利用重力和VLBI技术检测地球液态核的动力学效应
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摘要
利用最新的武汉地区高精度重力和全球高精度甚长基线干涉(very long baseline interferometry,VLBI)测量技术观测确定了地球液态地核的自由核章动本征参数(包括本征周期和品质因子等),同时获得了液核顶部的粘滞系数和液核的真实动力学椭率,使用Monte Carlo方法研究了本征周期的不确定度。结果表明,分别利用重力和VLBI确定的地球自由核章动本征周期值为430 sd(sd指恒星日)左右,两者间的差异为1.47 sd,粘滞系数为1 028 Pa·s。讨论了导致两者差异的主要原因,并将结果与国内外同类研究结果作了对比。
Based on the latest high-precision gravity data recorded in Wuhan and global high-accuracy VLBI(very long baseline interferometry) observations, we have determined the intrinsic parameters(including eigen-period and quality factor, et al) of FCN(free core nutation) of Earth's liquid core. Moreover, the viscosity at the top of the liquid core and its real dynamic ellipticity are obtained. By using the Monte Carlo method, we have calculated the uncertainty of the FCN's eigen-period. The results show that the FCN's eigen-periods determined by gravity and VLBI are about 430 sd and the difference between them is 1.47 sd, with the viscosity coefficient of 1 028 Pa·s. This paper discusses the main reasons for the above differences, and finally compares our results with similar research results from China and abroad.
Based on the latest high-precision gravity data recorded in Wuhan and global high-accuracy VLBI(very long baseline interferometry) observations, we have determined the intrinsic parameters(including eigen-period and quality factor, et al) of FCN(free core nutation) of Earth's liquid core. Moreover, the viscosity at the top of the liquid core and its real dynamic ellipticity are obtained. By using the Monte Carlo method, we have calculated the uncertainty of the FCN's eigen-period. The results show that the FCN's eigen-periods determined by gravity and VLBI are about 430 sd and the difference between them is 1.47 sd, with the viscosity coefficient of 1 028 Pa·s. This paper discusses the main reasons for the above differences, and finally compares our results with similar research results from China and abroad.
引文
[1] Buffett B A, Christensen U R. Magnetic and Viscous Coupling at the Core-Mantle Boundary: Infe-rences from Observations of the Earth’s Nutations[J]. Geophysical Journal International, 2007, 171(1):145-152
[2] Sun Heping, Cui Xiaoming, Xu Jianqiao, et al. Preliminary Application of Superconductive Gravity Technique on the Investigation of Viscosity at Core-Mantle Boundary[J]. Chinese Journal of Geophy-sics, 2009, 52(3):637-645(孙和平, 崔小明, 徐建桥,等. 超导重力技术在探讨核幔边界黏性特征中的初步应用[J]. 地球物理学报, 2009, 52(3):637-645)
[3] Wahr J M. Body Tides on an Elliptical, Rotating, Elastic and Oceanless Earth[J]. Geophysical Journal of the Royal Astronomical Society, 1981, 64(3):677-703
[4] Wahr J, Bergen Z. The Effects of Mantle Anelasticity on Nutations, Earth Tides, and Tidal Variations in Rotation Rate[J]. Geophysical Journal International, 1986, 87(2):633-668
[5] Mathews P M, Buffett B A, Herring T A, et al. Forced Nutations of the Earth: Influence of Inner Core Dynamics: 2. Numerical Results and Comparisons[J]. Journal of Geophysical Research: Solid Earth, 1991, 96(B5):8 243-8 257
[6] Vondrak J. Free Core Nutation: Direct Observations and Resonance Effects[J]. Astronomy & Astrophysics, 2005, 444(1): 297-304
[7] Chao B F, Hsieh Y. The Earth’s Free Core Nutation: Formulation of Dynamics and Estimation of Eigenperiod from the Very-Long-Baseline Interfe-rometry Data[J]. Earth & Planetary Science Letters, 2015, 432:483-492
[8] Zhou Y, Zhu Q, Salstein D A, et al.Estimation of the Free Core Nutation Period by the Sliding-Window Complex Least-Squares Fit Method[J]. Advances in Space Research, 2016, 57(10):2 136-2 140
