We studied the validity of qP-wave slowness and slowness-polarization methods for estimating local anisotropy parameters in transversely isotropic (TI) media by quantifying the estimation errors in a numerical exercise. We generated numerical slownesses and polarizations over two aperture ranges corresponding to a short offset walkaway vertical seismic profiling (VSP) and a long offset walkaway VSP for a range of TI models with vertical axis of symmetry (VTI). Synthetic data are equisampled over the phase angle range and contaminated with Gaussian noise. We inverted the data and compared the anisotropy parameters of the optimal model with the true model. We found that the selection of a proper methodology for VTI parameter estimation based on walkaway VSP measurements was mostly dependent on our ability to accurately estimate either horizontal components of qP-wave slowness vector or the polarization vector. With data contaminated with noise, methods that include the horizontal component of the slowness vector had greater accuracy than the methods that replace this information with polarization measurements. The estimations are particularly accurate when a wide range of propagation angle was available. For short offsets, only parameter could be reliably estimated. In the absence of long offsets, depending on the accuracy of polarization measurements, the method based on the weak anisotropy approximation for qP-wave velocity in VTI media or the method based on slowness and polarization vectors could be used to estimate and . If the horizontal components of the slowness vector were not available (a heterogeneous overburden), we used methods that were based on local measurements of the polarization vector. We found that, with accurate measurements of the polarization vector, the method based on exact relationship between vertical slowness and polarization dip could be used to estimate VTI parameters even for the cases in which the wide offset range was not available.