GRACE卫星时变重力场滤波方法研究进展
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摘要
GRACE卫星的成功发射为连续监测全球地表质量变化提供了直接有效的观测手段,在陆地水储量变化、冰川融化以及地震同震等领域得到了广泛应用,取得了重大研究进展.受卫星轨道特性和测量误差等因素影响,直接应用GRACE时变重力场模型的反演结果中会呈现严重条带误差,必须采用滤波方法进行处理.球谐系数法是当前GRACE卫星时变重力场研究中应用最广泛的方法,滤波作为球谐系数法的关键环节,对去条带误差具有至关重要的影响.本文从GRACE时变重力场数据处理方法入手,对高斯类滤波、去相关类滤波以及其他滤波方法进行了分类讨论,对不同方法的原理和特点进行了评述和对比分析,并对GRACE卫星时变重力场滤波方法后续的改进和发展进行了展望.
The successful launch of the GRACE satellites provides a direct and effective way of global surface mass variations monitoring. GRACE satellites time-variable gravity has been widely used in the fields of water storage,glacier melting,earthquake coseismic and so on. The study of time-variable gravity has made a great progress. Affected by satellites orbit characteristics and measurement errors,the inversion results are presented by serious stripes errors with using GRACE time-variable gravity models directly. Filtering as the key step of spherical harmonic coefficients method is necessary. It has a crucial influence on destripe. The Gaussian filtering,de-correlated filtering and other filtering methods are discussed. The principle and characteristics of different filtering methods are analyzed. Further improvements and developments are prospected at last.
The successful launch of the GRACE satellites provides a direct and effective way of global surface mass variations monitoring. GRACE satellites time-variable gravity has been widely used in the fields of water storage,glacier melting,earthquake coseismic and so on. The study of time-variable gravity has made a great progress. Affected by satellites orbit characteristics and measurement errors,the inversion results are presented by serious stripes errors with using GRACE time-variable gravity models directly. Filtering as the key step of spherical harmonic coefficients method is necessary. It has a crucial influence on destripe. The Gaussian filtering,de-correlated filtering and other filtering methods are discussed. The principle and characteristics of different filtering methods are analyzed. Further improvements and developments are prospected at last.
引文
Baur O,Sneeuw N.2011.Assessing Greenland ice mass loss by means of point-mass modeling:A viable methodology[J].Journal of Geodesy,85(9):607-615.
Belda S,David G-G,JoséM F.2015.On the decorrelation filtering of RL05 GRACE data for global applications[J].Geophysical Journal International,200(1):173-184.
Chambers D P.2006.Evaluation of new GRACE time-variable gravity data over the ocean[J].Geophysical Research Letters,33(17):389-390.
Chambers D P,Bonin J A.2012.Evaluation of release-05 GRACE timevariable gravity coefficients over the ocean[J].Ocean Science,8(5):859-868.
Davis J L,Tamisiea M E,Elósegui P,et al.2008.A statistical filtering approach for Gravity Recovery and Climate Experiment(GRACE)gravity data[J].Journal of Geophysical Research,113(B4):B04410.
Chen J L,Rodell M,Wilson C R,et al.2005.Low degree spherical harmonic influences on Gravity Recovery and Climate Experiment(GRACE)water storage estimates[J].Geophysical Research Letters,32(14):57-76.
Chen J L,Wilson C R,Famiglietti J S.2007a.Attenuation effect on seasonal basin-scale water storage changes from GRACE timevariable gravity[J].Journal of Geodesy,81(4):237-245.
Chen J L,Wilson C R,Seo K W.2006.Optimized smoothing of Gravity Recovery and Climate Experiment(GRACE)time-variable gravity observations[J].Journal of Geophysical Research,111(B6):B06408.
Chen J L,Wilson C R,Tapley B D,et al.2007b.GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake[J].Geophysical Research Letters,34(13):173-180.
Duan X J,Guo J Y,Shum C K,et al.2009.On the postprocessing removal correlated errors in GRACE temporal gravity field solutions[J].Journal of Geodesy(in Chinese),83:1095-1106.
Feng W.2013.Regional terrestrial water storage and sea level variations inferred from satellite gravimetry[D](in Chinese).Beijing:University of Chinese Academy of Sciences.
