三维层状孔隙介质中弹性波的一种积分表达式Ⅱ:正确性检验和数值模拟实验  

An integral expression of elastic waves in 3D stratified porous media Ⅱ:Validation and numerical simulation experiments

作　　者：李娜[1,2] 任恒鑫[1,3] 黄清华[4] 陈晓非[1,3] 

机构地区：[1]中国科学技术大学地球和空间科学学院,合肥230026 [2]西方科奇,斯伦贝谢中国分公司,北京100015 [3]中国科学技术大学地震与地球内部物理实验室,合肥230026 [4]北京大学地球与空间科学学院,北京100871

出　　处：《地球物理学报》2014年第7期2244-2257,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金面上项目(41274053;41274054);国家杰出青年基金项目(41025014)资助

摘　　要：基于前一篇文章中得到的关于三维层状孔隙介质中弹性波场的积分形式半解析解,本文通过离散波数法开展了数值模拟.将全空间均匀孔隙介质中单力点源和爆炸点源作用下弹性波场的解析解和我们的数值模拟结果进行对比,发现两者是完全一致的.而在一个两层半空间模型下的数值模拟,验证了固相位移Green函数的9组空间互易性情况.通过以上两种对比检验,验证了半解析解理论公式、数值模拟方法以及相应程序代码的正确性和可靠性.随后利用敏感度分析研究了不同的介质参数变化对爆炸点源在界面上会产生的反射波场的影响.通过垂直地震剖面模型的数值模拟,发现弹性波场能很好地反映孔隙介质物理性质的变化,同时也讨论了动力协调这一孔隙介质中的特殊现象.我们发展的基于半解析解的数值模拟方法可以为三维层状孔隙介质中弹性波传播特征的研究提供一种可供选择的有效工具和手段.Based on the integral expression of half-analytical solution for elastic waves in threedimensional （3D） stratified porous media derived in the companion paper, we carry out numerical simulations by using the discrete wave-number method in this study. Comparing the analytical solutions of the elastic waves generated by a point source of single-force or explosion in homogeneous full-space porous media with our numerical solutions, we find they are identical. We also confirm the special reciprocity of the solid displacement by the numerical simulation on a two-layer half-space model. Thus, we verify the validity and reliability of our half-analytical solution, the numerical simulation method and the program code used by us. Then we carry out sensitivity study to discuss the impact of the media parameter on the reflection waves induced by an explosion point source on the interface. In the numerical simulation of a model of vertical seismic profile, we find that solid displacement, seepage displacement and pore-fluid pressure all can reflect the variation of the media properties. Meanwhile, we also discuss the dynamic compatibility phenomenon in porous media. It can be concluded that the developed numerical simulation method based on our half-analytical solution provides an alternative and effective instrument for the study of elastic waves＇ propagation in 3D stratified porous media.

关 键 词：层状孔隙介质 弹性波 数值模拟 敏感度分析 垂直地震剖面 

分 类 号：P631[天文地球—地质矿产勘探] P315[天文地球—地质学]