Uncertainty of Approximate Relationship between GIA Induced Viscous Gravity and Radial Displacement
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摘要: 根据不同地幔粘滞度的冰川均衡调整(glacial isostatic adjustment, GIA)模型, 研究了地球内部各个圈层对GIA粘性重力扰动速率的贡献, 检验了粘性重力扰动速率与径向位移速率的近似关系及其是否独立于地幔粘滞度, 同时利用绝对重力和GPS(global positioning system)径向位移数据从实测角度对Wahr的近似关系进行比较和验证.结果表明: 岩石圈对GIA重力扰动速率和大地水准面异常速率的贡献都超过了86%, 而岩石圈以下5个圈层的总贡献不大于14%;利用近似关系, 由重力信号转换的径向位移速率与有限元模拟的结果相对差异大约为15%, 且相对差异的大小不依赖于地幔粘滞度的变化; 根据北美绝对重力和GPS径向位移数据得到实测的粘性重力-径向位移比值为0.141±0.014 μGal/mm, 与Wahr的理论值(0.154 μGal/mm)非常接近, 相对差异仅为9.2%.因此, 定量给出了粘性重力-径向位移近似关系的不确定性为9.2%~15.0%, 为利用此近似关系分离GIA和现今地表质量变化粘弹信号的不确定性估计提供了重要参考.Abstract: Based on glacial isostatic adjustment (GIA) models of different mantle viscosities, the contribution from different layers in the earth's interior to the GIA viscous gravity perturbation rates is investigated, and the approximate relation between GIA gravity perturbation rate and uplift rate and whether it is independent of the mantle viscosity are validated in this paper. Furthermore, the Wahr's approximate relation with the data from absolute gravimetry and global positioning system (GPS) was checked. It is found that the contribution of the lithosphere to GIA gravity perturbation rate and geoid anomaly rate is more than 86%, the contribution of the five layers under the lithosphere to GIA gravity signal is less than 14% yet. The relative difference between GIA uplift rate calculated by using approximate relation and that by the finite element method is about 15%, and the difference does not depend on changes in the mantle viscosity. The ratio of gravity versus uplift obtained by ground-based measurements in North America is 0.141±0.014 μGal/mm, which is very close to 0.154 μGal/mm of Wahr's theoretical ratio. The relative difference between the two ratio values above is just 9.2%. Therefore, this study gives the uncertainty value of the Wahr's approximate relation between 9.2%-15.0%, which can be used to evaluate the effects on the results of the separated GIA and present-day mass balance signals.
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Key words:
- glacial isostatic adjustment /
- gravity /
- radial displacement /
- approximate relation /
- uncertainty
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图 1 不同密度界面形变对GIA重力扰动速率(左)和大地水准面异常速率(右)的贡献
(a)，(b)岩石圈以下贡献；(c)，(d)岩石圈贡献；(e)，(f)总的GIA信号
Fig. 1. Contribution to GIA gravity perturbation (left) and geoid (right) from different boundaries
图 2 不同粘滞度GIA径向位移速率及与其近似值的残差
(a), (d), (g) GIA径向位移速率; (b), (e), (h) 残差$ \varDelta \dot{U}_{\mathrm{gdot}}$；(c), (f), (i) 残差$ \varDelta \dot{U}_{\mathrm{geoid}}$
Fig. 2. GIA uplift rates derived from different viscosity and their approximation residual
图 3 绝对重力-径向位移比值
黑色实线表示的是实测重力-径向位移比率拟合值；点虚线表示的是Wahr et al.(1995)的理论值(公式(8)中的A值)
Fig. 3. Ratio of absolute gravity-uplift rates
表 1 各圈层对GIA信号贡献率的统计
Table 1. Statistics of contribution to GIA from different boundaries