Gao C C,Lu Y,Zhang Z Z,et al.2015.Ice sheet mass balance in Antarctica measured by GRACE and its uncertainty[J].Chinese J.Geophys(in Chinese),58(3):780-792,doi:10.6038/cjg20150308.
Guo F X,Miao Y W,Xiao Y,et al.2017.Recovery water storage variation in China and its adjacent area by method of point-mass mode[J].Geomatics and Information Science of Wuhan University(in Chinese),42(7):1002-1007.
Guo F X,Xiao Y,Wang F F.2014.Mascon inversion method of earth surface mass anomaly using GRACE range rate data[J].Progress in Geophysics(in Chinese),29(6):2494-2497,doi:10.6038/pg20140602.
Guo J Y,Mu D P,Liu X,et al.2014.Equivalent water height extracted from GRACE gravity field model with robust independent component analysis[J].Acta Geophysica,62(4):953-972.
Han S C,Shum C K,Jekeli C,et al.2005a.Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement[J].Geophs.J.Int,163:18-25.
Han S C,Shum C K,Jekeli C,et al.2005b.Improved estimation of terrestrial water storage changes from GRACE[J].Geophysical Research Letters,32(7):99-119.
Han S C,Shum C K,Jekeli C,et al.2005c.Non-isotropic filtering of GRACE temporal gravity for geophysical[J].Geophysical Journal International,163(1):18-25.
Jekeli C.1981.Alternative methods to smooth the Earth’s gravity field[R].Technical Report Rep327,Columbus:Department of Geodesy and Science and Surveying,Ohio State University.
Ju X L,Shen Y Z,Chen Q J.2016.Analysis on GRACE gravity data based on a simple weighted average de-correlation filter[J].Journal of Geodesy and Geodynamics(in Chinese),36(2):129-133.
Klees R,Revtova E A,Gunter B C,et al.2008.The design of an optimal filter for monthly GRACE gravity models[J].Geophysical Journal Of the Royal Astronomical Society,175(2):417-432.
Kusche J.2007.Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models[J].Journal of Geodesy,81(11):733-749.
Kusche J,Schmidt R,Petrovic S,et al.2009.Decorrelated GRACEtime-variable gravity solutions by GFZ and their validation using a hydrological model[J].Journal of Geodesy,83(10):903-913.
Liao M S,Zhang X P,Huang H,et al.2016.Monitoring water storage changes in Dongting lake basin from GRACE gravity satellite[J].Progress in Geophysics(in Chinese),31(1):61-68,doi:10.6038/pg20160107.
Li Q,Luo Z C,Zhang B,et al.2013.Terrestrial water storage changes of the 2010 southwest China drought detected by GRACE temporal gravity field[J].Chinese Journal Geophysics(in Chinese),56(6):1843-1849,doi:10.6038/cjg20130606.
Li W D,Chang X T,Zhu G B,et al.2015.The inversion of terrestrial water storage changes by means of multi-channel singular spectrum combination filter[J].Science of Surveying and Mapping(in Chinese),40(12):16-20.
Lu F.2015.Global mass change analysis in recent ten years by GRACERL05 data[D].Chengdu:Southwest Jiaotong University.
Lu F,You W,Fan D M,et al.2015.Chinese continental water storage and ocean water mass variations analysis in recent ten years based on GRACE RL05 data[J].Acta Geodaetica et Cartographica Sinica(in Chinese),44(2):160-167.
Mu D P,Guo J Y,Sun Z C,et al.2014.Equivalent water height from GRACE gravity model based on principal component analysis[J].Progress in Geophysica(in Chinese),29(4):1512-1517,doi:10.6038/pg20140405.
Rowlands D D,Luthcke S B,Mc Carthy J J,et al.2010.Global mass flux solutions from GRACE:A comparison of parameter estimation strategies-Mass concentrations versus Stokes coefficients[J].Journal of Geophysical Research,115(B1),B01403.
Sasgen I,Martinec Z,Fleming K.2007.Wiener optimal combination and evaluation of the Gravity Recovery and Climate Experiment(GRACE)gravity fields over Antarctica[J].Journal of Geophysical Research,112(B4):B04401.
Seo K W,Wilson C R,Famiglietti J S,et al.2006.Terrestrial water mass load changes from Gravity Recovery and Climate Experiment(GRACE)[J].Water Resources Research,42(5),W05417.
