摘要
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 ratioα_0/β_0 equals 1.5,the maximum relative error of the phase-ve- locity 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 positiveεandδ.The applicability for P-wave extends a little whenα_0/β_0 in creases.However.the approximations of SV-wave are not as accu- rate 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 positiveεandδ.Asα_0/β_0 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 ap- proximations of SV-wave,especially the group-velocity approxima- tions,have a small applicability,sometimes high-order approxima- tions or exact solutions are necessary.
出处
《石油物探》
EI
CSCD
2008年第2期116-122,共7页
Geophysical Prospecting For Petroleum
基金
国家自然科学基金项目(40674023)资助
关键词
横向各向同性
各向异性参数
线性近似
相速度
群速度
transverse isotropy
anisotropic parameters
linear approximation
phase velocity
group velocity
