地球物理学报  2011, Vol. 54 Issue (9): 2348-2356 PDF

Study on SEM numerical simulation of airgun signal transition
TANG Jie
School of Geosciences, China University of Petroleum, Shandong Dongying 257061, China
Abstract: In order to study the wave field excited by signal gun, we deduce the seismic wave equation from the theory of porous media based on averaged method. We do the numerical simulation of seismic wave propagation by the spectral element method. We mainly do the following work: (1) We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral element method (SEM),the simulation result shows that SEM can simulate wave propagation effectively. (2) Validate the existence of the Biot's slow compressional wave. We study wave propagation at acoustic-poroelastic discontinuities. (3) We study wave propagation in compacted sediments with gradients in porosity, demonstrate the influence of porosity on phase velocity. (4) As the reservoir bottom is limited, we investigate the influence of fluctuant interface on wave propagation.
Key words: Airgun source      Field situation      SEM      Poroelastic      Biot's theory
1 引言

2 谱元法简介

3 双相介质中波场数值模拟

3.1 双相多孔介质中的弹性波的传播

 图 1 (a)固体相中的地震图；(b)流体相中的地震图 实线和虚线分别为黏滞模型和无黏滞模型的结果. Fig. 1 (a) Solid pressure seismograms； (b) Fluid pressure seismograms Solid line for viscous model, dotted line for inviscid model.
3.2 双相多孔介质中弹性波的反射与透射

 图 2 在上覆水层的双相介质里面的波传播模拟:(A)位移垂向分量波场快照；(B)水中和(C)双相介质中接收到的垂向归一化速度分量 Fig. 2 Simulation of wave propagation in a water layer over a homogeneous poroelastic half-space: (A) Snapshot of the vertical-component of displacement； (B)(C)Vertical-component velocity seismograms in water and poroelastic layer
3.3 孔隙度变化的沉积层研究

 图 3 上覆水层的坚实沉积层中波的传播模拟:(A)波场快照；(B)孔隙度变化；(C)(D)水中和双相介质中接收到的垂向速度分量地震图 Fig. 3 Simulation of wave propagation in a water layer over a compacted sedimentary layer: (A) Snapshot of the vertical- component displacement； (B) Porosity protile in the poroelastic layer； (C)(D) Vertical-component velocity seismograms in water and porosity layer

3.4 高速基岩层情况研究

 图 4 波的传播模拟:(a)(b)波场快照；(c)(d)垂直分量的合成地震图 Fig. 4 Simulation of wave propagation in a limited water layer: (a)(b) Snapshot；(c)(d) Vertical-component velocity seismograms
3.5 起伏水底情况

 图 5 (a)气枪近场子波信号；(b)功率谱图 Fig. 5 (a)Airgun wavelet signal；(b)Powers pectrum

 图 6 (a)模型；(b)波场快照；(c)10 Hz Ricker子波对应的合成地震图；(d)气枪子波信号对应的地震图 Fig. 6 (a)Model； (b)Snapshot； (c) Velocity seismograms for 10 Hz Ricker wavelet；(d) Velocity seismograms for airgun wavelet

4 结论及讨论

(1) 研究了使用SEM 方法模拟孔隙弹性介质中波的传播，使用平均理论实现了从微观到宏观尺度的过渡，研究了孔隙度的变化效果的影响.模拟结果表明，采用谱元法能有效模拟各向异性介质的波场传播.

(2) 双相介质中存在明显的慢纵波，流相波场的慢纵波比固相波场的明显，慢纵波具有很强的散射性质.慢纵波的存在是裂隙液体存在的重要标志，借助慢纵波的出现可以判断孔隙流体的存在，当然目前野外条件尚未获得慢纵波记录，有待于实际工作的努力.

(3) 研究了波在上覆水层的孔隙度变化的沉积层中传播，验证了孔隙度对于相速度的影响.

(4) 借助谱元法分析了高速层存在对于气枪激发信号波场的影响，研究表明低频信号具有较强的穿透高速屏蔽层的能力和较强的抗散射能力.

(5) 研究了起伏界面对波传播的影响，起伏界面会对地震波的传播起到调制和衰减作用.由于气枪源信号包含压力脉冲和气泡脉冲，会导致近源区接收到的干扰较多.

