俯冲岩石圈形在D“层发生过钙钛矿相变的数值模拟
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摘要
地幔对流作为地球动力学的一个基本概念,对地球以及类地行星的动力学演化研究起着重要作用。本文通过介绍对地幔对流的认识的发展,描述地幔对流的控制方程,简化条件以及无量纲化的方法,来初步介绍地幔对流的基础理论。
之后综述了当前地球物理学界关于D”层钙钛矿(PV)-过钙钛矿(PPV)相变对地幔对流的影响的一些研究进展。重点介绍了Nagakawa和Paul Tackley在过钙钛矿相变的克拉伯龙曲线斜率变化对地幔对流的影响,以及Marc Monnereau和David A.Yuen在研究相变截断温度对相变面的形态结构和地幔对流的影响。
以前面几位地球物理学家对D”层的研究结论为基础,为了探讨地幔底部以及核幔边界出现的异常结构,以及这些异常对我们认识地幔对流和地球动力学演化的帮助,更主要的是通过钙钛矿-过钙钛矿的相变这一强放热反应所能在核幔边界提供的强的温度约束条件来研究这些条件下俯冲岩石圈在下地幔形态结构。论文通过有限元方法在三维直角坐标下尝试了一个简单的数值模型,在加入了钙钛矿-过钙钛矿相变这一条件下进行演化计算。
通过数值模拟的结果我们可以得到一下结论:
1在地幔对流达到相对稳定的情况下,俯冲岩石圈可以达到下地幔底部,并进行堆积。
2尽管发生在核幔边界D”层上方的钙钛矿-过钙钛矿相变是一个强放热反应,但这个反应并不会使得地幔对流变得不稳定和与时间相关。
3钙钛矿-过钙钛矿相变为俯冲岩石圈在下地幔形态结构的研究提供了很好的温度约束条件,在温度场中我们可以看到清晰的下界面。
由于本研究仅仅考虑到了热-化学对流的一些基本参数以及相变面情况,而俯冲板块的形态结构的差异还可能由于热传导的横向不均匀性,介质的各向异性,以及地幔介质的可压缩性等等引起。所以把这些可能影响到俯冲板块形态结构的参数引入数值模型中对进一步完善实验结果会有很大的帮助。
As a fundimantle concept of geodynamics,’mantle convection’has played an important role in both the research in earth geodynamics process and the terrestrial planets geodynamics process.
The thesis briefly introduces the basic theories of‘Mantle Convection’by representing the Control function,Boussinesq approximation as well as the nondimensional method. Then introduced the numerical computing method– Finite Element Method(FEM) and the code we employ in our research- CitcomCu.
After that ,the thesis summarizes several viewpoints and previous works of the problem’the effect of the PPV phase trasition on the mantle convection’Mainly focus on the work Nagakawa and Paul Tackley have done on the Clayeron Slope’s value,and the research Marc Monnereau and David A. Yuen have taken on detecting the relationship between the Clayperon Slope and the temperature intercept. The PPV phase change provide us a strong constrain in the temperature field in CMB.
After the numerical calculation ,we come to the conclusions:
1 the subducted lithosphere could reach the CMB and the mantle convection can be still stable.
2 The exothermic reaction doesn’t destabilizes the thermal boundary.
3 With the PPV phase change in our numerical convection model, we could get a more obvious temperature field in CMB.
This study only take into account the effect of the PPV phase change into the thermal-chemical mantle convection.However,there are other different physical properties such as latent heating and elastic constants and thermal generation rate and so on.Therefore ,it would be a better research to take these properties into the numerical model.