SU Yong,YU Bing,YOU Wei,et al.2017.Surface mass distribution from gravity satellite observations by using three-dimensional pointmass modeling approach.Chinese Journal Of Geophysics,60(1):50-60,doi:10.6038/cjg20170105.
Swenson S,Wahr J.2002.Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment(GRACE)measurement of time-variable gravity[J].Journal of Geophysical,107(B9):2193.
Swenson S,Wahr J.2006.Post-pocessing removal of correlated errors in GRACE data[J].Geophysical Research Letter,33(8):L08402.
Swenson S,Wahr J.2007.Multi-sensor analysis of water storage variations of the Caspian Sea[J].Geophysical Research Letters,34(16):L16401.
Velicogna I,Wahr J.2006.Measurements of time-variable gravity snow mass loss in Antarctica[J].Science,311(5768):1754-1756.
Wahr J,Molenaar M,Bryan F.1998.Time variability of the Earth’s gravity field:Hydrological and oceanic effects and their possible detection using GRACE[J].Journal of Geophysical Research,103(B12):30205-30209.
Wouters B,Schrama E J O.2007.Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics[J].Geophysical Research Letters,34(23):229-241.
Xi H,Zhang Z Z,Lu Y,et al.2016.The Performances of Different Filtering Methods on Ocean Mass Change Estimated from GRACE[J].Journal of Geodesy and Geodynamics(in Chinese),36(5):380-386.
Xu C J,Gong Z.2016.Review of post-processing methods on GRACEtime varied gravity data[J].Geomatics and Information Science of Wuhan University(in Chinese),41(4):503-510.
Zhan J G,Wang Y,Hao X G.2011.Improved method for removal of correlated errors in GRACE data[J].Acta Geodaetica et Cartographica Sinica(in Chinese),40(4):442-447.
Zhan J G,Wang Y,Shi H L,et al.2015.Removing correlative errors in GRACE data by the smoothness priors method[J].Chinese Journal Geophysics(in Chinese),58(4):1135-1144,doi:10.6038/cjg20150404.
Zhang Z Z,Chao B F,Lu Y,et al.2009.An effective filtering for GRACE time-variable gravity:Fan filter[J].Geophysical Research Letter,36(17):1397-1413.
Zhou X,Sun W K,Fu G Yu.2011.Gravity satellite GRACE detects coseismic gravity changes caused by 2010 Chile MW8.8 earthquake[J].Chinese Journal Geophysics(in Chinese),54(7):1745-1749,doi:10.3969/j.issn.0001-5733.2011.07.007.
冯伟.2013.区域陆地水与海平面变化的卫星重力监测研究[D].北京:中国科学院大学.
高春春,陆洋,张子占,等.2015.GRACE重力卫星探测南极冰盖质量平衡及其不确定性[J].地球物理学报,58(3):780-792,doi:10.6038/cjg20150308.
郭飞霄,苗岳旺,肖云,等.2017.采用点质量模型方法反演中国大陆及周边地区陆地水储量变化[J].武汉大学学报信息科学版,42(7):1002-1007.
郭飞霄,肖云,汪菲菲.2014.利用GRACE星间距离变率数据反演地球表层质量变化的Mascon方法[J].地球物理学进展,29(6):2494-2497,doi:10.6038/pg20140602.
鞠晓蕾,沈云中,陈秋杰.2016.GRACE时变重力场条带误差加权平均去相关滤波方法[J].大地测量与地球动力学,36(2):129-133.
廖梦思,章新平,黄煌,等.2016.利用GRACE卫星监测近10年洞庭湖流域水储量变化[J].地球物理学进展,31(1):61-68,doi:10.6038/pg20160107.
李琼,罗志才,钟波,等.2013.利用GRACE时变重力场探测2010年中国西南干旱陆地水储量变化[J].地球物理学报,56(6):1843-1849,doi:10.6038/cjg20130606.
李武东,常晓涛,朱广彬,等.2015.多通道奇异谱组合滤波反演水储量变化[J].测绘科学,40(12):16-21.
卢飞.2015.基于GRACE RL05数据的近十年全球质量变化分析[D].成都:西南交通大学.