 [1] Tang J, Wang B S, Ge H K, et al. Experiment and simulation of large capacity air-guns in deep structure exploration. Earthquake Research in China , 2009, 23(4): 1-11. [2] Chen Y, Liu L B, Ge H K, et al. Using an airgun array in a land reservoir as the seismic source for seismotectonic studies in northern China: experiments and preliminary results. Geophysical Prospecting , 2007, 56(4): 601-612. [3] Biot M A. General theory of three-dimensional consolidation. J. Appl. Phys. , 1941, 12(2): 155-164. DOI:10.1063/1.1712886 [4] Biot M A. Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. , 1956a, 28(2): 168-178. DOI:10.1121/1.1908239 [5] Biot M A. Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. , 1956b, 28(2): 179-191. DOI:10.1121/1.1908241 [6] Biot M A. Mechanics of deformation and acoustic propagation in porous media. J. Appl. Phys. , 1962a, 33(4): 1482-1498. DOI:10.1063/1.1728759 [7] Biot M A. Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Am. , 1962b, 34(9A): 1254-1264. DOI:10.1121/1.1918315 [8] Plona T J. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies. Appl. Phys. Lett. , 1980, 36(4): 259-261. DOI:10.1063/1.91445 [9] 邵秀民, 蓝志凌. 非均匀各向同性弹性介质中地震波传播的数值模拟. 地球物理学报 , 1995, 38(Suppl.): 39–55. Shao X M, Lan Z L. Numerical simulation of the seismic wave propagation in homogeneous isotropic elastic media. Chinese J. Geophys. (Acta Geophysica Sinica) (in Chinese) , 1995, 38(Suppl.): 39-55. [10] 刘恩儒, 岳建华, 刘彦. 具有离散裂缝空间分布的二维固体中地震波传播的有限差分模拟. 地球物理学报 , 2006, 49(1): 180–188. Liu E R, Yue J H, Liu Y. Finite difference simulation of seismic wave propagation in 2-D solids with spatial distribution of discrete fractures. Chinese J. Geophys. (in Chinese) , 2006, 49(1): 180-188. [11] 杨顶辉. 双相各向异性介质中弹性波方程的有限元解法及波场模拟. 地球物理学报 , 2002, 45(4): 575–583. Yang D H. Finite element method of the elastic wave equation and wavefield simulation in two-phase anisotropic media. Chinese J. Geophys. (in Chinese) , 2002, 45(4): 575-583. [12] Orszag S A. Spectral methods for problems in complex geometries. J. Comput. Phys. , 1980, 37(1): 70-92. DOI:10.1016/0021-9991(80)90005-4 [13] Patera A T. A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Acoust. , 1984, 54(3): 468-488. [14] Priolo E, Seriani G. A numerical investigation of Chebyshev spectral element method for acoustic wave propagation. Proceedings of the 13th IMACS Conference on Comparative Applied Mathematics. Dublin, Ireland, 1991. 551~556 [15] Komatitsch D, Tromp J. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys. J. Int. , 1999, 139: 806-822. DOI:10.1046/j.1365-246x.1999.00967.x [16] Komatitsch D, Vilotte J P. The spectral-element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bull. Seism. Soc. Am. , 1998, 88(2): 368-392. [17] Morency C, Luo Y, Tromp J. Finite-frequency kernels for wave propagation in porous media based upon adjoint methods. Geophys. J. Int. , 2009, 179(2): 1148-1168. DOI:10.1111/gji.2009.179.issue-2 [18] Tromp J, Komatitsch D, Liu Q Y. Spectral-element and adjoint methods in seismology. Comm. in Comput. Phys. , 2008, 3(1): 1-32. [19] Luo Y, Zhu H J, Nissen-Meyer T, et al. Seismic modeling and imaging based upon spectral-element and adjoint methods. The Leading Edge , 2009, 28(5): 568. DOI:10.1190/1.3124932 [20] Morency C, Tromp J. Spectral-element simulations of wave propagation in poroelastic media. Geophys. J. Int. , 2008, 175: 301-345. DOI:10.1111/gji.2008.175.issue-1 [21] Zeng Y Q, Liu Q H. Acoustic detection of buried object in 3-D fluid saturated porous media: numerical modeling. IEEE Trans. Geosci. Remote Sens. , 2001, 39(6): 1165-1173. DOI:10.1109/36.927434 [22] Clayto R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Seism. Soc. Am. , 1977, 67(6): 1529-1540. [23] Higdon R L. Absorbing boundary conditions for acoustic and elastic waves in stratified media. J. Comput. Phys. , 1992, 101(2): 386-418. DOI:10.1016/0021-9991(92)90016-R [24] Yang D H, Wang S Q, Zhang Z J, et al. n-times absorbing boundary conditions for compact finite-difference modeling of acoustic and elastic wave propagation in the 2-D TI Medium. Bull. Seism. Soc.Am. , 2003, 93(6): 2389-2401. DOI:10.1785/0120020224 [25] Wang X M, Tang S Q. Analysis of multi-transmitting formula for absorbing boundary conditions. International Journal for Multicsale Computational Engineering , 2010, 8(2): 207-219. DOI:10.1615/IntJMultCompEng.v8.i2 [26] Arntsen B, Carcione J M. Numerical simulation of the Biot slow wave in water-saturated Nivelsteiner sandstone. Geophysics , 2001, 66(3): 890-896. DOI:10.1190/1.1444978 [27] Bear J. Dynamics of Fluids in Porous Media. New York: American Elsevier Publishing Company Inc., . [28] de Basabe J D, Sen M K. Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations. Geophysics , 2007, 72(6): T81-T95. DOI:10.1190/1.2785046 [29] 王童奎, 李瑞华, 李小凡, 等. 横向各向同性介质中地震波场谱元法数值模拟. 地球物理学进展 , 2007, 22(3): 778–784. Wang T K, Li R H, Li X F, et al. Numerical spectral-element modeling for seismic wave propagation in transversely isotropic medium. Progress in Geophysics (in Chinese) , 2007, 22(3): 778-784.