之后综述了当前地球物理学界关于D”层钙钛矿(PV)-过钙钛矿(PPV)相变对地幔对流的影响的一些研究进展。重点介绍了Nagakawa和Paul Tackley在过钙钛矿相变的克拉伯龙曲线斜率变化对地幔对流的影响,以及Marc Monnereau和David A.Yuen在研究相变截断温度对相变面的形态结构和地幔对流的影响。
以前面几位地球物理学家对D”层的研究结论为基础,为了探讨地幔底部以及核幔边界出现的异常结构,以及这些异常对我们认识地幔对流和地球动力学演化的帮助,更主要的是通过钙钛矿-过钙钛矿的相变这一强放热反应所能在核幔边界提供的强的温度约束条件来研究这些条件下俯冲岩石圈在下地幔形态结构。论文通过有限元方法在三维直角坐标下尝试了一个简单的数值模型,在加入了钙钛矿-过钙钛矿相变这一条件下进行演化计算。
通过数值模拟的结果我们可以得到一下结论:
1在地幔对流达到相对稳定的情况下,俯冲岩石圈可以达到下地幔底部,并进行堆积。
2尽管发生在核幔边界D”层上方的钙钛矿-过钙钛矿相变是一个强放热反应,但这个反应并不会使得地幔对流变得不稳定和与时间相关。
3钙钛矿-过钙钛矿相变为俯冲岩石圈在下地幔形态结构的研究提供了很好的温度约束条件,在温度场中我们可以看到清晰的下界面。
由于本研究仅仅考虑到了热-化学对流的一些基本参数以及相变面情况,而俯冲板块的形态结构的差异还可能由于热传导的横向不均匀性,介质的各向异性,以及地幔介质的可压缩性等等引起。所以把这些可能影响到俯冲板块形态结构的参数引入数值模型中对进一步完善实验结果会有很大的帮助。
As a fundimantle concept of geodynamics,’mantle convection’has played an important role in both the research in earth geodynamics process and the terrestrial planets geodynamics process.
The thesis briefly introduces the basic theories of‘Mantle Convection’by representing the Control function,Boussinesq approximation as well as the nondimensional method. Then introduced the numerical computing method– Finite Element Method(FEM) and the code we employ in our research- CitcomCu.
After that ,the thesis summarizes several viewpoints and previous works of the problem’the effect of the PPV phase trasition on the mantle convection’Mainly focus on the work Nagakawa and Paul Tackley have done on the Clayeron Slope’s value,and the research Marc Monnereau and David A. Yuen have taken on detecting the relationship between the Clayperon Slope and the temperature intercept. The PPV phase change provide us a strong constrain in the temperature field in CMB.
After the numerical calculation ,we come to the conclusions:
1 the subducted lithosphere could reach the CMB and the mantle convection can be still stable.
2 The exothermic reaction doesn’t destabilizes the thermal boundary.
3 With the PPV phase change in our numerical convection model, we could get a more obvious temperature field in CMB.
This study only take into account the effect of the PPV phase change into the thermal-chemical mantle convection.However,there are other different physical properties such as latent heating and elastic constants and thermal generation rate and so on.Therefore ,it would be a better research to take these properties into the numerical model.
引文
Garfunkel, Z., C. A. Anderson, and G. Schubert (1986), Mantle circulation and the lateral migration of subducted slabs, J. Geophys. Res., 91(B7), 7205–7223.
Moresi, L., and M. Gurnis (1996), Constraints on the lateral strength of slabs from three-dimensional dynamic flow models, Earth Planet. Sci. Lett., 138, 15–28.
Hager, B. H. (1991), Mantle viscosity: A comparison of models from postglacial rebound and from the geoid, plate driving forces, and advected heat flux, in NATO Advanced Research Workshop on Glacial Isostasy, Sea-Level, and Mantle Rheology, Erice, Italy, July 27–Aug. 4, 1990, NATOASI Ser., Ser. C, vol. 334, edited by E. B. R. Sabodini and K. Lambeck, pp. 493–513, Springer, New York.
Hall, C. E., M. Gurnis, M. Sdrolias, L. Lavier, and R. D. Mu¨ller (2003), Catastrophic initiation of subduction following forced convergence across fracture zones, Earth Planet.Sci. Lett., 212, 15–30.
Han, L., and M. Gurnis (1999), How valid are dynamic models of subduction and convection when plate motions are prescribed?, Phys. Earth Planet. Inter., 110, 235–246.
Hirth, G. (2003), Laboratory constraints on the rheology of the upper mantle, in Plastic Deformation of Minerals and Rocks, Rev. Mineral. Geochem., vol. 51, edited by S.-I. Karato and H-.R. Wenk, pp. 97–116, Mineral. Soc. of Am., Washington,D. C.
