摘要
由于反射地震在石油勘探中的重要作用,近年来岩石物理的研究偏重于岩石的地震特性,主要反映在地震波速度及衰减与岩石其他性质及岩石所处状态条件的关系。岩石物理学的研究成果在地震数据(属性参数)与油藏特性(储集参数)之间架起了一座桥梁,促使了地震岩石物理学的兴起与发展。地震岩石物理学研究致力于弄清储层岩石以及所含流体的性质与地震属性参数之间的关系,以便更准确地从地震数据中提取岩石、流体特性以及油藏参数。岩石物理性质的研究为地震勘探找油、油藏地震监测等技术奠定了物理基础,可以为地震模拟、地震反演以及地震解释的参数的正确性、物理意义起保障作用。
有关孔隙介质中的地震波传播的研究一直是地球物理与石油勘探的热点之一,有关波致流体流动引起的地震波的速度频散与衰减更是其中的核心内容。本文对有关波致流的实验和理论模型研究进行了详细介绍,了解了波致流相关的速度频散和衰减的主要研究方向及最新动态。多孔介质的复杂性包括微细观测结构的非均匀性、各向异性、孔隙流体的存在等,使得构建基于真实物理机制的多孔介质普适性模型非常困难。在实验室环境,抓住对问题的定性唯象描述,确定了以粘弹模型为基础的唯象理论模型研究方向。粘弹性模型可以模拟孔隙岩石中的粘弹行为,模型本身简单方便,而且可以针对实验结果加以调整,是一种非常好的研究手段。
由低频实验获得了符合Arrhenius关系的热弛豫规律,将其引入标准线性固体模型中,得到了同时含有频率和温度效应的热弛豫模型。热弛豫模型能够很好的反映饱和岩石的衰减和速度频散等性质。在频率域和温度域对饱和多孔岩石的波传播特性进行了分析,得到饱和岩石波速和衰减随频率和温度的变化规律。Biot耗散机制和热弛豫机制的共同存在使得饱和岩石的衰减曲线出现两个衰减峰,即Biot峰和热弛豫峰。两个衰减峰会随着频率或温度的变化发生相向移动,处于低频(或低温)区域的热弛豫峰随温度(或频率)的升高向高频(或高温)方向移动,与低频共振实验所得结果相吻合；处于高频(或高温)区域的Biot峰的移动与热弛豫峰相反。
对影响热弛豫模型特性的一些参数进行了分析。多孔岩石孔隙度的改变会对Biot衰减产生巨大的影响,由于孔隙空间的减少会造成Darcy渗流的减少,低孔隙度饱和岩石的Biot衰减比高孔隙度时要小得多,而热弛豫衰减受孔隙度的影响却相对较小；孔隙度对S波的影响比对P波更加明显。由于衰减和频散主要由流体的流动所造成,通过分析发现渗透率的改变会造成饱和岩石衰减峰位的移动。Cole-Cole分布系数βcole-cole是构建热弛豫模型的一个重要参数,它的取值对热弛豫衰减峰的大小以及峰宽有很大影响。当βcole-cole取值较小时,热弛豫衰减较大,衰减峰较窄；而当βcole-cole较大时,热弛豫衰减较小,峰宽则明显增大。将热弛豫模型同Biot、BISQ模型进行了对比,发现热弛豫模型能产生更大的频散和衰减,频散约为BISQ模型的2.5倍,并且几乎在全频段都存在速度频散。热弛豫模型克服了Biot模型衰减和频散小以及BISQ模型频散范围窄等缺点,对速度频散和衰减的预测与实验数据更吻合。热弛豫模型具有Biot、BISQ模型所不具备的优点,可以对波速和衰减随温度的变化规律进行分析。为了验证热弛豫模型的适用性,在更高频率范围进行了一系列不同流体饱和岩石的实验研究,得到了1-1000Hz频段范围的饱和岩石的波速和衰减的实验数据。所得波速和衰减随频率和温度的变化规律与低频共振实验结果类似,符合热弛豫规律,将热弛豫机制扩展到了更高频段,验证了热弛豫规律的普遍性。提出了一个“局部热流”的概念来解释热弛豫机制。实验发现了在较高温度区域存在的类似相变峰的衰减峰,通过类质同象分析了该衰减峰可能就是相变峰。在实验结果中还发现了类似Biot峰移动规律的衰减峰,通过引入“局部流”机制对其进行了数值模拟,其结果与实验数据很好地吻合。“局部流”机制的提出给出了一种理解Biot衰减的新尝试。
饱和孔隙岩石的衰减同岩石样品的微细观结构是密切相关的,因此引入了两个与岩石细观结构相关的特征尺度,分别对应于“局部热流”和“局部流”机制,概括性地给出了相关的特征频率。另外还进行了有关饱和多孔岩石的超声实验尝试,得到了不同流体饱和岩石的超声波速与衰减数据。由于样品的尺寸很小,使得不同的岩石样品所得实验结果有一定的差距,对其作了一些定性的解释。
本文研究的热弛豫模型能预测较强的衰减以及较宽范围的速度频散,更好地模拟了饱和多孔岩石中的粘弹性行为。对低频实验的扩展研究对相对匮乏的地震频段岩石物理实验数据有所补充,对地震资料的解释和反演有非常重要的意义。该实验技术包含了对岩石中粘弹性波和物理性质的研究,可以广泛用于无损检测技术、阻尼减震技术以及地震研究中。
Due to the important role of reflection seismology in oil exploration, in recent years, the study of rock physics focused on seismic properties of the rocks, which are mainly about the relationship between the seismic velocity and attenuation, and the properties and conditions of rocks. Rock physics research provides a connection between the seismic data (seismic parameters) and reservoir properties (reservoir parameters), prompting the formation and development of seismic rock physics. Seismic rock physics research dedicated to clarify the relationship between the properties of reservoir rock and the porous fluid contained in it, and the seismic property parameters, in order to more accurately acquire the rock and fluid properties, and reservoir parameters from seismic data. The study of physical properties of rock can provide physical foundation for seismic exploration for finding oil and oil reservoir seismic monitoring. It can also play a role in insuring the correctness and physical meaning of parameters used in seismic modeling, seismic inversion and seismic interpretation.
The study of the seismic wave propagation in porous media has so far been one of the hot spots of the geophysics and oil prospecting. And seismic wave velocity dispersion and attenuation caused by the wave-induced fluid flow is the key problem. This paper carried out a detailed review of the experimental and theoretical model research about the wave-induced flow, to find out the main research directions and the latest developments of the velocity dispersion and attenuation which related to the wave-induced flow. The porous rocks are very complex media. It's complexity include the heterogeneity in micro-and meso-scale structure of rock, anisotropy, and the presence of the pore fluid, which makes it very difficult to construct a universal porous medium model that based on real physical mechanisms. In the laboratory scenario, seizing the phenomenological phenomena of experiments, we can analyze the rock properties using a phenomenological theory model which based on viscoelastic model. And this is how I intend to start my research on velocity dispersion and attenuation caused by wave-induced fluid flow. Viscoelastic model can simulate the viscoelastic behavior of porous rocks, the model itself is simple and convenient, and can be adjusted for the experimental results, which makes it a very good research tool.
