Spherical Waves Scattering from Planar Boundaries

  • John A. DeSanto
Part of the Springer Series on Wave Phenomena book series (SSWAV, volume 12)


In this chapter we consider the scattering of a spherical wave from a planar boundary separating two different fluids with densities ρ j and sound speeds c j (j = 1, 2). This is the same geometry considered in Chap. 3 with the additional complication that all incidence angles are now possible. For the point source located at x′(z′ > 0) in the upper fluid (fluid 1) and the receiver at x which could occur in either fluid we have the geometry illustrated in Fig. 4.1.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 4.1
    K. Aki, P.G. Richards: Quantitative Seismology, Theory and Methods (Freeman, New York 1980) Vol. IGoogle Scholar
  2. 4.2
    N. Bleistein, R.A. Handelsman: Asymptotic Expansions of Integrals (Dover, New York 1986)Google Scholar
  3. 4.3
    L.M. Brekhovskikh: Waves in Layered Media (Academic, New York 1960)Google Scholar
  4. 4.4
    A. Erdelyi: Asymptotic Expansions (Dover, New York 1956).MATHGoogle Scholar
  5. 4.5
    L.B. Felsen, N. Marcuvitz: Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, NJ 1973)Google Scholar
  6. 4.6
    I.S. Gradshteyn, I.M. Ryzhik: Tables of Integrals, Series, and Products (Academic, New York 1965)Google Scholar
  7. 4.7
    W. Magnus, F. Oberhettinger, R.P. Soni: Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, New York 1966)MATHGoogle Scholar
  8. 4.8
    E.T. Whittaker, G.N. Watson: Modern Analysis (Cambridge Univ. Press, Cambridge 1962)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • John A. DeSanto
    • 1
  1. 1.Department of Mathematical and Computer SciencesColorado School of MinesGoldenUSA

Personalised recommendations