Enns, A., T.W. Becker, and H. Schmeling (2005), The dynamicsof subduction and trench migration for viscosity stratification, Geophys. J. Int., 160, 761–775.
Fukao, Y., S. Widiyantoro, and M. Obayashi (2001), Stagnant slabs in the upper and lower mantle transition region, Rev. Geophys., 39, 291–323.
Garnero, E. J., J. S. Revenaugh, Q. Williams, T. Lay, and L. H. Kellogg (1998), Ultralow velocity zone at the core-mantle boundary, in The Core-Mantle Boundary Region, Geodyn. Ser., vol. 28, edited by M. Gurnis et al., pp. 319–334, AGU, Washington, D. C.
Grand, S. P. (2002), Mantle shear-wave tomography and the fate of subducted slabs, Philos. Trans. R. Soc. London, Ser. A,360, 2475–2491
Huang J S, Zhong S, van Hunen J. Controls on sublithospheric small-scaleconvection. J Geophys Res, 2003, 108(B8), 2405. doi: 10.1029/2003JB002456
van Hunen J, Huang J S, Zhong S. The effects of shearing on the onset and vigor of small-scale convection in Newtonian rheology. Geophy Resarch Lett, 2003, 30(19), 1991. doi:10.1029/2003GL018101
Kneller, E.A., van Keken, P.E., Katayama, I., Karato, S., 2007. Stress, strain,and B-type olivine fabric in the fore-arc mantle: sensitivity tests using high-resolution steady state subduction zone models. J. Geophys. Res. 112, B04406, doi:10.1029/2006JB004544.
Kirby, S.H., Stein, S., Okal, E.A., Rubie, D.C., 1996. Metastable mantle phase transitions and deep earthquakes in subducting oceanic lithosphere. Rev.Geophys. 34, 261-306.
Kincaid, C., Sacks, I.S., 1997. Thermal and dynamical evolution of the upper mantle in subduction zones. J. Geophys. Res. 102, 12,295-12, 315.
King, S.D., Raefsky, A., Hager, B.H., 1990. Conman - vectorizing a _nite element code for incompressible 2-dimensional convection in the Earth's mantle. Phys. Earth Planet. Inter. 59, 195-207.
King, S.D., Hager, B.H., 1994. Subducted slabs and the geoid: 1. Numerical experiments with temperature-dependent viscosity. J. Geophys. Res., 99, 19843-19852.
McKenzie, D.P., 1969. Speculations on consequences and causes of plate motions. Geophys. J. Roy. Astron. Soc. 18, 1969.
Minear, J.W., Tokso z, M.N., 1970. Thermal regime of a downgoing slab and new global tectonics. J. Geophys. Res. 75, 1397.
Travis BJ, Olson P, and Schubert G (1990) The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection. Journal of Fluid Mechanics 216: 71–92.
Trompert RA and Hansen U (1996) The application of a finite-volume multigrid method to 3-dimensional flow problems in a highly viscous fluid with a variable viscosity. Geophysical and Astrophysical Fluid Dynamics 83: 261–291.
Trottenberg U, Oosterlee C, and Schueller A (2001) Multigrid, 631 pp. Orlando, FL: Academic Press. Turcotte DL, Torrance KE, and Hsui AT (1973) Convection in the Earth’s mantle in Methods. In: Bolt BA (ed.) Computational Physics, vol. 13, pp. 431–454. New York: Academic Press. van den Berg AP, van Keken PE, and Yuen DA (1993) The effects of a composite non-Newtonian and Newtonianrheology on mantle convection. Geophysical Journal International 115: 62–78.
van Keken PE and Zhong S (1999) Mixing in a 3D spherical model of present-day mantle convection. Earth and Planetary Science Letters 171: 533–547.
van Keken PE, King SD, Schmeling H, Christensen UR, Neumeister D, and Doin M-P (1997) A comparison of methods for the modeling of thermochemical convection. Journal of Geophysical Research 102: 22477–22496.
Verfurth R (1984) A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem. IMA Journal of Numerical Analysis 4: 441–455.
Weinberg RF and Schmeling H (1992) Polydiapirs: Multiwavelength gravity structures. Journal of Structural Geology 14: 425–436.
