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

We consider the second-order differential equations of P-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lam6's parameters 2, # oc r p and compressional and shear-wave velocities c~, flocr, where r 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 when p =-2. We obtain numerical results which agree with results obtained by other methods.