Calculating an accurate seismic velocity model serves an important role in many seismic imaging techniques. The process of velocity model building is often time-consuming, specifically for anisotropic areas, where more than a single parameter is involved in the process. In the past few years, more time-efficient approaches have been considered to estimate seismic velocity as well as anellipticity parameter or heterogeneity factor using local event slopes. Nevertheless, some of these techniques are not practical due to curvature-dependency, or due to the lack of near-offset data. To address such limitations, we have used a curvature-independent approach for normal-moveout correction as well as parameter estimation in vertical transverse isotropic media, which is based on local estimation of vertical traveltime using a shifted-hyperbola approximation in the absence of near-offset data. The performance of our approach is tested on synthetic and field common-midpoint gathers. It is also assessed in different signal-to-noise ratios and different missing-near-offset situations. Our findings are consistent with the results achieved by the previous methods that were not developed for sparse data.