卢飞,游为,范东明,等.2015.由GRACE RL05数据反演近10年中国大陆水储量及海水质量变化[J].测绘学报,44(2):160-167.
穆大鹏,郭金运,孙中昶,等.2014.基于主成分分析的GRACE重力场模型等效水高[J].地球物理学进展,29(4):1512-1517,doi:10.6038/pg20140405.
苏勇,于冰,游为,等.2017.基于重力卫星数据监测地表质量变化的三维点质量模型法.地球物理学报,60(1):50-60,doi:10.6038/cjg20170105.
郗慧,张子占,陆洋,等.2016.利用GRACE监测全球海水质量变化时滤波处理的影响分析[J].大地测量与地球动力学,36(5):380-386.
许才军,龚正.2016.GRACE时变重力数据的后处理方法研究进展[J].武汉大学学报信息科学版,41(4):503-510.
詹金刚,王勇,郝晓光.2011.GRACE时变重力位系数误差的改进去相关算法[J].测绘学报,40(4):0-441.
詹金刚,王勇,史红岭,等.2015.应用平滑先验信息方法移除GRACE数据中相关误差[J].地球物理学报,58(4):1135-1144,doi:10.6038/cjg20150404.
周新,孙文科,付广裕,等.2011.重力卫星GRACE检测出2010年智利MW8.8地震的同震重力变化[J].地球物理学报,54(7):1745-1749,doi:10.3969/j.issn.0001-5733.2011.07.007.
Belda S,David G-G,JoséM F.2015.On the decorrelation filtering of RL05 GRACE data for global applications[J].Geophysical Journal International,200(1):173-184.
Chambers D P.2006.Evaluation of new GRACE time-variable gravity data over the ocean[J].Geophysical Research Letters,33(17):389-390.
Chambers D P,Bonin J A.2012.Evaluation of release-05 GRACE timevariable gravity coefficients over the ocean[J].Ocean Science,8(5):859-868.
Davis J L,Tamisiea M E,Elósegui P,et al.2008.A statistical filtering approach for Gravity Recovery and Climate Experiment(GRACE)gravity data[J].Journal of Geophysical Research,113(B4):B04410.
Chen J L,Rodell M,Wilson C R,et al.2005.Low degree spherical harmonic influences on Gravity Recovery and Climate Experiment(GRACE)water storage estimates[J].Geophysical Research Letters,32(14):57-76.
Chen J L,Wilson C R,Famiglietti J S.2007a.Attenuation effect on seasonal basin-scale water storage changes from GRACE timevariable gravity[J].Journal of Geodesy,81(4):237-245.
Chen J L,Wilson C R,Seo K W.2006.Optimized smoothing of Gravity Recovery and Climate Experiment(GRACE)time-variable gravity observations[J].Journal of Geophysical Research,111(B6):B06408.
Chen J L,Wilson C R,Tapley B D,et al.2007b.GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake[J].Geophysical Research Letters,34(13):173-180.
Duan X J,Guo J Y,Shum C K,et al.2009.On the postprocessing removal correlated errors in GRACE temporal gravity field solutions[J].Journal of Geodesy(in Chinese),83:1095-1106.
Feng W.2013.Regional terrestrial water storage and sea level variations inferred from satellite gravimetry[D](in Chinese).Beijing:University of Chinese Academy of Sciences.
Gao C C,Lu Y,Zhang Z Z,et al.2015.Ice sheet mass balance in Antarctica measured by GRACE and its uncertainty[J].Chinese J.Geophys(in Chinese),58(3):780-792,doi:10.6038/cjg20150308.
Guo F X,Miao Y W,Xiao Y,et al.2017.Recovery water storage variation in China and its adjacent area by method of point-mass mode[J].Geomatics and Information Science of Wuhan University(in Chinese),42(7):1002-1007.
Guo F X,Xiao Y,Wang F F.2014.Mascon inversion method of earth surface mass anomaly using GRACE range rate data[J].Progress in Geophysics(in Chinese),29(6):2494-2497,doi:10.6038/pg20140602.
Guo J Y,Mu D P,Liu X,et al.2014.Equivalent water height extracted from GRACE gravity field model with robust independent component analysis[J].Acta Geophysica,62(4):953-972.
