基于BISQ机制的三维双相正交介质正演模拟及传播特性研究
|
摘要
Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制。近年来利用同时处理这两种力学机制的BISQ(Biot-Squirt)模型,进行波场数值模拟只限于二维二分量或二维三分量情况,三维三分量的波场模拟尚未见报道。只有三维模拟,才能全面认识双相各向异性介质中固相和流相弹性波场的耦合关系和空间分布特征。本文首先研究了三维情况下,交错网格有限差分算法的震源影响因素,确定了三维数值模拟中最佳的震源模式,再从BISQ模型的波动方程出发,采用交错网格高阶有限差分方法对三维双相正交各向异性介质的弹性波传播进行了数值模拟,研究并分析了不同时刻地震波场的传播快照、VSP记录和地面单炮记录。作为对比还给出了三维情况下的双相横向各向同性介质和方位各向异性介质的快照。
根据弹性波传播方程,推导了三维双相正交介质的Christoffel方程。相对以往对弹性波衰减和频散规律的研究多集中于超声频段,本文详细研究了测井频段(100-2000Hz)弹性波的相速度、逆品质因子与频率、孔隙度、流体粘滞系数、渗透率以及波的传播方向之间的关系。
The object of this paper is porous, cranny and crack 3D two-phase orthotropic medium which are filled with fluid. Firstly, we have had carried out the detailed review on the theory of porous medium and anisotropic medium and the technical Status of related seismic numerical modeling.
Based on the above theory, we derived the 3D elastic kinetic equation and elastic wave propagating equation in two-phase BISQ medium according to Dvorkin (1993) and Yang Dinghui’s studies. In view of the staggered grid high-order finite-difference method which had the numerous merits is quite popularly at present. We derived the forward numerical solution of staggered-grid finite difference method. Unifying predecessor's researches, we have given out the stable condition and boundary condition and studied systematically the source factor’s influence to wavefield simulation in the staggered grid finite-difference method. Through 16 kinds of isotropic medium models’research, we found out:The source add on the stress item, and the source function is sphere cavity source, S wave appeared in the wave field snapshot , it is not tally with classical theory’s conclusion, and the numerical frequency dispersion is very serious too. When the source function change to explosive point source, only the P-wave appeared in the wave field snapshot,this is tally with classical theory’s conclusion, but on the three orthogonal planes(the YoZ plane of X component、the XoZ plane of Y component and the XoY plane of Z component) appeared the numerical frequency dispersion (noise) seriously. When the source is single direction source of the above two source functions respectively, the wave fields are tally with classical theory’s conclusion, but exist obvious numerical frequency dispersion on the shapshots. On the other hand, the source add on the velocity item, there all exists S wave in the wave field snapshots when the source using cavity source and explosive point source respectively, it is not tally with classical theory’s conclusion, but the numerical frequency dispersion disappear when using the explosive point source (although the S-wave wavefront is is not very circular in certain planes). and the situation of the numerical frequency dispersion is not improved at all when using the cavity source. The simulations of using single direction source still exists obvious numerical frequency dispersion. In summary, The author concluded that the most appropriate type of source is explosive point source added on the velocity when we adopted the staggered grid finite-difference method to simulate elastic wave propagation. Under this kind of condition, although the S-wave wavefront is asymmetrical in certain planes, numerical dispersion (noise) is smallest, which is the most advantaged to explain to the complex wave field. On the meantime, the author consider that regarding anisotropic medium elastic wave numerical simulation, no matter the source function being used ,it can excitated the P wave and the S wave simultaneously in the wave field.
On the basis of these researches, First, based on BISQ mechanism, we simulated 3D-3C elastic wavefield of 3D two-phase orthotropic medium and analysed wavefield snapshots of different times、surface seismic records and VSP records. As a comparison, we have also presented the other two-phase medium wavefield snapshots: two-phase transversely isotropic medium、two-phase azimuth anisotropy medium. We analyzed the characters of wavefield. According to the above studies, we got the following conclusions: (1) There are four kinds of waves in two-phase anisotropy media, namely, fast quasi-P wave, slow quasi-P wave, fast quasi-S wave, and slow quasi-S wave. (2) For the viscous media, because the slow qP-wave have a strong attenuation property, we can not see clearly from the solid phase wavefield, but for the ideal non-viscous media, the clear slow qP-wave shown can be seen in both fluid and solid phase snapshots and records. (3) Assuming the anisotropy of solid-fluid coupling density and permeability, the propagation of slow qP-wave show anisotropy characteristic. The change of solid-fluid coupling density is more obvious to the influence of slow P-wave's propagation velocity. (4) In two phase anisotropy media, the wave field is much more complex due to the reflection, transmission, conversion and shear wave splitting on the interface. (5) From the two kinds of three-layers VSP records, we can see that seismic wavefield is more complex in two-phase medium. Fast qP wave propagation not only has the transmission, and reflection, but also has the conversion (convert to qSV wave and slow qP wave). The qS wave can converted to slow qP wave too. The reflection wave of slow qP-wave is quite weak, and also has not seen its conversion. Dispersion situation is quite serious on Y components of fluid-phase wavefield and Z components. The corresponding dispersion situation of solid-phase is quite slight. We analyzed the reason that slow P-wave velocity is low (less than 100/s) and does not satisfy the stable condition. This may be solved by decreasing the space and time domain sample interval(spatial sampling interval around 1m). However, because of the limitation of computer hardware at present, we can only be given such a result. (6) From the surface records we can see that X、Y component is quite sensitive to the S wave, the amplitude of reflection S-wave is more strong and P-wave is relatively quite weak. However, Z component is just right opposite. This is also evidence of our present exploration, especially the proof of P-wave exploration. For three-layers two-phase medium we may observe the slow p-wave’s direct wave and reflection on fluid-phase wavefield. But for the three-layers model with single-phase and two-phase interface, the slow p-wave’s direct wave and reflection cannot be seen even if on the fluid-phase wavefield.
Researching dispersion and attenuation of seismic wave have vital significance for predicting the existing and distribution of fluid in media and studying the pore construction. We deduced the Christoffel equation of 3D two phase media according to the elastic wave propagation equation based on the BISQ mechanism. By solving the Christoffel equation, we got the formulas of phase velocity, the inverse quality factor(Q-1)and the absorption coefficient of different waves, which thus has established relations between the two and solid media parameters、fluid permeability、porosity、glutinousness、frequency、fluid character ejection flow length、wave propagation direction. According to the derived formulas, we has calculated each kind of wave phase velocity and inverse quality factor(Q-1) in the well logging frequency band (100-2000Hz),and has studied the impact of solid flow parameters on the seismic wave dispersion and attenuation. This is important for oil parameter inversion using well log data. Because the massive predecessors study are aimed at high frequency situation(above ten thousand MHz),reflected the medium high frequency wave character, but high frequency characteristic of porous medium including fluid can not necessarily reflect the low frequency character. Through the researches, we can get the following conclusions: (1) In the well log frequency band,.the phase velocity of fast qP-wave, slow qP-wave, qSV-wave increases along with the frequency increasing, but has little influence on qSH-wave. The inverse quality factor(Q-1) of fast qP-wave, qSV-wave qSH-wave increases along with the frequency increasing gratwoly the slow qP-wave just right opposite (2) Porosity mainly affects on phase velocity to seismic wave dispersion and attenuation. Along with porosity increasing, phase velocity of the four waves is reducing gratwoly. However, slow P-wave’s reduce is quite small. But if the porosity were gratwoly reduced, the speed of slow qP-wave was increased gratwoly, when porosity were less than 10-8, slow P-wave would completely vanish. The wavefield of solid-phase and fluid-phase are almost the same, which is equal to the result of the theory of pure elastic. (3)Permeability mainly impacts dispersion and attenuation of the qP-wave and qSV, but has little influence on qSH-wave. (4) The viscosity also has the varying degree influence to four kinds of wave's phase velocity and attenuation. To compare with slow qP-wave, the change of other three kinds of waves is small. (5)The direction of wave propagation has great influence on wave attenuation and dispersion. Fast qP-wave has the strongest attenuation value in the axis of symmetry direction. This direction was usually considered as the direction of bearing permeability. The situation of slow qP-wave and fast qP-wave is opposite. (6) The dispersion and attenuation of seismic wave have anisotropic character,which were caused by the anisotropy of solid frame together with solid-fluid coupling anisotropy.
