基于弹性波动方程的叠后地震反演方法

本文提出一种新的基于弹性波动方程的叠后反演技术，即利用反射率法求解弹性波动方程的一维解析解。反射率法利用向量化的递推计算求取地震波反射系数并以此模拟全波场（反射波和多种转换波以及多次波），并考虑透射损失和地层厚度对波场的影响。新方法首先分析纵波速度、横波速度与密度之间的关系，然后直接从叠加数据中反演纵波速度。本文在贝叶斯反演框架基础上，通过微分拉普拉斯分布引入弹性参数的先验信息，降低了反演的不适定性，提高了反演分辨率和稳定性。模型数据和实际资料反演结果证明了新方法的有效性。

Poststack inversion based on the elastic wave equation

We propose in this paper a new poststack inversion method based on the elastic wave equation.This method adopts 1D analytical solution of the elastic wave equation with reflectivity method, which uses vectorized recursive calculation to obtain reflection coefficient and simulate the full-wave field with the consideration of transmission loss and layer thickness. The novel method analyzes the correlations between P-wave velocity and density from well logs, or S-wave velocity and this density, and then obtains P-wave velocity directly from stacked seismic data.Our study also introduces the Bayesian theorem and adds prior information of elastic parameters through differential Laplace constraint to solve the ill-posed inversion problem and improve the accuracy and stability of the inversion.Synthetic and field data applications demonstrate the validity and accuracy of the proposed method.