Yavneh I (2006) Why multigrid methods are so efficient? Computing in Science and Engineering 8: 12–23.
Yoshida M and Kageyama A (2004) Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell. Geophysical Research Letters 31: doi:10.1029/ 2004GL019970.
Yuen DA, Balachandar S, and Hansen U (2000) Modelling mantle convection: A significant challenge in geophysical fluid dynamics. In: Fox PA and Kerr RM (eds.) Geophysical and Astrophysical Convection pp. 257–294.
Zhang S and Christensen U (1993) Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle. Geophysical Jornal International 114: 531–547.
Morgan, J.P., Hasenclever, J., Hort, M., Ruepke, L., Parmentier, E.M., 2007.
On subducting slab entrainment of buoyant asthenosphere. Terra Nova 19,167-173
Zhong S (2006) Constraints on thermochemical convection of the mantle from plume heat flux, plume excess temperature and upper mantle temperature. Journal of Geophysical Research 111: B04409 (doi:10.1029/2005JB003972).
Zhong S (2005) Dynamics of thermal plumes in 3D isoviscous thermal convection. Geophysical Journal International 154(162): 289–300.
Zhong S and Hager BH (2003) Entrainment of a dense layer by thermal plumes. Geophysical Journal International 154: 666–676.
Zhong S, Zuber MT, Moresi LN, and Gurnis M (2000) Role of temperature dependent viscosity and surface plates in spherical shell models of mantle convection.Journal of Geophysical Research 105: 11063–11082.
Zhong S, Gurnis M, and Moresi LN (1998) The role of faults, nonlinear rheology, and viscosity structure in generating plates from instantaneous mantle flow models. Journal of Geophysical Research 103: 15255–15268.
Zhong S and Gurnis M (1994) The role of plates and temperature-dependent viscosity in phase change dynamics. Journal of Geophysical Research 99: 15903–15917
Backus, G. E. (1962), Long-wave elastic anisotropy produced by horizontal layering, J. Geophys. Res., 67, 4427–4440.
Batchelor, G. K. (1970), Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech., 44,419–440.
Beˇhounkova′, M., and H. Cˇ?′zˇkova′(2008), Long-wavelength character of subducted slabs in the lower mantle, Earth Planet.Sci. Lett., 275, 43–53.
Bellahsen, N., C. Faccenna, and F. Funiciello (2005), Dynamics of subduction and plate motion in laboratory experiments:Insights into the‘‘plate tectonics’’behavior of the Earth,J. Geophys. Res., 110, B01401, doi:10.1029/2004JB002999.
Christensen, U. R. (1996), The influence of trench migration on slab penetration into the lower mantle, Earth Planet. Sci. Lett., 140, 27–39.
叶正仁,王建.上地幔变黏度小尺度对流的数值研究.地球物理学报, 2003, 46(3): 335~339
叶正仁.地幔对流大地水准面异常和板块运动.现今地球动力学问题讨论会论文集.北京:地震出版社,1994. 72—8o
傅容珊,常筱华,黄建华,等.区域重力异常与上地幔小尺度对流模型.地球物理学报, 1994, 37(增刊): 249~258
傅容珊,董树谦,黄建华,等.利用地震层析成象数据反演地幔对流模型的研究.地球物理学报, 2002, 45(增刊): 136~143
傅容珊,黄建华,董树谦,等.利用地震层析成象数据计算地幔对流新模型的探讨.地球物理学报, 2003, 46(6): 772~778
Moresi, L., and M. Gurnis (1996), Constraints on the lateral strength of slabs from three-dimensional dynamic flow models, Earth Planet. Sci. Lett., 138, 15–28.
Hager, B. H. (1991), Mantle viscosity: A comparison of models from postglacial rebound and from the geoid, plate driving forces, and advected heat flux, in NATO Advanced Research Workshop on Glacial Isostasy, Sea-Level, and Mantle Rheology, Erice, Italy, July 27–Aug. 4, 1990, NATOASI Ser., Ser. C, vol. 334, edited by E. B. R. Sabodini and K. Lambeck, pp. 493–513, Springer, New York.
