基于岩石声弹理论的波速-静水围压关系耦合模型
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摘要
岩石的波速与静水围压的关系研究对于深部地球物质的判定、地壳应力评估等相关研究具有极其重要的意义.目前许多研究者基于静水围压作用下岩石超声波波速实验数据,仅从数学统计上考虑提出了不同的岩石波速-静水围压的关系模型,并且P波和S波的波速-静水围压统计关系互相不耦合.本文基于岩石声弹理论角度出发,给出岩石P波和S波波速-静水围压关系的耦合模型.其次,基于统计关系的非耦合模型和本文提出的耦合模型,对一系列岩石样本的P波和S波超声波波速-静水围压实验数据进行回归分析.最后,本文通过与非耦合模型的统计结果的对比分析,得出耦合模型相对于非耦合模型来说,不仅物理意义明确,而且更具有统计学意义.
Velocity changes in rocks subjected to hydrostatic confining pressure are of great importance for material determination in deep earth and crustal-stress assessment. At present, many statistical models based on the measured rock ultrasonic wave velocities in rock samples under hydrostatic confining pressure have been proposed, whose are lack of reasonable physical interpretation and the uncoupled statistical relation for P and S waves. In this paper, based on acoustoelastic theory of rocks, coupled model for P-and S-wave velocity changes in rocks subjected to hydrostatic confining pressure is firstly presented. Secondly, regression analysis for a series of the measured rock ultrasonic wave velocities in rock samples under hydrostatic confining pressure are conducted based on coupled and uncoupled model. Finally, the result comparison between coupled model and uncoupled model shows that the present coupled model not only has clear physical significance but also has more statistical significance than uncoupled model.
Velocity changes in rocks subjected to hydrostatic confining pressure are of great importance for material determination in deep earth and crustal-stress assessment. At present, many statistical models based on the measured rock ultrasonic wave velocities in rock samples under hydrostatic confining pressure have been proposed, whose are lack of reasonable physical interpretation and the uncoupled statistical relation for P and S waves. In this paper, based on acoustoelastic theory of rocks, coupled model for P-and S-wave velocity changes in rocks subjected to hydrostatic confining pressure is firstly presented. Secondly, regression analysis for a series of the measured rock ultrasonic wave velocities in rock samples under hydrostatic confining pressure are conducted based on coupled and uncoupled model. Finally, the result comparison between coupled model and uncoupled model shows that the present coupled model not only has clear physical significance but also has more statistical significance than uncoupled model.
引文
Bates D M, Watts D G. 1988. Nonlinear regression analysis and its applications [M]. New York: John wiley & sons, inc.
Bridgman P W. 1922. The compressibility of metals at high pressures [J]. Proceedings of the National Academy of Sciences of the United States of America, 8(12): 361-365, doi: 10.2307/84446.
Chen Z, Du J G, Zhou W G, et al. 2009. Wave velocity and attenuation characteristics of gabbro at 100～300 ℃ and 0.5～4.0 GPa [J]. Chinese Journal of High Pressure Physics (in Chinese), 23(5): 338-344, doi: 10.3969/j.issn.1000-5773.2009.05.004.
Cheng X, Niu F L,Wang B S. 2010. Coseismic velocity change in the rupture zone of the 2008 MW 7.9 Wenchuan earthquake observed from ambient seismic noise [J]. Bulletin of the Seismological Society of America, 100(5B): 2539-2550, doi: 10.1785/0120090329.
Freund D. 1992. Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity, clay content, and confining Pressure [J]. Geophysical Journal International, 108(1): 125-135, doi: 10.1111/j.1365-246X.1992.tb00843.x.
Ge H K, Chen Y, Han D H. 2001. The effect of effective stress on rock elastic wave velocities [J]. Chinese Journal of Geophysics (in Chinese), 44(z1): 152-160, doi: 10.3321/j.issn:0001-5733.2001.z1.019.
Greenfield R J, Graham E K. 1996. Application of a simple relation for describing wave velocity as a function of pressure in rocks containing microcracks [J]. Journal of Geophysical Research: Solid Earth, 101(B3): 5643-5652, doi: 10.1029/95JB03462.
