Attenuation is one of the most important quantities in describing seismic wave propagation, which is also anisotropic because of the dispersion relationship between the seismic wave and the symmetry direction. Transverse isotropic media with titled symmetry-axis (TTI) is a widespread approximation of the Earth’s surface. For 2D TTI attenuating media, we firstly use the acoustic assumption to simplify the exact eikonal equation for the complex-valued quasi P-wave traveltime. Then we design a perturbation method to obtain the new approximation by solving the acoustic attenuating eikonal equation of TTI media and use Shanks transform to increase precision. Compared with former studies, the new approximation considers the symmetry-axis angles of the media as a factor, which will improve its robustness. The approximation is tested in several medium to demonstrate its effectiveness. The energy velocity which derived by the steepest-descent method is used to calculate the exact complex-valued traveltime. We test the accuracy of the approximations developed with and without Shanks transform in the following. Finally, we discussed the possibility to apply this approximation to the methods like fast marching methods.

衰减是描述地震波传播最重要的量之一，由于地震波与对称方向的频散关系，衰减也是各向异性的。具有标题对称轴 (TTI) 的横向各向同性介质是地球表面的广泛近似。对于二维 TTI 衰减介质，我们首先使用声学假设来简化复值准 P 波旅行时的精确方程。然后，我们设计了一种扰动方法，通过求解 TTI 介质的声学衰减特征方程来获得新的近似值，并使用 Shanks 变换来提高精度。与以往的研究相比，新的近似将介质的对称轴角度作为一个因素，这将提高其鲁棒性。该近似在几种介质中进行了测试以证明其有效性。最速下降法推导出的能量速度用于计算精确的复值走时。我们在下面测试使用和不使用香克斯变换开发的近似值的准确性。最后，我们讨论了将这种近似应用于快速行进方法等方法的可能性。