pure and applied geophysics

, Volume 147, Issue 3, pp 515–536 | Cite as

Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell

  • Swarn Arora
  • S. N. Bhattacharya
  • M. L. Gogna
Article

Abstract

We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters λ, μ ∞r p and compressional and shear-wave velocities α, β ∞r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=−2. We obtain numerical results which agree with results obtained by other methods.

Key words

Spherical earth heterogeneous shells Rayleigh waves dispersion equation decoupling 

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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Swarn Arora
    • 1
  • S. N. Bhattacharya
    • 2
  • M. L. Gogna
    • 3
  1. 1.D.A.V. College for WomenKarnalIndia
  2. 2.Seismological Observatory, Meteorological DepartmentNew DelhiIndia
  3. 3.Department of MathematicsKurukshetra UniversityKurukshetraIndia

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