Guo B B, Wang H C, Zhao W H, et al. 2014. Analysis of seismic anisotropy of slate and its application of slate [J]. Chinese Journal of Geophysics (in Chinese), 57(3): 837-846, doi: 10.6038/cjg20140313.
Huang C X,Song D W. 1991. Study on elastic wave velocity of rock under confining pressure [J]. Chinese Journal of Geotechnical Engineering (in Chinese), 13(2): 32- 41, doi: 10.3321/j.issn:1000- 4548.1991.02.004.
Huang X J, Burns D R, Toksoz M N. 2001. The effect of stresses on the sound velocity in rocks: theory of acoustoelasticity and experimental measurements [R]. Massachusetts Institute of Technology Earth Resources Laboratory.
Ji S C. 1997. Fracturing of garnet crystals in anisotropic metamorphic rocks during uplift: reply [J]. Journal of Structural Geology, 19(11): 1433-1435, doi: 10.1016/S0191-8141(97)00086-2.
Ji S C, Long C X, Martignole J, et al. 1997. Seismic reflectivity of a finely layered, granulite-facies ductile shear zone in the Southern Grenville Province (Quebec) [J]. Tectonophysics, 279(1- 4): 113-133, doi: 10.1016/S0040-1951(97)00133-9.
Ji S C, Wang Q, Marcotte D, et al. 2007. P Wave velocities, anisotropy and hysteresis in ultrahigh-pressure metamorphic rocks as a function of confining pressure [J]. Journal of Geophysical Research-Solid Earth, 112(B9): 685- 693, doi: 10.1029/2006JB004867.
Ji S C, Wang Q, Xia B. 2002. Handbook of seismic properties of minerals, rocks and ores [M]. Montreal: Polytechnic International Press.
Ji Z L, Li J, Xiong S, et al. 1993. Elastic character of oil-rock and the relation with oil-gas formation [J]. Chinese Journal of Geophysics (in Chinese), 36(2): 242-255 doi:10.3321/j.issn:0001-5733.1993.02.013.
Li A W, Sun D S,Wang H C. 2014. Seismic anisotropy and elastic parameter of tight sandstone with confining pressure [J]. Progress in Geophysics (in Chinese), 29(2): 754-760, doi: 10.6038/pg20140238.
Ma H F. 2016. Incremental algorithm for acoustoelastic theory of large static pre-deformed media [D]. Beijing: The Institute of Crustal Dynamics.
Ma H F, Tian J Y, Wang M. 2017. Incremental algorithm for acoustoelastic theory of large static pre-deformed fluid-saturated porous media [J]. Progress in Computational Fluid Dynamics An International Journal, 17(1): 42-51, doi: 10.1504/PCFD.2017.081718.
Ma Z G, Wu X Y,Wang Z H. 2006. Effect of effective pressure on compressional and shear wave velocities [J]. Progress in Exploration Geophysics (in Chinese), 29(3): 183-186.
Nakata N, Snieder R. 2011. Near-surface weakening in Japan after the 2011 Tohoku-Oki earthquake [J]. Geophysical Research Letters, 38(17): 245-255, doi: 10.1029/2011GL048800.
Nur A, Simmons G. 1969. Stress-induced velocity anisotropy in rock: An experimental study [J]. Journal of Geophysical Research, 74(27): 6667- 6674, doi: 10.1029/JB074i027p06667.
Pao Y H, 1984. Acoustoelasticity and ultrasonic measurement of residual stress[A]. Physical Acoustics[M]: 61-143.
Sayers C M, Schlumberger. 2010. Geophysics under stress: geomechanical applications of seismic and borehole acoustic waves [M]. Tulsa: Society of Exploration Geophysicist.
Shapiro S A. 2003. Elastic piezosensitivity of porous and fractured rocks [J]. Geophysics, 68(2): 482- 486, doi: 10.1190/1.1567215.
Shi G, Shen L D. 1990. Evaluations of the lithological character and physical property of rocks from the relation between wave velocity and pressure-an experimental study [J]. Chinese Journal of Geophysics (in Chinese), 33(2): 212-219.