[9] Neuberg J, Hinderer J, Zürn W. Stacking Gravity Tide Observations in Central Europe for the Retrieval of the Complex Eigenfrequency of the Nearly Diurnal Free-Wobble[J]. Geophysical Journal International, 1987, 91(3):853-868
[10] Xu J Q, Sun H P, Luo S C.Study of the Earth’s Free Core Nutation by Tidal Gravity Data Recorded with International Superconducting Gravimeters[J]. Sci China Earth Sci, 2002, 45(4):337-347
[11] Xu Houze, Sun Heping.GGP Project and Observations Using Wuhan Superconducting Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2003, 28(S1):18-22(许厚泽, 孙和平. 国际GGP计划和武汉超导重力仪观测[J]. 武汉大学学报·信息科学版, 2003, 28(S1):18-22)
[12] Sun H P, Jentzsch G, Xu J Q, et al. Earth’s Free Core Nutation Determined Using C032 Superconducting Gravimeter at Station Wuhan/China[J]. Journal of Geodynamics, 2004, 38(3-5):451-460
[13] Lambert S B, Dehant V. The Earth’s Core Parameters as Seen by the VLBI[J]. Astronomy & Astrophysics, 2007, 469(2):777-781
[14] Cui Xiaoming. Investigation of the Earth’s Free Core Nutation and Core-Mantle Coupling[D]. Wuhan: University of Chinese Academy of Sciences,2013(崔小明. 地球自由核章动及核幔耦合的研究[D].武汉: 中国科学院大学,2013)
[15] Lambert S, Ziegler Y, Huda N, et al.Earth’s Nutation: Recent Advances in Improving the Accuracy of Their Measurement by VLBI and in Constraining the Fluid and Inner Core Resonances[C]. EGU General Assembly Conference, Vienna, Italy, 2018
[16] Ducarme B, Sun H P, Xu J Q, et al. Determination of the Free Core Nutation Period from Tidal Gravity Observations of the GGP Superconducting Gravimeter Network[J]. Journal of Geodesy, 2007, 81(3):179-187
[17] Rosat S, Florsch N, Hinderer J, et al. Estimation of the Free Core Nutation Parameters from SG Data: Sensitivity Study and Comparative Analysis Using Linearized Least-Squares and Bayesian Methods[J]. Journal of Geodynamics, 2009, 48(3):331-339
[18] Rajner M, Brzeziński A. Free Core Nutation Period Inferred from the Gravity Measurements at Józefosław[J]. Studia Geophysica et Geodaetica, 2017, 61(4):639-656
[19] Tamura Y.A Harmonic Development of the Tide Generating Potential[J]. Bulletin d’Informations de Marees Terrestres, 1987, 99: 6 817-6 855
[20] Wenzel H G. The Nanogal Software: Earth Tide Data Processing Pakage Eterna3.30[J]. Bulletin d’ Information de Marees Terrestres, 1996, 124:9 425-9 439
[21] Xu Jianqiao, Zhou Jiangcun, Chen Xiaodong, et al. Long-Term Observations of Gravity Tides from a Superconducting Gravimeter at Wuhan[J]. Chinese Journal of Geophysics, 2014, 57(10):3 091-3 102(徐建桥, 周江存, 陈晓东,等. 武汉台重力潮汐长期观测结果[J]. 地球物理学报, 2014, 57(10):3 091-3 102)
[22] Jia Jiangang, Luan Wei, Shen Wenbin. Accurate Determination of the Calibration Factor of iGrav-007 Superconducting Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2015, 40(10):1 366-1 370(贾剑钢, 栾威, 申文斌. iGrav-007超导重力仪格值的精密测定[J]. 武汉大学学报·信息科学版, 2015, 40(10):1 366-1 370)
[23] Florsch N, Hinderer J. Bayesian Estimation of the Free Core Nutation Parameters from the Analysis of Precise Tidal Gravity Data[J]. Physics of the Earth & Planetary Interiors, 2000, 117(1-4):21-35
[24] Herring T A, Gwinn C R, Shapiro I I. Geodesy by Radio Interferometry: Studies of the Forced Nutations of the Earth: 1. Data Analysis[J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B5):4 745-4 754
[25] Koot L, Rivoldini A, Viron O D, et al.Estimation of Earth Interior Parameters from a Bayesian Inversion of very Long Baseline Interferometry Nutation Time Series[J]. Journal of Geophysical Research: Solid Earth, 2008, 113:B08414