圈层 $ \delta \dot{g}_{\mathrm{RMS}}$ $ \dot{N}_{\mathrm{RMS}}$ 贡献率($\delta \dot{g} $) 贡献率($\dot{N}$) 岩石圈以下 0.050 0.049 13.9% 12.8% 岩石圈 0.308 0.334 86.1% 87.2% 总信号 0.358 0.383 100% 100% 
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表 2 GIA径向位移速率残差统计
Table 2. Statistics for residual of GIA uplift rate
粘滞度模型 $\dot{U}^{\mathrm{RMS}} $ $ \Delta \dot{U}_{\text {gdot }}^{\mathrm{RMS}}$ $ \Delta \dot{U}_{\text {geoid }}^{\mathrm{RMS}}$ $ \Delta \dot{U}_{\mathrm{gdot}}^{\mathrm{RMS}} / \dot{U}^{\mathrm{RMS}} $ $ \Delta \dot{U}_{\mathrm{geoid}}^{\mathrm{RMS}} / \dot{U}^{\mathrm{RMS}}$ RF3L20(β=0.4) 2.14 0.33 0.30/0.28* 15.4 14.0%/13.1%* RF3 2.08 0.34 0.29/0.25* 16.3% 13.9%/12.0%* RF2 2.16 0.40 0.34/0.26* 18.5% 15.7%/12.0%* *根据 Purcell et al.(2011) 的研究所得结果.
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表 3 绝对重力和GPS台站位置及速率
Table 3. Absolute gravity and GPS station locations and rates
站点 经度(°) 纬度(°) 重力(μGal/a) 径向位移(mm/a) Churchill -94.086 58.762 1.45 10.38 Flin Flon -101.978 54.725 0.38 2.05 Pinawa -95.865 50.259 -0.12 -0.17 International Falls -93.162 48.585 -0.14 -0.12 Wausau -89.680 44.920 -0.17 -0.99 Iowa City -91.543 41.658 -0.08 -1.90 Saskatoon -106.399 52.195 -0.30 -1.01 Priddis -114.293 50.871 -0.30 -0.33
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[1] Altamimi, Z., Collilieux, X., Legrand, J., et al., 2007. ITRF2005: A New Release of the International Terrestrial Reference Frame Based on Time Series of Station Positions and Earth Orientation Parameters. Journal of Geophysical Research, 112(B9): B09401. doi: 10.1029/2007JB004949 [2] Bevis, M., Kendrick, E., Jr. Smalley, R., 2009. Geodetic Measurements of Vertical Crustal Velocity in West Antarctica and the Implications for Ice Mass Balance. Geochem. Geophys. Geosyst., 10(10): Q10005. doi: 10.1029/2009GC002642 [3] Blewitt, G., Lavallee, D., 2002. Effect of Annual Signals on Geodetic Velocity. Journal of Geophysical Research, 107(B7): 2145. doi: 10.1029/2001JB000570 [4] Chambers, D.P., 2006. Observing Seasonal Steric Sea Level Variations with GRACE and Satellite Altimetry. Journal of Geophysical Research, 111(C3): C03010. doi: 10.1029/2005JC002914 [5] Dziewonski, A.M., Anderson, D.L., 1981. Preliminary Reference Earth Model. Phys. Earth Planet. Int. , 25(4): 297-356. doi: 10.1016/0031-9201(81)90046-7 [6] E, D.C., Yang, Y.D., Chao, D.B., 2009. The Sea Level Change from the Antarctic Ice Sheet Based on GRACE. Chinese J. Geophys., 52(9): 2222-2228(in Chinese with English abstract). [7] Ekman, M., Mäkinen, J., 1996. Recent Postglacial Rebound, Gravity Change and Mantle Flow in Fennoscandia. Geophysical Journal International, 126(1): 229-234. doi: 10.1111/j.1365-246X.1996.tb05281.x [8] Fang, M., Hager, B.H., 2001. Vertical Deformation and Absolute Gravity. Geophysical Journal International, 146(2): 539-548. doi: 10.1046/j.0956-540x.2001.01483.x [9] Feng, W., Zhong, M., Lemoine, J.M., et al., 2013. Evaluation of Groundwater Depletion in North China Using the Gravity Recovery