Siegesmund S, Kern H. 1990. Velocity anisotropy and shear-wave splitting in rocks from the mylonite belt along the Insubric Line (Ivrea Zone, Italy) [J]. Earth & Planetary Science Letters, 99(1-2): 29- 47, doi: 10.1016/0012-821X(90)90068-9.
Simmons G. 1964. Velocity of shear waves in rocks to 10 kilobars, 1 [J]. Journal of Geophysical Research, 69(6): 1123-1130, doi: 10.1029/JZ069i006p01123.
Tian J Y, Hu L L. 2010. Progress in theories and experimental technologies of solid acoustoelasticity and its application [J]. Advances in Mechanics (in Chinese), 40(6): 652- 662, doi: 10.6052/1000- 0992-2010- 6-lxjzJ2009- 042.
Tosaya C A. 1982. Acoustical properties of clay-bearing rocks [D]. Stanford: Stanford University.
Wang H W. 1999. Partial least-squares regression-method and application [M]. Beijing: National Defense Industry Press.
Wang Q. 2007. Experimental and theoretical study on seismic properties of rocks [J]. Bulletin of Mineralogy, Petrology & Geochemistry (in Chinese), 26(2): 118-126, doi: 10.3969/j.issn.1007-2802.2007.02.003.
Wang Q, Ji S C, Salisbury M H, et al. 2005. Pressure dependence and anisotropy of P-wave velocities in ultrahigh-pressure metamorphic rocks from the Dabie-Sulu orogenic belt (China): Implications for seismic properties of subducted slabs and origin of mantle reflections [J]. Tectonophysics, 398(1-2): 67-99, doi: 10.1016/j.tecto.2004.12.001.
Wepfer W W, Christensen N I. 1991. A seismic velocity-confining pressure relation, with applications [J]. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts, 28(5): 451- 456, doi: 10.1016/0148-9062(91)90083-x.
Xie Y. 2013. Regression analysis.Second edtion [M]. Beijing: Social Science Academic Press(China).
Zang C J, Wang M L, Liu Y G, et al. 2014. The elastic wave velocities of the granitoids from Eastern Junggar of Xinjiang at high temperature and high pressure and their geological constraints on the crustal structure [J]. Chinese Journal of Geophysics (in Chinese), 57(5): 2099-2112, doi: 10.6038/cjg20140707.
Zhang J F, Wang Y F, Jin Z M. 2007. The seismic wave velocity anisotropy of ultrahigh pressure eclogite caused by deformation fabric [J]. Science in China(D) (in Chinese), 37(11): 1433-1443, doi: 10.3969/j.issn.1674-7240.2007.11.002.
Zhao H, Li X P, Luo Y, et al. 2017. Characteristics of elastic wave propagation in jointed rock mass and development of constitutive model by coupling macroscopic and mesoscopic damage [J]. Rock and Soil Mechanics (in Chinese), 38(10): 2939-2948, doi: 10.16285/j.rsm.2017.10.022.
Zhou B, Sun F, Xue S F, et al. 2014. Numerical simulation on the changes of elastic wave velocities of rocks under reservoir bottom during water storage and drainage [J]. Seismology & Geology (in Chinese), 36(1): 39-51, doi: 10.3969/j.issn.0253- 4967.2014.01.004.
陈志, 杜建国, 周文戈, 等. 2009. 0.5～4.0 GPa、100～300 ℃条件下辉长岩弹性波速及衰减特征[J]. 高压物理学报, 23(5): 338-344, doi: 10.3969/j.issn.1000-5773.2009.05.004.
葛洪魁, 陈颙, 韩德华. 2001. 有效应力对岩石弹性波速的影响[J]. 地球物理学报, 44(z1): 152-160, doi: 10.3321/j.issn:0001-5733.2001.z1.019.
郭彬彬, 王红才, 赵卫华, 等. 2014. 云南高黎贡山典型板岩地震波各向异性研究[J]. 地球物理学报, 57(3): 837-846, doi: 10.6038/cjg20140313.
黄承贤, 宋大卫. 1991. 在围压下岩石弹性波速的研究[J]. 岩土工程学报, 13(2): 32- 41, doi: 10.3321/j.issn:1000- 4548.1991.02.004.