Thermal relaxation regularities that consistent with the Arrhenius relationship are observed in the low-frequency experiments. Introducing the thermal relaxation regularities into the standard linear solid model, the thermal relaxation model with effects of both frequency and temperature is obtained. The thermal relaxation model can well simulate the properties of the saturated rocks, such as attenuation and velocity dispersion. In the frequency domain and the temperature domain, the characteristics of wave propagation are analyzed for saturated porous rock, to get saturated rock wave velocity and attenuation versus frequency and temperature variation. The co-existence of Biot dissipation mechanism and thermal relaxation mechanism results in the appearance of two attenuation peaks in the attenuation curve of the saturated rock, i.e., the Biot peak and the thermal relaxation peak. The two attenuation peaks will move toward each other when the frequency or temperature changes. The thermal relaxation peak at low-frequency area(or low-temperature area) will shift to high-frequency area(or high-temperature area) when the temperature (or frequency) increases, which is consistent with the experimental results obtained in low-frequency resonance experiments. The shift of the Biot peak locates at the high-frequency area(or high temperature area) is opposite to the movement of thermal relaxation peak.
The influence of parameters on characteristics of the thermal relaxation model is analyzed. The change of rock porosity may remarkably change the Biot attenuation. The reduction of the pore space will result in the reduction of Darcy flow, the Biot attenuation of low porosity saturated rock is much smaller than high porosity saturated rock. The influence of porosity variation on thermal relaxation attenuation is much smaller. The effect of porosity for S-wave is more obvious than for P-wave. Since the attenuation and dispersion of saturated rock are mainly caused by the flow of the fluid, the change of the permeability may bring about the shift of the attenuation peaks. Cole-Cole distribution coefficient βcole-cole is an important parameter for constructing the thermal relaxation model, and its value has a great influence on the thermal relaxation peak value and the peak width. When βcole-cole is small, the attenuation is large and the peak is sharp. When βcole-cole is large, the attenuation is small, and the peak width significantly increases. Thermal relaxation model is compared with the Biot and BISQ model in this dissertation. The thermal relaxation model can produce bigger dispersion and attenuation. The dispersion of thermal relaxation model is about2.5times as that of the BISQ model. The frequency range of dispersion is wider, and there is velocity dispersion almost in full-frequency band, which is consistent with the experimental data. The thermal relaxation model overcome the defects of Biot and BISQ model that the Biot attenuation and dispersion are rather small, and the frequency band of dispersion in BISQ model is narrow. The thermal relaxation model can analyze the velocity and attenuation variation with temperature, which could not be carried out for Biot and BISQ model.
In order to verify the applicability of the thermal relaxation model, the experimental study of a series of different fluid-saturated rocks is carried out in a higher frequency range, i.e.,1-1000Hz. The experimental data of velocity and attenuation for these saturated rocks are obtained. Variation of velocity and attenuation with frequency and temperature is similar to the low-frequency resonance experimental results, and is consistent with the thermal relaxation regularities. The thermal relaxation mechanism is extended to higher frequency band, and that verifies the universality of the thermal relaxation regularities. A "local thermal flux" mechanism is proposed to explain the thermal relaxation mechanism. An attenuation peak that is similar to phase transition peak was observed in the high temperature region. We use isomorphism to argue that this may be the phase transition peak. We found attenuation peak that has similar shifts with frequency as the Biot peak in the experimental results. Introducing a mechanism of "local fluid flow", the experimental data are well simulated numerally. The "local fluid flow" mechanism proposed a new attempt for understanding the Biot attenuation.
Attenuation in saturated porous rocks is closely related with the micro-and meso-scale structure of the rock samples. Thus we have introduced two rock mesostructure characteristic scales, corresponding to the "local thermal flux" and the "local fluid flow" mechanism, respectively. The characteristic frequencies are showed in general terms. Also ultrasound experiments for saturated porous rock are carried out to obtain the ultrasonic velocity and attenuation data for different fluid-saturated rocks. The experimental results obtained for different rock samples are quite different due to the small sample size. The small size of samples makes the interaction between the wave and the sample very complicated. We made some qualitative explanation for the experimental data.
The thermal relaxation model can predict strong attenuation as well as a wide range of velocity dispersion, which can well simulate the viscoelastic behavior of saturated porous rocks. The expansion of the low-frequency experiments has supplemented the relative lack of experimental data in the earthquake frequency band, and is of important significance to the interpretation and inversion of seismic data. These rock physics experiments contain research about the viscoelastic wave and physical properties of saturated rocks. The experimental techniques can be widely used for nondestructive testing techniques, damping and seismic studies.
引文
Adam L, Batzle ML, Lewallen KT.2009. Seismic wave attenuation in carbonates [J]. Journal of Geophysical Research,114(B6), B06208.
Adelinet M, Fortin J, Gueguen Y, et al.2010. Frequency and fluid effects on elastic properties of basalt:Experimental investigations [J]. Geophysical Research Letters,37, L02303.
Agersborg R, Jakobsen M, Ruud BO, et al.2007. Effects of pore fluid pressure on the seismic response of a fractured carbonate reservoir[J]. Studia Geophysica et Geodaetica,51(1): 89-118.
Aki K, Richards PG.1980. Quantitative seismology: Theory and methods[M]. Freeman and Co., San Francisco.
Allard JF.1993. Propagation of sound in porous media: Modelling sound absorbing materials[M]. Chapman&Hall.
Auriault JL, Boutin C.1994. Deformable porous media with double porosity III:Acoustics[J]. Transport in Porous Media,14(2):143-162.
Auriault JL, Boutin C, Royer P, et al.2002. Acoustics of a porous medium saturated by a bubbly fluid undergoing phase change[J]. Transport in Porous Media,46(1):43-76.
Ba J, Nie JX, Cao H, et al.2008. Mesoscopic fluid flow simulation in double-porosity rocks[J]. Geophysical Research Letters,35, L04303.
Bacri JC, Salin D.1986. Sound-velocity of a sandstone saturated with oil and brine at different concentrations [J]. Geophysical Research Letters,13:326-328.
Batzle ML, Han DH, Hofmann R.2006. Fluid mobility and frequency-dependent seismic velocity—Direct measurements [J]. Geophysics,71(1):N1-N9.
Bedford A, Stern M.1983. A model for wave propagation in gassy sediments[J], Journal of the Acoustical Society of America,73:409-417.
Berryman JG.1980a. Long-wavelength propagation in composite elastic media I. Spherical inclusions[J]. Journal of the Acoustical Society of America,68(6):1809-1819.
Berryman JG.1980b. Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions[J]. Journal of the Acoustical Society of America,68(6):1820-1831.
Berryman JG.2007. Seismic waves in rocks with fluids and fractures[J]. Geophysical Journal International,171:954-974.
