各向异性及双相介质弹性波正演模拟与波场特征分析
|
摘要
对地震波传播的研究是地震学、测震学、地震勘探与探测和地震工程学科的基础,因此受到国内外地震学界的广泛重视。一方面地球物理学者们已认识到从地幔到地壳上部的沉积岩都存在不同程度的各向异性;另一方面传统的地震波理论将地下介质近似为单相介质,但储层实际是双相介质或多相介质,当岩石孔隙较大或者孔隙中流体的弹性模量、密度与岩石骨架的弹性模型、密度差值较时,大采用基于单相介质的弹性波理论就会有较大的误差,因此基于各向异性介质及多相介质的地震波理论研究,对于越来越复杂的油气储藏勘探具有重要的理论及实际意义。
本文深入研究了各向异性及双相介质中的地震波理论,分别从弹性波方程的建立、弹性波方程的数值求解、相速度及群速度特征方程、弹性波在弹性界面上散射方面来探讨了各向异性及双相介质中的波场特征以及弹性波传播机理。
论文首先在分析、研究国内外关于各向异性介质理论、双相介质理论及其相关的正演模拟技术研究成果的基础上,从柯西方程、虎克定律和运动微分方程出发论证了各向异性介质、粘弹性各向异性介质、双相各向同性介质及双相各向异性介质以位移为变量的弹性波方程。其次引入了目前比较流行的交错网格高阶有限差分方法,先对有限差分方法的边界条件、频散、差分格式以及震源加载方式进行了讨论,结合前人的研究成果,选取完全匹配层法处理人工边界、采用通量校正传输方法消除数值频散及选择胀缩震源加载在速度项上,再利用交错网格有限差分方法求解与二阶偏微分方程等价的一阶速度-应力方程,数值模拟各种介质中波场特征,并对不同地质模型的多波波场进行分析,通过上述分析进一步认识了弹性波在各向异性介质和双相介质中的传播规律,这对多波信息的识别具有一定的指导意义。
由于弹性波的频散和衰减以及弹性波在分界面处的能量分配规律是地震波传播理论中很重要的问题之一,因此本文从弹性波方程出发,导出相速度和群速度及其特征方程、弹性波在自由界面和弹性界面能量分配方程等。在具体研究中结合各向异性介质的克里斯托夫方程,首次分析了汤姆森参数对相速度随相位角、群速度随群角的影响情况;结合基于BISQ理论的双相介质的克里斯托夫方程,详细地研究了弹性波的相速度、逆品质因子与频率、孔隙度、渗透率、饱和度及波的传播方向之间的关系。联合基于Biot理论的双相各向同性介质的弹性波方程和4个边界条件证明了牟氏方程,讨论了储层顶界面、储层内分界面以及储层底界面处的AVA特征曲线,并与基于单相介质的佐普里兹方程计算结果进行了对比,在此基础上并分析了储层内孔隙度的变化对AVA特征曲线的影响。通过上述分析进一步认识了弹性波衰减特性以及储层参数对弹性波的影响程度,这为多波联合叠前AVA反演岩性参数和储层参数及流体识别奠定了基础。
本文以河南油田泌阳地区某口井测井曲线为储层参数,基于Biot理论建立了无耗散情形时的双相层状模型,并采用高阶交错网格有限差分技术模拟了层状介质中的波场记录,分析了孔隙度的改变、孔隙内流体成份差异对共炮点记录的影响,并且对相应的地质模型分界面上的AVA特征曲线及各模型AVA正演记录进行了分析。
综上所述,本文通过正演模拟方法分析研究了各向异性介质及双相介质中的弹性波多波波场特征,所取得的成果对于研究地震波传播理论和认识弹性波场特征具有参考意义,对复杂介质的地震勘探与开发、油气横向预测等均具有实际应用价值。
The worldwide experts in seismology attaches great importance to the research ofseismic wave propagation ,which is the basis for seismology, seismological, seismicprospecting and exploration and earthquake engineering .On the one hand,the scholarsof the geophysics have recognized that the sedimentary rock from the mantle to theupper crust have varying degrees of anisotropy;on the other hand, the traditionaltheory of seismic wave treat the subsurface medium as the single-phase mediumapproximatively,and actually the reservoir is the two-phase or multi-phasemedium.When the porosity of the rock and the elastic modulus and density of thefluids in the pore are large,the seismic wave theory based on single-phase media willhave large error.Thus the theoretical studies of seismic wave based on anisotropicmedia and multi-phase media has important theoretical and practical significance forthe complex exploration of oil and gas reserves.
This thesis discusses the seismic wave theory of anisotropic and two-phasemedium in detail.Specifically, this thesis discuss and analysis wave fieldcharacteristics and mechanism of seismic wave propagation in the anisotropic andtwo-phase medium by establishing、solving in the way of numerical method andextending the wave equation.
First,this thesis overview the research status quo of anisotropic medium theory、two-phase medium theory and numerical simulation technology. Unifyingpredecessor’s researches, we derived the anisotropic media、viscoelastic anisotropicmedia、two-phase isotropic media and two-phase anisotropic medium’s the secondorder partical differential wave equation with a displacement variable by using theCauchy equations、Hooke’s Law and differential equations of motion. Second thispaper introduces and discuses the staggered grid high-order finite-difference method,including the boundary conditions、dispersion、differential format of the finitedifference method and the way of loading souce.Unifying predecessor’s researches, weuse PML to deal with the artificial boundaries、use FCT to eliminate numericaldispersion and add the source on the velocity item. By solving the first-order velocitystressequations which is equal with the second order partial differential equations using staggered grid finite difference method、simulating the propagation of seismicwave of various mediums and analysising the multi-wave field of different geologicalmodels, we have understood better the law of the wave propagation in anisotropicmedia and two-phase media, which has some signigicances for distinguishing themulti-wave information.
