VTI介质弹性波相速度扩展各向异性线性近似  

Extended anisotropic linear approximation for elastic phase velocity in VTI media

作　　者：谷一鹏 印兴耀[1,2] 梁锴 张佳佳[1,2] GU Yipeng;YIN Xingyao;LIANG Kai;ZHANG Jiajia(School of Geosciences,China University of Petroleum(East China),Qingdao,Shandong 266580,China;Evaluation and Detection Technology Laboratory for Marine Mineral Resources,Qingdao,Shandong 266071,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,山东青岛266580 [2]海洋国家实验室海洋矿产资源评价与探测技术功能实验室,山东青岛266071

出　　处：《石油地球物理勘探》2020年第3期635-642,472,共9页Oil Geophysical Prospecting

基　　金：中国石油科学研究与技术开发项目“碎屑岩薄储层地震反演技术研究与集成应用”(2017D-3504);中国石油科技创新基金项目“深层碳酸盐岩储层地震岩石物理建模及孔隙结构表征方法研究”(2016D-5007-0301);中央高校基本科研业务费专项资金项目“基于岩石物理的天然气水合物饱和度预测方法”(18CX02061A);“多组裂隙介质地震波传播与方位响应特征研究”(19CX02002A)联合资助

摘　　要：Thomsen给出的弱各向异性线性近似的条件为各向异性参数的绝对值小于0.2,针对某些各向异性较强的岩石,因为各向异性参数绝对值很大,所以由弱各向异性线性近似计算的相速度误差较大。为此,提出了VTI介质弹性波相速度扩展各向异性线性近似公式,该公式保持了对各向异性参数的线性关系。从VTI介质弹性波精确相速度公式出发,在相速度精确表达式函数曲线与线性近似式函数曲线切点处进行一阶Taylor展开,由切点处相速度对各向异性参数的一阶偏导数构成雅可比矩阵,得到扩展各向异性线性近似公式。理论分析和数值示例表明:在各向异性参数绝对值较小时,弱各向异性线性近似和扩展各向异性线性近似所得结果均与理论值吻合较好;当各向异性参数绝对值较大时,弱各向异性近似所得结果与理论值偏差较大,扩展各向异性线性近似所得结果与理论值吻合较好。说明扩展各向异性线性近似通过调节线性近似的切点,可以适用于各向异性较强的情况。The condition for linear approximation of weak anisotropy given by Thomsen is that absolute anisotropy is less than 0.2.However,for some highly anisotropic rocks,because the absolute value of anisotropy is large,the phase velocity error calculated by weak anisotropy linear approximation is large.A linear approximation formula for extended anisotropy of elastic wave phase velocity in VTI media is proposed.The formula maintains a linear relationship to anisotropic parameters.Starting from the accurate phase velocity formula of elastic wave in VTI media,a first-order Taylor expansion is performed at the tangent point of the accurate expression function curve and linear approximation function curve of phase velocity,a Jacobi matrix is formed from the first-order partial derivative of the phase velocity at the tangent point to the anisotropic parameter,and the extended anisotropic linear approximation formula is obtained.Theoretical analysis and numerical examples show that,when the absolute value of anisotropy is small,the results obtained by the weak anisotropy linear approximation and the extended anisotropy linear approximation agree well with theoretical values;when the absolute value of anisotropy is larger,the result obtained by the weak anisotropy approximation is larger than the theoretical value,and the result obtained by the linear anisotropy extension is in good agreement with the theoretical value.It’s proved that the extended anisotropic linear approximation is applicable for strong anisotropy by adjusting the tangent point of linear approximation.

关 键 词：VTI介质 弱各向异性线性近似 扩展各向异性线性近似 一阶Taylor展开 切点 

分 类 号：P631.4[天文地球—地质矿产勘探]