An Accurate Method of Computing the Gradient of Seismic Wave Reflection Coefficients (SWRCs) for the Inversion of Stratum Parameters

作者：Liu Xiao Bo; Liu Fu Ping^*; Meng Xian Jun; Xiao Jia Qi

来源：Surveys in Geophysics, 2012, 33(2): 293-309.

DOI：10.1007/s10712-011-9149-8

• Jacobian matrix
• Zoeppritz equations
• Gradient of seismic wave reflection coefficients (SWRCs)

The optimization inversion method based on derivatives is an important inversion technique in seismic data processing, where the key problem is how to compute the Jacobian matrix. The computational precision of the Jacobian matrix directly influences the success of the optimization inversion method. Currently, most of the AVO (amplitude versus offset) inversions are based on approximate expressions for the Zoeppritz equations to obtain the derivatives of the seismic wave reflection coefficients (SWRCs) with respect to the stratum parameters. As a result, the computational precision and range of applications of these AVO inversions are restricted undesirably. In order to improve the computational precision and to extend the range of applications of AVO inversions, the partial derivative equations of the Zoeppritz equations are established, with respect to the ratios of wave velocities and medium densities. By solving the partial derivative equations of the Zoeppritz equations accurately, we obtained the partial derivative of SWRCs with respect to the ratios of seismic wave velocities and medium densities. With the help of the chain rule for derivatives, the gradient of the SWRCs can be accurately computed. To better understand the behavior of the gradient of the SWRCs, we plotted the partial derivative curves of the SWRCs, analyzed the characteristics of these curves, and gained some new insight into the derivatives. Because only a linear system of equations is solved in our method without adding any new restrictions, the new computational method has both high precision and a quick running speed; it is not only suitable for small incident angles and weak reflection seismic waves but also for large incident angles and strong reflection seismic waves. With the theoretical foundations established in the article, we can further study inversion problems for layered stratum structures and we can further improve the computational speed and precision of the inversions.

• 出版日期2012-3
• 单位北京印刷学院; 中国石油大学（北京）