This thesis has extended the phase velocity、group velocity and energydistribution equation in the free and flexibility interface from elastic wave equation,because seismic wave dispersion、attenuation and the energy distribution law ofseismic wave propagation are very important issues of the theory of seismic wave.This part of the work include: we have derived Chrisotoffel equations of theanisotropic media and analyzed the phase velocity and group velocity with the changeof the phase and group angle when the Thomson parameter had different values; wehave derived the Chrisotoffel equation of the two-phase medium based on BISQtheory and studied the relationship between the phase velocity of elastic waves、Qfactor and frequency、porosity、permeability、saturation and the direction of wavepropagation; Jointing the wave equation of two-phase isotropic medium based on theBiot thory and four boundary conditions, we have proved the Mou’s equation anddiscussed the AVA characteristic curves of the top reservoir interface、the interfacewithin the reservoir and the bottom reservoir interface, which is compared with theresult calculated using the single-phase medium’s Zoeppritz equation, at the same timewe have analysed the AVA curves changes with the reservoir porosity.Through theanalysis,we further understand the elastic wave attenuation characteristics and thedegree of influence about elastic wave caused by reservoir parameters,which isfoundation for inversing lithology parameters using multi-wave joint prestack AVAand identifying the reservoir parameters and fluid parameters.
Finally,this thesis has established layer model without dissipation based on Biotthory using reservoir parameters of a certain well in the region of Miyan of Henanoilfield、have simulated the wave field records using high-order staggered-grid finitedifference technique and have analysed the impact of common shot records caused bythe change of porosity and AVA characteristic curves of each interface.
Overall, this paper analysis the wave field characteristics and seismic wavepropagation characteristics of the anisotropic medium and two-phase medium usingforward simulation, the research results have a reference value for studying the seismicwave propagation and understanding the seismic wave propagation,and have practicalapplication value for the seismic exploration and development in the complex media、forecasting the oil and gas,etc.
本文深入研究了各向异性及双相介质中的地震波理论,分别从弹性波方程的建立、弹性波方程的数值求解、相速度及群速度特征方程、弹性波在弹性界面上散射方面来探讨了各向异性及双相介质中的波场特征以及弹性波传播机理。
论文首先在分析、研究国内外关于各向异性介质理论、双相介质理论及其相关的正演模拟技术研究成果的基础上,从柯西方程、虎克定律和运动微分方程出发论证了各向异性介质、粘弹性各向异性介质、双相各向同性介质及双相各向异性介质以位移为变量的弹性波方程。其次引入了目前比较流行的交错网格高阶有限差分方法,先对有限差分方法的边界条件、频散、差分格式以及震源加载方式进行了讨论,结合前人的研究成果,选取完全匹配层法处理人工边界、采用通量校正传输方法消除数值频散及选择胀缩震源加载在速度项上,再利用交错网格有限差分方法求解与二阶偏微分方程等价的一阶速度-应力方程,数值模拟各种介质中波场特征,并对不同地质模型的多波波场进行分析,通过上述分析进一步认识了弹性波在各向异性介质和双相介质中的传播规律,这对多波信息的识别具有一定的指导意义。
由于弹性波的频散和衰减以及弹性波在分界面处的能量分配规律是地震波传播理论中很重要的问题之一,因此本文从弹性波方程出发,导出相速度和群速度及其特征方程、弹性波在自由界面和弹性界面能量分配方程等。在具体研究中结合各向异性介质的克里斯托夫方程,首次分析了汤姆森参数对相速度随相位角、群速度随群角的影响情况;结合基于BISQ理论的双相介质的克里斯托夫方程,详细地研究了弹性波的相速度、逆品质因子与频率、孔隙度、渗透率、饱和度及波的传播方向之间的关系。联合基于Biot理论的双相各向同性介质的弹性波方程和4个边界条件证明了牟氏方程,讨论了储层顶界面、储层内分界面以及储层底界面处的AVA特征曲线,并与基于单相介质的佐普里兹方程计算结果进行了对比,在此基础上并分析了储层内孔隙度的变化对AVA特征曲线的影响。通过上述分析进一步认识了弹性波衰减特性以及储层参数对弹性波的影响程度,这为多波联合叠前AVA反演岩性参数和储层参数及流体识别奠定了基础。
本文以河南油田泌阳地区某口井测井曲线为储层参数,基于Biot理论建立了无耗散情形时的双相层状模型,并采用高阶交错网格有限差分技术模拟了层状介质中的波场记录,分析了孔隙度的改变、孔隙内流体成份差异对共炮点记录的影响,并且对相应的地质模型分界面上的AVA特征曲线及各模型AVA正演记录进行了分析。
综上所述,本文通过正演模拟方法分析研究了各向异性介质及双相介质中的弹性波多波波场特征,所取得的成果对于研究地震波传播理论和认识弹性波场特征具有参考意义,对复杂介质的地震勘探与开发、油气横向预测等均具有实际应用价值。
The worldwide experts in seismology attaches great importance to the research ofseismic wave propagation ,which is the basis for seismology, seismological, seismicprospecting and exploration and earthquake engineering .On the one hand,the scholarsof the geophysics have recognized that the sedimentary rock from the mantle to theupper crust have varying degrees of anisotropy;on the other hand, the traditionaltheory of seismic wave treat the subsurface medium as the single-phase mediumapproximatively,and actually the reservoir is the two-phase or multi-phasemedium.When the porosity of the rock and the elastic modulus and density of thefluids in the pore are large,the seismic wave theory based on single-phase media willhave large error.Thus the theoretical studies of seismic wave based on anisotropicmedia and multi-phase media has important theoretical and practical significance forthe complex exploration of oil and gas reserves.