Berryman JG, Thigpen L, Chin RCY.1988. Bulk elastic wave propagation in partially saturated porous solids[J]. Journal of the Acoustical Society ofAmerica,84:360-372.
Best A, McCann C.1995. Seismic attenuation and pore-fluid viscosity in clay-rich reservoir sandstones[J]. Geophysics,60:1386-1397.
Biot M A.1956a. Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low frequency range[J]. J Acoust Soc Am,28(2):168-178.
Biot M A.1956b. Theory of propagation of elastic waves in a fluid saturated porous solid. II. Hight frequency range [J]. J Acoust Soc Am,28(2):179-191.
Biot M A.1962. Mechanics of deformation and acoustic propagation in porous media[J]. J Appl Phys,33(4):1482-1498.
Borcherdt RD.2009. Viscoelastic waves in layered media[M]. Cambridge University Press.
Born WT.1941. The attenuation constant of earth materials[J]. Geophysics,6(2):132-148.
Bourbie T, Coussy O, Zinszner B.1987. Acoustics of porous media[M]. EditionsTECHNIP.
Brajanovski M, Gurevich B, Schoenberg M.2005. A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures[J]. Geophysical Journal International, 163(1):372-384.
Brajanovski M, Muller TM, Gurevich B.2006. Characteristic frequencies of seismic attenuation due to wave-induced fluid flow in fractured porous media[J]. Geophysical Journal International,166(2):574-578.
Brajanovski M, Muller TM, Parra JO.2010. A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir[J]. Science China Physics, Mechanics and Astronomy,53(8):1383-1387.
Brie AF, Pampuri AF, Marsala F, et al.1995. Shear sonic interpretation in gas-bearing sands[J]. Society of Petroleum Engineers Annual Technical Conference and Exhibition, paper 30595-MS.
Brown RJS, Korringa J.1975. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid[J]. Geophysics,40:608-616.
Cadoret T, Marion D, Zinszner B.1995. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones[J]. Journal of Geophysical Research,100: 9789-9803.
Cadoret T, Mavko G, Zinszner B.1998. Fluid distribution effect on sonic attenuation in partially saturated limestones[J]. Geophysics,63:154-160.
Cheng CHA.1978. Seismic velocities in porous rocks:Direct and inverse problems[D]:[Ph.D thesis]. MIT, Cambridge, MA.
Cheng CH.1993. Crack models for a transversely isotropic medium[J]. J Geophys Res,98(B1): 675-684.
Cheng YF, Yang DH, Yang HZ.2002. Biot/Squirt model in viscoelastic porous media[J]. Chinese Physics Letters,19(3):445-448.
Carcione JM.1998. Viscoelastic effective rheologies for modelling wave propagation in porous media[J]. Geophysical Prospecting,46:249-270.
Carcione JM.2001. Wave fields in real media: wave propagation in anisotropic, anelastic and porous media:Handbook of Geophysical Exploration[M]. Oxford, Pergamon Press,219-293.
Carcione JM.2007. Wave fields in real media: Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media[M].2nd ed. Elsevier Scientific Publ Co, Inc.
Carcione JM, Helle HB.1999. Numerical solution of the poroviscoelastic wave equation on a staggered mesh[J]. Journal of Computational Physics,154:520-527.
Carcione JM, Helle HB, Pham NH.2003. White's model for wave propagation in partially saturated rocks, comparison with poroelastic numerical experiments[J]. Geophysics,67: 1389-1398.
Carcione JM, Morency C, Santos JE.2010. Computational poroelasticity[J]. Geophysics,75(5): 75A229-75A243.
Carcione JM, Picotti S.2006. P-wave seismic attenuation by slow wave diffusion: Effects of inhomogeneous rock properties[J], Geophysics,71(3):01-08.
Carcione JM, Picotti S, Gei D, and et al.2006. Physics and seismic modeling for monitoring CO2 storage[J]. Pure and Applied Geophysics,163:175-207.
Cerveny V, Psencik I.2008. Quality factor Q in dissipative anisotropic media[J]. Geophysics, 73(4):T63-T75.
Chandler RN, Johnson DL.1981. The equivalence of quasistatic flow in fluid-saturated porous media and Biot's slow wave in the limit of zero frequency[J]. Journal ofApplied Physics,52: 3391-3395.
Chapman M.2003. Frequency dependent anisotropy due to mesoscale fractures in the presence of equant porosity[J]. Geophysical Prospecting,51:369-379.
Chapman M.2009. Modeling the effect of multiple fracture sets of mesoscale fractures in porous rock on frequency-dependent anisotropy[J]. Geophysics,74(6):D97-D103.
Chapman M, Zatsepin SV, Crampin S.2002. Derivation of a microstructural poroelastic model[J]. Geophysical Journal International,151:427-451.
Ciz R, Gurevich B.2005. Amplitude of Biot's slow wave scattered by a spherical inclusion in a fluid-saturated poroelastic medium [J]. Geophysical Journal International,160:991-1005.
Ciz R, Gurevich B, Markov M.2006. Seismic attenuation due to waveinduced fluid flow in a porous rock with spherical heterogeneities [J]. Geophysical Journal International,165: 957-968.
Clark RA, Benson PM, Carter AJ, et al.2009. Anisotropic P-wave attenuation measured from a multi-azimuth surface seismic reflection survey[J]. Geophysical Prospecting,57:835-845.
Commander KW, Prosperetti A.1989. Linear pressure waves in bubbly fluids:Comparison between theory and experiments [J]. Journal of the Acoustical Society of America,85: 732-746.
Crampin S.1984. Effective anisotropic elastic constants for wave propagation through cracked solids[J]. J Roy Astr Soc,76(1):135-145.
Das A, Batzle M.2010. Frequency dependent elastic properties and attenuation in heavy-oil sands: Comparison between measured and modeled data[C].2010 SEG Annual Meeting, Denver, Colorado.
Digby PJ.1981. The effective elastic moduli of porous granular rocks[J]. Journal ofApplied Mechanics,48(4):803-808.
Domenico SN.1976. Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir[J]. Geophysics,41(5):882-894.
Dutta NC, Ode H.1979a. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation(White model); Part I, Biot theory[J]. Geophysics, 44(11):1777-1788.
Dutta NC, Ode H.1979b. Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation(White model); Part II, Results[J]. Geophysics,44(11): 1789-1805.
Dutta NC, Seriff AJ.1979. On White's model of attenuation in rocks with partial gas saturation[J]. Geophysics,44(11):1806-1812.
Dvorkin J, Mavko G.2006. Modeling attenuation in reservoir and nonreservoir rock[J]. The Leading Edge,25(2):194-197.
Dvorkin J, Mavko G, Nur A.1995. Squirt flow in fully saturated rocks[J]. Geophysics,60(1): 97-107.
Dvorkin J, Nolen-Hoeksema R, Nur A.1994. The squirt-flow mechanism: Macroscopic description[J]. Geophysics,59(3):428-438.
Dvorkin J, Nur A.1993. Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms [J]. Geophysics,58(4):524-533.