根据弹性波传播方程,推导了三维双相正交介质的Christoffel方程。相对以往对弹性波衰减和频散规律的研究多集中于超声频段,本文详细研究了测井频段(100-2000Hz)弹性波的相速度、逆品质因子与频率、孔隙度、流体粘滞系数、渗透率以及波的传播方向之间的关系。
The object of this paper is porous, cranny and crack 3D two-phase orthotropic medium which are filled with fluid. Firstly, we have had carried out the detailed review on the theory of porous medium and anisotropic medium and the technical Status of related seismic numerical modeling.
Based on the above theory, we derived the 3D elastic kinetic equation and elastic wave propagating equation in two-phase BISQ medium according to Dvorkin (1993) and Yang Dinghui’s studies. In view of the staggered grid high-order finite-difference method which had the numerous merits is quite popularly at present. We derived the forward numerical solution of staggered-grid finite difference method. Unifying predecessor's researches, we have given out the stable condition and boundary condition and studied systematically the source factor’s influence to wavefield simulation in the staggered grid finite-difference method. Through 16 kinds of isotropic medium models’research, we found out:The source add on the stress item, and the source function is sphere cavity source, S wave appeared in the wave field snapshot , it is not tally with classical theory’s conclusion, and the numerical frequency dispersion is very serious too. When the source function change to explosive point source, only the P-wave appeared in the wave field snapshot,this is tally with classical theory’s conclusion, but on the three orthogonal planes(the YoZ plane of X component、the XoZ plane of Y component and the XoY plane of Z component) appeared the numerical frequency dispersion (noise) seriously. When the source is single direction source of the above two source functions respectively, the wave fields are tally with classical theory’s conclusion, but exist obvious numerical frequency dispersion on the shapshots. On the other hand, the source add on the velocity item, there all exists S wave in the wave field snapshots when the source using cavity source and explosive point source respectively, it is not tally with classical theory’s conclusion, but the numerical frequency dispersion disappear when using the explosive point source (although the S-wave wavefront is is not very circular in certain planes). and the situation of the numerical frequency dispersion is not improved at all when using the cavity source. The simulations of using single direction source still exists obvious numerical frequency dispersion. In summary, The author concluded that the most appropriate type of source is explosive point source added on the velocity when we adopted the staggered grid finite-difference method to simulate elastic wave propagation. Under this kind of condition, although the S-wave wavefront is asymmetrical in certain planes, numerical dispersion (noise) is smallest, which is the most advantaged to explain to the complex wave field. On the meantime, the author consider that regarding anisotropic medium elastic wave numerical simulation, no matter the source function being used ,it can excitated the P wave and the S wave simultaneously in the wave field.
On the basis of these researches, First, based on BISQ mechanism, we simulated 3D-3C elastic wavefield of 3D two-phase orthotropic medium and analysed wavefield snapshots of different times、surface seismic records and VSP records. As a comparison, we have also presented the other two-phase medium wavefield snapshots: two-phase transversely isotropic medium、two-phase azimuth anisotropy medium. We analyzed the characters of wavefield. According to the above studies, we got the following conclusions: (1) There are four kinds of waves in two-phase anisotropy media, namely, fast quasi-P wave, slow quasi-P wave, fast quasi-S wave, and slow quasi-S wave. (2) For the viscous media, because the slow qP-wave have a strong attenuation property, we can not see clearly from the solid phase wavefield, but for the ideal non-viscous media, the clear slow qP-wave shown can be seen in both fluid and solid phase snapshots and records. (3) Assuming the anisotropy of solid-fluid coupling density and permeability, the propagation of slow qP-wave show anisotropy characteristic. The change of solid-fluid coupling density is more obvious to the influence of slow P-wave's propagation velocity. (4) In two phase anisotropy media, the wave field is much more complex due to the reflection, transmission, conversion and shear wave splitting on the interface. (5) From the two kinds of three-layers VSP records, we can see that seismic wavefield is more complex in two-phase medium. Fast qP wave propagation not only has the transmission, and reflection, but also has the conversion (convert to qSV wave and slow qP wave). The qS wave can converted to slow qP wave too. The reflection wave of slow qP-wave is quite weak, and also has not seen its conversion. Dispersion situation is quite serious on Y components of fluid-phase wavefield and Z components. The corresponding dispersion situation of solid-phase is quite slight. We analyzed the reason that slow P-wave velocity is low (less than 100/s) and does not satisfy the stable condition. This may be solved by decreasing the space and time domain sample interval(spatial sampling interval around 1m). However, because of the limitation of computer hardware at present, we can only be given such a result. (6) From the surface records we can see that X、Y component is quite sensitive to the S wave, the amplitude of reflection S-wave is more strong and P-wave is relatively quite weak. However, Z component is just right opposite. This is also evidence of our present exploration, especially the proof of P-wave exploration. For three-layers two-phase medium we may observe the slow p-wave’s direct wave and reflection on fluid-phase wavefield. But for the three-layers model with single-phase and two-phase interface, the slow p-wave’s direct wave and reflection cannot be seen even if on the fluid-phase wavefield.
Researching dispersion and attenuation of seismic wave have vital significance for predicting the existing and distribution of fluid in media and studying the pore construction. We deduced the Christoffel equation of 3D two phase media according to the elastic wave propagation equation based on the BISQ mechanism. By solving the Christoffel equation, we got the formulas of phase velocity, the inverse quality factor(Q-1)and the absorption coefficient of different waves, which thus has established relations between the two and solid media parameters、fluid permeability、porosity、glutinousness、frequency、fluid character ejection flow length、wave propagation direction. According to the derived formulas, we has calculated each kind of wave phase velocity and inverse quality factor(Q-1) in the well logging frequency band (100-2000Hz),and has studied the impact of solid flow parameters on the seismic wave dispersion and attenuation. This is important for oil parameter inversion using well log data. Because the massive predecessors study are aimed at high frequency situation(above ten thousand MHz),reflected the medium high frequency wave character, but high frequency characteristic of porous medium including fluid can not necessarily reflect the low frequency character. Through the researches, we can get the following conclusions: (1) In the well log frequency band,.the phase velocity of fast qP-wave, slow qP-wave, qSV-wave increases along with the frequency increasing, but has little influence on qSH-wave. The inverse quality factor(Q-1) of fast qP-wave, qSV-wave qSH-wave increases along with the frequency increasing gratwoly the slow qP-wave just right opposite (2) Porosity mainly affects on phase velocity to seismic wave dispersion and attenuation. Along with porosity increasing, phase velocity of the four waves is reducing gratwoly. However, slow P-wave’s reduce is quite small. But if the porosity were gratwoly reduced, the speed of slow qP-wave was increased gratwoly, when porosity were less than 10-8, slow P-wave would completely vanish. The wavefield of solid-phase and fluid-phase are almost the same, which is equal to the result of the theory of pure elastic. (3)Permeability mainly impacts dispersion and attenuation of the qP-wave and qSV, but has little influence on qSH-wave. (4) The viscosity also has the varying degree influence to four kinds of wave's phase velocity and attenuation. To compare with slow qP-wave, the change of other three kinds of waves is small. (5)The direction of wave propagation has great influence on wave attenuation and dispersion. Fast qP-wave has the strongest attenuation value in the axis of symmetry direction. This direction was usually considered as the direction of bearing permeability. The situation of slow qP-wave and fast qP-wave is opposite. (6) The dispersion and attenuation of seismic wave have anisotropic character,which were caused by the anisotropy of solid frame together with solid-fluid coupling anisotropy.
引文
[1] Aki. K., Richards, P. G., Quantitative seismology: theory and methods. W. N. Freeman & Co, 1980, Vol.1. 778-84.
[2] Akbar N, Dvorkin J., Nur A., Relating P-waves attenuation to permeability, Geophysics, 1993, Vol.58, 20-29.
[3] Auriault, J. L., et al., Dynamics of porous saturated media, checking of the generalized law of Darcy. J. Acoust. Soc. Am., 1985, Vol.77, 1641-1650.
