The single-station surface wave inversion is a powerful tool for crustal structure exploration. High quality earthquake recordings at far-field seismic stations can be used to perform such kind of inversion. In this process, the frequency dependent phase shift that seismic waves acquire at the focal area should be removed from the observed dispersion curves. This is often a difficult task to achieve particularly for minor earthquakes. In the present work, we attempt a numerical simulation of this problem by employing synthetic seismograms and investigate the case where no correction is made for the source phase shift before the group velocity inversion. After performing the inversion, very satisfactory results were obtained particularly for shallow depths, i.e. upper and middle crustal levels. In some cases, inversion gave poor resolution for velocities at lower crustal levels, for which a forward synthetic seismogram modelling is suggested in order to recover the missing information at those levels. The results of the present study show that synthetic modelling is necessary for modelling surface wave recordings at local and regional distances. The case of anisotropic wave propagation in the crust has also been studied with an emphasis on the false identification of anisotropy provided that no corrections are applied for the source phase shift. This erroneous anisotropy identification is caused by the Rayleigh and Love wave incompatibility and can have serious practical consequences for surface wave modelling.