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基于导数的最优化反演方法是求解反问题的重要方法之一,实现的关键是Jacobian矩阵的计算,其精度直接影响反演结果的优劣,然而目前的AVO(Amplitude VersusOffset)技术几乎都是基于Zoeppritz方程近似式实现的,致使计算的精度和适应范围受到很大限制.利用Zoeppritz方程建立了反射系数对地震纵横波速度的偏导方程(反演纵横波速度的Jacobian矩阵方程),导出了Zoeppritz方程各矩阵元对纵横波速度的导数.通过求解Jacobian矩阵方程获得了精确的反射系数对地震波速度的偏导数,实现了反演纵横波速度Jacobian矩阵的精确计算,绘制了反射系数对纵横波速度的偏导数曲线,分析了曲线的变化特点,获得了规律性认识.由于Jacobian矩阵的计算是采用直接解法求解线性方程组,使计算不仅具有高的精度而且还具有较快的计算速度,为进一步研究地层参数反演(包括大角度入射波的反演)、提高反演的速度和精度提供了重要的理论依据和计算方法.
Derivative-based inversion method is one of the important methods to solve the inverse problem. The key to realize is the calculation of Jacobian matrix, whose accuracy directly affects the quality of the inversion results. However, the current AVO (Amplitude Versus Offset) techniques are almost always Based on the Zoeppritz equation approximation, the precision and the range of the calculation are greatly limited. The partial derivative equation (the Jacobian matrix equation of the inverse S-wave velocity) of the reflection coefficient to the seismic P- and S-wave velocities is established by the Zoeppritz equation, Zoeppritz equation. By solving the Jacobian matrix equation, the partial derivative of the reflection coefficient to the seismic wave velocity is obtained, and the exact calculation of the Jacobian matrix of the inverse S-wave velocity is achieved. The effects of the reflection coefficient on the P- Speed of the partial derivative curve, analysis of the curve characteristics of change, access to the regularity of understanding.As the Jacobian matrix is calculated using the direct solution of linear equations, the calculation not only with high accuracy but also has a faster computational speed, as Further study of the inversion of formation parameters (including the inversion of large-angle incident waves) and increase the inversion Performing speed and accuracy provides an important theoretical basis and calculation methods.