[4] Banik N. C., Velocity anisotropy of shale and depth estimation in the North Sea basin, Geophysics, 1984, Vol.49, 1411-1419.
[5] Backus G. E., 1962, Long-Wave elastic anisotropy produced by horizontal layering, J. Geophys. Res., Vol.67, 4427-4440.
[6] Berryman J. G., Long-wave elastic anisotropy in transversely isotropic media, Geophysics, 1979, Vol.44, 896-917.
[7] Berryman, J. G., Scattering by a spherical in homogeneity in a fluid saturated porous medium. J. Math. Phys., 1985, Vol.26, 1408-1419.
[8] Berryman, J. G., Effective medium approximation for elastic constants of porous solids with microscopic heterogeneity. J. Appl. Phys., 1986, Vol.59, 1136-1140.
[9] Berryman, J. G., Milton G. W., Exact results for generalized Gassmann’s equation in composite porous media with two constitutes. Geophysics, 1956, Vol.56, 1950-1960.
[10] Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid, Part I: low frequency range, J. Acoust. Soc. Am., 1956a, Vol.28, 168-178.
[11] Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid, Part II: high frequency range, J. Acoust. Soc. Am., 1956b, Vol.28, 179-191.
[12] Biot, M. A. and Willis, D. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech., 1957, Vol.24, 594-601.
[13] Biot, M. A., , Mechanics of deformations and acoustic propagation in porous media, J. Appl. Phys., 1962a ,Vol.33, 1592-1498.
[14] Biot, M. A., Generalized theory of acoustic propagation in porous dissipative media, J. Acoust. Soc. Am., 1962b, Vol.34, 1254-1264.
[15] Brown R., Korringa J. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics 1975, Vol.40, 608-616.
[16] Brodov et al., Some result of the experimental study of seismic anisotropy of sedimentary rocks using different type of wave, Geophys. J. R. astr. Soc., 1984, Vol.76, 191-200.
[17] Bush I., Crampin, S., Paris Basin VSPs: Case history establishing combinations offine-layer (or lithologic). Anisotropy and crack anisotropy from modeling shear wavefields near point singularities, Geophys, J. Int., 1991, Vol.107, 433-447.
[18] Bush I., Crampin S., Observations of EDA and PTL anisotropy in shear-wave VSPs, 57th Ann. Int. SEG Meeting, Eapanded Abstracts, 1987, 646-649.
[19] Bush I., Crampin S., Paris Basin VSPs: Case history establishing combinations of fine-layer (or lithologic) Anisotropy and crack anisotropy from modeling shear wavefields near point singularities, Geophys, J. Int., 1991, Vol.107, 433-447.
[20] Carcione J.M., Herman, G. C., ten Kroode, A.P.E., Seismic modeling, Geophysics, 2002, Vol.67(4), 1304-1325.
[21] Carcione J.M., Kosloff D., Kosloff R., Wave propagation simulation in a linear viscoacoustic medium, Geophys, 1988, Vol.93, 393-407.
[22] Carcione J.M., Kosloff D., Kosloff R., Viscoacoustic wave propagation simulation in the Earth, Geophysics, 1988, Vol.53, 769-777.
[23] Carcione J.M., Kosloff, D., Kosloff R., Wave propagation simulation in a linear viscoelastic medium, Geophys, J, 1988, Vol.95, 597-611.
[24] Carcione J.M., Seismic modeling in viscoelastic media, Geophysics, 1993, Vol.58(1), 110-120.
[25] Carcione J.M., Wave propagation in anisotropic linear viscoelastic media, Geophys. J. Int., 1990, Vol.101, 739-950.
[26] Cerjan, C., Kosloff, D. et al., A non-reflection boundary condition for discrete acoustic and elastic wave equation, Geophysics, 1985, Vol.50, 705-708.
[27] Crampin S., Evaluation of anisotropy by shear-wave splitting. Geophysics, 1985, Vol.50(1), 142-152.
[28] Crampin S., Evidence for aligned cracks in the Earth's crust, First Break, 1985, Vol.3(1), 12-15.
[29] Crampin S., The geological and industrial implications of extensive-dilatancy anisotropy, Nature, 1987, Vol.328, 491-496.
[30] Crampin S., Evaluation of anisotropy by shear-wave splitting. Geophysics, 1985. Vol.50, 142-152.
[31] Crampin S., Anisotropy in exploration seismic, First Break, 1984b, Vol.23, 19-21.
[32] Crampin S., et al., Observation of dilatancy-induced polarization anomalies and earthquake prediction, Nature, 1980, Vol.286, 874-877.
[33] Crampin S., Effective anisotropic elastic constants for wave propagation through cracked solids, in proc First Int. Workshop on Seismic Anisotropy , Suzdahl, 1982, 135-145.
[34] Crampin S. Anisotropy in exploration seismics, First Break, 1984b, Vol.23, 19-21.
[35] Crampin S., et al. Observation of dilatancy-induced polarization anomalies and earthquake prediction, Nature, 1980, Vol.286, 874-877.
[36] Crampin S., The geological and industrial implications of extensive-dilatancy anisotropy, Nature, 1987, Vol.328, 491-496
[37] Dai N., Vafidis A., and Kamasewich E. R., Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method. Geophysics, 1995, Vol.60(2), 327-340.
[38] Daley P. F., Hron F., Reflection and transmission coefficients for transversely isotropic solids, Bull. Seis. Soc. Am., 1977, Vol.67, 661-675.
[39] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: I. Reflection of Plane Waves at a Free Plane Boundary (Non-Dissipative Case), Bull. Seism. Soc. Am., 1960, Vol.50, 599-607.
[40] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: III. Reflection of Plane Waves at a Free Plane Boundary (general Case), Bull. Seism. Soc. Am., 1962, Vol.52, 505-625.
[41] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: V. transmission across a Plane interface, Bull. Seism. Soc. Am., 1964, Vol.54, 409-416.
[42] Dvorkin J., Nur A., Dynamic poroelasticity: A unified model model with the squirt and the Biot mechanisms: Geophyscis, 1993, Vol.58, 524-533.
[43] Dvorkin J., Hoeksema R N., The squirt-flow mechanism: Macroscopic description: Geophysics, 1994, Vol.59, 428-438.
[44] Dvorkin J., Mavko G, and Nur A, Squirt flow in fully saturated rocks: Geophyscis, 1995, Vol.60, 97-107.
[45] Faria E. L. Stoffa P. L., Finite-difference modeling in transversely isotropic media. Geophysics, 1994, Vol.59(2), 282-289.
[46] Gassmann F., Elastic waves through a packing of spheres, Geophysics, 1951, Vol.16, 673-685.
[47] Geeertsma J., Smit D. C., Some aspect of elastic wave propogation in fluid-saturated porous solids, Geophysics, 1961, Vol.26, 169-181.
[48] Graebner M., Plane-wave reflection and transmission coefficients for a transversely isotropic solid (short note), Geophysics, 1992, Vol.57(11), 1512-1519.
[49] Hassanzadeh S., 1991, Acoustic modeling in fluid saturated porous media, Geophysics, Vol.56(4), 424-435.
[50] Han Q. Y., Wang S. X., et al., Simulation of 3D Wave fields using Biot theory: A 1-D finite element algorithm, 68th SEG abstract, ST12.2. 1998.
[51] Helbig K., Transverse isotropy in exploration seismics, Geophys. J. R. astr. Soc., 1984, Vol.76, 79-88.
[52] Hudson J. A., Overall properties of a cracked solid, Math. Proc. Camb. Phil. Soc., 1980, Vol.88, 371-384.
[53] Hudson J. A., A higher order approximation to the wave propagation constants for cracked solid, Geophys. J. R. Astr. Soc. 1986, Vol.87, 265-274.
[54] Hudson J. A., Liu E., Crampin S., The mechanical properties of materials with interconnected cracks and pores, Geophys, J. Internat., 1996, Vol.124, 105-112.
[55] Hudson J. A., Wave Speeds and Attenuation of elastic waves in material containing cracks, Geophy, J. R. Astr. Soc, 1981, Vol.64, 133-150.
[56] Hamdi F, Smith D. T., The influence of permeability on compressional wave velocity in marine sediments, Geophysical Prospecting, 1982, Vol.30, 622-640.
