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

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 Lame'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.