This thesis discusses the seismic wave theory of anisotropic and two-phasemedium in detail.Specifically, this thesis discuss and analysis wave fieldcharacteristics and mechanism of seismic wave propagation in the anisotropic andtwo-phase medium by establishing、solving in the way of numerical method andextending the wave equation.
First,this thesis overview the research status quo of anisotropic medium theory、two-phase medium theory and numerical simulation technology. Unifyingpredecessor’s researches, we derived the anisotropic media、viscoelastic anisotropicmedia、two-phase isotropic media and two-phase anisotropic medium’s the secondorder partical differential wave equation with a displacement variable by using theCauchy equations、Hooke’s Law and differential equations of motion. Second thispaper introduces and discuses the staggered grid high-order finite-difference method,including the boundary conditions、dispersion、differential format of the finitedifference method and the way of loading souce.Unifying predecessor’s researches, weuse PML to deal with the artificial boundaries、use FCT to eliminate numericaldispersion and add the source on the velocity item. By solving the first-order velocitystressequations which is equal with the second order partial differential equations using staggered grid finite difference method、simulating the propagation of seismicwave of various mediums and analysising the multi-wave field of different geologicalmodels, we have understood better the law of the wave propagation in anisotropicmedia and two-phase media, which has some signigicances for distinguishing themulti-wave information.
This thesis has extended the phase velocity、group velocity and energydistribution equation in the free and flexibility interface from elastic wave equation,because seismic wave dispersion、attenuation and the energy distribution law ofseismic wave propagation are very important issues of the theory of seismic wave.This part of the work include: we have derived Chrisotoffel equations of theanisotropic media and analyzed the phase velocity and group velocity with the changeof the phase and group angle when the Thomson parameter had different values; wehave derived the Chrisotoffel equation of the two-phase medium based on BISQtheory and studied the relationship between the phase velocity of elastic waves、Qfactor and frequency、porosity、permeability、saturation and the direction of wavepropagation; Jointing the wave equation of two-phase isotropic medium based on theBiot thory and four boundary conditions, we have proved the Mou’s equation anddiscussed the AVA characteristic curves of the top reservoir interface、the interfacewithin the reservoir and the bottom reservoir interface, which is compared with theresult calculated using the single-phase medium’s Zoeppritz equation, at the same timewe have analysed the AVA curves changes with the reservoir porosity.Through theanalysis,we further understand the elastic wave attenuation characteristics and thedegree of influence about elastic wave caused by reservoir parameters,which isfoundation for inversing lithology parameters using multi-wave joint prestack AVAand identifying the reservoir parameters and fluid parameters.
Finally,this thesis has established layer model without dissipation based on Biotthory using reservoir parameters of a certain well in the region of Miyan of Henanoilfield、have simulated the wave field records using high-order staggered-grid finitedifference technique and have analysed the impact of common shot records caused bythe change of porosity and AVA characteristic curves of each interface.
Overall, this paper analysis the wave field characteristics and seismic wavepropagation characteristics of the anisotropic medium and two-phase medium usingforward simulation, the research results have a reference value for studying the seismicwave propagation and understanding the seismic wave propagation,and have practicalapplication value for the seismic exploration and development in the complex media、forecasting the oil and gas,etc.
引文
[1] Hudson J .Overall properties of cracked solid, Math.Proc.Camb.Phil.Soc. 1980, Vol.88,371~384
[2] Crampin S., Evaluation of anisotropy by shear-wave splitting.Geophysics, 1985, Vol.50 (1),142~152
[3] Crampin S., Evidence for aligned cracks in the Earth’s crust.First Break, 1985, Vol.3 (1), 12~15
[4] Crampin S., Anisotropy in exploration seismic.First Break, 1984b, Vol.23, 19~21
[5] Crampin S.,et al.,Observation of dilatnacy-induced polarization anomalies and earthquakeprediction.Nature,1980,Vol.286,874~877
[6] Crampin S.Effective anisotropic elastic constants for wave propagation through crackedsolids,In proc First Int.Workshop on Seismic Anisotropy,Suzdahl,1982,135~145
[7] Crampin S., The geological and industial implications of extensive-dilatancy anisotropy.Nature,1987, Vol.328, 491~496
[8] Brodov L U,et al .,Estimating physical parameter of cracked-porous reservoirs by invertingshear-wave splitting.Geophys J R.Astr.Soc,1992,107:429~432
