Abstract：The paper analyzed and discussed the functional relationship among phase velocity, group velocity, group angle and phase angle in transverse isotropic media given by Mr. Thomsen (1986); defined a parameter C0 relative to V_P/V_S ratio in vertical directions; illustrated that Thomsen parameters ε, δ and C0 are not totally independent, their evaluated range should be constrained by each other. The paper pointed out the evaluated ranges of Thomsen parameters ε, δ and C_0 should satisfy this constrained interrelation theoretically; proved the group angle of q-P wave φ(θ) is monotonously increasing function of phase angle θ and have consistent monotonicity of group velocity and phase velocity of q-P wave versus phase angle θ; gave monotonous conditions of group angle of q-SV wave φ(θ) versus phase angle θ and summarized the monotony of group velocity and phase velocity of q-SV wave versus phase angle θ is not always consistent. Analyzed results mentioned above provided a theoretical basis for using linear or non-linear interpolation method to determine the phase angle as well as phase velocity and group velocity relative to the known group angle