[57] Igel H ,Riollet B ,Mora P. Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation. 62th Ann. Internat . Mtg , Soc. Expl., Geophys., Expanded Abstracts, 1992,1244 —1246.
[58] Jones L. E. A., Wang H. F., Ultrasonic velocities in Cretaceous shale from Williston Basin, Geophysics, 1981, Vol.46, 288-297.
[59] Julin C., Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media, Geophysical Prospecting, 1995, Vol.43, 843-858.
[60] Kaarsberg E. A., Introductory studies of natural and artificial argillaceous aggregates by sound propagation and X-ray diffraction methods, J. Geol., 1959, Vol.67, 447-472.
[61] Kosloff D. D., Carcione J. M., Three dimension wave propagation simulation in elastic anisotropy media, Expanded Abstracts of 59th SEG Annual Meeting, 1989, 1016-1018.
[62] Levander, A. R., Fourth-order finite difference P-SV seismograms, Geophysics, 1988, Vol.53, 1425-1436.
[63] Levin F. K., P-wave anisotropy of Pierre Shale, Geophysics, 1992, Vol.57, 1346-1347.
[64] Levin F. K., Seismic Velocity in transversely isotropic media, Geophysics, 1979, Vol.44, 918-936.
[65] Levin F. K., Seismic Velocity in transversely isotropic media II, Geophysics, 1980, Vol.45, 3-17.
[66] Madariaga R. Dynamics of an expanding circular fault . BSSA ,1976 ,66 (3) :639 —666.
[67] Mavko G., Nur A., Melt Squirt in asthenosphere, J. Geophys. Res. 1975, Vol.80, 1444-1448.
[68] Mavko G., Nur A., Wave attenuation in partially saturated rocks. Geophysics, 1979, Vol.44, 161-178.
[69] Nur A M, Wang Z. Seismic and acoustic velocities in reservoir rocks: Experimental Studies, Society of Exploration Geophysicists, 1989, Vol.1, 30-36.
[70] ?zdenvar T, McMechan G. A., Algorithms for staggered-grid computations forporoelastic, elastic, and scalar equations, Geophysical Prospecting., 1997, Vol.45, 403-420.
[71] Parra J. O., The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms, Theory and application. Geophysics, 1997, Vol.62, 309-318.
[72] Parra J. O., Xu P. C., Dispersion and attenuation of acoustic guided waves in layered fluid porous media: J. Acoust. Soc. Am., 1994, Vol.95, 91-98.
[73] Plona T J., Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies., Appl. Phys. Lett., 1980, Vol.36, 259-261.
[74] Postma G. W., Wave propagation in stratified medium, Geophysics, 1958, Vol.4, 780-806.
[75] Ramos-Martinez J., Ortega A. A., McMechan G. A., 3D seismic modeling for cracked media: shear-wave splitting at zero-offset, Geophysics, 2000, Vol.65(1), 211-221.
[76] Ren J. X., Gang A. F., Reflections and transmissions of plane waves on an interface between dissimilar fluid-saturated porous media. 64th Ann Internat.Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1994, 1167-1170.
[77] Richard P. G., Frasier C. W., Scattering of elastic waves from depth dependent inhomogeneities, Geophysics, 1976, Vol.41(3), 441-458.
[78] Robertson J. D., Corrigan D., Radiation studies on shear-wave vibrator in near-surface shale, Geophysics, 1983, Vol.48, 19-26.
[79] Ruan A. G., Li Q. H., Anisotropy elastic constitutive relation of the crust media.North western seismological journal, 2001, Vol.23(2), 206-216.
[80] Ruger A., P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry, Geophysics, 1997, Vol.62, 713-722.
[81] Ruger A., Variation of P-wave reflectivity with offset and azimuth in anisotropic media, Geophysics, 1998, Vol.63, 935-947.
[82] Sharma M. D., Surface-wave propagation in a cracked poroelastic half-space lying under a uniform layer of fluid, Geophys. J. Int., 1996, Vol.127, 31-39.
[83] Siamak H., Acustic modeling in fluid-saturated porous media, Geophysics, 1991, Vol. 56(4), 424-435.
[84] Thomsen L., Poisson was not a geophysicist. The Leading Edge, 1990, Vol.9(12), 27-29.
[85] Thomsen L., Seismic anisotropy, Geophysics, 2001,Vol.66(1), 40-41.
[86] Thomsen L., Reflection seismology in azimthally anisotropic media, Geophysics, 1988, Vol.53, 304-313.
[87] Thomsen L., M. M. Backus, Weak anisotropic reflections in: Offset dependent reflectivity, Geophysical Prospecting, 1988, Vol.35, 993-1014.
[88] Virieux J . SH-wave propagation in heterogeneous media:Velocity-stress finite-difference method. Geophisics , 1984 , Vol.49(11) :1933 —1957.
[89] Virieux J. P-SV wave propagation in heterogeneous media :Velocity-stress finite-difference method. Geophisics , 1986,Vol.51(4) :889 —901.
[90] Wu N., Jerry M. Harris, Seismic wave modeling in poroelastic media using the generalized reflection transmission (R/T) coefficients method, 68th SEG Technical Program Expanded Abstracts, 1998, 1799-1802
[91] White J. E., Computed seismic speeds and attenuation in rocks with partial gas saturation, Geophysics, 1975, Vol.40, 224-232.
[92] Wright, J., The effects of transverse isotropy on reflection amplitude versus offset, Geophysics, 1987, Vol.53, 564-567.
[93] Wang Z., Nur A., Seismic and acoustic velocities in reservoir rocks, Theoretical and model studies, Society of Exploration Geophysicists, 1992, Vol.2, pp. 285-296.
[94] Zeng Y. Q., H, J. Q., Liu Q.H., The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media, Geophysics, 2001, Vol.66(4), 1258-1266.
[95] Zdenvar T., McMechan G. A., Algorithms for staggered-grid computations for poroelastic, elastic, and scalar equations, Geophysical Prospecting, 1997, Vol.45, 403-420.
[96] Zhu X., McMechan G. A., Numerical simulation of seismic response of poroelastic reservoirs using Biot Theory. Geophysics, 1991. Vol.56, 328-339.
[97] Zhu X., McMechan G. A., Numerical simulation of seismic response of poroelastic reservoirs using Biot Theory, Geophysics, 1991, Vol.56, 328-339.
[98] Anos Nur 等著,许云译, 双相介质中波的传播. 北京, 石油工业出版社. 1986.
[99] 陈敬国, 一种有效吸收边界条件的 matlab 实现,中国科技论文在线, 2006, Vol.6, 71-80.
[100] 董良国,马在田,曹景忠,一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411—419.
[101] 董敏煜, 多波多分量地震勘探, 石油工业出版社, 北京, 2002.
[102] 范祯祥, 郑仙种编著, 地震波数值模拟与偏移成像,河南科学技术出版社. 1994.
[103] 郭建, 双相介质中P波波场的有限差分模拟,石油地球物理勘探, 1992, Vol.27(2), 565-571.
[104] 郭建, 马爱珍, 双相介质与弹性介质混合模型的有限差分声波模拟, 石油地球物理勘探, 1992, Vol.27(5), 1-8.
[105] 桂志先, 贺振华, 黄济德, 含垂直裂隙地层中弹性波相速度, 石油地球物理勘探, 2001, Vol.36(2), 180-186.
[106] 桂志先, 贺振华, 汪德雯, 正交介质中地震波传播数值模拟与分析, 江汉石油学院学报, 2001, Vol.23(3), 21-23.
[107] 黄晓葛, 白武明, 地震波各向异性的研究进展, 地球物理学进展, 1999, Vol.14(3), 54-65.
[108] 何樵登, 地震勘探原理和方法, 地质出版社. 1986.
[109] 何樵登, 地震波理论, 地质出版社. 1988.
[110] 何樵登, 熊维纲主编, 应用地球物理教程-地震勘探, 地质出版社. 1991
[111] 何樵登, 张中杰,横向各向同性介质中地震波及其数值模拟, 吉林大学出版社. 1996.
