The domain is the natural domain for anisotropy parameter estimation in horizontally layered media. The need to transform the data to the domain or to pick traveltimes in the domain is, however, a practical disadvantage. To overcome this, we combine -derived traveltimes and offsets in horizontally layered transversely isotropic media with a vertical symmetry axis (VTI) with a rational interpolation procedure applied in the domain. This combination results in an accurate and efficient -based semblance analysis for anisotropy parameter estimation from the moveout of qP-waves in horizontally layered VTI media. The semblance analysis is applied to the moveout to search directly for the interval values of the relevant parameters. To achieve this, the method is applied in a layer-stripping fashion. We demonstrate the method using synthetic data examples and show that it is robust in the presence of random noise and moderate statics.