and Climate Experiment (GRACE) Data and Ground-Based Measurements. Water Resources Research, 49(4): 2110-2118. doi: 10.1002/wrcr.20192 [10] Guo, J.Y., Huang, Z.W., Shum, C.K., et al., 2012. Comparisons among Contemporary Glacial Isostatic Adjustment Models. Journal of Geodynamics, 61: 129-137. doi: 10.1016/j.jog.2012.03.011 [11] Hu, X.G., Chen, J.L., Zhou, Y.H., et al., 2006. Seasonal Water Storage Change of the Yangtze River Basin Detected by GRACE. Science China Earth Sciences, 36(3): 225-232(in Chinese). [12] Jia, L.L., Wang, H.S., Xiang, L.W., et al., 2011. Effects of Glacial Isostatic Adjustment on the Estimate of Ice Mass Balance over Antarctica and the Uncertainties. Chinese J. Geophys. , 54(6): 1466-1477(in Chinese with English abstract). [13] King, M.A., Bingham, R.J., Moore, P., et al., 2012. Lower Satellite-Gravimetry Estimates of Antarctic Sea-Level Contribution. Nature, 491(7425): 586-589. doi: 10.1038/nature11621 [14] Kuo, C.Y., Shum, C.K., Braun, A., et al., 2008. Vertical Motion Determined Using Satellite Altimetry and Tide Gauges. Terrestrial Atmospheric and Oceanic Sciences, 19(1-2): 21-35. doi: 10.3319/TAO.2008.19.1-2.21(SA) [15] Kuo, C.Y., Shum, C.K., Braun, A., et al., 2004. Vertical Crustal Motion Determined by Satellite Altimetry and Tide Gauge Data in Fennoscandia. Geophysical Research Letters, 31(1): L01608. doi: 10.1029/2003GL019106 [16] Lidberg, M., Johansson, J.M., Scherneck, H.G., et al., 2010. Recent Results Based on Continuous GPS Observations of the GIA Process in Fennoscandia from BIFROST. Journal of Geodynamics, 50(1): 8-18. doi: 10.1016/j.jog.2009.11.010 [17] Luo, Z.C., Li, Q., Zhang, K., et al., 2012. Trend of Mass Change in the Antarctic Ice Sheet Recovered from the GRACE Temporal Gravity Field. Science China Earth Sciences, 55(1): 76-82. doi: 10.1007/s11430-011-4275-1 [18] Mazzotti, S., Lambert, A., Henton, J., et al., 2011. Absolute Gravity Calibration of GPS Velocities and Glacial Isostatic Adjustment in Mid-Continent North America. Geophysical Research Letters, 38(24): L24311. doi: 10.1029/2011GL049846. [19] Milne, G.A., Mitrovica, J.X., Schrag, D.P., 2002. Estimating Past Continental Ice Volume from Sea-Level Data. Quaternary Science Reviews, 21(1-3): 361-376. doi: 10.1016/S0277-3791(01)00108-1 [20] Mitrovica, J.X., Forte, A.M., 1997. Radial Profile of Mantle Viscosity: Results from the Joint Inversion of Convection and Post-Glacial Rebound Observables. Journal of Geophysical Research, 102(B2): 2751-2769. doi: 10.1029/96JB03175 [21] Peltier, W.R., 1998. Postglacial Variations in the Level of the Sea: Implications for Climate Dynamics and Solid-Earth Geophysics. Reviews of Geophysics, 36(4): 603-689. doi: 10.1029/98RG02638 [22] Peltier, W.R., 2002. Global Glacial Isostatic Adjustment: Palaeogeodetic and Space-Geodetic Tests of the ICE-4G (VM2) Model. Journal of Quaternary Science, 17(5-6): 491-510. doi: 10.1002/jqs.713 [23] Purcell, A., Dehecq, A., Tregoning, P., et al., 