Hall, C. E., M. Gurnis, M. Sdrolias, L. Lavier, and R. D. Mu¨ller (2003), Catastrophic initiation of subduction following forced convergence across fracture zones, Earth Planet.Sci. Lett., 212, 15–30.
Han, L., and M. Gurnis (1999), How valid are dynamic models of subduction and convection when plate motions are prescribed?, Phys. Earth Planet. Inter., 110, 235–246.
Hirth, G. (2003), Laboratory constraints on the rheology of the upper mantle, in Plastic Deformation of Minerals and Rocks, Rev. Mineral. Geochem., vol. 51, edited by S.-I. Karato and H-.R. Wenk, pp. 97–116, Mineral. Soc. of Am., Washington,D. C.
Enns, A., T.W. Becker, and H. Schmeling (2005), The dynamicsof subduction and trench migration for viscosity stratification, Geophys. J. Int., 160, 761–775.
Fukao, Y., S. Widiyantoro, and M. Obayashi (2001), Stagnant slabs in the upper and lower mantle transition region, Rev. Geophys., 39, 291–323.
Garnero, E. J., J. S. Revenaugh, Q. Williams, T. Lay, and L. H. Kellogg (1998), Ultralow velocity zone at the core-mantle boundary, in The Core-Mantle Boundary Region, Geodyn. Ser., vol. 28, edited by M. Gurnis et al., pp. 319–334, AGU, Washington, D. C.
Grand, S. P. (2002), Mantle shear-wave tomography and the fate of subducted slabs, Philos. Trans. R. Soc. London, Ser. A,360, 2475–2491
Huang J S, Zhong S, van Hunen J. Controls on sublithospheric small-scaleconvection. J Geophys Res, 2003, 108(B8), 2405. doi: 10.1029/2003JB002456
van Hunen J, Huang J S, Zhong S. The effects of shearing on the onset and vigor of small-scale convection in Newtonian rheology. Geophy Resarch Lett, 2003, 30(19), 1991. doi:10.1029/2003GL018101
Kneller, E.A., van Keken, P.E., Katayama, I., Karato, S., 2007. Stress, strain,and B-type olivine fabric in the fore-arc mantle: sensitivity tests using high-resolution steady state subduction zone models. J. Geophys. Res. 112, B04406, doi:10.1029/2006JB004544.
Kirby, S.H., Stein, S., Okal, E.A., Rubie, D.C., 1996. Metastable mantle phase transitions and deep earthquakes in subducting oceanic lithosphere. Rev.Geophys. 34, 261-306.
Kincaid, C., Sacks, I.S., 1997. Thermal and dynamical evolution of the upper mantle in subduction zones. J. Geophys. Res. 102, 12,295-12, 315.
King, S.D., Raefsky, A., Hager, B.H., 1990. Conman - vectorizing a _nite element code for incompressible 2-dimensional convection in the Earth's mantle. Phys. Earth Planet. Inter. 59, 195-207.
King, S.D., Hager, B.H., 1994. Subducted slabs and the geoid: 1. Numerical experiments with temperature-dependent viscosity. J. Geophys. Res., 99, 19843-19852.
McKenzie, D.P., 1969. Speculations on consequences and causes of plate motions. Geophys. J. Roy. Astron. Soc. 18, 1969.
Minear, J.W., Tokso z, M.N., 1970. Thermal regime of a downgoing slab and new global tectonics. J. Geophys. Res. 75, 1397.
Travis BJ, Olson P, and Schubert G (1990) The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection. Journal of Fluid Mechanics 216: 71–92.
Trompert RA and Hansen U (1996) The application of a finite-volume multigrid method to 3-dimensional flow problems in a highly viscous fluid with a variable viscosity. Geophysical and Astrophysical Fluid Dynamics 83: 261–291.
