A new acoustic traveltime approximation for attenuating transversely isotropic media

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 frstly 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 symmetryaxis angles of the media as a factor, which will improve its robustness. The approximation is tested in several medium to demonstrate its efectiveness. 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.