[9] Mueller M C. Prediction of lateral variability in fracture intensity using multi-component shearwavesurface seismic as a processor to horizontal drilling I the Austin Chalk.Geophys J R.,AStr.Soc, 1991, 107:409~416
[10] Ebrom D.（万有林译）．各向异性和油藏开发．石油物探译丛，1995，No.2:11~16
[11] Gassmann F. Uberdie elastizitt porser media .Vierteliah rssch rift der Natur for schendenGesellschaft in Zurich,1951,96:1~23
[12] Biot M A .Theorry of propagation of elastic waves in a fluid-saturated porous solid, I: Lowfrequencyrange J.Acoust Soc Amer., 1956a, 28:168~178
[13] Biot M A .Theorry of propagation of elastic waves in a fluid-saturated porous solid,II: Higherfrequencyrange J.Acoust Soc Amer.,1956b,28:179~191
[14] White J E.Computed seismic speeds and attenuation in rocks with partial gas satueation.Geophysics, 1975, 40:224~232
[15] Plona T J.Observation of a second bulk compressional wave in a porous medium at ultrasonicfrequencies .Appl.Phys.Lett. 1980, 36:259~261
[16] Nur A M, Wang Z. Seismic and acoustic velocities in reservoir rocks: Experimental Studies.Society of Exploration Geophysicists.1989, 1
[17] Wang Z,Nur A.Seismic and acoustic velocities in reservoir rocks:Theoretical and modelstudies.Society of Exploration Geophysicists.1992,2
[18] Parra J O,Xu P C.Dispersion and attenuation of acoustic guides waves in layered fluid-filledporous media:J.Acoust.Soc.Am.,1994,95:91~98
[19] Sharma M D.Surface-wave propagation in a cracked poroelastic half-space lying under auniform layer of fluid.Giophys J.Int.,1996,127:31~39
[20] Dvorkin J,Nur A.Dynamic poroelasticity: A unified model with the squirt and the Biotmechanisms.Geophysics,1993,58:524~533
[21] Dvorkin J, Nolen-Hoelsema R,Nur A. The squirt-flow mechanism: Macroscopic description.Geophysics, 1994, 59:428~438
[22]王尚旭．双相介质中弹性波问题有限元数值解和AVO问题.中国石油大学博士学位论文,1990
[23]乔文孝,王宁,严治培.声波在两种多孔介质界面上的反射和透射[J].地球物理学报,1992,35(2):242~248
[24]张应波.Biot理论应用于地震勘探的探索[J].石油物探,1994,33(4):29~38
[25] Kazi-Azoual.Green’s function in an infinite transversely isotropic saturated poroelasticmedium .J. A coust Soc Am., 1988, 84:1883~1889
[26] Auriault J L. Dynamic behavior of a porous medium saturated by a Newtonian fluid, Int.J.Engng.Sci, 1984, 18:775~785
[27] Auriault J L., etc Dynamic behavior of a porous media, checking of the generalized law ofDarcy. J.Acoust.Soc Am., 1985, 77:1641~1650
[28] Schmitt D P.Acoustic multipole logging in transversely isotropic poroelastic formation J.Acoust Soc Am, 1989, 86:2397~2420
[29] Mukerji T, Mavko G.Pore fluid affects on seismic velocity in anisotropic rocks.Geophysics,1994, 59:223~224
[30] Xu S Y. Modeling the effect of pore fluid communication on seismic anisotropy. 67th Ann. Int.SEG meeting, Expanded Abstracts, 1997, 991~994
[31] Pointer, Numerical modeling of seismic waves scattered by hydro fractures: application of theindirect boundary element method. Geophysics J.Int, 1998, 135:289~303
[32] Sayers C M. Stress-dependent seismic anisotropy of shales.Geophysics, 1999, 64:93~98
[33] Berryman J G. Scattering by a spherical in homogeneity in a fluid saturated porous medium .J.Math. Phys, 1985, 26:1408~1419
[34] Berryman J G. .Effective medium approximation for elastic constants of porous solids withmicroscopic heterogeneity.J.Appl.Phys, 1986, 59:1136~1140
[35] Berryman J G., Milton GW. Exact results for generalized Gassmann’s equations in compositeporous media with two constitutes .Geophysics, 1995, 56:1950~1960
[36] Rathore J S, Fjaer E ,Holt R M, ect .P-wave and S-wave anisotropy of synthetics sandstonewith controlled crack geometry .Geophysics Prosp.1994,43:711~728.
[37] Thomsen L. Elastic anisotropy due to aligned cracks in porous rock. Geophysics Prosp.1995,43:805~829
[38] Hudson J , A Liu, Cramp in S . The mechanical properties of materials with interconnectedcracks and pores, Geophysics.J.Int, 1996, 124:105~112
[39] Gelinsky S, Shapiro SA. Dynamic-equivalent medium approach for thinly layered saturatedsediments, Geophysics .J.Int,1997, 128: F1～F4 .
[40]牟永光储层地球物理学[M].北京：石油工业出版社，1996
[41]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, 1994,37 (4):499～513
[42]牛滨华,何樵登,孙春岩.六方各向异性介质方位矢量波动方程及其相速度.石油物探,1994,33 (1):19～29 .
[43]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.
[44]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
[45] Parra J O. The transversely isotropic poroelastic wave equation including the Biot and thesquirt mechanisms: Theory and application. Geophysics, 1997, 62: 309～318 .
[46]杨顶辉,陈小宏,牟永光.双相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方程.中国学术期刊文摘(科技快报专栏),1999
[47]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
[48]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,2006,41(5):550~556
[49]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,2007,22(2):514~520
[50]杨顶辉，张中杰等.双相各向异性研究、问题与应用前景.地球物理学进展,2000,15(2):7~21
[51] Dvorkin J, Nur A. Dynamic poroelastic: A unified model with the squirt and the Biotmechanisms [J] .Geophysics, 1993, 58: 524 533.
[52] Dvorkin J, Hoeksema R N. The squirt-flow mechanism: Macroscopic description [J].Geophysics, 1994, 59: 428 438.