[112] 侯安宁, 何樵登, 分形反射序列的合成记录与生物遗传算法反演的初步研究, SEG/CPS 北京 93 届国际地球物理会议论文集,石油物探, 1993, 44-49.
[113] 侯安宁, 各向异性弹性波及其波动方程正反演研究, 博士学位论文, 吉林, 长春地质学院. 1994.
[114] 侯安宁, 何樵登, 各向异性介质中弹性波动方程高阶差分及其稳定性研究, 地球物理学报, 1995, Vol.38(4), 519-527.
[115] 侯安宁, 何樵登, 马在田, 各向异性弹性波动交错网格高阶差分法的误差研究. 长春科技大学学报, 1995, Vol.25(4), 446-451.
[116] 刘克安, 刘宏伟, 双相介质二维波动方程三参数同时反演的时卷正则迭代法, 石油地球物理勘探, 1997, Vol.32(5), 615-622.
[117] 刘希强,周蕙兰,地震各向异性研究进展,地震研究,1998, Vol.4(2), 185-195.
[118] 刘洋, 董敏煜, 各向异性介质中的方位 AVO, 石油地球物理勘探, 1999, Vol.34(3), 260-267.
[119] 刘洋, 李承楚,双相各向异性介质中弹性波传播伪谱法数值模拟研究, 地震学报, 2000, Vol.22, 132-138.
[120] 刘银斌, 李幼铭, 吴如山, 横向各向同性多孔介质中的地震波传播. 地球物理学进展, 1994, Vol.37(4), 499-513.
[121] 马在田, 三维地震勘探方法, 北京, 石油工业出版社. 1989.
[122] 孟庆生, 基于 BISQ 机制双相裂隙介质弹性波场正演及其方位属性研究, 博士学位论文, 吉林, 吉林大学. 2003.
[123] 孟庆生, 何樵登等, 基于 BISQ 模型双相各向同性介质中地震波数值模拟, 吉林大学学报(地球科学版), 2003, Vol.33(2), 217-221.
[124] 孟庆生, 何樵登等, 基于 BISQ 机制三维双相 EDA 介质中的反射与透射, 地球物理学进展, 2005, Vol.20(2), 323-327.
[125] 牟永光, 储层地球物理学, 北京, 石油工业出版社.1996.
[126] 牟永光, 三维复杂介质地震物理模拟, 北京, 石油工业出版社, 003.
[127] 牟永光, 裴正林, 三维复杂介质地震数值模拟, 北京, 石油工业出版社. 2005.
[128] 牛滨华, 裂隙各向异性介质中地震波传播规律研究及其波场数值模拟, 博士学位论文, 吉林, 长春地质学院. 1992.
[129] 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模拟, 中国石油大学学报, 2004, Vol28(5), 23-29.
[130] 裴正林, 三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟, 中国石油大学学报, 2006, Vol30(2), 16-20.
[131] 裴正林,双相各向异性介质弹性波传播交错网格高阶有限差分法模拟, 石油地球物理勘探, 2006, Vol.41(2), 137-143.
[132] 乔文孝, 王宁, 严炽培,声波在两种多孔介质界面上的反射和透射, 地球物理学报, 1992, Vol.35(2), 242-248.
[133] 阮爱国, 李清河,地壳介质各向异性弹性本构关系讨论, 华南地震, 2000, Vol.20(3), 14-23.
[134] 石双虎, 何樵登等, 基于 BISQ 模型双相 EDA 介质中 VSP 记录模拟, 地球物理学进展, 2007, Vol.22(2), 466-473.
[135] 邵治龙, 贺振华, 黄德济, 正交各向异性介质中地震记录的有限差分数值模拟, 物探化探计算技术, 1998, Vol.20(4), 300-305.
[136] 石双虎, HTI 介质中断裂大小、各向异性及频率之间依赖关系, 博士学位论文, 吉林, 吉林大学. 2007.
[137] 滕吉文, 王光杰等,地球各向异性介质中地震波动理论、检测与应用研究, 地学前缘, 1998, Vol.5(1), 83-90.
[138] 王德利, 单斜介质弹性波场的数值模拟与 Thomsen 参数反演方法研究, 博士学位论文, 吉林, 吉林大学. 2002.
[139] 王尚旭, 双相介质中弹性波问题有限元数值解和 AVO 问题, 博士学位论文, 北京, 中国石油大学. 1990.
[140] 魏修成, 双相各向异性介质中的地震波场研究, 博士学位论文, 北京, 中国石油大学. 1995.
[141] 吴望一, 流体力学, 北京大学出版社, 1982.
[142] 席道瑛, 易良坤, 砂岩中孔隙流体的黏性与衰减、模量和速度色散. 石油地球物理勘探, 1999, Vol.34(4), 420-425.
[143] 轩义华, 何樵登等, 基于BISQ机制的双相EDA介质的波场分析, 石油地球物理勘探, 2006, Vol.41(5), 550-556.
[144] 轩义华,倾斜横向各向同性介质(TTI)参数反演方法研究, 博士学位论文, 吉林, 吉林大学. 2007.
[145] 肖建华, 孔隙岩石的一般波动理论, 石油地球物理勘探, 1998, 33, 增刊, 1-11.
[146] 杨宝俊, 何樵登, 有限元素法的一种频率域计算方法及其应用, 1982, Vol.21(1), 56-64.
[147] 杨顶辉, 牟永光,孔隙各向异性介质中基于微观流场的 BISQ 理论, 北京, 中国地球物理学会年刊, 1998, 58-59.
[148] 杨顶辉,孔隙各向异性介质中基于 BISQ 模型的弹性波传播理论及有限元方法, 博士后研究报告, 北京, 中国石油大学. 1998.
[149] 杨顶辉, 陈小宏, 牟永光,各向异性介质中基于固-流质量耦合密度各向异性的应力波动方程, 中国学术期刊文摘(科技快报专栏). 2000, Vol.6(1), 75-77.
[150] 杨顶辉, Biot 和喷射流动耦合作用对各向异性弹性波的影响, 科学通报, 2000, Vol.45(12), 1333-1340.
[151] 杨顶辉, 张中杰, 滕吉文, 王光杰, 双相各向异性研究、问题与应用前景, 地球物理学进展, 2000, Vol.15, 7-21.
[152] 杨宽德, 杨顶辉, 王书强,基于 Biot-Squirt 方程的波场模拟, 地球物理学报, 2002, Vol.45(6), 853-861.
[153] 杨宽德, 杨顶辉, 王书强,基于 BISQ 高频极限方程的交错网格法数值模拟, 2002, Vol.37(5), 463-468.
[154] 杨宽德,杨顶辉,王书强,基于横向各向同性 BISQ 方程的弹性波传播数值模拟,地震学报,2002,Vol.24(6):599-606
[155] 张文生, 何樵登,二维横向各向同性介质的伪谱法正演模拟, 石油地球物理勘探, 1998, Vol.33(3), 310-319.
[156] 张文生, 宋海斌,三维正交各向异性介质三分量高精度有限差分正演模拟, 石油地球物理勘探, 2001, Vol.36(4), 422-432.
[157] 张应波, Biot 理论应用于地震勘探的探索, 石油物探, 1994, Vol.33(4), 29-38.
[158] 张中杰, 何樵登,含裂隙介质中地震波运动学问题的正演模拟, 石油地球物理勘探, 1989, Vol.24(3), 290-300.
[159] 张中杰, 滕吉文, EDA 介质中地震波速度、衰减与品质因子方位异性研究, 中国科学(E 辑), 1999, Vol.29(6), 569-574.
[160] 张中杰,地震各向异性研究进展, 地球物理学进展, 2002, Vol.17(2), 281-293.
[161] 朱建伟, 含流体孔隙介质基于 BISQ 机制的弹性波波动方程及传播特性, 博士学位论文, 吉林, 长春科技大学. 2000.
[162] 朱建伟, 何樵登, 李云辉,含油水各向异性孔隙介质中地震波传播方程, 长春科技大学学报, 2001, Vol.31, 193-196.
[2] Akbar N, Dvorkin J., Nur A., Relating P-waves attenuation to permeability, Geophysics, 1993, Vol.58, 20-29.
[3] Auriault, J. L., et al., Dynamics of porous saturated media, checking of the generalized law of Darcy. J. Acoust. Soc. Am., 1985, Vol.77, 1641-1650.
