流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法  

A wavelet finite element method for the 2-D wave equation in fluid-saturated porous media

作　　者：张新明[1] 刘克安[1] 刘家琦[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《地球物理学报》2005年第5期1156-1166,共11页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(40374046);哈尔滨工业大学跨学科交叉研究基金项目(HIT.MD2002.26).

摘　　要：本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的.The wavelet finite element method is applied to forward simulation of the wave equation in fluidsaturated porous media. The 2-D scaling functions of Daubechies wavelet are used as the interpolation basis function to replace the polynomial functions, then the tensor wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression of the Daubechies wavelet, a kind of character functions are introduced. The recursive expression of calculating the function value of Daubechies wavelet on the fraction node is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation show that the method is effective.

关 键 词：小波有限元法 流体饱和多孔隙介质 DAUBECHIES小波 尺度函数 快速小波变换 

分 类 号：P631[天文地球—地质矿产勘探]