A reliable description of seismic anisotropy in the overburden is necessary for accurate seismic imaging, reflection amplitude analysis, and the correction of borehole sonic logs. A walkaway VSP provides an opportunity of local determination of anisotropy parameters in the overburden from recorded polarization vectors and vertical components of slowness vectors. On synthetic examples, we study quality of the estimates of the local transverse isotropy (TI) and of the orientation of its symmetry axis, from Pwave data recorded along a single line of the walkaway VSP. We study sensitivity of the estimates to the used type of the wave (direct, reflected or both), to the varying level of noise applied separately to each component of recorded direct and reflected waves and sensitivity to other parameters.