基于非均匀各向同性介质的黏弹性波正演数值模拟

Viscoelastic wave modeling in heterogeneous and isotropic media

本文基于广义线性黏弹性体,通过引入黏弹性拉梅常量,提出拉梅差异矩阵,给出了非均匀各向刚性介质的黏弹性波简化方程.拉梅差异矩阵具有和物性矩阵相似的形式,与弹性、黏弹性物性矩阵之间具有特定的数量关系,体现了黏弹性与弹性物性参数之间的差异程度,可以大大简化方程.并利用该简化方程对SEG/EAGE二维盐丘模型进行了正演数值模拟,将模拟得到的单炮记录和声波、Carcione黏弹性波方程模拟得到的单炮记录进行了对比分析.结果表明该简化方程模拟得到的单炮记录不仅具有较好的效果,而且比Carcione黏弹性波方程计算效率高,与理论分析基本相符.

In this paper, the authors present simplified viscoelastic wave equations in heterogeneous and isotropic media based on generalized linear viscoelasticity. Viscoelastic Lame constants are introduced and Lame difference matrix is put forward. Lame difference matrix that has the similar form with physical property matrix holds a certain quantitative relation with elastic and viscoelastic physical property matrices. It makes the viscoelastic equations more concise. The viscoelastic modeling in 2-D SEG/EAGE salt dome model is carried out by using the simplified viscoelastic equations. A comparison of the viscoelastic single-shot records derived from acoustic equations, Carcione＇s equations and the simplified viscoelastic equations is made. The results show that the simplified viscoelastic equations not only have the better effects of single-shot records, but also have a better computational efficiency than Carcione＇s viscoelastic equations and it agrees well with the theoretical analysis.