Endres AL, Knight RJ.1997. Incorporating pore geometry and fluid pressure communication into modeling the elastic behavior of porous rocks[J]. Geophysics,62:106-117.
Eshelby JD.1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems[J]. Proc Roy Soc London, A241 (1226):376-396.
Frenkel J.1944. On the theory of seismic and seismoelectric phenomena in moist soil[J]. Journal of Physics—USSR,8:230-241.
Galvin RJ, Gurevich B.2007, Scattering of a longitudinal wave by a circular crack in a fluid-saturated porous medium[J]. International Journal of Solids and Structures,44: 7389-7398.
Galvin RJ, Gurevich B.2009. Effective properties of a poroelastic medium containing a distribution of aligned cracks[J]. Journal of Geophysical Research—Solid Earth,114, B07305.
Gassmann F.1951. Uber die elastizitt poroser medien[J]. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich,96(76):1-23.
Gelinsky S, Shapiro SA.1997. Dynamic-equivalent medium approach for thinly layered saturated sediments[J]. Geophysical Journal International,128:F1-F4.
Gelinsky S, Shapiro SA, Muller TM, et al.1998. Dynamic poroelasticity of thinly layered structures [J]. International Journal of Solids and Structures,35:4739-4752.
Gerner A, Saenger EH, Shapiro SA.2007. Attenuation of P-waves due to interlayer flow in hydrate-bearing sediments[J]. Journal of Geophysics and Engineering,4:394-403.
Gist GA.1994. Interpreting laboratory velocity measurements in partially gas-saturated rocks [J]. Geophysics,59:1100-1109.
Gregory, A. R.,1976, Fluid saturation effects on dynamic elastic properties of sedimentary rocks[J]. Geophysics,41:895-921.
Gueguen Y, Gavrilenko P, LeRavalec M.1996. Scales of rock permeability [J]. Surveys in Geophysics,17:245-263.
Gueguen Y, Palciauskas V.1994. Introduction to the physics of rocks[M]. Princeton University Press.
Gurevich B.2003. Elastic properties of saturated porous rocks with aligned fractures [J]. Journal ofApplied Geophysics,54:203-218.
Gurevich B, Brajanovski M, Galvin R, et al.2009a. P-wave dispersion and attenuation in fractured and porous reservoirs—Poroelasticity approach: Geophysical Prospecting,57:225-237.
Gurevich B, Galvin RJ, Brajanovski M, et al.2007. Fluid substitution, dispersion and attenuation in fractured and porous reservoirs—Insights from new rock physics models[J]. The Leading Edge,26:1162-1168.
Gurevich B, Lopatnikov SL.1995. Velocity and attenuation of elastic waves in finely layered porous rocks[J]. Geophysical Journal International,121:933-947.
Gurevich B, Makarynska D, Pervukhina M.2009b, Ultrasonic moduli for fluid-saturated rocks: Mavko-Jizba relations rederived and generalized[J]. Geophysics,74(4):N25-N30.
Gurevich B, Makarynska D, Pervukhina M.2009c. A new squirt-flow model of elastic wave attenuation and dispersion in fluid-saturated rocks[C]. Proceedings of 4th Biot Conference on Poromechanics,700-705.
Gurevich B, Sadovnichaja AP, Lopatnikov SL, et al.1998. Scattering of a compressional wave in a poroelastic medium by an ellipsoidal inclusion[J]. Geophysical Journal International,133: 91-103.
Gurevich B, Zyrianov VB, Lopatnikov SL.1997. Seismic attenuation in finely layered porous rocks:Effects of fluid flow and scattering[J]. Geophysics,62:319-324.
Helle HB, Pham NH, Carcione JM.2003. Velocity and attenuation in partially saturated rock: Poroelastic numerical experiments [J]. Geophysical Prospecting,51:551-566.
Hill R.1952. The elastic behavior of crystalline aggregate[J]. Proc Physical Soc A,65(5): 349-354.
Hill R.1963. Elastic properties of reinforced solids:Some theoretical principles[J]. Journal of Mechanics and Physics of Solids,11:357-72.
Hudson JA.1980. Overall properties of a cracked solid[J]. Math Proc Cambridge Phil Soc,88: 371-384.
Hudson JA.1981. Wave speeds and attenuation of elastic waves in materiral containing cracks [J]. Geophys J Roy Astron Soc,64(1):133-150.
Hudson JA.1990. Overall elastic properties of isotropic materials with arbitrary distribution of circular cracks[J]. Geophys J Int,102(2):465-469.
Hudson JA, Liu E, Crampin S.1996. The mechanical properties of materials with interconnected cracks and pores [J]. Geophysical Journal International,124:105-112.
Hudson JA, Pointer T, Liu E.2001. Effective-medium theories for fluid-saturated materials with aligned cracks[J]. Geophysical Prospecting,49:509-522.
Hughes DS, Kelly JL.1952. Variation of elastic wave velocity with saturation in sandstone[J]. Geophysics,17:739-752.
Jakobsen M.2004. The interacting inclusion model of wave-induced fluid flow[J]. Geophysical Journal International,158:1168-1176.
Jakobsen M, Chapman M.2009. Unified theory of global flow and squirt flow in cracked porous media[J]. Geophysics,74(2):WA65-WA76.
Jakobsen M, Johansen TA, McCann C.2003. The acoustic signature of fluid flow in complex porous media[J]. Journal ofApplied Geophysics,54:219-246.
Jaquin CH.1964. Correlation entre la permeabilite et les caracteristiques geometriques du gres de Fontainebleau[J]. Rev Inst Franc du Petrole, XIX:921-937.
Johansen TA, Jakobsen M, Ruud BO.2002. Estimation of the internal structure and anisotropy of shales from borehole data[J]. J Seism Explor,11(4):363-381.
Johnson DL.2001. Theory of frequency dependent acoustics in patchy saturated porous media[J]. Journal of the Acoustical Society of America,110:682-694.
Johnson DL, Koplik J, Dashen R.1987. Theory of dynamic permeability and tortuosity in fluid-saturated porous media[J]. Journal of Fluid Mechanics,176:379-402.
Johnston DH, Toksoz NM, Timur A.1979. Attenuation of seismic waves in dry and saturated rocks:II. Mechanisms [J]. Geophysics,44:691-711.
Jones TD.1986. Pore fluids and frequency-dependent wave propagation in rocks[J]. Geophysics, 51:1939-1953.
Karal FC, Keller JB.1964. Elastic, electromagnetic and other waves in random media[J]. Journal of Mathematical Physics,5:537-547.
Kan TK, Batzle ML, Gaiser JE.1983. Attenuation measured from VSP:Evidence of frequency-dependent Q[J]. Soc Expl Geophys Expanded Abstracts,2:589-590.
King MS.2005. Rock-physics developments in seismic exploration: a personal 50-year perspective[J]. Geophysics,70(6):3-8.
King MS.2009. Recent developments in seismic rock physics[J]. International Journal of Rock Mechanics and Mining Sciences,46:1341-1348.
