We present a new technique in surface wave tomography that takes the finite frequency of surface waves into account using first-order scattering theory in a SNREI Earth. Physically, propagating surface waves with a finite frequency are diffracted by heterogeneity distributed on a sphere and then interfere at the receiver position. Paradoxically, surface waves have the largest sensitivity to velocity anomalies off the path of the geometrical ray. The non-ray geometrical effect is increasingly important for increasing period and distance. Therefore, it is expected that the violation of ray theory in surface wave tomography is most significant for the longest periods.
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Spetzler et al. (2002) studied this question.