[26] Vondrák J, Ron C. New Method for Determining Free Core Nutation Parameters, Considering Geophysical Effects[J]. Astronomy & Astrophysics, 2017, 604(A56):1-7
[27] Vondrák J, Ron C. Stability of Period and Quality Factor of Free Core Nutation[J]. Acta Geodynamica et Geomaterialia, 2009, 6(3):217-224
[28] Cui Xiaoming, Sun Heping, Xu Jianqiao, et al. Temporal Variation of the Period of Free Core Nutation Derived from VLBI and Superconducting Gravity Data[J]. Chinese Journal of Geophysics, 2014, 57(2):384-391(崔小明, 孙和平, 徐建桥,等. 利用VLBI和超导重力资料研究自由核章动周期时变特征[J]. 地球物理学报, 2014, 57(2):384-391)
[29] Palmer A,Smylie D E. VLBI Observations of Free Core Nutations and Viscosity at the Top of the Core[J]. Physics of the Earth & Planetary Interiors, 2005, 148(2-4):285-301
[30] Smylie D E, Palmer A. Viscosity of Earth’s Outer Core[OL]. http://arxiv.org/abs/0709.3333, 2007
[31] Cui Xiaoming, Sun Heping, Xu Jianqiao, et al. Application of Superconductive Gravity Technique on the Constraints of Core-Mantle Coupling Parameters[J]. Sci China: Earth Sci, 2012, 55(3):513-520(崔小明, 孙和平, 徐建桥,等. 利用超导重力技术约束核幔耦合参数[J]. 中国科学:地球科学, 2012,55(3):513-520)
[2] Sun Heping, Cui Xiaoming, Xu Jianqiao, et al. Preliminary Application of Superconductive Gravity Technique on the Investigation of Viscosity at Core-Mantle Boundary[J]. Chinese Journal of Geophy-sics, 2009, 52(3):637-645(孙和平, 崔小明, 徐建桥,等. 超导重力技术在探讨核幔边界黏性特征中的初步应用[J]. 地球物理学报, 2009, 52(3):637-645)
[3] Wahr J M. Body Tides on an Elliptical, Rotating, Elastic and Oceanless Earth[J]. Geophysical Journal of the Royal Astronomical Society, 1981, 64(3):677-703
[4] Wahr J, Bergen Z. The Effects of Mantle Anelasticity on Nutations, Earth Tides, and Tidal Variations in Rotation Rate[J]. Geophysical Journal International, 1986, 87(2):633-668
[5] Mathews P M, Buffett B A, Herring T A, et al. Forced Nutations of the Earth: Influence of Inner Core Dynamics: 2. Numerical Results and Comparisons[J]. Journal of Geophysical Research: Solid Earth, 1991, 96(B5):8 243-8 257
[6] Vondrak J. Free Core Nutation: Direct Observations and Resonance Effects[J]. Astronomy & Astrophysics, 2005, 444(1): 297-304
[7] Chao B F, Hsieh Y. The Earth’s Free Core Nutation: Formulation of Dynamics and Estimation of Eigenperiod from the Very-Long-Baseline Interfe-rometry Data[J]. Earth & Planetary Science Letters, 2015, 432:483-492
[8] Zhou Y, Zhu Q, Salstein D A, et al.Estimation of the Free Core Nutation Period by the Sliding-Window Complex Least-Squares Fit Method[J]. Advances in Space Research, 2016, 57(10):2 136-2 140
[9] Neuberg J, Hinderer J, Zürn W. Stacking Gravity Tide Observations in Central Europe for the Retrieval of the Complex Eigenfrequency of the Nearly Diurnal Free-Wobble[J]. Geophysical Journal International, 1987, 91(3):853-868
[10] Xu J Q, Sun H P, Luo S C.Study of the Earth’s Free Core Nutation by Tidal Gravity Data Recorded with International Superconducting Gravimeters[J]. Sci China Earth Sci, 2002, 45(4):337-347
[11] Xu Houze, Sun Heping.GGP Project and Observations Using Wuhan Superconducting Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2003, 28(S1):18-22(许厚泽, 孙和平. 国际GGP计划和武汉超导重力仪观测[J]. 武汉大学学报·信息科学版, 2003, 28(S1):18-22)
[12] Sun H P, Jentzsch G, Xu J Q, et al. Earth’s Free Core Nutation Determined Using C032 Superconducting Gravimeter at Station Wuhan/China[J]. Journal of Geodynamics, 2004, 38(3-5):451-460
[13] Lambert S B, Dehant V. The Earth’s Core Parameters as Seen by the VLBI[J]. Astronomy & Astrophysics, 2007, 469(2):777-781
[14] Cui Xiaoming. Investigation of the Earth’s Free Core Nutation and Core-Mantle Coupling[D]. Wuhan: University of Chinese Academy of Sciences,2013(崔小明. 地球自由核章动及核幔耦合的研究[D].武汉: 中国科学院大学,2013)
