Rayleigh waves are investigated numerically on a subsurface model composed of a layer over a substratum, and a basin embedded in the layer. The basin elastic parameters are varied to obtain three laterally heterogeneous models of different velocity contrast between the basin and the layer. The wave incident upon the basin is defined to be a pure fundamental mode having wavelengths comparable to the basin dimensions. Analysis of the wave transmitted reveals mode conversion, i.e., higher mode excitation which is increasingly important with increased velocity contrast. In terms of (rate of transport of) energy, the contribution of the first higher mode (being the only higher mode in the analysis interval) is relatively small, which differs from earlier results for the case of Love waves. To enable direct comparison, a fundamental Love mode having spectral properties analogous to the Rayleigh wave, is propagated across the subsurface models of the present paper, Hence, the discrepancy between the two waves basically arises from the structure of the subsurface transfer functions. The fraction of modal energy transmitted across the basin proves a sensitive indicator of the velocity contrast, showing similarity in amount and frequency dependence for Rayleigh and Love waves. In terms of modal amplitudes, conventionally considered in practice, the first higher mode contribution (due to mode conversion) is roughly comparable to the fundamental mode contribution, for both transmitted waves. It implies that the amplitude spectrum of the transmitted surface wave is modulated in the horizontal direction. The effect adds to the spectral distortion due to reflection at the basin. Hence, standard interpretation based upon a laterally homogeneous model, of measurements is corresponding regions, may be significantly biased.