井间地震粘弹性波场特征的数值模拟研究
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摘要
以数值模拟方法为基础,研究了井间地震粘弹性波场特征及传播规律,并重点研究了井间地震波的粘滞衰减和散射衰减。从本构方程和运动方程出发,给出了二维粘弹性波方程交错网格任意偶数阶有限差分数值模拟方法。对均匀模型、含洞均匀背景模型和含洞层状模型进行了井间地震粘弹性波场数值模拟。结果表明,该方法模拟精度高,边界吸收效果好。介质的粘滞性使得波振幅明显衰减、波形和相位畸变严重,主频向低频偏移显著,且有效频带变窄。洞的散射波同相轴为双曲型,但其同相轴曲率大于直达波的曲率。洞的散射引起直达波振幅衰减明显,而对直达波主频的影响较小。当洞的直径小于一个波长时,洞散射波的主频高于直达波的主频,且与洞的大小关系密切。
Based on both general Hooke's equation and motion equation in 2-D inhomogeneous viscoelastic media, this paper presents a stag-gered-grid any even-order accurate finite-difference scheme of first-order stress-velocity viscoelastic wave equation. The results of numerical modeling for the homogeneous model, homogeneous model with a cave and layers model with a cave indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. It is significant for cross-hole seismic exploration to be viscosity absorption and scattered attenuation; the scattered attenuation mainly depends on the relation between the length of seismic wave and the size of scattered body in inhomogeneous media. Events of scattered wave from cave are hy-perbolic; its curvature is larger than that of direct wave. The effect of the scattered wave from cave on amplitude of the direct wave is significant while the effect on main frequency of the direct wave is small. When the diameter of cave is smaller than the length of crosshole seismic wave, the main frequency of scattered wave from the cave is higher than that of the direct wave and significantly affected by the diameter of cave.
Based on both general Hooke's equation and motion equation in 2-D inhomogeneous viscoelastic media, this paper presents a stag-gered-grid any even-order accurate finite-difference scheme of first-order stress-velocity viscoelastic wave equation. The results of numerical modeling for the homogeneous model, homogeneous model with a cave and layers model with a cave indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. It is significant for cross-hole seismic exploration to be viscosity absorption and scattered attenuation; the scattered attenuation mainly depends on the relation between the length of seismic wave and the size of scattered body in inhomogeneous media. Events of scattered wave from cave are hy-perbolic; its curvature is larger than that of direct wave. The effect of the scattered wave from cave on amplitude of the direct wave is significant while the effect on main frequency of the direct wave is small. When the diameter of cave is smaller than the length of crosshole seismic wave, the main frequency of scattered wave from the cave is higher than that of the direct wave and significantly affected by the diameter of cave.
引文
1牟永光,裴正林．三维复杂介质地震数值模拟[M]．北京:石油工业出版社,2005．1
2 Madariaga R. Dynamics of an expanding circular fault [J]. BSSA, 1976,66(3): 639-666
3 Virieux J. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method [J]. Geophysics, 1986,51(4): 889-901
4 Carcione J M, Kosloff D. Kosloff R. Viscoacoustic wave propagation simulation in the earth [J]. Geophysics, 1988,53(6): 769-777
5 Carcione J M. Seismic modeling in viscoelastic media [J]. Geophysics, 1993,58(1): 110-120
6 Robertsson J O, Blanch J O, Symes W W. Viscoelastic finite-difference modeling[J]. Geophysics, 59(9): 1444-1456
7 Blanch J O, Robertsson J O A, Symes W W. Modeling of a constant Q: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic tech-nique[J]. Geophysics, 1995,60(1): 176-184
8 Aki K.Richards P G. Quantitative Seismology: Theory and practice[M]. New York:W H Freeman, 1980
9 Day S M, Minster J B. Numerical simulation of attenuated wavefields using a Fade approximant method[J]. Geophys J Roy Astr Soc, 1984, 78(1).105- 118
10 Emmerich E, Korn M. Incorporation of attenuation into time-domain computations of seismic wavefields [J]. Geophysics, 1987,52(9): 1 252-1 264
11裴正林．三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟[J]．石油大学学报(自然科学版),2004,28(5):23-29
12裴正林．三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J]．石油物探,2005,44(4):308 315
2 Madariaga R. Dynamics of an expanding circular fault [J]. BSSA, 1976,66(3): 639-666
3 Virieux J. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method [J]. Geophysics, 1986,51(4): 889-901
4 Carcione J M, Kosloff D. Kosloff R. Viscoacoustic wave propagation simulation in the earth [J]. Geophysics, 1988,53(6): 769-777
5 Carcione J M. Seismic modeling in viscoelastic media [J]. Geophysics, 1993,58(1): 110-120
6 Robertsson J O, Blanch J O, Symes W W. Viscoelastic finite-difference modeling[J]. Geophysics, 59(9): 1444-1456
7 Blanch J O, Robertsson J O A, Symes W W. Modeling of a constant Q: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic tech-nique[J]. Geophysics, 1995,60(1): 176-184
8 Aki K.Richards P G. Quantitative Seismology: Theory and practice[M]. New York:W H Freeman, 1980
9 Day S M, Minster J B. Numerical simulation of attenuated wavefields using a Fade approximant method[J]. Geophys J Roy Astr Soc, 1984, 78(1).105- 118
10 Emmerich E, Korn M. Incorporation of attenuation into time-domain computations of seismic wavefields [J]. Geophysics, 1987,52(9): 1 252-1 264
11裴正林．三维各向异性介质中弹性波方程交错网格高阶有限差分法数值模拟[J]．石油大学学报(自然科学版),2004,28(5):23-29
12裴正林．三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J]．石油物探,2005,44(4):308 315
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