2011. Relationship between Glacial Isostatic Adjustment and Gravity Perturbations Observed by GRACE. Geophysical Research Letters, 38(18): L18305. doi: 10.1029/2011GL048624 [24] Sella, G.F., Stein, S., Dixon, T.H., 2007. Observation of Glacial Isostatic Adjustment in "Stable" North America with GPS. Geophysical Research Letters, 34(2): L02306. doi: 10.1029/2006GL027081 [25] Sun, W.K., Miura, S., Sato, T., et al., 2010. Gravity Measurements in Southeastern Alaska Reveal Negative Gravity Rate of Change Caused by Glacial Isostatic Adjustment. Journal of Geophysical Research, 115(B12): B12406. doi: 10.1029/2009JB007194 [26] Tamisiea, M.E., 2011. Ongoing Glacial Isostatic Contributions to Observations of Sea Level Change. Geophysical Journal International, 186(3): 1036-1044. doi: 10.1111/j.1365-246X.2011.05116.x [27] Thomas, I.D., King, M.A., Bentley, M.J., et al., 2011. Widespread Low Rates of Antarctic Glacial Isostatic Adjustment Revealed by GPS Observations. Geophysical Research Letters, 38(22): L22302. doi: 10.1029/2011GL049277 [28] Velicogna, I., Wahr, J., 2006. Measurements of Time-Variable Gravity Show Mass Loss in Antarctica. Science, 311(5768): 1754-1756. doi: 10.1126/science.1123785 [29] Wahr, J., Han, D., Trupin, A., 1995. Predictions of Vertical Uplift Caused by Changing Polar Ice volumes on a Viscoelatic Earth. Geophysical Research Letters, 22(8): 977-980. doi: 10.1029/94GL02840 [30] Wahr, J., Wingham, D., Bentley, C., 2000. A Method of Combing ICESat and GRACE Satellite Data to Constrain Antarctica Mass Balance. Journal of Geophysical Research, 105(B7): 16279-16294. doi: 10.1029/2000JB900113 [31] Wang, H.S., Wu, P., Wouter, V.D.W., et al., 2009. Glacial Isostatic Adjustment Model Constrained by Geodetic Measurments and Relative Sea Level. Chinese J. Geophys. , 52(10): 2450-2460(in Chinese with English abstract). [32] Wang, H.S., Wu, P., Xu, H.Z., 2009. A Review of Research in Glacial Isostatic Adjustment. Progress in Geophys. , 24(6): 1958-1967(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200906006.htm [33] Wang, H.S., Jia, L.L., Wu, P., et al., 2010. Effects of Global Glacial Isostatic Adjustment on the Secular Changes of Gravity and Sea Level in East Asia. Chinese J. Geophys. , 53(11): 2590-2602(in Chinese with English abstract). [34] Wang, H.S., Jia, L.L., Steffen, H., et al., 2013. Increased Water Storage in North America and Scandinavia from GRACE Gravity Data. Nature Geoscience, 6(1): 38-42. doi: 10.1038/NGEO1652 [35] Wang, H.S., Wu, P., Jia, L.L., et al., 2011. The Role of Glacial Isostatic Adjustment in the Present-Day Crustal Motion and Sea Levels of East Asia. Earth Planets Space, 63(8): 915-928. doi: 10.5047/eps.2011.05.002 [36] Wang, H.S., Wu, P., 2006., Effects of Lateral Variations in Lithospheric Thickness and Mantle Viscosity on Glacially Induced Surface Motion on a Spherical, Self-Gravitating Maxwell Earth. Earth and Planetary Science Letters, 244(3-4): 576-589. doi: 10.1016/j.epsl.2006.02.026 [37] Wang, H.S., Wu, P., Wal, W.V.D., 2008. Using Postglacial Sea Level, Crustal Velocities and Gravity-Rate-of-Change to Constrain the Influence of Thermal Effects on Mantle Lateral Heterogeneities. Journal of Geodynamics, 46(3-5): 104-117. doi: 10.1016/j.jog.2008.03.003 [38] Wang, H.S., Wang, Z.Y., Yuan, X.D., et al., 2007. Water Storage Changes in Three Gorges Water Systems Area Inferred from GRACE Time-Variable Gravity Data. Chinese J. Geophys., 50(3): 730-736(in Chinese with English abstract). [39] Wessel, P., Smith, W.H., 1991. Free Software Helps Map and Display Data. Eos, Transactions American Geophysical Union, 72(41): 441-446. doi: 10.1029/90EO00319 [40] Wu, J., Liu, Q., 2012. Pollen-Recorded Vegetation and Climate Changes from Moon Lake since Late Glacial. Earth Science—Journal of China University of Geoscience, 37(5): 947-954(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQKX201205010.htm [41] Wu, P., 2004. Using Commercial Finite Element Packages for the Study of Earth Deformations, Sea Levels and the State of Stress. Geophysical Journal International, 158(2): 401-408. doi: 10.1111/j.1365-246X.2004.02338.x [42] Wu, P., Wang, H.S., Steffen, H., 2013. The Role of Thermal Effect on Mantle Seismic Anomalies under Laurentia and Fennoscandia from Observations of Glacial Isostatic Adjustment. Geophysical Journal International, 192(1): 7-17. doi: 10.1093/gji/ggs009 [43] Wu, X.P., Heflin, M.B., Schotman, H., et al., 2010. Simultaneous Estimation of Global Present-Day Water Transport and Glacial Isostatic Adjustment. Nature Geoscience, 3(9): 642-646. doi: 10.1038/ngeo938 [44] Zhou, X., Sun, W.K., Zhao, B., et al., 2012. Geodetic Observations Detecting Coseismic Displacements and Gravity Changes Caused by the Mw=9.0 Tohoku-Oki Earthquake. Journal of Geophysical Research, 117(B5): B05408. doi: 10.1029/2011JB008849H [45] 鄂栋臣, 杨元德, 晁定波, 2009. 基于GRACE资料研究南极冰盖消减对海平面的影响. 地球物理学报, 52(9): 2222-2228. doi: 10.3969/j.issn.0001-5733.2009.09.005 [46] 胡小工, 陈剑利, 周永宏, 等, 2006. 利用GRACE空间重力测量监测长江流域水储量的季节性变化. 中国科学, 36(3): 225-232. https://www.cnki.com.cn/Article/CJFDTOTAL-JDXK200603002.htm [47] 贾路路, 汪汉胜, 相龙伟, 等, 2011. 冰川均衡调整对南极冰质量平衡监测的影响及其不确定性. 地球物理学报, 54(6): 1466-1477. doi: 10.3969/j.issn.0001-5733.2011.06.006 [48] 汪汉胜, Wu, P., Wouter, V.D.W., 等, 2009. 大地测量观测和相对海平面联合约束的冰川均衡调整模型. 地球物理学报, 52(10): 2450-2460. doi: 10.3969/j.issn.0001-5733.2009.10.004 [49] 汪汉胜, Wu, P., 许厚泽, 2009. 冰川均衡调整(GIA)的研究. 地球物理学进展, 24(6): 1958-1967. doi: 10.3969/j.issn.1004-2903.2009.06.005 [50] 汪汉胜, 贾路路, Wu, P., 等, 2010. 冰川均衡调整对东亚重力和海平面变化的影响. 地球物理学报, 53(11): 2590-2602. https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX201011010.htm [51] 汪汉胜, 王志勇, 袁旭东, 等, 2007. 基于GRACE时变重力场的三峡水库补给水系水储量变化. 地球物理学报, 50(3): 730-736. doi: 10.3321/j.issn:0001-5733.2007.03.011 [52] 伍婧, 刘强, 2012. 晚冰期以来月亮湖孢粉记录反映的古植被与古气候演化. 地球科学——中国地质大学学报, 37(5): 947-954 https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201205010.htm -
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