基于Lebedev网格的TTI介质二维三分量正演模拟  

2D three-component seismic forward modeling in TTI media based on the Lebedev grid

作　　者：刘东洋 彭苏萍[1] 师素珍[1] 赵太郎 

机构地区：[1]中国矿业大学(北京)煤炭资源与安全开采国家重点实验室,北京100083

出　　处：《石油地球物理勘探》2018年第2期288-296,共9页Oil Geophysical Prospecting

基　　金：国家重点研发计划课题(2016YFC0501102);国家科技重大专项课题(2016ZX05066-001);国家自然科学基金煤炭项目(U1261203)联合资助

摘　　要：传统交错网格有限差分法是研究地震波传播规律的一种较为常用的数值模拟方法,但是在交错网格中每个变量的不同分量都是交错定义的,对于没有定义的点需要进行变量插值,从而降低了模拟精度。为此,在前人的研究基础上,推导了TTI介质二维三分量的应力—速度方程,采用Lebedev网格对其进行了高精度的差分离散处理,避免了传统交错网格在处理各向异性介质时波场插值引起的误差,提高了模拟精度,并将多轴完全匹配层吸收边界(M-PML)引入了Lebedev网格。分别对单层TTI介质和含透镜体的复杂TTI介质模型进行了正演模拟,结果表明:(1)由于Lebedev网格对各向异性介质的弹性波方程做离散时无需进行波场插值,与传统交错网格有限差分方法相比,模拟精度更高;对TTI介质进行模拟时可以清晰地观察到纵波、快横波和慢横波,并且快、慢横波的偏振方向相反,在单炮记录中观测到的三种波的速度特征也符合波场传播规律。(2)引入多轴完全匹配层(M-PML)吸收边界条件后,在不影响模拟效果的情况下边界反射现象被有效地压制。The conventional staggered grid finite difference method is a numerical simulation method which is often used to study seismic wave propagation.However,different components of each variable in the staggered grid is staggered defined.For undefined points,their variables need to be interpolated,which reduces the accuracy of simulation.Therefore,the 2 D3 Cvelocity-stress elastic wave equation of the TTI media is deduced on the basis of previous studies and the Lebedev grid is used to process the high accuracy differential separation.This scheme can avoid errors caused by the wave field interpolation in the conventional staggered grid when dealing with anisotropic media and it improves the modulated precision.Meanwhile,the multi-axis perfectly matched layer(MPML)method is introduced into this method.The forward modeling of the single layer TTI medium and the complex TTI medium with the lens is carried out.The results indicate as follows:A.The Lebedev grid does not need to interpolate the wavefield when the elastic wave equation of the anisotropic medium is discrete.Compared with the conventional staggered grid method,the simulation accuracy is higher.The test shows that P-wave,fast S-wave and slow S-wave can be clearly observed when the TTI medium is simulated and the polarization direction of fast S-wave and slow S-wave is opposite.The velocity characteristics of the three kinds of waves observed in single gun record also conform to the propagation regulation of seismic wavefield;B.After introducing MPML into this method,the phenomenon of boundary reflection is effectively suppressed without affecting the simulation effect.

关 键 词：TTI介质 Lebedev网格 多轴完全匹配层 透镜体模型 

分 类 号：P631[天文地球—地质矿产勘探]