[4] Banik N. C., Velocity anisotropy of shale and depth estimation in the North Sea basin, Geophysics, 1984, Vol.49, 1411-1419.
[5] Backus G. E., 1962, Long-Wave elastic anisotropy produced by horizontal layering, J. Geophys. Res., Vol.67, 4427-4440.
[6] Berryman J. G., Long-wave elastic anisotropy in transversely isotropic media, Geophysics, 1979, Vol.44, 896-917.
[7] Berryman, J. G., Scattering by a spherical in homogeneity in a fluid saturated porous medium. J. Math. Phys., 1985, Vol.26, 1408-1419.
[8] Berryman, J. G., Effective medium approximation for elastic constants of porous solids with microscopic heterogeneity. J. Appl. Phys., 1986, Vol.59, 1136-1140.
[9] Berryman, J. G., Milton G. W., Exact results for generalized Gassmann’s equation in composite porous media with two constitutes. Geophysics, 1956, Vol.56, 1950-1960.
[10] Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid, Part I: low frequency range, J. Acoust. Soc. Am., 1956a, Vol.28, 168-178.
[11] Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid, Part II: high frequency range, J. Acoust. Soc. Am., 1956b, Vol.28, 179-191.
[12] Biot, M. A. and Willis, D. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech., 1957, Vol.24, 594-601.
[13] Biot, M. A., , Mechanics of deformations and acoustic propagation in porous media, J. Appl. Phys., 1962a ,Vol.33, 1592-1498.
[14] Biot, M. A., Generalized theory of acoustic propagation in porous dissipative media, J. Acoust. Soc. Am., 1962b, Vol.34, 1254-1264.
[15] Brown R., Korringa J. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics 1975, Vol.40, 608-616.
[16] Brodov et al., Some result of the experimental study of seismic anisotropy of sedimentary rocks using different type of wave, Geophys. J. R. astr. Soc., 1984, Vol.76, 191-200.
[17] Bush I., Crampin, S., Paris Basin VSPs: Case history establishing combinations offine-layer (or lithologic). Anisotropy and crack anisotropy from modeling shear wavefields near point singularities, Geophys, J. Int., 1991, Vol.107, 433-447.
[18] Bush I., Crampin S., Observations of EDA and PTL anisotropy in shear-wave VSPs, 57th Ann. Int. SEG Meeting, Eapanded Abstracts, 1987, 646-649.
[19] Bush I., Crampin S., Paris Basin VSPs: Case history establishing combinations of fine-layer (or lithologic) Anisotropy and crack anisotropy from modeling shear wavefields near point singularities, Geophys, J. Int., 1991, Vol.107, 433-447.
[20] Carcione J.M., Herman, G. C., ten Kroode, A.P.E., Seismic modeling, Geophysics, 2002, Vol.67(4), 1304-1325.
[21] Carcione J.M., Kosloff D., Kosloff R., Wave propagation simulation in a linear viscoacoustic medium, Geophys, 1988, Vol.93, 393-407.
[22] Carcione J.M., Kosloff D., Kosloff R., Viscoacoustic wave propagation simulation in the Earth, Geophysics, 1988, Vol.53, 769-777.
[23] Carcione J.M., Kosloff, D., Kosloff R., Wave propagation simulation in a linear viscoelastic medium, Geophys, J, 1988, Vol.95, 597-611.
[24] Carcione J.M., Seismic modeling in viscoelastic media, Geophysics, 1993, Vol.58(1), 110-120.
[25] Carcione J.M., Wave propagation in anisotropic linear viscoelastic media, Geophys. J. Int., 1990, Vol.101, 739-950.
[26] Cerjan, C., Kosloff, D. et al., A non-reflection boundary condition for discrete acoustic and elastic wave equation, Geophysics, 1985, Vol.50, 705-708.
[27] Crampin S., Evaluation of anisotropy by shear-wave splitting. Geophysics, 1985, Vol.50(1), 142-152.
[28] Crampin S., Evidence for aligned cracks in the Earth's crust, First Break, 1985, Vol.3(1), 12-15.
[29] Crampin S., The geological and industrial implications of extensive-dilatancy anisotropy, Nature, 1987, Vol.328, 491-496.
[30] Crampin S., Evaluation of anisotropy by shear-wave splitting. Geophysics, 1985. Vol.50, 142-152.
[31] Crampin S., Anisotropy in exploration seismic, First Break, 1984b, Vol.23, 19-21.
[32] Crampin S., et al., Observation of dilatancy-induced polarization anomalies and earthquake prediction, Nature, 1980, Vol.286, 874-877.
[33] Crampin S., Effective anisotropic elastic constants for wave propagation through cracked solids, in proc First Int. Workshop on Seismic Anisotropy , Suzdahl, 1982, 135-145.
[34] Crampin S. Anisotropy in exploration seismics, First Break, 1984b, Vol.23, 19-21.
[35] Crampin S., et al. Observation of dilatancy-induced polarization anomalies and earthquake prediction, Nature, 1980, Vol.286, 874-877.
[36] Crampin S., The geological and industrial implications of extensive-dilatancy anisotropy, Nature, 1987, Vol.328, 491-496
[37] Dai N., Vafidis A., and Kamasewich E. R., Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method. Geophysics, 1995, Vol.60(2), 327-340.
[38] Daley P. F., Hron F., Reflection and transmission coefficients for transversely isotropic solids, Bull. Seis. Soc. Am., 1977, Vol.67, 661-675.
[39] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: I. Reflection of Plane Waves at a Free Plane Boundary (Non-Dissipative Case), Bull. Seism. Soc. Am., 1960, Vol.50, 599-607.
[40] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: III. Reflection of Plane Waves at a Free Plane Boundary (general Case), Bull. Seism. Soc. Am., 1962, Vol.52, 505-625.
[41] Deresiewicz H., The Effect of Boudaries on Wave Propagation in a Liquid-Filled Porous Solid: V. transmission across a Plane interface, Bull. Seism. Soc. Am., 1964, Vol.54, 409-416.
[42] Dvorkin J., Nur A., Dynamic poroelasticity: A unified model model with the squirt and the Biot mechanisms: Geophyscis, 1993, Vol.58, 524-533.
[43] Dvorkin J., Hoeksema R N., The squirt-flow mechanism: Macroscopic description: Geophysics, 1994, Vol.59, 428-438.
[44] Dvorkin J., Mavko G, and Nur A, Squirt flow in fully saturated rocks: Geophyscis, 1995, Vol.60, 97-107.
[45] Faria E. L. Stoffa P. L., Finite-difference modeling in transversely isotropic media. Geophysics, 1994, Vol.59(2), 282-289.
[46] Gassmann F., Elastic waves through a packing of spheres, Geophysics, 1951, Vol.16, 673-685.
[47] Geeertsma J., Smit D. C., Some aspect of elastic wave propogation in fluid-saturated porous solids, Geophysics, 1961, Vol.26, 169-181.
[48] Graebner M., Plane-wave reflection and transmission coefficients for a transversely isotropic solid (short note), Geophysics, 1992, Vol.57(11), 1512-1519.
[49] Hassanzadeh S., 1991, Acoustic modeling in fluid saturated porous media, Geophysics, Vol.56(4), 424-435.
[50] Han Q. Y., Wang S. X., et al., Simulation of 3D Wave fields using Biot theory: A 1-D finite element algorithm, 68th SEG abstract, ST12.2. 1998.
[51] Helbig K., Transverse isotropy in exploration seismics, Geophys. J. R. astr. Soc., 1984, Vol.76, 79-88.
[52] Hudson J. A., Overall properties of a cracked solid, Math. Proc. Camb. Phil. Soc., 1980, Vol.88, 371-384.
[53] Hudson J. A., A higher order approximation to the wave propagation constants for cracked solid, Geophys. J. R. Astr. Soc. 1986, Vol.87, 265-274.
[54] Hudson J. A., Liu E., Crampin S., The mechanical properties of materials with interconnected cracks and pores, Geophys, J. Internat., 1996, Vol.124, 105-112.
[55] Hudson J. A., Wave Speeds and Attenuation of elastic waves in material containing cracks, Geophy, J. R. Astr. Soc, 1981, Vol.64, 133-150.