季钟霖, 李建林, 熊舜华, 等. 1993. 含油岩石弹性特征及其与油气的关系[J]. 地球物理学报, 36(2): 242-255, doi:10.3321/j.issn:0001-5733.1993.02.013.
李阿伟, 孙东生, 王红才. 2014. 致密砂岩波速各向异性及弹性参数随围压变化规律的实验研究[J]. 地球物理学进展, 29(2): 754-760, doi: 10.6038/pg20140238.
马洪飞. 初始静态大变形介质声弹理论的增量算法研究[D]. 北京: 中国地震局地壳应力研究所.
马中高, 伍向阳, 王中海. 2006. 有效压力对岩石纵横波速度的影响[J]. 勘探地球物理进展, 29(3): 183-186
史謌, 沈联蒂. 1990. 根据波速—压力关系评价岩石岩性,物性的实验研究[J]. 地球物理学报, 33(2): 212-219.
田家勇, 胡莲莲. 2010. 固体声弹性理论、实验技术及应用研究进展[J]. 力学进展, 40(6): 652- 662, doi: 10.6052/1000- 0992-2010- 6-lxjzJ2009- 042.
王惠文. 1999. 偏最小二乘回归方法及其应用[M]. 北京: 国防工业出版社.
王勤. 2007. 岩石地震波性质的实验与理论研究[J]. 矿物岩石地球化学通报, 26(2): 118-126, doi: 10.3969/j.issn.1007-2802.2007.02.003.
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Bridgman P W. 1922. The compressibility of metals at high pressures [J]. Proceedings of the National Academy of Sciences of the United States of America, 8(12): 361-365, doi: 10.2307/84446.
Chen Z, Du J G, Zhou W G, et al. 2009. Wave velocity and attenuation characteristics of gabbro at 100～300 ℃ and 0.5～4.0 GPa [J]. Chinese Journal of High Pressure Physics (in Chinese), 23(5): 338-344, doi: 10.3969/j.issn.1000-5773.2009.05.004.
Cheng X, Niu F L,Wang B S. 2010. Coseismic velocity change in the rupture zone of the 2008 MW 7.9 Wenchuan earthquake observed from ambient seismic noise [J]. Bulletin of the Seismological Society of America, 100(5B): 2539-2550, doi: 10.1785/0120090329.
Freund D. 1992. Ultrasonic compressional and shear velocities in dry clastic rocks as a function of porosity, clay content, and confining Pressure [J]. Geophysical Journal International, 108(1): 125-135, doi: 10.1111/j.1365-246X.1992.tb00843.x.
Ge H K, Chen Y, Han D H. 2001. The effect of effective stress on rock elastic wave velocities [J]. Chinese Journal of Geophysics (in Chinese), 44(z1): 152-160, doi: 10.3321/j.issn:0001-5733.2001.z1.019.
Greenfield R J, Graham E K. 1996. Application of a simple relation for describing wave velocity as a function of pressure in rocks containing microcracks [J]. Journal of Geophysical Research: Solid Earth, 101(B3): 5643-5652, doi: 10.1029/95JB03462.
Guo B B, Wang H C, Zhao W H, et al. 2014. Analysis of seismic anisotropy of slate and its application of slate [J]. Chinese Journal of Geophysics (in Chinese), 57(3): 837-846, doi: 10.6038/cjg20140313.
Huang C X,Song D W. 1991. Study on elastic wave velocity of rock under confining pressure [J]. Chinese Journal of Geotechnical Engineering (in Chinese), 13(2): 32- 41, doi: 10.3321/j.issn:1000- 4548.1991.02.004.
Huang X J, Burns D R, Toksoz M N. 2001. The effect of stresses on the sound velocity in rocks: theory of acoustoelasticity and experimental measurements [R]. Massachusetts Institute of Technology Earth Resources Laboratory.
Ji S C. 1997. Fracturing of garnet crystals in anisotropic metamorphic rocks during uplift: reply [J]. Journal of Structural Geology, 19(11): 1433-1435, doi: 10.1016/S0191-8141(97)00086-2.
Ji S C, Long C X, Martignole J, et al. 1997. Seismic reflectivity of a finely layered, granulite-facies ductile shear zone in the Southern Grenville Province (Quebec) [J]. Tectonophysics, 279(1- 4): 113-133, doi: 10.1016/S0040-1951(97)00133-9.
