复杂介质多尺度变网格地震波数值模拟

The difference methods with variable grids Seismic wave numerical simulation in Multi-scale complex media

在应用有限差分法地震波场数值模拟过程中,模拟精度和计算效率是关键问题之一,特别是对于速度变化剧烈的含小尺度地质体的数值模拟尤为重要.为了既能精细刻画介质的局部结构,又能保证模拟的时效性,本文在传统交错网格有限差分算法的基础上,将变网格有限差分方法引入到交错网格高阶差分数值模拟中,对交错网格空间算法进行了改进,并避免了因插值因素影响模拟精度和计算效率.本文采用完全匹配层吸收边界条件实现对可变网格数值模拟的边界处理,根据完全匹配层吸收边界原理和参量的分裂思想,在不同的方向分别加相应的阻尼衰减因子,解决边界的反射问题.此外还分析了数值频散对于模拟结果的影响.文中分别设计了地堑和生物礁两个介质模型对可变交错网格算法的有效性和稳定性进行了验证.数值模拟结果表明,可变交错网格有限差分算法数值模拟能够对地下介质物性的空间变化进行准确刻画,进一步增强数值模拟对复杂介质的适应性,同时为地震数据的波场成像、纵横波联合解释等提供可靠依据.

In the process of seismic wave field numerical simulation using finite difference method,the simulation accuracy and computational efficiency is one of the keys to the problem which is especially important to the numerical simulation of small scale geological body which velocity changes violently.In order to describe the local structure of medium subtly and guarantee the efficiency of the simulation,this article introduces the variable grid finite difference method to the staggered grid high-order finite difference numerical simulation on the basic of the traditional staggered grid finite difference algorithm to improve the staggered grid spatial algorithm and avoid the reduction of the simulation accuracy and computational efficiency caused by the interpolation factor.This article uses the PML absorbing boundary conditions for the boundary treatment of the variable grid numerical simulation that in different directions respectively introduce the corresponding damping factor to solve the problem of boundary reflection which according to the principle of perfectly matched layer absorbing boundary and the parameters of disunion.In addition,this article analyzes the affection of numerical frequency dispersion on the simulation results.In this article,,the graben and organic reef two medium model have been designed to verify the effectiveness and stability of variable staggered grid algorithm.The results show that the variable staggered grid numerical simulation of finite difference algorithm can accurately depict the space variation of underground medium physical properties to further enhance the adaptability of numerical simulation of complex medium,it also can provide reliable basis for wave field imaging and the combined interpretation of p-wave and s-wave.