Explicit approximations in traveltime are usually used in seismic data processing such as simulation through ray tracing, velocity analysis for model building, and imaging from time migration. Accurate approximation is key to achieving high-resolution imaging of the structure. We have proposed a perturbation-based approximation for P- and S-waves traveltime in a transversely isotropic medium with a vertical symmetry axis. The perturbation coefficients in this approximation are derived directly from the implicit parametric offset-traveltime equation. The comparison with the generalized moveout approximation (GMA) for P and S waves is applied in numerical examples. We find that our proposed approximation indicates higher accuracy than the GMA counterpart for P and S waves. The error sensitivity of P and S waves in the depth, vertical velocity ratio, and the anellipticity parameter also is analyzed to examine the influence of these factors. In addition, we investigate the anisotropy estimation through two approximations for P and S waves and find that our proposed perturbation method results in high accuracy, which can significantly improve the data processing quality. For the S wave, our approximation also is more accurate than the GMA counterpart and could be implemented for joint tomographic inversions.

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