[56] Hamdi F, Smith D. T., The influence of permeability on compressional wave velocity in marine sediments, Geophysical Prospecting, 1982, Vol.30, 622-640.
[57] Igel H ,Riollet B ,Mora P. Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation. 62th Ann. Internat . Mtg , Soc. Expl., Geophys., Expanded Abstracts, 1992,1244 —1246.
[58] Jones L. E. A., Wang H. F., Ultrasonic velocities in Cretaceous shale from Williston Basin, Geophysics, 1981, Vol.46, 288-297.
[59] Julin C., Finite-difference elastic wave propagation in 2D heterogeneous transversely isotropic media, Geophysical Prospecting, 1995, Vol.43, 843-858.
[60] Kaarsberg E. A., Introductory studies of natural and artificial argillaceous aggregates by sound propagation and X-ray diffraction methods, J. Geol., 1959, Vol.67, 447-472.
[61] Kosloff D. D., Carcione J. M., Three dimension wave propagation simulation in elastic anisotropy media, Expanded Abstracts of 59th SEG Annual Meeting, 1989, 1016-1018.
[62] Levander, A. R., Fourth-order finite difference P-SV seismograms, Geophysics, 1988, Vol.53, 1425-1436.
[63] Levin F. K., P-wave anisotropy of Pierre Shale, Geophysics, 1992, Vol.57, 1346-1347.
[64] Levin F. K., Seismic Velocity in transversely isotropic media, Geophysics, 1979, Vol.44, 918-936.
[65] Levin F. K., Seismic Velocity in transversely isotropic media II, Geophysics, 1980, Vol.45, 3-17.
[66] Madariaga R. Dynamics of an expanding circular fault . BSSA ,1976 ,66 (3) :639 —666.
[67] Mavko G., Nur A., Melt Squirt in asthenosphere, J. Geophys. Res. 1975, Vol.80, 1444-1448.
[68] Mavko G., Nur A., Wave attenuation in partially saturated rocks. Geophysics, 1979, Vol.44, 161-178.
[69] Nur A M, Wang Z. Seismic and acoustic velocities in reservoir rocks: Experimental Studies, Society of Exploration Geophysicists, 1989, Vol.1, 30-36.
[70] ?zdenvar T, McMechan G. A., Algorithms for staggered-grid computations forporoelastic, elastic, and scalar equations, Geophysical Prospecting., 1997, Vol.45, 403-420.
[71] Parra J. O., The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms, Theory and application. Geophysics, 1997, Vol.62, 309-318.
[72] Parra J. O., Xu P. C., Dispersion and attenuation of acoustic guided waves in layered fluid porous media: J. Acoust. Soc. Am., 1994, Vol.95, 91-98.
[73] Plona T J., Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies., Appl. Phys. Lett., 1980, Vol.36, 259-261.
[74] Postma G. W., Wave propagation in stratified medium, Geophysics, 1958, Vol.4, 780-806.
[75] Ramos-Martinez J., Ortega A. A., McMechan G. A., 3D seismic modeling for cracked media: shear-wave splitting at zero-offset, Geophysics, 2000, Vol.65(1), 211-221.
[76] Ren J. X., Gang A. F., Reflections and transmissions of plane waves on an interface between dissimilar fluid-saturated porous media. 64th Ann Internat.Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1994, 1167-1170.
[77] Richard P. G., Frasier C. W., Scattering of elastic waves from depth dependent inhomogeneities, Geophysics, 1976, Vol.41(3), 441-458.
[78] Robertson J. D., Corrigan D., Radiation studies on shear-wave vibrator in near-surface shale, Geophysics, 1983, Vol.48, 19-26.
[79] Ruan A. G., Li Q. H., Anisotropy elastic constitutive relation of the crust media.North western seismological journal, 2001, Vol.23(2), 206-216.
[80] Ruger A., P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry, Geophysics, 1997, Vol.62, 713-722.
[81] Ruger A., Variation of P-wave reflectivity with offset and azimuth in anisotropic media, Geophysics, 1998, Vol.63, 935-947.
[82] Sharma M. D., Surface-wave propagation in a cracked poroelastic half-space lying under a uniform layer of fluid, Geophys. J. Int., 1996, Vol.127, 31-39.
[83] Siamak H., Acustic modeling in fluid-saturated porous media, Geophysics, 1991, Vol. 56(4), 424-435.
[84] Thomsen L., Poisson was not a geophysicist. The Leading Edge, 1990, Vol.9(12), 27-29.
[85] Thomsen L., Seismic anisotropy, Geophysics, 2001,Vol.66(1), 40-41.
[86] Thomsen L., Reflection seismology in azimthally anisotropic media, Geophysics, 1988, Vol.53, 304-313.
[87] Thomsen L., M. M. Backus, Weak anisotropic reflections in: Offset dependent reflectivity, Geophysical Prospecting, 1988, Vol.35, 993-1014.
[88] Virieux J . SH-wave propagation in heterogeneous media:Velocity-stress finite-difference method. Geophisics , 1984 , Vol.49(11) :1933 —1957.
[89] Virieux J. P-SV wave propagation in heterogeneous media :Velocity-stress finite-difference method. Geophisics , 1986,Vol.51(4) :889 —901.
[90] Wu N., Jerry M. Harris, Seismic wave modeling in poroelastic media using the generalized reflection transmission (R/T) coefficients method, 68th SEG Technical Program Expanded Abstracts, 1998, 1799-1802
[91] White J. E., Computed seismic speeds and attenuation in rocks with partial gas saturation, Geophysics, 1975, Vol.40, 224-232.
[92] Wright, J., The effects of transverse isotropy on reflection amplitude versus offset, Geophysics, 1987, Vol.53, 564-567.
[93] Wang Z., Nur A., Seismic and acoustic velocities in reservoir rocks, Theoretical and model studies, Society of Exploration Geophysicists, 1992, Vol.2, pp. 285-296.
[94] Zeng Y. Q., H, J. Q., Liu Q.H., The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media, Geophysics, 2001, Vol.66(4), 1258-1266.
[95] Zdenvar T., McMechan G. A., Algorithms for staggered-grid computations for poroelastic, elastic, and scalar equations, Geophysical Prospecting, 1997, Vol.45, 403-420.
[96] Zhu X., McMechan G. A., Numerical simulation of seismic response of poroelastic reservoirs using Biot Theory. Geophysics, 1991. Vol.56, 328-339.
[97] Zhu X., McMechan G. A., Numerical simulation of seismic response of poroelastic reservoirs using Biot Theory, Geophysics, 1991, Vol.56, 328-339.
[98] Anos Nur 等著,许云译, 双相介质中波的传播. 北京, 石油工业出版社. 1986.
[99] 陈敬国, 一种有效吸收边界条件的 matlab 实现,中国科技论文在线, 2006, Vol.6, 71-80.
[100] 董良国,马在田,曹景忠,一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(3):411—419.
[101] 董敏煜, 多波多分量地震勘探, 石油工业出版社, 北京, 2002.
[102] 范祯祥, 郑仙种编著, 地震波数值模拟与偏移成像,河南科学技术出版社. 1994.
[103] 郭建, 双相介质中P波波场的有限差分模拟,石油地球物理勘探, 1992, Vol.27(2), 565-571.
[104] 郭建, 马爱珍, 双相介质与弹性介质混合模型的有限差分声波模拟, 石油地球物理勘探, 1992, Vol.27(5), 1-8.
[105] 桂志先, 贺振华, 黄济德, 含垂直裂隙地层中弹性波相速度, 石油地球物理勘探, 2001, Vol.36(2), 180-186.
[106] 桂志先, 贺振华, 汪德雯, 正交介质中地震波传播数值模拟与分析, 江汉石油学院学报, 2001, Vol.23(3), 21-23.
[107] 黄晓葛, 白武明, 地震波各向异性的研究进展, 地球物理学进展, 1999, Vol.14(3), 54-65.
[108] 何樵登, 地震勘探原理和方法, 地质出版社. 1986.
[109] 何樵登, 地震波理论, 地质出版社. 1988.
