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.
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Arora, S., Bhattacharya, S.N. & Gogna, M.L. Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell. PAGEOPH 147, 515–536 (1996). https://doi.org/10.1007/BF00878842
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DOI: https://doi.org/10.1007/BF00878842