraham, 1905–1970;
  • Geophysics;
  • Geophysicists—United States—Biography

Summary

  • Introductio

  • Wave Equation

  • Normal Mode Solutions of the Wave Equation

  • Approximate Expressions for the Function N(z, k)

  • The Roots of N′(0, k)

  • Asymptotic Approximation for ϕ

  • Geometrical Interpretation of the Normal Modes

  • Phase and Group Velocities of the Normal Modes

  • Integral Representation of ϕ

  • Approximate Evaluation of the Integrals