[53] Cerveny V, Molotkov I. Ray method in seismology.Univ.Karlova, 1977
[54] Pao Y H, Varatharajulu V. Huygens’Principle radiation conditions and integral formulas forthe scattering of elastic waves. J. Acoust.Soc.Am., 1976, 59:1361~1371
[55] Bouchon M. Diffraction of elastic waves by cracks or cavities using the discrete wave numbermethod. J. Acoust Soc.Am., 1987, 81:1671~1676
[56] Bakamjian B. Boundary integrals: An efficient method for modeling seismic wave propagationin 3-D.62th Ann. Internat. Mtg. Sco. Expl. Geophys. Expanded Abstracts, 1992, 1232~1235
[57]符力耘，牟永光.弹性波边界元法正演模拟.地球物理学报. 1994, 37(4): 521~ 529
[58] Lysmer J, Drake L A finite element method foe seismology,In Alder B,Fernbach S,Bolt B A,Eds.,Methods in computational physics,Seismilogy,Academic Press., 1972,181~216
[59] Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elasticwave equations.Geophysics, 1984, 49:553~549
[60] Seron F J,Sanz F J,Kindelan M et al.Finite-element method for elastic wave propagation.Comm.Appl. Numerical Method. 1990, 6:359~368
[61] Seron F J,Badal J,Sabadell F J.A numerical laboratory for simulation and visualization ofseismic wavefields.Gedophy.Prosp.,1996,44:603~642
[62]Padovani E,Priolo E,Seriani G. Low and high order finite element method :experience inseismic modeling.J.Comp.Acoust.,1994,2:371~422
[63] Saema G S,Mallick K,Gadhinglajkar V R. Nonreflecting boundary condition in finite elementformulation for an elastic wave equation. Geophysics, 1998,63: 1006~1016
[64] Kosloff D D,Baysal E.Forward modeling by a Fourier method.Geophysics,1982，47（10）：1402～1412
[65] Gazdag J. Modeling of the acoustic wave equation with transform methods, Geophysics, 1981,46(6):854~859
[66] Reshef M, Kosloff D D., Three-dimensional elastic modeling by the Fouriermethod.Geophysics,1988,53:611~624
[67] Alterman Z,Karal Jr F C .Propagation of elastic waves in layered media by finite differencemethods.Bull.Seism.Soc.Am.,1968,58:367~398
[68] Boore D M.Finite difference methods for seismic wave propagation in heterogeneousmaterial.In:Methods in Bolt B A Ed.Computational physics.Academic Press.Inc,1972
[69] Alford R M,Kelly K R,Boore D M.Accuracy of finite difference modeling of the acousticwave equation.Geophysics,1974,39:838~842
[70] Kelly K R,Ward R W,Treitel S,et al. Synthetic seismograms, a finite differenceapproach.Geophysics.,1976,41:2~27
[71] Virieux J.P-SV wave propagation in heterogeneous media: Velocity-stress finite differencemethod.Geophysics, 1986, 51(4):889~901
[72] Dablain M A.The application of high-order differencing to scalar wave equation.Geophysics,1986, 51(1):54~66
[73] Bayliss A ,Jordan K E,LeMesurier B J,Turkel E.A fourth-order accurate finite differencescheme for the computation of elastic waves.Bull.Seism.Soc.Am。，76：1115～1132
[74] Levander A R.Fourth-order difference P-SV seismograms. Geophysics, 1988,53(11):1425~1436
[75] Graves R W. Simulating seismic wave propagation in 3D elastic media using staggered-griddifference.Bull.Seism.Soc.Am, 1996, 96:1091~1106
[76] Caricone J,Kosloff D,Kosloff R. Viscoacoustic wave propagation simulation in theearth.Geophysics,1988,53:769~777
[77] Tal-EzerH,Carcione J,Kosloff D.An accurate and efficient scheme for wave propagation inlinear viscoelastic media.Geophysics.,1900,55:1366~1397
[78] Robertsson J O,Blanch J O,Symes W W. Viscoelastic finite-difference modeling.Geophysics,1994,59(9):1444~1456
[79] Dai N,Vafidis A,Kanasewich E R.Wave propagation in heterogeneous,porous media:Avelocity-stress,finite difference method.Geophysics,1995,60(2):327~340
[80] Carcione J M,Quiroga-Goode G.Some aspects of the physics and numerical modeling of Biotcompressional wave.J.Comput.Acous.,1996,3:261~280
[81] Ozdenvar T.McMechan G. Algorithms for staggered-grid computation for poroelastic,elastic,acoustic and scalar wave equation .Geophys.Prosp., 1997, 45: 403~ 420
[82] Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on astaggered mesh.J.Comput.Phys.,1999,154:520~527
[83]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，2002,45(6),853~861
[84]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,2002,37(5),463~468
[85]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.2002,24(6):599~606
[86]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
[87]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）,2003,33(2):217~221
[88]李红星,刘财,陶春辉.基于BISQ模型的各向同性孔隙介质弹性波三维交错网格高阶有限差分数值模拟.世界地质,2007，26(4):501~508
[89]周怀来.多波波场正演模拟与波场特征分析研究.博士学位论文,成都理工大学.2009
[90]刘庆敏.高阶差分数值模拟方法研究.硕士学位论文.中国石油大学,2007
[91] Reynolds A C..Boundary conditions for the numerical solution of wave propagation problems[J].Geophysics, 1978; 43(6):895~904.
[92] Clayton R, Engquist B.Absorbing boundary conditions for acoustic and elastic waveequations[J].Bull.Seis.Soc.Am.,1977;67(6):1529~540.
[93]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):45~56
[94] Kosloff R, Kosloff D. Absorbing boundaries for wave propagation problems [J]. J.ComputPhys.1986; 63:363~376.
[95] Collino F, Tsohka C. Application of the perfectly matched layer model to the linearastodynamic problem in anisotropic heterogeneous media [J].Geophysics, 2001 66:294~307.
[96] Crampin S. Suggestions for a consistent terminology for seismic anisotropy [J]. Prosp. 1989,37:753~770.
[97] Crampin S. A review of wave motion in anisotropic and cracked elastic–medium [J].Wavemotion ,1981,3:343~391.
[98]郑治真.S波分裂的研究[J].地球物理学进展,1991,4(1): 26~32.