King MS, Marsden JR, Dennis JW.2000. Biot dispersion for P- and S-wave velocities in partially and fully saturated sandstones [J]. Geophysical Prospecting,48:1075-1089.
Kirstetter O, Corbett P, Somerville J.2006. Elasticity/saturation relationships using flow simulation from an outcrop analogue for 4D seismic modelling[J]. Petroleum Geoscience,12: 205-219.
Kjartansson E.1979. Constant Q—Wave propagation and attenuation[J]. Journal of Geophysical Research,84:4737-4748.
Kjartansson E.1980. Attenuation of seismic waves in rocks and application in energy exploration[D]:[Ph.D thesis]. Standord University.
Klimentos T, McCann C.1990. Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones [J]. Geophysics,55:998-1014.
Knight R, Dvorkin J, Nur A.1998. Acoustic signatures of partial saturation[J]。 Geophysics,63; 132-138.
Knight R, Nolen-Hoeksema R.1990. A laboratory study of the dependence of elastic wave velocities on pore scale fluid distribution[J]. Geophysical Research Letters,17:1529-1532.
Koh YK, Cahill DG.2007. Frequency dependence of the thermal conductivity of semiconductor alloys[J]. Physical Review B,76,075207.
Konishi C, Azuma H, Nobuoka D, et al.2009. Quantitative CO2 saturation estimation from P-wave velocity changes by considering patchy saturation[C]. SEG Summer Research Workshop, Banff, Canada.
Krzikalla F, Miiller TM, Hardy B, et al.2006. Seismic wave attenuation and dispersion in patchy-saturated rocks:Numerical experiments[C].68th Conference & Technical Exhibition, EAGE, Extended Abstracts, E038.
Lambert G, Gurevich B, Brajanovski M.2006. Attenuation and dispersion of P-waves in porous rocks with planar fractures:Comparison of theory and numerical simulation[J]. Geophysics, 71(3):N41-N45.
Lebedev M, Gurevich B, Toms J, et al.2009a, Laboratory observation of velocity-saturation relation transition during water imbibition of porous rock[M].4th Biot Conference on Poromechanics, Abstracts,941-946.
Lebedev M, Toms-Stewart J, Clennell B, et al.2009b. Direct laboratory observation of patchy saturation and its effects on ultrasonic velocities[J]. The Leading Edge,28(1):24-27.
Lee MW, Collett TS.2009. Unique problems associated with seismic analysis of partially gas-saturated unconsolidated sediments[J]. Marine and Petroleum Geology,26:775-781.
Lei X, Xue Z.2009. Ultrasonic velocity and attenuation during CO2 injection into water-saturated porous sandstone: Measurements using difference seismic tomography[J]. Physics of the Earth and Planetary Interiors,176:224-234.
le Ravalec M, Gueguen Y, Chelidze T.1996. Elastic wave velocities in partially saturated rocks: Saturation hysteresis [J]. Journal of Geophysical Research,101(B1):837-844.
Li X, Zhong L, Pyrak-Nolte LJ.2001. Physics of partially saturated porous media: Residual saturation and seismic-wave propagation [J]. Annual Review of Earth and Planetary Sciences, 29:419-460.
Liu E, Chapman M, Varela I, et al.2007. Velocity and attenuation anisotropy:Implication of seismic fracture characterizations[J]. The Leading Edge,26:1170-1174.
Liu E, Queen JH, Li XY, et al.2003. Observation and analysis of frequency-dependent anisotropy from a multicomponent VSP at Bluebell-Altamont field, Utah[J]. Journal of Applied Geophysics,54:319-333.
Liu J, Ba J, Ma JW, et al.2010. An analysis of seismic attenuation in random porous media[J]. Science China Physics, Mechanics & Astronomy,53:628-637.
Liu J, Yamada H, Kozaki T, et al.2003. Effect of silica sand on activation energy for diffusion of sodium ions in montmorillonite and silica sand mixture[J]. J Constam Hydrol,61(1-4): 85-93.
Liu X, Greenhalgh S, Zhou B.2009. Transient solution for poro-viscoacoustic wave propagation in double porosity media and its limitations [J]. Geophysical Journal International,178: 375-393.
Lo WC, Sposito G, Majer E.2005. Wave propagation through elastic porous media containing two immiscible fluids[J]. Water Resources Research,41, W02025.
Lopatnikov SL, Gorbachev PY.1987. Propagation and attenuation of longitudinal waves in a partially gas-saturated porous media[J]. Izvestiya Earth Physics,23:683-689.
Lopatnikov SL, Gurevich B.1986. Attenuation of elastic waves in a randomly inhomogeneous saturated porous medium[J]. Doklady Earth Science Section,291(6):19-22.
Mandelis A.2000. Diffusion waves and their uses[J]. PhysicsToday,53(8):29-34.
Makse HA, Gland N, Johnson DL, Schwartz LM.1999. Why effective medium theory fails in granular materials[J]. Phys Rev Lett,83(24):5070-5073.
Markov MG, Yumatov AY.1988. Acoustic properties of a porous laminated medium[J]. Journal of Applied Mechanics and Technical Physics,29:107-111.
MassonYJ, Pride SR.2007. Poroelastic finite difference modeling of seismic attenuation and dispersion due to mesoscopic-scale heterogeneity[J]. Journal of Geophysical Research,112, B03204.
Masson YJ, Pride SR, Nihei KT.2006. Finite difference modelling of Biot's poroelastic equations at seismic frequencies [J]. Journal of Geophysical Research,111, B10305.
Maultzsch S, Chapman M, Liu E, et al.2003. Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures:Implication of fracture size estimation from anisotropic measurements [J]. Geophysical Prospecting,51:381-392.
Maultzsch S, Chapman M, Liu E, et al.2007. Modelling and analysis of attenuation anisotropy in multi-azimuth VSP data from the Clair field[J]. Geophysical Prospecting,55:627-642.
Mavko G.1980. Velocity and attenuation in partially molten rocks[J]. J Geophys Res,85(B10): 5173-5189.
Mavko G, Jizba D.1991. Estimating grain-scale fluid effects on velocity dispersion in rocks[J]. Geophysics,56(12):1940-1949.
Mavko G, Jizba D.1994. The relation between seismic P-and S-wave velocity dispersion in saturated rocks[J]. Geophysics,59:87-92.
Mavko G, Mukerji T.1998. Bounds on low frequency seismic velocities in partially saturated rocks[J]. Geophysics,63:918-924.
Mavko G, Mukerji T, Dvorkin J.2009. The rock physics handbook[M].2nd ed. Cambridge University Press.
Mavko G, Nolen-Hoeksema R.1994. Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks[J]. Geophysics,59:252-258.
Mavko G, Nur A.1975. Melt squirt in the aesthenosphere[J]. Journal of Geophysical Research, 80(11):1444-1448.
Mavko G, Nur A.1978. The effect of nonelliptical cracks on the compressibility of rocks[J]. Journal of Geophysical Research,83(B9):4459-4468.
