基于Zoeppritz方程的叠前和叠后混合多参数非线性地震反演

目前通过Shuey近似式或Gray近似式及基追踪理论反演泊松比，或依据叠前反演获得的纵、横波速度计算纵横波速度比，但不可避免地降低了参数反演精度。为此，尝试通过精确的Zoeppritz方程直接反演纵横波速度比或泊松比。基于垂直入射反射系数和精确Zoeppritz方程的褶积模型，结合边界保护正则化建立叠前和叠后地震反演的目标函数，以降低反演不适定性的不利影响，并使用快速模拟退火算法进行全局非线性优化。由于多参数之间的量级差异以及多参数同步随机搜索增大了不确定性，在反演时通过在改进Fatti方程中引入密度与纵波速度、横波速度与纵波速度两个拟合式提高反演精度与稳定性。实际资料反演结果表明：精确Zoeppritz方程直接反演纵横波速度比的精度明显高于间接反演，各参数反演结果与测井数据基本吻合；叠后反演获得的纵波速度和密度精度较高，叠前反演获得的纵横波速度比的精度高于叠后反演，18°~24°角度道集的反演效果好于3°~9°和33°~39°角度道集。

Nonlinear multi-parameter hybrid inversion of pre-stack and post-stack seismic data based on Zoeppritz equation

At present, Shuey or Gray approximate formula and basis pursuit theory are widely applied in inversion of Poisson ratio. The same is true for the velocity ratio which is calculated from P- and S- waves velocity obtained from pre-stack inversion. But it is not avoidable to reduce the accuracy of inversion parameters. We try to apply Zoeppritz equation in inversion for velocity ratio and Poisson ratio. First we developed a hybrid pre-stack and post-stack seismic inversion workflow by the convolution model based on the reflection coefficient of vertical incidence and Zoeppritz equation. Then we constructed a new objective function which includes edge-preserving regularization to reduce the adverse effect of inversion unsuitability. We applied a fast simulated annealing algorithm to achieve global non-linear optimization. To reduce the influence from the magnitude difference of multiple parameters and the poor stability of multi-parameter simultaneous random search, we used an improved Fatti equation in inversion, which introduces two fitting formulas, a density and P-wave velocity formula, and a S-velocity and P-wave velocity formula, to improve the accuracy and stability of inversion. The inverted results of field data indicate that the velocity ratio obtained by direct Zoeppritz equation inversion is better than that obtained by approximate formulas. The inversion results from the new workflow have good consistency with the logging data. In a word, post-stack inversion obtained more accurate P-wave velocity and density, while the accuracy of velocity ration obtained by pre-stack inversion is higher than that obtained by post-stack inversion, and the inversion of 18°~24° angular trace gathers is better than that of 3°~9° and 33°~39° gathers.