[99]李录明,罗省贤.多波多分量地震勘探原理及数据处理方法[M].成都:成都科技大学出版社,1997
[100].刘莲莲.各向异性粘弹性孔隙介质伪谱法波场正演模拟.中国石油大学硕士学位论文,2007
[101].杜启振，王延光，付水华.方位各向异性粘弹性介质波场数值模拟[J].地球物理学进展,2006, 21(2): 502～504
[102].刘财，张智，邵志刚，等.线性粘弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2006,21(2):360～369
[103].杜启振，杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010～2015
[104].范帧祥.准各向异性粘弹介质地震波的数值仿真[J].地球物理学报,1988,31(2):184～210
[105].谭末一，赵兵，张中杰.粘弹性VTI介质地震波模拟特征分析[J].地球物理学进展,2007,22(4):1305～1311
[106]李军，苏云，李录明.各向异性黏弹性介质波场数值模拟[J].大庆石油学院学报,2009，33(6):38～42
[107] Berryman J G .Long-Wave elastic anisotropy produced by horizontal layering [J].GeophysRes., 1979, 67(11): 4427~4440
[108]韩颜颜,郭智奇,刘财等.弹性各向异性介质速度特征分析.[J].吉林大学学报(地球科学版).,2008,38(增刊):80~84
[109]苏云,李军，唐娟等.弱各向异性介质地震波传播特征分析.[J].物探化探计算技术,2010,32（2）:144~148
[110].Greertsma J,Smith D C.Some aspects of elastic wave propagation in fluid saturated poroussolid[J].Geophysics,1961,33(2):169~181
[111]撒利明.储层反演油气检测理论方法研究及其应用.博士学位论文，中国科院学广州地球化学研究所，2003
[112]腾吉文，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[J].地学前缘,1998，5(1),83~90
[2] Crampin S., Evaluation of anisotropy by shear-wave splitting.Geophysics, 1985, Vol.50 (1),142~152
[3] Crampin S., Evidence for aligned cracks in the Earth’s crust.First Break, 1985, Vol.3 (1), 12~15
[4] Crampin S., Anisotropy in exploration seismic.First Break, 1984b, Vol.23, 19~21
[5] Crampin S.,et al.,Observation of dilatnacy-induced polarization anomalies and earthquakeprediction.Nature,1980,Vol.286,874~877
[6] Crampin S.Effective anisotropic elastic constants for wave propagation through crackedsolids,In proc First Int.Workshop on Seismic Anisotropy,Suzdahl,1982,135~145
[7] Crampin S., The geological and industial implications of extensive-dilatancy anisotropy.Nature,1987, Vol.328, 491~496
[8] Brodov L U,et al .,Estimating physical parameter of cracked-porous reservoirs by invertingshear-wave splitting.Geophys J R.Astr.Soc,1992,107:429~432
[9] Mueller M C. Prediction of lateral variability in fracture intensity using multi-component shearwavesurface seismic as a processor to horizontal drilling I the Austin Chalk.Geophys J R.,AStr.Soc, 1991, 107:409~416
[10] Ebrom D.（万有林译）．各向异性和油藏开发．石油物探译丛，1995，No.2:11~16
[11] Gassmann F. Uberdie elastizitt porser media .Vierteliah rssch rift der Natur for schendenGesellschaft in Zurich,1951,96:1~23
[12] Biot M A .Theorry of propagation of elastic waves in a fluid-saturated porous solid, I: Lowfrequencyrange J.Acoust Soc Amer., 1956a, 28:168~178
[13] Biot M A .Theorry of propagation of elastic waves in a fluid-saturated porous solid,II: Higherfrequencyrange J.Acoust Soc Amer.,1956b,28:179~191
[14] White J E.Computed seismic speeds and attenuation in rocks with partial gas satueation.Geophysics, 1975, 40:224~232
[15] Plona T J.Observation of a second bulk compressional wave in a porous medium at ultrasonicfrequencies .Appl.Phys.Lett. 1980, 36:259~261
[16] Nur A M, Wang Z. Seismic and acoustic velocities in reservoir rocks: Experimental Studies.Society of Exploration Geophysicists.1989, 1
[17] Wang Z,Nur A.Seismic and acoustic velocities in reservoir rocks:Theoretical and modelstudies.Society of Exploration Geophysicists.1992,2
[18] Parra J O,Xu P C.Dispersion and attenuation of acoustic guides waves in layered fluid-filledporous media:J.Acoust.Soc.Am.,1994,95:91~98
[19] Sharma M D.Surface-wave propagation in a cracked poroelastic half-space lying under auniform layer of fluid.Giophys J.Int.,1996,127:31~39
[20] Dvorkin J,Nur A.Dynamic poroelasticity: A unified model with the squirt and the Biotmechanisms.Geophysics,1993,58:524~533
[21] Dvorkin J, Nolen-Hoelsema R,Nur A. The squirt-flow mechanism: Macroscopic description.Geophysics, 1994, 59:428~438
[22]王尚旭．双相介质中弹性波问题有限元数值解和AVO问题.中国石油大学博士学位论文,1990
[23]乔文孝,王宁,严治培.声波在两种多孔介质界面上的反射和透射[J].地球物理学报,1992,35(2):242~248
[24]张应波.Biot理论应用于地震勘探的探索[J].石油物探,1994,33(4):29~38
[25] Kazi-Azoual.Green’s function in an infinite transversely isotropic saturated poroelasticmedium .J. A coust Soc Am., 1988, 84:1883~1889
[26] Auriault J L. Dynamic behavior of a porous medium saturated by a Newtonian fluid, Int.J.Engng.Sci, 1984, 18:775~785
[27] Auriault J L., etc Dynamic behavior of a porous media, checking of the generalized law ofDarcy. J.Acoust.Soc Am., 1985, 77:1641~1650
[28] Schmitt D P.Acoustic multipole logging in transversely isotropic poroelastic formation J.Acoust Soc Am, 1989, 86:2397~2420
[29] Mukerji T, Mavko G.Pore fluid affects on seismic velocity in anisotropic rocks.Geophysics,1994, 59:223~224
[30] Xu S Y. Modeling the effect of pore fluid communication on seismic anisotropy. 67th Ann. Int.SEG meeting, Expanded Abstracts, 1997, 991~994
[31] Pointer, Numerical modeling of seismic waves scattered by hydro fractures: application of theindirect boundary element method. Geophysics J.Int, 1998, 135:289~303
[32] Sayers C M. Stress-dependent seismic anisotropy of shales.Geophysics, 1999, 64:93~98
[33] Berryman J G. Scattering by a spherical in homogeneity in a fluid saturated porous medium .J.Math. Phys, 1985, 26:1408~1419
[34] Berryman J G. .Effective medium approximation for elastic constants of porous solids withmicroscopic heterogeneity.J.Appl.Phys, 1986, 59:1136~1140
[35] Berryman J G., Milton GW. Exact results for generalized Gassmann’s equations in compositeporous media with two constitutes .Geophysics, 1995, 56:1950~1960
[36] Rathore J S, Fjaer E ,Holt R M, ect .P-wave and S-wave anisotropy of synthetics sandstonewith controlled crack geometry .Geophysics Prosp.1994,43:711~728.