[15] Lambert S, Ziegler Y, Huda N, et al.Earth’s Nutation: Recent Advances in Improving the Accuracy of Their Measurement by VLBI and in Constraining the Fluid and Inner Core Resonances[C]. EGU General Assembly Conference, Vienna, Italy, 2018
[16] Ducarme B, Sun H P, Xu J Q, et al. Determination of the Free Core Nutation Period from Tidal Gravity Observations of the GGP Superconducting Gravimeter Network[J]. Journal of Geodesy, 2007, 81(3):179-187
[17] Rosat S, Florsch N, Hinderer J, et al. Estimation of the Free Core Nutation Parameters from SG Data: Sensitivity Study and Comparative Analysis Using Linearized Least-Squares and Bayesian Methods[J]. Journal of Geodynamics, 2009, 48(3):331-339
[18] Rajner M, Brzeziński A. Free Core Nutation Period Inferred from the Gravity Measurements at Józefosław[J]. Studia Geophysica et Geodaetica, 2017, 61(4):639-656
[19] Tamura Y.A Harmonic Development of the Tide Generating Potential[J]. Bulletin d’Informations de Marees Terrestres, 1987, 99: 6 817-6 855
[20] Wenzel H G. The Nanogal Software: Earth Tide Data Processing Pakage Eterna3.30[J]. Bulletin d’ Information de Marees Terrestres, 1996, 124:9 425-9 439
[21] Xu Jianqiao, Zhou Jiangcun, Chen Xiaodong, et al. Long-Term Observations of Gravity Tides from a Superconducting Gravimeter at Wuhan[J]. Chinese Journal of Geophysics, 2014, 57(10):3 091-3 102(徐建桥, 周江存, 陈晓东,等. 武汉台重力潮汐长期观测结果[J]. 地球物理学报, 2014, 57(10):3 091-3 102)
[22] Jia Jiangang, Luan Wei, Shen Wenbin. Accurate Determination of the Calibration Factor of iGrav-007 Superconducting Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2015, 40(10):1 366-1 370(贾剑钢, 栾威, 申文斌. iGrav-007超导重力仪格值的精密测定[J]. 武汉大学学报·信息科学版, 2015, 40(10):1 366-1 370)
[23] Florsch N, Hinderer J. Bayesian Estimation of the Free Core Nutation Parameters from the Analysis of Precise Tidal Gravity Data[J]. Physics of the Earth & Planetary Interiors, 2000, 117(1-4):21-35
[24] Herring T A, Gwinn C R, Shapiro I I. Geodesy by Radio Interferometry: Studies of the Forced Nutations of the Earth: 1. Data Analysis[J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B5):4 745-4 754
[25] Koot L, Rivoldini A, Viron O D, et al.Estimation of Earth Interior Parameters from a Bayesian Inversion of very Long Baseline Interferometry Nutation Time Series[J]. Journal of Geophysical Research: Solid Earth, 2008, 113:B08414
[26] Vondrák J, Ron C. New Method for Determining Free Core Nutation Parameters, Considering Geophysical Effects[J]. Astronomy & Astrophysics, 2017, 604(A56):1-7
[27] Vondrák J, Ron C. Stability of Period and Quality Factor of Free Core Nutation[J]. Acta Geodynamica et Geomaterialia, 2009, 6(3):217-224
[28] Cui Xiaoming, Sun Heping, Xu Jianqiao, et al. Temporal Variation of the Period of Free Core Nutation Derived from VLBI and Superconducting Gravity Data[J]. Chinese Journal of Geophysics, 2014, 57(2):384-391(崔小明, 孙和平, 徐建桥,等. 利用VLBI和超导重力资料研究自由核章动周期时变特征[J]. 地球物理学报, 2014, 57(2):384-391)
[29] Palmer A,Smylie D E. VLBI Observations of Free Core Nutations and Viscosity at the Top of the Core[J]. Physics of the Earth & Planetary Interiors, 2005, 148(2-4):285-301
[30] Smylie D E, Palmer A. Viscosity of Earth’s Outer Core[OL]. http://arxiv.org/abs/0709.3333, 2007
[31] Cui Xiaoming, Sun Heping, Xu Jianqiao, et al. Application of Superconductive Gravity Technique on the Constraints of Core-Mantle Coupling Parameters[J]. Sci China: Earth Sci, 2012, 55(3):513-520(崔小明, 孙和平, 徐建桥,等. 利用超导重力技术约束核幔耦合参数[J]. 中国科学:地球科学, 2012,55(3):513-520)