基于谱元法的各向异性黏弹性介质地震波场模拟和分析
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摘要
基于谱元法计算理论,通过坐标旋转算法实现任意各向异性黏弹性介质中的地震波场计算,研究复合介质中地震波场特征。根据计算结果,qSV波表现为剪切滞弹性形变,qP波表现为膨胀滞弹性形变;品质因子不仅影响地震波振幅,还影响其传播频率;黏弹性介质吸收高频快,在一定频率范围内,黏弹性介质没有频散现象。
Based on the calculation theory of spectral element method,the authors used the coordinate rotation algorithm to calculate seismic wave field of arbitrary anisotropic viscoelastic medium to understand the characteristics of seismic wave field in complex media. The results of calculation indicate that qSV wave is a shear anelastic deformation and qP wave is expansion of anelastic deformation. Moreover,the quality factor not only affects the amplitude of seismic wave,but also the frequency of propagation. The viscoelastic medium absorbs high-frequency quickly and there is no frequency dispersion in certain frequency range.
Based on the calculation theory of spectral element method,the authors used the coordinate rotation algorithm to calculate seismic wave field of arbitrary anisotropic viscoelastic medium to understand the characteristics of seismic wave field in complex media. The results of calculation indicate that qSV wave is a shear anelastic deformation and qP wave is expansion of anelastic deformation. Moreover,the quality factor not only affects the amplitude of seismic wave,but also the frequency of propagation. The viscoelastic medium absorbs high-frequency quickly and there is no frequency dispersion in certain frequency range.
引文
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[2]Emmerich H,Korn M.Incorporation of attenuation into time-domain computations of seismic wave fields[J].Geophysics,1987,52(9):1252-1264.
[3]宋守根,袁修贵,白尤军.黏弹性介质地震复合波变焦分离与波场外推技术[J].中南工业大学学报,1996,27(6):632-637.SONG Shou-gen,YUAN Xiu-gui,BAI You-jun.Zoom separation and wave field extrapolation technique for seismic compound wave in viscoelastic medium[J].Journal of Central South University of Technology,1996,27(6):632-637.
[4]Xu T,Mc Mechan G A.Efficient 3-D viscoelastic modeling with application to near-surface land seismic data[J].Geophysics,1998,63(2):601-612.
[5]张中杰,膝吉文,贺振华.EDA介质中地震波速度,衰减与品质因子方位异性研究[J].中国科学,1999,29(6):569-574.ZHANG Zhong-jie,TENG Ji-wen,HE Zhen-hua.Study on seismic wave velocity,attenuation and quality factor in EDA medium[J].Chinese science,1999,29(6):569-574.
[6]邵志刚,傅容珊,黄建华,等.线性黏弹性介质中地震波场数值模拟[J].地球物理学进展,2007,22(4):1135-1141.SHAO Zhi-gang,FU Rong-shan,HUANG Jian-hua,et al.Numerical simulation of seismic wave field in linear viscoelastic medium[J].Advances in geophysics,2007,22(4):1135-1141.
[7]唐启军,韩立国,王恩利,等.基于随机各向异性背景的黏弹性单斜介质二维三分量正演模拟[J].西北地震学报,2009,30(1):35-39.TANG Qi-jun,HAN Li-guo,WANG En-li,et al.Two dimensional three component forward modeling of viscoelastic medium based on random anisotropic background[J].Journal of Northwest China earthquake,2009,30(1):35-39.
[8]李金泉,韩立国,罗金梅,等.基于qp波及qs波衰减系数检测裂缝的方法[J].世界地质,2011,30(2):282-288.LI Jin-quan,HAN Li-guo,LUO Jin-mei,et al.Method for detecting cracks based on qp and qs wave attenuation coefficient[J].Global Geology,2011,30(2):282-288.
[9]梁全有,韩立国,巩向博.各向异性Radon变换在深水地震多次波压制中的应用[J].世界地质,2014,33(2):484-487.LIANG Quan-you,HAN Li-guo,GONG Xiang-bo.Application of anisotropic radon transform in deep sea seismic multiple wave attenuation[J].Global Geology,2014,33(2):484-487.
[10]Patera A T.A spectral element method for fluid dynamics laminar flow in a channel expansion[J].Journal of Computational Physics,1984,54(3):468-488.
[11]Aki K,Richards P G.Quantitative seismology the theory and method(the first volume)(in Chinese)[M].Beijing:Beijing Seismological,1986:41-130.
[12]Chaljub E,Komatitsch D,Vilotte J P.The spectral element method:an efficient tool to simulate the seismic response of 2D and 3D geological structures[J].Bulletin of the Seismological Society of America,1998,88,368-392.
[13]王宁,吕希华,闫磊,等.三维方位各向异性介质数值模拟及波场分析[J].世界地质,2010,29(1):130-138.WANG Ning,LXi-hua,YAN Lei,et al.Numerical simulation and wave field analysis of 3-D azimuthal anisotropy media[J].Global Geology,2010,29(1):130-138.
[14]祝贺君,张伟,陈晓非.二维各向异性介质中地震波场的高阶同位网格有限差分模拟[J].地球物理学报,2009,52(6):1536-1546.ZHU He-jun,ZHANG Wei,CHEN Xiao-fei.Two dimensional anisotropic medium seismic wave field with high order staggered grid finite difference simulation[J].Chinese Journal of Geophysics,2009,52(6):1536-1546.
[15]Hughes T J R.The finite element method,linear static and dynamic finite element analysis[M].Dover:Dover Publications,2000:206-319.
[16]De Martin F.Verification of a spectral-element method code for the southern California earthquake center LOH3 viscoelastic case[J].Bulletin of the Seismological Society of America,2011,101(6):2855-2865.
[17]Peter D,Komatitsch D,Luo Y,et al.Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes[J].Geophysical Journal International,2011,186(2):721-739.
[18]李洪建,韩立国,巩向博.复杂构造网格化及高精度地震波场谱元法数值模拟[J].石油物探,2014,53(4),1000-1441.LI Hong-jian,HAN Li-guo,GONG Xiang-bo.Numerical simulation of complex structure and high accuracy seismic wave field spectroscopy[J].Petroleum geophysical prospecting,2014,53(4),1000-1441.