Surface wave tomography routinely uses empirically scaled density model in the inversion of dispersion curves for shear wave speeds of the crust and uppermost mantle. An improperly selected empirical scaling relationship between density and shear wave speed can lead to unrealistic density models beneath certain tectonic formations such as sedimentary basins. Taking the Sichuan basin east to the Tibetan plateau as an example, we investigate the differences between density profiles calculated from four scaling methods and their effects on Rayleigh wave phase velocities. Analytical equations for 1-D layered models and adjoint tomography for 3-D models are used to examine the trade-off between density and S-wave velocity structures at different depth ranges. We demonstrate that shallow density structure can significantly influence phase velocities at short periods, and thereby affect the shear wave speed inversion from phase velocity data. In particular, a deviation of 25 per cent in the initial density model can introduce an error up to 5 per cent in the inverted shear velocity at middle and lower crustal depths. Therefore one must pay enough attention in choosing a proper velocity-density scaling relationship in constructing initial density model in Rayleigh wave inversion for crustal shear velocity structure.