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Recently, a formalism for three-dimensional surface-wave scattering in a plane geometry was derived. Since teleseismic surface-wave data are generally recorded at epicentral distances large enough to be influenced by the sphericity of the Earth, it is necessary to find the effects of a spherical geometry on surface-wave scattering. The theory of surface-wave scattering relies heavily on a dyadic decomposition of the Green's function, and a new derivation is given for the (dyadic) Green's function of a spherically symmetric Earth. This new derivation employs Poisson's sum formula and is more rigorous than previous derivations. Using the dyadic Green's function, a relation is established with the scattering theory in a flat geometry. This finally leads to a linearized formalism for three-dimensional surface-wave scattering on a sphere. Even for shallow surface waves the effects of sphericity are important and necessitate a modification of the propagator terms in the expression for the scattered surface waves.
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