Trottenberg U, Oosterlee C, and Schueller A (2001) Multigrid, 631 pp. Orlando, FL: Academic Press. Turcotte DL, Torrance KE, and Hsui AT (1973) Convection in the Earth’s mantle in Methods. In: Bolt BA (ed.) Computational Physics, vol. 13, pp. 431–454. New York: Academic Press. van den Berg AP, van Keken PE, and Yuen DA (1993) The effects of a composite non-Newtonian and Newtonianrheology on mantle convection. Geophysical Journal International 115: 62–78.
van Keken PE and Zhong S (1999) Mixing in a 3D spherical model of present-day mantle convection. Earth and Planetary Science Letters 171: 533–547.
van Keken PE, King SD, Schmeling H, Christensen UR, Neumeister D, and Doin M-P (1997) A comparison of methods for the modeling of thermochemical convection. Journal of Geophysical Research 102: 22477–22496.
Verfurth R (1984) A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem. IMA Journal of Numerical Analysis 4: 441–455.
Weinberg RF and Schmeling H (1992) Polydiapirs: Multiwavelength gravity structures. Journal of Structural Geology 14: 425–436.
Yavneh I (2006) Why multigrid methods are so efficient? Computing in Science and Engineering 8: 12–23.
Yoshida M and Kageyama A (2004) Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell. Geophysical Research Letters 31: doi:10.1029/ 2004GL019970.
Yuen DA, Balachandar S, and Hansen U (2000) Modelling mantle convection: A significant challenge in geophysical fluid dynamics. In: Fox PA and Kerr RM (eds.) Geophysical and Astrophysical Convection pp. 257–294.
Zhang S and Christensen U (1993) Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle. Geophysical Jornal International 114: 531–547.
Morgan, J.P., Hasenclever, J., Hort, M., Ruepke, L., Parmentier, E.M., 2007.
On subducting slab entrainment of buoyant asthenosphere. Terra Nova 19,167-173
Zhong S (2006) Constraints on thermochemical convection of the mantle from plume heat flux, plume excess temperature and upper mantle temperature. Journal of Geophysical Research 111: B04409 (doi:10.1029/2005JB003972).
Zhong S (2005) Dynamics of thermal plumes in 3D isoviscous thermal convection. Geophysical Journal International 154(162): 289–300.
Zhong S and Hager BH (2003) Entrainment of a dense layer by thermal plumes. Geophysical Journal International 154: 666–676.
Zhong S, Zuber MT, Moresi LN, and Gurnis M (2000) Role of temperature dependent viscosity and surface plates in spherical shell models of mantle convection.Journal of Geophysical Research 105: 11063–11082.
Zhong S, Gurnis M, and Moresi LN (1998) The role of faults, nonlinear rheology, and viscosity structure in generating plates from instantaneous mantle flow models. Journal of Geophysical Research 103: 15255–15268.
Zhong S and Gurnis M (1994) The role of plates and temperature-dependent viscosity in phase change dynamics. Journal of Geophysical Research 99: 15903–15917
Backus, G. E. (1962), Long-wave elastic anisotropy produced by horizontal layering, J. Geophys. Res., 67, 4427–4440.
Batchelor, G. K. (1970), Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech., 44,419–440.
Beˇhounkova′, M., and H. Cˇ?′zˇkova′(2008), Long-wavelength character of subducted slabs in the lower mantle, Earth Planet.Sci. Lett., 275, 43–53.
Bellahsen, N., C. Faccenna, and F. Funiciello (2005), Dynamics of subduction and plate motion in laboratory experiments:Insights into the‘‘plate tectonics’’behavior of the Earth,J. Geophys. Res., 110, B01401, doi:10.1029/2004JB002999.
Christensen, U. R. (1996), The influence of trench migration on slab penetration into the lower mantle, Earth Planet. Sci. Lett., 140, 27–39.
叶正仁,王建.上地幔变黏度小尺度对流的数值研究.地球物理学报, 2003, 46(3): 335~339
叶正仁.地幔对流大地水准面异常和板块运动.现今地球动力学问题讨论会论文集.北京:地震出版社,1994. 72—8o
傅容珊,常筱华,黄建华,等.区域重力异常与上地幔小尺度对流模型.地球物理学报, 1994, 37(增刊): 249~258
傅容珊,董树谦,黄建华,等.利用地震层析成象数据反演地幔对流模型的研究.地球物理学报, 2002, 45(增刊): 136~143
傅容珊,黄建华,董树谦,等.利用地震层析成象数据计算地幔对流新模型的探讨.地球物理学报, 2003, 46(6): 772~778