基于散射矩阵分解的反射系数二阶近似

常规AVO反演利用精确Zoeppritz方程的一阶近似式，更加适用于弱介质变化的反射界面、小角度或小炮检距反射问题，其假设条件导致计算误差，不利于准确提取密度参数，不能很好地预测复杂储层或中深部储层，且无法充分利用近临界角数据；基于反射/透射系数精确表达式进行高阶近似过于繁琐，利用上、下行波特征向量矩阵及矩阵对称性对反射/透射系数进行泰勒二阶展开，其过程物理意义不够明确，且得到的二阶近似式亦不够完善。为此，直接从P-SV平面波入射/散射矩阵出发，给出了一种求取散射矩阵高阶近似的方法，即利用扰动思想将散射矩阵分解为背景矩阵与一阶、二阶扰动矩阵，求取纵波反射系数背景项与一阶、二阶扰动项，推得纵波反射系数的二阶近似公式。模型对比分析表明，所推公式在中高角度乃至近临界角入射情况下具有较高的精度，对密度参数的敏感性更高，为充分利用大炮检距地震数据准确地反演物性参数提供了基础。

Second-order approximation of reflection coefficient based on decomposition of scattering matrix

The first-order approximation of the exact Zoeppritz equation is widely used in conventional AVO inversions,which is more suitable for the interface with weak medium variations and the problem of small angle or short offset.The assumptions will lead to calculation errors,which are not conducive to accurate inversion of density and prediction of complex reservoirs and medium-deep reservoirs.And seismic data near the critical angle cannot be fully used.The high-order approximation method based on the exact equation of reflection/transmission coefficients is too complicated.The physical meaning of the process of second-order Taylor expansion of the reflection/transmission coefficients based on the eigenvector matrices of up-and-down waves and matrix symmetry is not clear enough.And the second-order approximation is also not perfect enough.In this paper,a high-order approximation of the scattering matrix based on the incident/scattering matrix of P-SV plane wave is presented.The scattering matrix can be decomposed into the background matrix,the first-and second-order perturbation matrices,and the background term based on the theory of perturbations.The background term,first-and second-order perturbation terms can be derived respectively and the second-order approximation of P wave reflection coefficient can be further obtained.The model comparison analysis shows that the second-order approximation obtained in this paper has higher accuracy in the case of medium-high angle and even near-critical angle incidence and more sensitive to the density variations.It provides a basis for making full use of large-angle or long-offset seismic data and the accurate inversion of physical parameters.