基于波动方程理论的地震波场数值模拟方法综述

Review on the seismic wavefield forward modelling

地震波场数值模拟的重要性日益凸显,其在地震勘探、各向异性介质属性研究、强地面振动预测、理论地震图合成等方面的应用日渐增多.基于波动方程理论的模拟方法有很多,如:有限差分法、伪谱法、有限元法、谱元法、边界元法等,而现有的综述性文献仅仅是关注某一种或是几种算法,还未有融入最新的文献后系统论述以上五种方法的综述性文献.鉴于此,本文就地震波场数值模拟的主要算法进行了回顾性分析,讨论了这五种算法的优点与不足.一般而言,有限差分法计算速度快,但其频散较严重,而且难以应付地表起伏问题;伪谱法计算精度高,占用内存相对较小,但不适于复杂的地质体模型,也不利于并行计算;有限元法处理地表起伏问题的能力强,但计算量较大;谱元法和边界元法便于处理边界问题,但也存在计算量大的问题.综合考虑,谱元法虽然存在模型参数化困难的问题,却是目前值得推荐的模拟算法.最后,文中对未来地震波场数值模拟的发展进行了展望.

The seismic wavefield modelling becomes more and more important in the seismic exploration, anisolropie study, strong motion prediction, synthetic seismogram and etc. There are many methodologies based on the theory of seismic wave equation, such as finite difference method, pseudospectral method, finite element method, speclral element method, boundary element method and etc. So far there are only some specified articles in lhe lileralure reviewing on some of the total methods. It is necessary to overview the main methodologies on seismic wavefieht modelling in a whole, and summarize their advantages and shortcomings, which is more important to new comer in this field. Generally speaking, the finite difference method has fast CPU time, but relatively heavy frequency dispersion and uneasy treatment for the undulated topography; while the pseudospectral method has high accuracy and less memory requirement, but inflexible for complex model and unsuitable for paralleling computation; lbe finite element method is capable of simulating an undulated topography, but with relatively longer CPU time and both the boundary element method and the spectral element method are able to deal with any boundary problems, but also have longer CPU time. Based on the above discussion, the spectral element method is a favorable choice. Finally, we try to prospect the near future in the seismic wavefield modelling.