正交各向异性介质反射系数精确解

中国陆相沉积岩大多具有薄互层特征，当受到构造运动的影响时，会发育垂向或近似垂向的高角度裂缝，呈现出典型的正交各向异性，可看作是VTI和HTI各向异性的叠置。研究正交各向异性介质的AVO响应特征对裂缝型储层的精细刻画有重要的意义。针对VTI背景介质中发育的一组直立裂缝诱导的正交各向异性，采用Tsvankin提出的各向异性参数构建刚度系数矩阵，再根据Christoffel方程和边界条件推导了精确反射系数和透射系数的计算方法。理论模型试算表明：①若P波从低阻抗各向同性介质入射至高阻抗正交各向异性介质，背景介质VTI各向异性强度的增大会导致PP波反射系数增大、PS1波和PS2波的反射系数减小；而随着裂缝弱度的增强会导致PP波反射系数的减小、PS1波和PS2波的反射系数的增大。②若P波从高阻抗各向同性介质入射到低阻抗正交各向异性介质，PP波、PS1波和PS2波的反射系数变化规律与①相反。③PP波反射系数的方位各向异性远小于PS1波和PS2波。与Rüger反射系数近似公式计算结果的对比，验证了该反射系数计算方法的正确性。

Exact reflection coefficients of orthorhombic anisotropic media

Most of continental sedimentary formations in China are characterized by thin interbeds.Under the influence of tectonic movement,in sedimentary formations,vertical or nearly vertical high-dip fractures are developed,which result in typical orthorhombic anisotropy.This kind of orthorhombic anisotropy can be regarded as the superposition of VTI and HTI.Therefore,the study on AVO responses of orthorhombic anisotropic media is significant for fine characterization of fractured reservoirs.To the orthor-hombic anisotropy induced by a set of upright frac-tures developed in a VTI background,Tsvankin aniso- tropy parameters are used to construct the stiffness coefficient matrix.Then,the method for calculating exact reflection and transmission coefficients is presented based on the Christoffel equations and the correspon-ding boundary conditions.Model test shows that: ①if P-wave is incident from a low-impedance isotropic medium to a high-impedance orthorhombic anisotropic medium,the increase of the VTI anisotropy coefficient in the background media will lead to the increase of the PP-wave reflection coefficient and the decrease of the PS1- and PS2-wave reflection coefficients; and the increase of fracture weakness will lead to the decrease of the PP-wave reflection coefficient and the increase of the PS1- and PS2-wave reflection coefficients; ②if P-wave is incident from a high-impedance isotropic medium to a low-impedance orthorhombic anisotropic medium,the reflection coefficients of PP-,PS1- and PS2-waves present the opposite characteristics; ③the azimuthal anisotropy of PP-wave reflection coefficients are much smaller than those of PS1- and PS2-waves.By comparing with the results of Rüger approximate reflection coefficient formulas,the accuracy of our calculation method is verified.