[37] Thomsen L. Elastic anisotropy due to aligned cracks in porous rock. Geophysics Prosp.1995,43:805~829
[38] Hudson J , A Liu, Cramp in S . The mechanical properties of materials with interconnectedcracks and pores, Geophysics.J.Int, 1996, 124:105~112
[39] Gelinsky S, Shapiro SA. Dynamic-equivalent medium approach for thinly layered saturatedsediments, Geophysics .J.Int,1997, 128: F1～F4 .
[40]牟永光储层地球物理学[M].北京：石油工业出版社，1996
[41]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, 1994,37 (4):499～513
[42]牛滨华,何樵登,孙春岩.六方各向异性介质方位矢量波动方程及其相速度.石油物探,1994,33 (1):19～29 .
[43]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.
[44]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
[45] Parra J O. The transversely isotropic poroelastic wave equation including the Biot and thesquirt mechanisms: Theory and application. Geophysics, 1997, 62: 309～318 .
[46]杨顶辉,陈小宏,牟永光.双相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方程.中国学术期刊文摘(科技快报专栏),1999
[47]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
[48]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,2006,41(5):550~556
[49]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,2007,22(2):514~520
[50]杨顶辉，张中杰等.双相各向异性研究、问题与应用前景.地球物理学进展,2000,15(2):7~21
[51] Dvorkin J, Nur A. Dynamic poroelastic: A unified model with the squirt and the Biotmechanisms [J] .Geophysics, 1993, 58: 524 533.
[52] Dvorkin J, Hoeksema R N. The squirt-flow mechanism: Macroscopic description [J].Geophysics, 1994, 59: 428 438.
[53] Cerveny V, Molotkov I. Ray method in seismology.Univ.Karlova, 1977
[54] Pao Y H, Varatharajulu V. Huygens’Principle radiation conditions and integral formulas forthe scattering of elastic waves. J. Acoust.Soc.Am., 1976, 59:1361~1371
[55] Bouchon M. Diffraction of elastic waves by cracks or cavities using the discrete wave numbermethod. J. Acoust Soc.Am., 1987, 81:1671~1676
[56] Bakamjian B. Boundary integrals: An efficient method for modeling seismic wave propagationin 3-D.62th Ann. Internat. Mtg. Sco. Expl. Geophys. Expanded Abstracts, 1992, 1232~1235
[57]符力耘，牟永光.弹性波边界元法正演模拟.地球物理学报. 1994, 37(4): 521~ 529
[58] Lysmer J, Drake L A finite element method foe seismology,In Alder B,Fernbach S,Bolt B A,Eds.,Methods in computational physics,Seismilogy,Academic Press., 1972,181~216
[59] Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elasticwave equations.Geophysics, 1984, 49:553~549
[60] Seron F J,Sanz F J,Kindelan M et al.Finite-element method for elastic wave propagation.Comm.Appl. Numerical Method. 1990, 6:359~368
[61] Seron F J,Badal J,Sabadell F J.A numerical laboratory for simulation and visualization ofseismic wavefields.Gedophy.Prosp.,1996,44:603~642
[62]Padovani E,Priolo E,Seriani G. Low and high order finite element method :experience inseismic modeling.J.Comp.Acoust.,1994,2:371~422
[63] Saema G S,Mallick K,Gadhinglajkar V R. Nonreflecting boundary condition in finite elementformulation for an elastic wave equation. Geophysics, 1998,63: 1006~1016
[64] Kosloff D D,Baysal E.Forward modeling by a Fourier method.Geophysics,1982，47（10）：1402～1412
[65] Gazdag J. Modeling of the acoustic wave equation with transform methods, Geophysics, 1981,46(6):854~859
[66] Reshef M, Kosloff D D., Three-dimensional elastic modeling by the Fouriermethod.Geophysics,1988,53:611~624
[67] Alterman Z,Karal Jr F C .Propagation of elastic waves in layered media by finite differencemethods.Bull.Seism.Soc.Am.,1968,58:367~398
[68] Boore D M.Finite difference methods for seismic wave propagation in heterogeneousmaterial.In:Methods in Bolt B A Ed.Computational physics.Academic Press.Inc,1972
[69] Alford R M,Kelly K R,Boore D M.Accuracy of finite difference modeling of the acousticwave equation.Geophysics,1974,39:838~842
[70] Kelly K R,Ward R W,Treitel S,et al. Synthetic seismograms, a finite differenceapproach.Geophysics.,1976,41:2~27
[71] Virieux J.P-SV wave propagation in heterogeneous media: Velocity-stress finite differencemethod.Geophysics, 1986, 51(4):889~901
