横向各向同性介质Thomsen近似公式的适用范围

Applicability of Thomsen approximate formula in transversely isotropic media

（中国地震局地质研究所，北京100029）

Thomsen为横向各向同性（TI）介质提出的各向异性参数和线性近似公式被广泛采用，但目前对Thomsen近似公式的适用范围的认识仍很模糊。针对这一问题，研究了TI介质P波和SV波Thomsen近似公式最大相对误差随各向异性参数变化的特征以及近似公式的适用范围。研究结果表明，波速比α₀/β₀ =1.5时，在-0.12≤ε≤0.16且-0.16≤δ≤0.24，或
|ε-δ|<0.17（ε和δ为正）时， P波相速度近似公式的最大相对误差不超过1%，随着
α₀/β₀的增大，适用范围略有扩大。SV波近似公式的精度比P波要低一些，在|ε|≤0.1且|δ|≤0.14，或|ε-δ|<0.02（ε和δ为正）时， SV波相速度平方线性近似公式的最大相对误差不超过1%，随着α₀/β₀的增大，适用范围明显缩小。总体来说，P波近似公式适用范围较大，对一些中等强度的各向异性也适用； SV波近似公式尤其是群速度近似公式适用范围很小，必要时需要使用高阶近似或者精确解。

Thomsen anisotropy parameters and linear approximations for transversely isotropic (TI) media are widely used. However, the applicability of the approximations is still obscure. Aiming at this problem, we studied the characteristics of maximum relative errors varying with Thomsen’s parameters and the applicable range of the approximations in TI media. The result shows when the velocity ratio α₀/β₀ equals 1.5, the maximum relative error of the phase-velocity approximations of P-waves is no more than 1% for -0.12≤ε≤0.16 and -0.16≤δ≤0.24,or ｜ε-δ｜<0.17 with positive ε and δ.The applicability for P-wave extends a little when α₀/β₀ increases. However, the approximations of SV-wave are not as accurate as those of P-wave. Maximum relative errors of the squared phase-velocity approximation of SV-waves are less than 1% if ｜ε｜≤0.1 and ｜δ｜≤0.4,or ｜ε-δ｜<0.02 with positive εand δ. As α₀/β₀ grows, the applicability for SV-waves shrinks obviously. In a word, the approximations of P-wave have larger applicability and are applicable for medium tenacity anisotropy media. But the approximations of SV-wave, especially the group-velocity approximations, have a small applicability, sometimes high-order approximations or exact solutions are necessary.