[110] 何樵登, 熊维纲主编, 应用地球物理教程-地震勘探, 地质出版社. 1991
[111] 何樵登, 张中杰,横向各向同性介质中地震波及其数值模拟, 吉林大学出版社. 1996.
[112] 侯安宁, 何樵登, 分形反射序列的合成记录与生物遗传算法反演的初步研究, SEG/CPS 北京 93 届国际地球物理会议论文集,石油物探, 1993, 44-49.
[113] 侯安宁, 各向异性弹性波及其波动方程正反演研究, 博士学位论文, 吉林, 长春地质学院. 1994.
[114] 侯安宁, 何樵登, 各向异性介质中弹性波动方程高阶差分及其稳定性研究, 地球物理学报, 1995, Vol.38(4), 519-527.
[115] 侯安宁, 何樵登, 马在田, 各向异性弹性波动交错网格高阶差分法的误差研究. 长春科技大学学报, 1995, Vol.25(4), 446-451.
[116] 刘克安, 刘宏伟, 双相介质二维波动方程三参数同时反演的时卷正则迭代法, 石油地球物理勘探, 1997, Vol.32(5), 615-622.
[117] 刘希强,周蕙兰,地震各向异性研究进展,地震研究,1998, Vol.4(2), 185-195.
[118] 刘洋, 董敏煜, 各向异性介质中的方位 AVO, 石油地球物理勘探, 1999, Vol.34(3), 260-267.
[119] 刘洋, 李承楚,双相各向异性介质中弹性波传播伪谱法数值模拟研究, 地震学报, 2000, Vol.22, 132-138.
[120] 刘银斌, 李幼铭, 吴如山, 横向各向同性多孔介质中的地震波传播. 地球物理学进展, 1994, Vol.37(4), 499-513.
[121] 马在田, 三维地震勘探方法, 北京, 石油工业出版社. 1989.
[122] 孟庆生, 基于 BISQ 机制双相裂隙介质弹性波场正演及其方位属性研究, 博士学位论文, 吉林, 吉林大学. 2003.
[123] 孟庆生, 何樵登等, 基于 BISQ 模型双相各向同性介质中地震波数值模拟, 吉林大学学报(地球科学版), 2003, Vol.33(2), 217-221.
[124] 孟庆生, 何樵登等, 基于 BISQ 机制三维双相 EDA 介质中的反射与透射, 地球物理学进展, 2005, Vol.20(2), 323-327.
[125] 牟永光, 储层地球物理学, 北京, 石油工业出版社.1996.
[126] 牟永光, 三维复杂介质地震物理模拟, 北京, 石油工业出版社, 003.
[127] 牟永光, 裴正林, 三维复杂介质地震数值模拟, 北京, 石油工业出版社. 2005.
[128] 牛滨华, 裂隙各向异性介质中地震波传播规律研究及其波场数值模拟, 博士学位论文, 吉林, 长春地质学院. 1992.
[129] 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模拟, 中国石油大学学报, 2004, Vol28(5), 23-29.
[130] 裴正林, 三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟, 中国石油大学学报, 2006, Vol30(2), 16-20.
[131] 裴正林,双相各向异性介质弹性波传播交错网格高阶有限差分法模拟, 石油地球物理勘探, 2006, Vol.41(2), 137-143.
[132] 乔文孝, 王宁, 严炽培,声波在两种多孔介质界面上的反射和透射, 地球物理学报, 1992, Vol.35(2), 242-248.
[133] 阮爱国, 李清河,地壳介质各向异性弹性本构关系讨论, 华南地震, 2000, Vol.20(3), 14-23.
[134] 石双虎, 何樵登等, 基于 BISQ 模型双相 EDA 介质中 VSP 记录模拟, 地球物理学进展, 2007, Vol.22(2), 466-473.
[135] 邵治龙, 贺振华, 黄德济, 正交各向异性介质中地震记录的有限差分数值模拟, 物探化探计算技术, 1998, Vol.20(4), 300-305.
[136] 石双虎, HTI 介质中断裂大小、各向异性及频率之间依赖关系, 博士学位论文, 吉林, 吉林大学. 2007.
[137] 滕吉文, 王光杰等,地球各向异性介质中地震波动理论、检测与应用研究, 地学前缘, 1998, Vol.5(1), 83-90.
[138] 王德利, 单斜介质弹性波场的数值模拟与 Thomsen 参数反演方法研究, 博士学位论文, 吉林, 吉林大学. 2002.
[139] 王尚旭, 双相介质中弹性波问题有限元数值解和 AVO 问题, 博士学位论文, 北京, 中国石油大学. 1990.
[140] 魏修成, 双相各向异性介质中的地震波场研究, 博士学位论文, 北京, 中国石油大学. 1995.
[141] 吴望一, 流体力学, 北京大学出版社, 1982.
[142] 席道瑛, 易良坤, 砂岩中孔隙流体的黏性与衰减、模量和速度色散. 石油地球物理勘探, 1999, Vol.34(4), 420-425.
[143] 轩义华, 何樵登等, 基于BISQ机制的双相EDA介质的波场分析, 石油地球物理勘探, 2006, Vol.41(5), 550-556.
[144] 轩义华,倾斜横向各向同性介质(TTI)参数反演方法研究, 博士学位论文, 吉林, 吉林大学. 2007.
[145] 肖建华, 孔隙岩石的一般波动理论, 石油地球物理勘探, 1998, 33, 增刊, 1-11.
[146] 杨宝俊, 何樵登, 有限元素法的一种频率域计算方法及其应用, 1982, Vol.21(1), 56-64.
[147] 杨顶辉, 牟永光,孔隙各向异性介质中基于微观流场的 BISQ 理论, 北京, 中国地球物理学会年刊, 1998, 58-59.
[148] 杨顶辉,孔隙各向异性介质中基于 BISQ 模型的弹性波传播理论及有限元方法, 博士后研究报告, 北京, 中国石油大学. 1998.
[149] 杨顶辉, 陈小宏, 牟永光,各向异性介质中基于固-流质量耦合密度各向异性的应力波动方程, 中国学术期刊文摘(科技快报专栏). 2000, Vol.6(1), 75-77.
[150] 杨顶辉, Biot 和喷射流动耦合作用对各向异性弹性波的影响, 科学通报, 2000, Vol.45(12), 1333-1340.
[151] 杨顶辉, 张中杰, 滕吉文, 王光杰, 双相各向异性研究、问题与应用前景, 地球物理学进展, 2000, Vol.15, 7-21.
[152] 杨宽德, 杨顶辉, 王书强,基于 Biot-Squirt 方程的波场模拟, 地球物理学报, 2002, Vol.45(6), 853-861.
[153] 杨宽德, 杨顶辉, 王书强,基于 BISQ 高频极限方程的交错网格法数值模拟, 2002, Vol.37(5), 463-468.
[154] 杨宽德,杨顶辉,王书强,基于横向各向同性 BISQ 方程的弹性波传播数值模拟,地震学报,2002,Vol.24(6):599-606
[155] 张文生, 何樵登,二维横向各向同性介质的伪谱法正演模拟, 石油地球物理勘探, 1998, Vol.33(3), 310-319.
[156] 张文生, 宋海斌,三维正交各向异性介质三分量高精度有限差分正演模拟, 石油地球物理勘探, 2001, Vol.36(4), 422-432.
[157] 张应波, Biot 理论应用于地震勘探的探索, 石油物探, 1994, Vol.33(4), 29-38.
[158] 张中杰, 何樵登,含裂隙介质中地震波运动学问题的正演模拟, 石油地球物理勘探, 1989, Vol.24(3), 290-300.
[159] 张中杰, 滕吉文, EDA 介质中地震波速度、衰减与品质因子方位异性研究, 中国科学(E 辑), 1999, Vol.29(6), 569-574.
[160] 张中杰,地震各向异性研究进展, 地球物理学进展, 2002, Vol.17(2), 281-293.
[161] 朱建伟, 含流体孔隙介质基于 BISQ 机制的弹性波波动方程及传播特性, 博士学位论文, 吉林, 长春科技大学. 2000.
[162] 朱建伟, 何樵登, 李云辉,含油水各向异性孔隙介质中地震波传播方程, 长春科技大学学报, 2001, Vol.31, 193-196.