[72] Dablain M A.The application of high-order differencing to scalar wave equation.Geophysics,1986, 51(1):54~66
[73] Bayliss A ,Jordan K E,LeMesurier B J,Turkel E.A fourth-order accurate finite differencescheme for the computation of elastic waves.Bull.Seism.Soc.Am。，76：1115～1132
[74] Levander A R.Fourth-order difference P-SV seismograms. Geophysics, 1988,53(11):1425~1436
[75] Graves R W. Simulating seismic wave propagation in 3D elastic media using staggered-griddifference.Bull.Seism.Soc.Am, 1996, 96:1091~1106
[76] Caricone J,Kosloff D,Kosloff R. Viscoacoustic wave propagation simulation in theearth.Geophysics,1988,53:769~777
[77] Tal-EzerH,Carcione J,Kosloff D.An accurate and efficient scheme for wave propagation inlinear viscoelastic media.Geophysics.,1900,55:1366~1397
[78] Robertsson J O,Blanch J O,Symes W W. Viscoelastic finite-difference modeling.Geophysics,1994,59(9):1444~1456
[79] Dai N,Vafidis A,Kanasewich E R.Wave propagation in heterogeneous,porous media:Avelocity-stress,finite difference method.Geophysics,1995,60(2):327~340
[80] Carcione J M,Quiroga-Goode G.Some aspects of the physics and numerical modeling of Biotcompressional wave.J.Comput.Acous.,1996,3:261~280
[81] Ozdenvar T.McMechan G. Algorithms for staggered-grid computation for poroelastic,elastic,acoustic and scalar wave equation .Geophys.Prosp., 1997, 45: 403~ 420
[82] Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on astaggered mesh.J.Comput.Phys.,1999,154:520~527
[83]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，2002,45(6),853~861
[84]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,2002,37(5),463~468
[85]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.2002,24(6):599~606
[86]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
[87]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）,2003,33(2):217~221
[88]李红星,刘财,陶春辉.基于BISQ模型的各向同性孔隙介质弹性波三维交错网格高阶有限差分数值模拟.世界地质,2007，26(4):501~508
[89]周怀来.多波波场正演模拟与波场特征分析研究.博士学位论文,成都理工大学.2009
[90]刘庆敏.高阶差分数值模拟方法研究.硕士学位论文.中国石油大学,2007
[91] Reynolds A C..Boundary conditions for the numerical solution of wave propagation problems[J].Geophysics, 1978; 43(6):895~904.
[92] Clayton R, Engquist B.Absorbing boundary conditions for acoustic and elastic waveequations[J].Bull.Seis.Soc.Am.,1977;67(6):1529~540.
[93]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):45~56
[94] Kosloff R, Kosloff D. Absorbing boundaries for wave propagation problems [J]. J.ComputPhys.1986; 63:363~376.
[95] Collino F, Tsohka C. Application of the perfectly matched layer model to the linearastodynamic problem in anisotropic heterogeneous media [J].Geophysics, 2001 66:294~307.
[96] Crampin S. Suggestions for a consistent terminology for seismic anisotropy [J]. Prosp. 1989,37:753~770.
[97] Crampin S. A review of wave motion in anisotropic and cracked elastic–medium [J].Wavemotion ,1981,3:343~391.
[98]郑治真.S波分裂的研究[J].地球物理学进展,1991,4(1): 26~32.
[99]李录明,罗省贤.多波多分量地震勘探原理及数据处理方法[M].成都:成都科技大学出版社,1997
[100].刘莲莲.各向异性粘弹性孔隙介质伪谱法波场正演模拟.中国石油大学硕士学位论文,2007
[101].杜启振，王延光，付水华.方位各向异性粘弹性介质波场数值模拟[J].地球物理学进展,2006, 21(2): 502～504
[102].刘财，张智，邵志刚，等.线性粘弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2006,21(2):360～369
[103].杜启振，杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010～2015
[104].范帧祥.准各向异性粘弹介质地震波的数值仿真[J].地球物理学报,1988,31(2):184～210
[105].谭末一，赵兵，张中杰.粘弹性VTI介质地震波模拟特征分析[J].地球物理学进展,2007,22(4):1305～1311
[106]李军，苏云，李录明.各向异性黏弹性介质波场数值模拟[J].大庆石油学院学报,2009，33(6):38～42
[107] Berryman J G .Long-Wave elastic anisotropy produced by horizontal layering [J].GeophysRes., 1979, 67(11): 4427~4440
[108]韩颜颜,郭智奇,刘财等.弹性各向异性介质速度特征分析.[J].吉林大学学报(地球科学版).,2008,38(增刊):80~84
[109]苏云,李军，唐娟等.弱各向异性介质地震波传播特征分析.[J].物探化探计算技术,2010,32（2）:144~148
[110].Greertsma J,Smith D C.Some aspects of elastic wave propagation in fluid saturated poroussolid[J].Geophysics,1961,33(2):169~181
[111]撒利明.储层反演油气检测理论方法研究及其应用.博士学位论文，中国科院学广州地球化学研究所，2003
[112]腾吉文，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[J].地学前缘,1998，5(1),83~90
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |