Computation of Phase and Group Velocities of Surface Waves in a Spherical Earth Using the Generalized Reflection-Transmission Coefficient Method

We present a new approach to evaluate phase and group velocities of Love and Rayleigh waves in a spherical layered earth using the generalized reflection-transmission coefficient method. The approach is simple and self-efficient to give numerically stable results at all frequency ranges. The method has been previously used for computing phase velocities in a flat layered earth. For spherical earth, we apply the exact flattening transformation to find out the dispersion equation in a spherical layered earth. This equation is then used to compute phase velocities of Love and Rayleigh waves for periods between 20 s and 300 s. Further, group velocities are obtained through analytic differentiation of the dispersion function. We denote Cs, Us as the phase velocity and group velocity respectively for a model in a spherical earth and Cf, Uf as corresponding values for the same model in a flat earth. Computed results on PREM model show that Cs-Cf at 300 s is about 0.26 km/s for fundamental mode Rayleigh wave and about 0.07 km/s for fundamental mode Love wave. On the other hand, Us-Uf at 300 s is about -0.07 km/s for fundamental Rayleigh wave and about 0.07 km/s for fundamental mode Love wave. The both Cs-Cf and Us-Uf are negligible at period 20 s.