介质密度反演偏导矩阵的精确计算方法

实现反演偏导矩阵的计算是基于导数最优化反演方法的关键,然而目前的地震反演几乎都是基于Zoeppritz方程近似实现的,使计算精度和适应范围受到限制.本文利用Zoeppritz方程建立了反射系数对地层介质密度比偏导方程,导出了Zoeppritz方程矩阵元对介质密度比的导数.通过求解偏导方程获得了反射系数对介质密度比偏导数的精确计算(考虑了速度中含介质密度的问题).利用数值算例分析了反射系数对介质密度比偏导数的变化特点.本文采用直接解法求解偏导矩阵方程组,获得了快的计算速度和高的计算精度,为实现地层介质密度反演(包括大角度反演)提供了偏导矩阵的计算方法.

Accurate method for calculating derivative matrix in medium density ratio inversion

Realization of derivative computation is the key for derivative-based inversion. Its computational precision directly influences the inversion result. However, at present almost all AVO (Amplitude Versus Offset) inversions are based on the approximate expressions of Zoeppritz equations. The computational precision and the application scope of AVO inversions are restricted. With the help of Zoeppritz equations, this paper sets up the partial derivative equation of the reflection coefficients of seismic wave with respect to the ratio of medium densities, and derives the derivative of any matrix element with respect to the ratio of medium densities. Through solving the derivative matrix equation, we have obtained the partial derivative of reflection coefficients of seismic wave with respect to the ratio of medium densities, realized the accurate calculation of derivative matrix equation, which can be used to inverse for the ratio of medium densities. We have also analyzed the derivative curves of reflection coefficients of seismic wave, and achieved some new cognitions for the derivative. Because the method of computational derivative matrix adopted is directly solving the linear system of equations, the computation not only has high precision but also has fast computational speed. This paper offers a computational method for us to further research the inversion of stratum densities (including the inversion problem of large angle incident wave) and to improve the computational speed and precision of inversion.