We present a study of anisotropic parameter estimation in the near-surface layers for P-wave and converted-wave (C-wave) data. Near-surface data is affected by apparent anisotropy due to a vertical velocity compaction gradient. We have carried out a modelling study, which showed that a velocity gradient introduces apparent anisotropy into an isotropic medium. Thus, parameter estimation will give anomalous values that affect the imaging of the target area. The parameter estimation technique is also influenced by phase reversals with diminishing amplitude, leading to erroneous parameters. In a modelling study using a near-surface model, we have observed phase reversals in near-surface PP reflections. The values of the P-wave anisotropy parameter eta estimated from these events are about an order of magnitude larger than the model values. Next, we use C-wave data to estimate the effect of anisotropy (chi) and compute eta from these values. These calculated eta-values are closer to the model values, and NMO correction with both eta-values shows a better correction for the calculated value. Hence, we believe that calculating eta from chi gives a better representation of the anisotropy than picked eta from the P-wave. Finally, we extract the anisotropy parameters eta and chi from real data from the Alba Field in the North Sea. Comparing the results with reference values from a model built according to well-log, VSP and surface data, we find that the parameters show differences of up to an order of magnitude. The eta-values calculated from the C-wave anisotropy parameter chi fit the reference values much better and show values of the same order of magnitude.