The sensitivity of a surface wave to the lateral structure of the Earth's mantle depends on the local structure and thickness of the crust; particularly at short periods, the strong lateral heterogeneity of the crust has a significant nonlinear effect on the surface wave sensitivity functions. Thus far, this effect has not been quantified, and tomographic studies of the upper mantle based on surface wave observations have not taken it into account. On the basis of a Jeffreys-Wentzel-Kramers-Brillouin (JWKB) description of surface wave propagation we find and discuss the lateral variations of the sensitivity of Love and Rayleigh waves to mantle seismic anomalies, associated with a realistic model of the crust <Mooney et al., 1998>. We then use the resulting laterally varying sensitivity kernels to determine a new tomographic image of horizontally and vertically polarized shear velocity in the upper mantle from Love and Rayleigh wave phase velocity measurements (periods from 35 to 300 s). In terms of large-scale patterns of high and low velocity our model is similar to previously published ones, confirming, among other features, the anomalous anisotropy underlying the central Pacific <Ekstr¿m and Dziewonski, 1998>; we find, however, that the lateral dependence of the surface wave sensitivity kernels has a significant effect on the absolute amplitude of the anomalies, which should not be neglected as we attempt to obtain higher-resolution images of the upper mantle.