基于波动方程差分和Kirchhoff积分的被动源弹性波逆时成像对比研究

The comparison of passive source elastic time-reversal migration based on wave equation and Kirchhoff integral

对地壳和上地幔地下结构成像是地震学研究的重点问题,传统上接收函数法的原理是基于水平层状介质和远震平面波近垂直出射假设的叠加方法,难以适用于复杂地下结构的成像。勘探地震学中的叠前深度偏移类方法(如被动源逆时偏移(PS-RTM)),可以用于复杂结构成像,与传统接收函数的共转换点叠加方法相比有更高的成像精度。基于双程弹性波动方程差分法的PS-RTM必需满足计算的稳定性,对模型网格尺寸和时间步长有较高要求,其巨大的计算量导致成像效率太低。而Kirchhoff类叠前深度偏移具有很高的计算效率,并且对观测方式和时空采样间隔的要求更加灵活,在勘探地震的三维偏移和速度分析中得以广泛应用。首先介绍被动源PS-RTM实现中的波场分离和成像条件,进一步提出适用于单分量和多分量被动源弹性波的叠前Kirchhoff逆时偏移方法,利用Kirchhoff积分方法重构纵波和横波的波场,通过应用被动源成像条件获得地下结构的图像。利用西藏某区的深部构造模型合成理论数据进行测试,对莫霍面成像与PS-RTM方法的成像效果相近,表明所提出方法的有效性。为了讨论观测台站疏密程度对被动源弹性波逆时偏移的影响,用几组不同台站间距合成测试检验,对比被动源弹性波波动方程和Kirchhoff偏移的适应性差异。

The discovery of subsurface structure has always been the hot-discussed issue.The receiver function method based on the hypothesis that subsurface structure is horizontally layered and teleseismic plane wave eject nearly vertically into surface,is a popular method because of its practicality.Thus it is not applicable to the imaging of complex medium.The pre-stack depth migration based on exploration seismology suits this situation.Passive source reverse time migration(PS-RTM)has much higher resolution than the common conversion point(CCP)stack.Finite difference(FD)modelling based on two-way wave equation needs to meet stability condition of numerally computation and requires fine space sampling interval and small temporal sampling interval,which has low imaging efficiency because of its great computation.On the other hand,Kirchhoff pre-stack depth migration has incomparable calculation efficiency and its parameter choice is more flexible,which has been widely applied in 3D seismic migration and migration velocity analysis.In this paper,we first introduce P-and S-wave field decomposition and imaging condition and develop a passive source elastic wave pre-stack Kirchhoff depth migration method based on one component and multi-component data respectively,we reconstruct P-and S-wave field by using Kirchhoff integral and then apply imaging conditions to obtain the image of subsurface structure.We test passive source time-reversal imaging based on wave equation and Kirchhoff integral with the synthetic model of Tibet region.The imaging result of Moho discontinuity of these two methods are close,which indicates validity and practicability of the proposed method.In order to discuss the influence of station density on passive source elastic time-reversal migration,we employ four groups different station intervals to compare feasibility difference between wave equation and Kirchhoff method.