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During the analysis of azimuthal anisotropy from migrated seismic 3D gathers, an automatic residual NMO correction is performed. Since it is done gather by gather, it often produces a noisy residual velocity field with high frequency of vertical stripes. Using this velocity field for further calculations may result in large artifacts in the final sections. It is thus necessary to filter the azimuthal velocity field, which is described, in the case of anisotropy, as an ellipse with three components for every point in the 3D space. To filter out the stripes and artifacts, we use a special implementation of the Vector Median Filter method. A straightforward calculation of the Vector Median Filter can be very expensive, and therefore we suggest an effective approximation.