Mavko G, Nur A.1979. Wave propagation in partially saturated rocks[J]. Geophysics,44: 161-178.
Mayr SI, Burkhardt H.2006. Ultrasonic properties of sedimentary rocks:Effect of pressure, saturation, frequency and microcracks[J]. Geophysical Journal International,164:246-258.
Meissner R.1983. Attenuation of seismic waves in sediments[C]. Proceedings of the 11th World Petroleum Congress, London:363-381.
Milton GW.2002. The theory of composites[M]. Cambridge University Press.
Mindlin RD.1949. Compliance of elastic bodies in contact[J]. J Appl Mech,16:259-268.
Monsen K, Johnstad SE.2005. Improved understanding of velocity saturation relationships using 4D computer-tomography acoustic measurements [J]. Geophysical Prospecting,53:173-181.
Muller TM, Gurevich B.2004. One-dimensional random patchy saturation model for velocity and attenuation in porous rocks[J]. Geophysics,69:1166-1172.
Muller TM, Gurevich B.2005a. A first-order statistical smoothing approximation for the coherent wave field in random porous media[J]. Journal of the Acoustical Society ofAmerica,117: 1795-1805.
Muller TM, Gurevich B.2005b. Wave induced fluid flow in random porous media:Attenuation and dispersion of elastic waves[J]. Journal of theAcoustical Society ofAmerica,117: 2732-2741.
Muller TM, Gurevich B, Shapiro SA.2008a. Attenuation of seismic waves due to wave-induced flow and scattering in random porous media[C]. In Sato H, and Fehler M, eds, Earth heterogeneity and scattering effects on seismic waves. Elsevier Scientific Publ Co, Inc, 123-166.
Muller TM, Lambert G, Gurevich B.2007. Dynamic permeability of porous rocks and its seismic signatures[J]. Geophysics,72(5):E149-E158.
Muller TM, Rothert E.2006. Seismic attenuation due to wave-induced flow: Why Q scales differently in random structures[J]. Geophysical Research Letters,33, L16305.
Muller TM, Toms-Stewart J, Wenzlau F.2008b. Velocity-saturation relation for partially saturated rocks with fractal pore fluid distribution [J]. Geophysical Research Letters,26, L09306.
Murphy WE 1982. Effects of partial water saturation on attenuation in Massilon sandstone andVycor porous glass[J]. Journal of the Acoustical Society ofAmerica,71:1458-1468.
Murphy WE 1984. Acoustic measures of partial gas saturation in tight sandstones [J]. Journal of Geophysical Research,89(B13):11549-11559.
Murphy WF, Roberts JN, Yale D, et al.1984. Centimeter scale heterogeneities and microstratification in sedimentary rocks[J]. Geophysical Research Letters,11:697-700.
Murphy WF, Winkler KW, Kleinberg RL.1986. Acoustic relaxation in sedimentary rocks: Dependence on grain contacts and fluid saturation [J]. Geophysics,51:757-766.
Nelson RA.2001. Geological analysis of naturally fractured reservoirs[M].2nd ed. Gulf Publ Co.
Norris AN.1993. Low-frequency dispersion and attenuation in partially saturated rocks [J]. Journal of the Acoustical Society of America,94:359-370.
Norris AN, Johnson DL.1997. Nonlinear elasticity of granular media[J]. J Appl Mech,64(1): 39-49.
O'Connell RJ, Budiansky B.1974. Seismic velocities in dry and saturated cracked solids[J]. Journal of Geophysical Research,79:5412-5426.
O'Connell RJ, Budiansky B.1977. Viscoelastic properties of fluid-saturated cracked solids[J]. Journal of Geophysical Research,82:5719-5740.
Paffenholz J, Burkhardt H.1989. Absorption and modulus measurements in the seismic frequency and strain range on partially saturated sedimentary rocks[J]. Journal of Geophysical Research—Solid Earth,94:9493-9507.
Palmer ID, Traviolia ML.1980. Attenuation by squirt flow in undersaturated gas sands[J]. Geophysics,45:1780-1792.
Parra JO.2000. Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy[J]. Geophysics,65:202-210.
Picotti S, Carcione JM, Rubino JG, et al.2007. P-wave seismic attenuation by slow-wave diffusion: Numerical experiments in partially saturated rocks[J]. Geophysics,72(4):N11-N21.
Picotti S, Carcione JM, Rubino JG, et al.2010. A visoelastic representation of wave attenuation in porous media[J]. Computers and Geosciences,36:44-53.
Pride SR.2005. Relationships between seismic and hydrological properties [J]. Hydrogeophysics, 50:253-290.
Pride SR, Berryman JG.2003a. Linear dynamics of double-porosity and dual-permeability materials. Ⅰ. Governing equations and acoustic attenuation[J]. Physical Review E,68, 036603.
Pride SR, Berryman JG.2003b. Linear dynamics of double-porosity and dual-permeability materials. Ⅱ. Fluid transport equations[J]. Physical Review E,68,036604.
Pride SR, Berryman JG, Harris JM.2004. Seismic attenuation due to wave induced flow[J]. Journal of Geophysical Research,109(B1), B01201.
Pride SR, Harris JH, Johnson DL, et al.2003. Permeability dependence of seismic amplitudes[J]. The Leading Edge,22:518-525.
Pride SR, Masson YJ.2006. Acoustic attenuation in self-affine porous structures [J]. Physical Review Letters,97,184301.
Pride SR, Morgan FD, Gangi AF.1993. Drag forces of porous medium acoustics[J]. Physical Review B,47:4964-4978.
Pride SR, Tromeur E, Berryman JG.2002. Biot slow-wave effects in stratified rock[J]. Geophysics, 67:271-281.
Pyrak-Nolte LJ, Myer LR, Nicoletis S.1990a. Transmission of seismic waves across single natural fractures[J]. Journal of Geophysical Research,95(B6):8617-8638.
Pyrak-Nolte LJ, Myer LR, Nicoletis S.1990b. Anisotropy in seismic velocities and amplitudes from multiple parallel fractures[J]. Journal of Geophysical Research,95(B7):11345-11358.
Quintal B, Schmalholz SM, Podladchikov YY.2009. Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow[J]. Geophysics,74(1):N14-N22.
Rasolofosaon PNJ.2009. Unified phenomenological model for the mechanical behavior of rocks[J]. Geophysics,74(5):WB107-WB116.
Ren H, Goloshubin G, Hilterman FJ.2009. Poroelastic analysis of amplitude-versus-frequency variations[J]. Geophysics,74(6):N41-N48.
Reuss A.1929. Berechnung der Flieβgrenze von Mischkristallen auf Grund der Plastizitatsbedingung fur Einkristalle[J]. Zeitschrift fur Angewandte Mathematik und Mechanik,9(1):49-58.
Rice JR., Cleary MP. 1976. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents [J]. Reviews of Geophysics and Space Physics,14: 227-241.
