几种典型地质模型的地震波场数值模拟  

Seismic wave field simulation of several typical geological models

作　　者：徐佼[1,2] 张智[1,2] 董超[1,2] 陈立波[1,2] 李飞[3] 

机构地区：[1]桂林理工大学 广西隐伏金属矿产勘查重点实验室 [2]桂林理工大学 地球科学学院,广西桂林541004 [3]中国石油 塔里木油田分公司勘探开发研究院,新疆库尔勒841000

出　　处：《桂林理工大学学报》2014年第3期416-422,共7页Journal of Guilin University of Technology

基　　金：国家自然科学基金项目(41274070;41174075;41074033;41174043;40804017);国家科技专项(SinoProbe02-02-02);广西自然科学基金项目(2013GXNSFAA019271);桂林市“漓江学者”经费专项(2013);广西壮族自治区地质资源与地质工程“八桂学者”经费专项(2013)

摘　　要：在地震波场数值模拟中,边界条件的选取、差分方程的稳定性条件和收敛性以及频散的消除对于模拟质量至关重要。在综合考虑这些影响因素的基础上,对二维声波方程采用有限差分方法,利用二阶吸收边界条件,模拟了均匀模型、层状模型、断层模型、背斜模型等几种典型介质模型的地震波场。模拟结果揭示了参数的选取对模拟精度的影响程度。通过泰勒级数展开推导得到有限差分波动方程,造成离散的波动方程固有误差的存在。差分阶数越低,频散越严重;相反,有限差分的误差就越小,就越接近于精确解;此外,空间和时间采样间隔越大,会加快计算速度,同时可能会产生网格频散,故在有限差分数值模拟的过程中必须同时兼顾模拟的精度和速度。Stability condition and astringency of difference equation,the elimination of dispersion are important in seismic wave numerical modeling. From the factors in modeling result,based on two-dimensional acoustic wave equation,the seismic wave numerical modeling is shown by finite difference method with two-order absorbing boundary condition in the wave-field of heterogeneous media and inhomogeneous media. By theory calculation and finite difference wave equation numerical modeling in the heterogeneous model,the strata model,the fault model and the anticline model,this method can achieve ideal results if the parameters are reasonable.Through the finite difference method,the wave equation is derived by Taylor series,which makes inherent errors in scattering the wave equation. The low-order difference method may increase the numerical dispersion,and vice versa,the high-order difference method leads to small errors and exact solutions. Meanwhile,larger spatial sampling interval and sampling time interval are better in the calculation rate,but may decrease the corresponding numerical dispersion. So consideration must be given to both the accuracy and speed in the finite difference wave equation numerical modeling.

关 键 词：地震波场 数值模拟 有限差分法 吸收边界条件 稳定条件 数值频散 

分 类 号：P315.31[天文地球—地震学] P631.41[天文地球—固体地球物理学]