井中震源的远场波场特征研究  

Far-field wavefield characteristics of downhole seismic sources

作　　者：徐逸鹤 徐涛[1,3] 王敏玲[1,2] 白志明[1] 张忠杰[1] 滕吉文[1] 

机构地区：[1]中国科学院地质与地球物理研究所,岩石圈演化国家重点实验室,北京100029 [2]中国科学院大学,北京100049 [3]中国科学院青藏高原地球科学卓越创新中心,北京100101

出　　处：《地球物理学报》2015年第8期2912-2926,共15页Chinese Journal of Geophysics

基　　金：中国地震局公益性行业科研专项(20140823);国家自然科学基金(41174075,41274070,41374062,41474068)联合资助

摘　　要：井中震源在逆VSP、随钻地震和采矿地球物理研究中都有广泛应用.满足"小井孔"(井孔半径远小于特征波长)及"远场"(炮检距大于特征波长)假设时,井中震源的远场波场存在解析解.为了检验解析解在不同情况下的适用性,本文使用最速下降积分计算了不满足上述假设时井中震源远场波场的合成地震记录,即半解析解.模型试验表明,解析解只能在同时满足"小井孔"和"远场"假设时使用;当这两个假设条件不满足时,解析解的振幅和波形相对于半解析解会有明显的偏差.随着假设不满足程度的增加,偏差会逐渐增加,并会逐渐影响走时的准确拾取;这种条件下,采用半解析解才能获得准确的井中震源波场.Borehole sources,whose scope goes far beyond sources in boreholes,are of extreme importance in research with active seismic sources,including deep seismic sounding,reverse vertical seismic profiling（RVSP）,seismic while drilling,mining geophysics,etc.Sources used in these studies are all of cylindrical structures,which is the reason why they are called borehole sources and why their wave fields has unique characteristics.Previous studies on borehole sources are mostly based on analytical solutions obtained when small-borehole assumption（the borehole radius is significantly smaller than the characteristic wave length）and far-field assumption（the offset is greater than the characteristic wave length）are satisfied.It is still an open question whether the analytical solutions are applicable to cases that violate the two assumptions.This study is based on the synthetic seismograms computed by both analytical solutions and semi-analytical solutions.The analytical solutions used in previous studies are obtained through asymptotic analysis,while the semi-analytical solutions are computed by numerical integration.The semi-analytical solutions are of higher accuracy and therefore regarded as＂true solutions＂.Synthetic seismograms from the analytical solutions are compared to true solutions to validate whether the analytical solutions are applicable to certain cases or not.Accuracy is crucial to the comparison.Yet the high oscillation of solutions in frequency-wavenumber domain brings out a great challenge.We developed a brand-new numerical method called Steepest Descent Integration Method（SDIM）.The new method is inspired by the Method of Steepest Descent（SDM）in asymptotic analysis that is specially designed for highly oscillatory integral and is the very method used to obtain the analytical solutions.Replacing approximate integration path and approximate integrand in SDM with accurate ones,SDIM breaks the restraints of small borehole and far field and can compute seismograms at arbitrary offset and ar

关 键 词：井中震源 远场波场 解析解 最速下降积分 最速下降法 

分 类 号：P631[天文地球—地质矿产勘探]