Ji S C, Wang Q, Marcotte D, et al. 2007. P Wave velocities, anisotropy and hysteresis in ultrahigh-pressure metamorphic rocks as a function of confining pressure [J]. Journal of Geophysical Research-Solid Earth, 112(B9): 685- 693, doi: 10.1029/2006JB004867.
Ji S C, Wang Q, Xia B. 2002. Handbook of seismic properties of minerals, rocks and ores [M]. Montreal: Polytechnic International Press.
Ji Z L, Li J, Xiong S, et al. 1993. Elastic character of oil-rock and the relation with oil-gas formation [J]. Chinese Journal of Geophysics (in Chinese), 36(2): 242-255 doi:10.3321/j.issn:0001-5733.1993.02.013.
Li A W, Sun D S,Wang H C. 2014. Seismic anisotropy and elastic parameter of tight sandstone with confining pressure [J]. Progress in Geophysics (in Chinese), 29(2): 754-760, doi: 10.6038/pg20140238.
Ma H F. 2016. Incremental algorithm for acoustoelastic theory of large static pre-deformed media [D]. Beijing: The Institute of Crustal Dynamics.
Ma H F, Tian J Y, Wang M. 2017. Incremental algorithm for acoustoelastic theory of large static pre-deformed fluid-saturated porous media [J]. Progress in Computational Fluid Dynamics An International Journal, 17(1): 42-51, doi: 10.1504/PCFD.2017.081718.
Ma Z G, Wu X Y,Wang Z H. 2006. Effect of effective pressure on compressional and shear wave velocities [J]. Progress in Exploration Geophysics (in Chinese), 29(3): 183-186.
Nakata N, Snieder R. 2011. Near-surface weakening in Japan after the 2011 Tohoku-Oki earthquake [J]. Geophysical Research Letters, 38(17): 245-255, doi: 10.1029/2011GL048800.
Nur A, Simmons G. 1969. Stress-induced velocity anisotropy in rock: An experimental study [J]. Journal of Geophysical Research, 74(27): 6667- 6674, doi: 10.1029/JB074i027p06667.
Pao Y H, 1984. Acoustoelasticity and ultrasonic measurement of residual stress[A]. Physical Acoustics[M]: 61-143.
Sayers C M, Schlumberger. 2010. Geophysics under stress: geomechanical applications of seismic and borehole acoustic waves [M]. Tulsa: Society of Exploration Geophysicist.
Shapiro S A. 2003. Elastic piezosensitivity of porous and fractured rocks [J]. Geophysics, 68(2): 482- 486, doi: 10.1190/1.1567215.
Shi G, Shen L D. 1990. Evaluations of the lithological character and physical property of rocks from the relation between wave velocity and pressure-an experimental study [J]. Chinese Journal of Geophysics (in Chinese), 33(2): 212-219.
Siegesmund S, Kern H. 1990. Velocity anisotropy and shear-wave splitting in rocks from the mylonite belt along the Insubric Line (Ivrea Zone, Italy) [J]. Earth & Planetary Science Letters, 99(1-2): 29- 47, doi: 10.1016/0012-821X(90)90068-9.
Simmons G. 1964. Velocity of shear waves in rocks to 10 kilobars, 1 [J]. Journal of Geophysical Research, 69(6): 1123-1130, doi: 10.1029/JZ069i006p01123.
Tian J Y, Hu L L. 2010. Progress in theories and experimental technologies of solid acoustoelasticity and its application [J]. Advances in Mechanics (in Chinese), 40(6): 652- 662, doi: 10.6052/1000- 0992-2010- 6-lxjzJ2009- 042.
Tosaya C A. 1982. Acoustical properties of clay-bearing rocks [D]. Stanford: Stanford University.
Wang H W. 1999. Partial least-squares regression-method and application [M]. Beijing: National Defense Industry Press.
Wang Q. 2007. Experimental and theoretical study on seismic properties of rocks [J]. Bulletin of Mineralogy, Petrology & Geochemistry (in Chinese), 26(2): 118-126, doi: 10.3969/j.issn.1007-2802.2007.02.003.