Rubino JG, Ravazzoli CL, Santos JE.2009. Equivalent viscoelastic solids for heterogeneous fluid-saturated porous rocks [J]. Geophysics,74(1):N1-N13.
Rubino JG, Santos JE, Picotti S, et al.2007. Simulation of upscaling effects due to wave-induced fluid flow in Biot media using the finite-element method[J]. Journal ofApplied Geophysics, 62:193-203.
Rudnicki JW.1986. Fluid mass sources and point forces in linear elastic diffusive solidspJ]. Mechanics of Materials,5:383-393.
Rytov SM, Kravtsov YA, Tatarskii VI.1989. Wave propagation through random media[M]. Springer-Verlag, Berlin.
Sams MS, Neep JP, Worthington MH.1997. The measurement of velocity dispersion and frequency-dependent intrinsic attenuation in sedimentary rocks [J]. Geophysics,62: 1456-1464.
Santos JE, Douglas J, Corbero J, et al.1990. A model for wave propagation in a porous medium saturated by a two-phase fluid[J]. Journal of the Acoustical Society of America,87: 1439-1448.
Sayers CM, Kachanov M.1995. Microcrack-induced elastic wave anisotropy of brittle rocks[J]. Journal of Geophysical Research, B100:4149-4156.
Schmidt H, Tango G.1986. Efficient global matrix approach to the computation of synthetic seismograms[J]. Geophysical Journal of the Royal Astronomical Society,84:331-359.
Schoenberg M.1980. Elastic wave behavior across linear slip interfaces [J]. Journal of the Acoustical Society of Am erica,68:1516-1521.
Schoenberg M.1983. Reflection of elastic waves from periodically stratified media with interfacial slip[J]. Geophys Prospecting,31(2):265-292.
Schoenberg M, Sayers CM.1995. Seismic anisotropy of fractured rock[J]. Geophysics,60: 204-211.
Sengupta M, Mavko G, Mukerji T.2003. Quantifying subresolution saturation scales from time-lapse seismic data:A reservoir monitoring case study[J]. Geophysics,68:803-814.
Shapiro SA.2003, Elastic piezosensitivity of porous and fractured rocks[J]. Geophysics,68: 482-486.
Shapiro SA, Muller TM.1999. Seismic signatures of permeability in heterogeneous porous media[J]. Geophysics,64:99-103.
Shapiro SA, Rothert E, Rath V, et al.2002. Characterization of fluid transport properties of reservoirs using induced microseismicity[J]. Geophysics,67:212-220.
Smeulders DMJ, van Dongen MEH.1997. Wave propagation in porous media containing a dilute gas-liquid mixture: Theory and experiments [J]. Journal of Fluid Mechanics,343:351-373.
Smith TM, Sondergeld CH, Rai CS.2003. Gassmann fluid substitutions:Atutorial[J]. Geophysics, 68:430-440.
Spencer JW.1981. Stress relaxations at low frequencies in fluid-saturated rocks:Attenuation and modulus dispersion [J]. Journal of Geophysical Research,86:1803-1812.
Stoll RD, Bryan GM.1970. Wave attenuation in saturared sediments[J]. J Acoust Soc Am,47(5B): 1440-1447.
Taylor SR, Knight RJ.2003. An inclusion-based model of elastic wave velocities incorporating patch-scale fluid pressure relaxation [J]. Geophysics,68:1503-1509.
Thomsen L.1995. Elastic anisotropy due to aligned cracks in porous rock[J]. Geophysical Prospecting,43:805-829.
Timmerman EH.1982. Practical reservoir engineering[M]. Pennwell Pub.
Toksoz MN, Johnston DH, Timur A.1979. Attenuation of seismic waves in dry and saturated rocks:I. Laboratory measurements [J]. Geophysics,44:681-690.
Toms J.2008. Effect of fluid distribution on compressional wave propagation in partially saturated rocks[D]:[Ph.D dissertation]. Curtin University of Technology.
Toms J, Muller TM, Ciz R, et al.2006a. Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks[J]. Soil Dynamics and Earthquake Engineering,26:548-565.
Toms J, Muller TM, Gurevich B.2007. Seismic attenuation in porous rocks with random patchy saturation[J]. Geophysical Prospecting,55:671-678.
Toms J, Muller TM, Gurevich B, et al.2006b. Attenuation and dispersion in partially saturated rock:Random vs periodic models[M].68th Conference&Technical Exhibition, EAGE, Extendend Abstracts, E039.
Toms-Stewart J, Muller TM, Gurevich B, et al.2009. Statistical characterization of gas-patch distributions in partially saturated rocks [J]. Geophysics,74(2):WA51-WA64.
Tserkovnyak Y, Johnson DL.2001. Can one hear the shape of a saturation patch[J]. Geophysical Research Letters,29:1108-1112.
Tserkovnyak Y, Johnson DL.2003. Capillary forces in the acoustics of patchy-saturated porous media[J]. Journal of the Acoustical Society ofAmerica,114:2596-2606.
Voigt W.1910. Lehrbuch der Kristallphysik[M]. Leipzig:Teubner.
Walsh JB.1965. The effect of cracks on the compressibility of rock[J]. Journal of Geophysical Research,70:381-389.
Walsh JB.1995. Seismic attenuation in partially saturated rock[J]. Journal of Geophysical Research—Solid Earth,100:15407-15424.
Walton K.1987. The effective elastic moduli of a random packing of spheres[J]. J Mech Phys Solids,35(2):213-226.
Wang Z.2001. Fundamentals of seismic rock physics[J]. Geophysics,66(2):398-412.
Waterman PC, Truell R.1961. Multiple scattering of waves[J]. Journal of Mathematical Physics,2: 512-537.
Wei CF, Muraleetharan KK.2006. Acoustical characterization of fluid-saturated porous media with local heterogeneities: Theory and application[J]. International Journal of Solids and Structures,43:982-1008.
Wenzlau F, Altmann JB, Muller TM.2010. Anisotropic dispersion and attenuation due to wave-induced fluid flow: Quasi-static finite-element modeling in poroelastic solids[J]. Journal of Geophysical Research,115, B02074.
Wenzlau F, Muller TM.2009. Finite-difference modeling of wave propagation and diffusion in poroelastic media[J]. Geophysics,74(4):T55-T66.
White JE.1975. Computed seismic speeds and attenuation in rocks with partial gas saturation[J]. Geophysics,40:224-232.
White JE.1986. Underground sound: Applications of seismic waves[J]. Elsevier Scientific Publ. Co., Inc.
White JE, Mikhaylova NG, Lyakhovitskiy FM.1976. Low-frequency seismic waves in fluid-saturated layered rocks[J]. Physics of the Solid Earth,11:654-659.
Winkler K.1983. Contact stiffness in granular porous materials:Comparison between theory and experimen[J]. Geophysical Research Letters,10:1073-1076.
Winkler K.1985. Dispersion analysis of velocity and attenuation in Berea sandstone[J]. Journal of Geophysical Research,90:6793-6800.
Winkler K, Nur A.1982. Seismic attenuation—Effects of pore fluids and frictional sliding[J]. Geophysics,47:1-15.
