Abstract：The paper directly uses the precious functional relationship among the phase velocity,group angle and phase angle as well as group velocity and phase velocity in transversely isotropic medium deduced by Mr.Thomsen to present a new method for computing the traveltimes of seismic first breaks in transversely isotropic medium with arbitrary anisotropic strength that different from the computational method of traveltimes of seismic first breaks presented by Mr.Faria et al that uses approximation of group velocity and is only suitable for weak anisotropy.The new algorithm does not significantly increase computational times when computing the traveltimes of seismic first breaks in transversely isotropic medium with arbitrary anisotropic strength.It is shown by analysis and correlation between isochron sections of travel-times of seismic first breaks given by new algorithm and snapshots of wavefields simulated by staggering mesh finite-difference that the new algorithm has higher precision either in weak anisotropy or in strong-weak anisotropy; the difference of computational results between new algorithm and approximation increases along with the increase of anisotropic strength