Wang Q, Ji S C, Salisbury M H, et al. 2005. Pressure dependence and anisotropy of P-wave velocities in ultrahigh-pressure metamorphic rocks from the Dabie-Sulu orogenic belt (China): Implications for seismic properties of subducted slabs and origin of mantle reflections [J]. Tectonophysics, 398(1-2): 67-99, doi: 10.1016/j.tecto.2004.12.001.
Wepfer W W, Christensen N I. 1991. A seismic velocity-confining pressure relation, with applications [J]. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts, 28(5): 451- 456, doi: 10.1016/0148-9062(91)90083-x.
Xie Y. 2013. Regression analysis.Second edtion [M]. Beijing: Social Science Academic Press(China).
Zang C J, Wang M L, Liu Y G, et al. 2014. The elastic wave velocities of the granitoids from Eastern Junggar of Xinjiang at high temperature and high pressure and their geological constraints on the crustal structure [J]. Chinese Journal of Geophysics (in Chinese), 57(5): 2099-2112, doi: 10.6038/cjg20140707.
Zhang J F, Wang Y F, Jin Z M. 2007. The seismic wave velocity anisotropy of ultrahigh pressure eclogite caused by deformation fabric [J]. Science in China(D) (in Chinese), 37(11): 1433-1443, doi: 10.3969/j.issn.1674-7240.2007.11.002.
Zhao H, Li X P, Luo Y, et al. 2017. Characteristics of elastic wave propagation in jointed rock mass and development of constitutive model by coupling macroscopic and mesoscopic damage [J]. Rock and Soil Mechanics (in Chinese), 38(10): 2939-2948, doi: 10.16285/j.rsm.2017.10.022.
Zhou B, Sun F, Xue S F, et al. 2014. Numerical simulation on the changes of elastic wave velocities of rocks under reservoir bottom during water storage and drainage [J]. Seismology & Geology (in Chinese), 36(1): 39-51, doi: 10.3969/j.issn.0253- 4967.2014.01.004.
陈志, 杜建国, 周文戈, 等. 2009. 0.5～4.0 GPa、100～300 ℃条件下辉长岩弹性波速及衰减特征[J]. 高压物理学报, 23(5): 338-344, doi: 10.3969/j.issn.1000-5773.2009.05.004.
葛洪魁, 陈颙, 韩德华. 2001. 有效应力对岩石弹性波速的影响[J]. 地球物理学报, 44(z1): 152-160, doi: 10.3321/j.issn:0001-5733.2001.z1.019.
郭彬彬, 王红才, 赵卫华, 等. 2014. 云南高黎贡山典型板岩地震波各向异性研究[J]. 地球物理学报, 57(3): 837-846, doi: 10.6038/cjg20140313.
黄承贤, 宋大卫. 1991. 在围压下岩石弹性波速的研究[J]. 岩土工程学报, 13(2): 32- 41, doi: 10.3321/j.issn:1000- 4548.1991.02.004.
季钟霖, 李建林, 熊舜华, 等. 1993. 含油岩石弹性特征及其与油气的关系[J]. 地球物理学报, 36(2): 242-255, doi:10.3321/j.issn:0001-5733.1993.02.013.
李阿伟, 孙东生, 王红才. 2014. 致密砂岩波速各向异性及弹性参数随围压变化规律的实验研究[J]. 地球物理学进展, 29(2): 754-760, doi: 10.6038/pg20140238.
马洪飞. 初始静态大变形介质声弹理论的增量算法研究[D]. 北京: 中国地震局地壳应力研究所.
马中高, 伍向阳, 王中海. 2006. 有效压力对岩石纵横波速度的影响[J]. 勘探地球物理进展, 29(3): 183-186
史謌, 沈联蒂. 1990. 根据波速—压力关系评价岩石岩性,物性的实验研究[J]. 地球物理学报, 33(2): 212-219.
田家勇, 胡莲莲. 2010. 固体声弹性理论、实验技术及应用研究进展[J]. 力学进展, 40(6): 652- 662, doi: 10.6052/1000- 0992-2010- 6-lxjzJ2009- 042.
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