Wood AB.1941. Atextbook of sound[M]. Bell.
Wulff AM, Burkhardt H.1997. Mechanisms affecting ultrasonic wave propagation in fluid-containing sandstones under high hydrostatic pressure[J]. Journal of Geophysical Research,102B:3043-3050.
Wyllie MRJ, Gregory AR, Gardner LW.1956. Elastic wave velocities in heterogeneous and porous media[J]. Geophysics,21:41-70.
Xi DY. Liu XY, Zhang C Y.2007. The frequency(or time)-temperature equivalence of relaxation in saturated rocks[J]. Pure Appl Geophys,164(11):2157-2173.
Xi DY, Xu Songlin, Du Yun, et al.2011. Wave propatation analysis of porous rocks with thermal activated relaxation mechanism[J]. Journal of Applied Geophysics,73(3):289-303.
Yang DH, Zhang ZJ.2000. Effects of the Biot and the Squirt-flow coupling interaction onanisotropic elastic waves[J]. Chinese Science Bulletin,45(23):2130-2138.
Yang DH, Zhang ZJ.2002. Poroelastic wave equation including the Biot/Squirt mechanism and the solid/fluid coupling anisotropy[J]. Wave Motion,35(3):223-245.
Yang KD, Yang DH, Wang S Q.2002. Numerical simulation of elastic wave propagation based on the transversely isotropic BISQ equation[J]. ACTA Seismologica Sinica,15(6):628-635.
Yin CS, Batzle ML, Smith BJ.1992. Effects of partial liquid gas saturation on extensional wave attenuation in Berea sandstone[J]. Geophysical Research Letters,19:1399-1402.
Zeller R, Dederich PH.1973. Elastic constants of polycrystals[J]. Physica Status SolidiB—Basic Research,55:831-842.
Zener C.1948. Elasticity and anelasticity of metals[M]. University of Chicago Press.
Zhang HL, Wu XS, Chen CS, et al.2005. Excess oxygen ordering in the La2NiO4+δ system studie by low-frequency internal friction[J]. Physical Review B,71,064422.
Zhu Y, Tsvankin I.2006. Plane-wave propagation in attenuative transversely isotropic media[J]. Geophysics,71(2):T17-T30.
巴晶.2008.复杂多孔介质中的地震波传播机理研究[D]：[博士论文].清华大学.
陈颙,黄庭芳.2001.岩石物理学[M].北京：北京大学出版社.
杜贇,席道瑛,徐松林,等.2009.多孔岩石波传播的热激活弛豫模型修正[J].地球物理学报,52(12)：3051-3060.
葛瑞·马沃可,塔潘·木克基,杰克·德沃金,编著.2008.岩石物理手册：孔隙介质中地震分析工具[M].徐海滨,戴建春,翻译.合肥：中国科学技术大学出版社.
葛庭燧.2000.固体内耗理论基础[M].北京：科学出版社。
李维新,史謌,王红等.2007.岩石物理弹性参数规律研究[J].地球物理学进展,22(5)：1380-1385.
刘浩杰.2009.地震岩石物理研究综述[J].油气地球物理,3：1-8.
刘小燕.2006.二氧化碳深含水层隔离的二相渗流模拟与岩石物理学研究[D]：[博士论文].中国科学技术大学.
马淑芬,韩大匡,甘利灯,等.2010.地震岩石物理模型综述[J].地球物理学进展,25(2)：460-471.
马中高,周巍,孙成龙.2006.地震岩石物理分析软件系统设计和实现[J].物探与化探,30(3)：260-265.
谭启,席道瑛,周光泉,等.1995.花岗岩的低频内耗研究[J].科大学报,25(3)：368-372.
唐建伟.2008.地震岩石物理学研究有关问题的探讨[J].石油物探,47(4)：398-404.
王炳章.2008.地震岩石物理学及其应用研究[D]：[博士论文].成都理工大学.
王炳章,朱晔,王丹.2008.多孔介质的流体机制模型极其频散机理[J].勘探地球物理进展, 31(6)：405-413.
席道瑛,陈运平,陶月赞,等.2006.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,25(6)：1086-1093.
席道瑛,程经毅,易良坤,等.1999.饱和砂岩中衰减、模量和速度的流体效应[J].石油物探,38(3)：43-49.
席道瑛,杜赞,席军,等.2011a.饱和砂岩在疲劳载荷作用下的粘弹性性质[J].岩石力学与工程学报,30(5)：865-870.
席道瑛,杜赞,薛彦伟,等.2007.岩石非线性细观响应中温度对岩石力学性能的影响[J].岩石力学与工程学报,26(增1)：3342-3347.
席道瑛,刘斌,刘卫,等.2000a.饱和多孔岩石弛豫衰减对时间和温度的依赖性[J].地球物理学报,43(6)：827-834.
席道瑛,刘斌,田象燕.2002.饱和岩石的各向异性及非线性粘弹性响应[J].地球物理学报,45(1)：109-118。
席道瑛,刘斌,谢端,等.1998.孔隙流体饱和砂岩的衰减与频率的相关性[J].石油地球物理勘探,33(1)：66-77.
席道瑛,徐松林.2012.岩石物理学基础[M].合肥：中国科学技术大学出版社.
席道瑛,徐松林,席军,等.2011b.饱和砂岩的粘弹行为的实验研究[J].地球物理学报,54(9)：2302-2308.
席道瑛,徐松林,杜贇.2012.泵油饱和砂岩的粘弹行为的实验研究[J].物理学报,61(11),119102.
席道瑛,易良坤,田象燕.2003Biot理论的唯象修正对S波持性的影响[J].地球物理学报,46(6)：814-820.
席道瑛,易良坤,张程远.2004Biot理论的唯象修正对P波特性的影响[J].岩石力学与工程学报,23(18)：3162-3167.
席道瑛,张程远,刘小燕,等.2000b.饱和岩石的时温等效关系[J].物探化探计算技术,22(2)：127-131.
席军,杜贇,徐松林,等.2011.饱和岩石滞弹性弛豫机理的实验研究[J].实验力学,26(3)：316-321.
徐胜峰,李勇根,曹宏,等.2009.地震岩石物理研究概述[J].地球物理学进展,24(2)：680-691.
徐松林,席道瑛,唐志平.2005.短脉冲激光与岩石相互作用机理初探[J].石力学与工程学报,24(增Ⅰ)：4694-4699.
薛彦伟,席道瑛,徐松林.2005.岩石非经典非线性频率效应的细观研究[J].岩石力学与工程学报,24(增I)：5020-5025.
杨顶辉.1998.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：石油大学.
杨宽德,杨顶辉,王书强.2002.基于Biot-Squirt方程的波场模拟[J].地球物理学报,45(6)：853-861.
杨宽德,杨顶辉,王书强.2002.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探,37(5)：463-468.
易良坤,席道瑛,刘小燕.2003.孔隙介质热激活弛豫波动理论[J].岩石力学与工程学报,22(5)：803-809.