In an anisotropic model, traveltime can be determined approximately by numerical solution of the eikonal equation in terms of an anellipticity parameter η, using perturbation theory. However, its accuracy decreases under the effect of strong anisotropy at larger offsets. It becomes invalid for determining normal moveout velocity and anellipticity parameter in seismic processing. We propose a new approach using Levin T-transformation to transform the expanded traveltime in the transversely isotropic medium with vertical axis of symmetry (VTI) into rational form. The objective of this study is to provide a new traveltime approximation that is more accurate at larger offsets. In this study, we derive Levin algorithm and determine the optimal value of Levin parameters, which is a key step in achieving better accuracy. In a numerical experiment, we compare the accuracy between Levin T-transformation and second sequence of Shanks transformation in a homogeneous VTI medium. We also implement both approximations in a velocity analysis and stacking traces using synthetic common midpoint gathers on a multilayer earth model. The proposed method shows a superiority in accuracy to existing methods over a range of offsets with offset-to-depth ratio up to 6 and anellipticity parameter 0–0.5.

在各向异性模型中，可以使用扰动理论，通过基于椭圆率参数η的方程式的数值解来近似确定行进时间。但是，其精度在较大的偏移量下受到强各向异性的影响而降低。在地震处理中确定法向运动速度和椭圆率参数无效。我们提出了一种使用Levin T变换将具有垂直对称轴（VTI）的横向各向同性介质中的扩展传播时间转换为有理形式的新方法。这项研究的目的是提供一个新的行进时间近似值，该近似值在较大的偏移量处更准确。在本研究中，我们推导了Levin算法并确定Levin参数的最佳值，这是获得更好精度的关键步骤。在数值实验中 我们比较了均质VTI培养基中Levin T转化和Shanks转化第二序列之间的准确性。我们还使用多层地球模型上的合成公共中点道集，在速度分析中实现了逼近，并实现了叠加轨迹。所提出的方法在一定范围的偏移量上具有优于现有方法的精度，偏移量与深度的比值最高为6，而椭圆度参数为0-0.5。