Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell |
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| Authors: | Swarn Arora S N Bhattacharya M L Gogna |
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| Institution: | (1) D.A.V. College for Women, 132001 Karnal, India;(2) Seismological Observatory, Meteorological Department, Lodi Road, 110003 New Delhi, India;(3) Department of Mathematics, Kurukshetra University, 132119 Kurukshetra, Haryana, India |
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| 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  ,   r
p
and compressional and shear-wave velocities  ,  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. |
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| Keywords: | Spherical earth heterogeneous shells Rayleigh waves dispersion equation decoupling |
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