Han S C,Shum C K,Jekeli C,et al.2005a.Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement[J].Geophs.J.Int,163:18-25.
Han S C,Shum C K,Jekeli C,et al.2005b.Improved estimation of terrestrial water storage changes from GRACE[J].Geophysical Research Letters,32(7):99-119.
Han S C,Shum C K,Jekeli C,et al.2005c.Non-isotropic filtering of GRACE temporal gravity for geophysical[J].Geophysical Journal International,163(1):18-25.
Jekeli C.1981.Alternative methods to smooth the Earth’s gravity field[R].Technical Report Rep327,Columbus:Department of Geodesy and Science and Surveying,Ohio State University.
Ju X L,Shen Y Z,Chen Q J.2016.Analysis on GRACE gravity data based on a simple weighted average de-correlation filter[J].Journal of Geodesy and Geodynamics(in Chinese),36(2):129-133.
Klees R,Revtova E A,Gunter B C,et al.2008.The design of an optimal filter for monthly GRACE gravity models[J].Geophysical Journal Of the Royal Astronomical Society,175(2):417-432.
Kusche J.2007.Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models[J].Journal of Geodesy,81(11):733-749.
Kusche J,Schmidt R,Petrovic S,et al.2009.Decorrelated GRACEtime-variable gravity solutions by GFZ and their validation using a hydrological model[J].Journal of Geodesy,83(10):903-913.
Liao M S,Zhang X P,Huang H,et al.2016.Monitoring water storage changes in Dongting lake basin from GRACE gravity satellite[J].Progress in Geophysics(in Chinese),31(1):61-68,doi:10.6038/pg20160107.
Li Q,Luo Z C,Zhang B,et al.2013.Terrestrial water storage changes of the 2010 southwest China drought detected by GRACE temporal gravity field[J].Chinese Journal Geophysics(in Chinese),56(6):1843-1849,doi:10.6038/cjg20130606.
Li W D,Chang X T,Zhu G B,et al.2015.The inversion of terrestrial water storage changes by means of multi-channel singular spectrum combination filter[J].Science of Surveying and Mapping(in Chinese),40(12):16-20.
Lu F.2015.Global mass change analysis in recent ten years by GRACERL05 data[D].Chengdu:Southwest Jiaotong University.
Lu F,You W,Fan D M,et al.2015.Chinese continental water storage and ocean water mass variations analysis in recent ten years based on GRACE RL05 data[J].Acta Geodaetica et Cartographica Sinica(in Chinese),44(2):160-167.
Mu D P,Guo J Y,Sun Z C,et al.2014.Equivalent water height from GRACE gravity model based on principal component analysis[J].Progress in Geophysica(in Chinese),29(4):1512-1517,doi:10.6038/pg20140405.
Rowlands D D,Luthcke S B,Mc Carthy J J,et al.2010.Global mass flux solutions from GRACE:A comparison of parameter estimation strategies-Mass concentrations versus Stokes coefficients[J].Journal of Geophysical Research,115(B1),B01403.
Sasgen I,Martinec Z,Fleming K.2007.Wiener optimal combination and evaluation of the Gravity Recovery and Climate Experiment(GRACE)gravity fields over Antarctica[J].Journal of Geophysical Research,112(B4):B04401.
Seo K W,Wilson C R,Famiglietti J S,et al.2006.Terrestrial water mass load changes from Gravity Recovery and Climate Experiment(GRACE)[J].Water Resources Research,42(5),W05417.
SU Yong,YU Bing,YOU Wei,et al.2017.Surface mass distribution from gravity satellite observations by using three-dimensional pointmass modeling approach.Chinese Journal Of Geophysics,60(1):50-60,doi:10.6038/cjg20170105.
Swenson S,Wahr J.2002.Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment(GRACE)measurement of time-variable gravity[J].Journal of Geophysical,107(B9):2193.
Swenson S,Wahr J.2006.Post-pocessing removal of correlated errors in GRACE data[J].Geophysical Research Letter,33(8):L08402.
Swenson S,Wahr J.2007.Multi-sensor analysis of water storage variations of the Caspian Sea[J].Geophysical Research Letters,34(16):L16401.
Velicogna I,Wahr J.2006.Measurements of time-variable gravity snow mass loss in Antarctica[J].Science,311(5768):1754-1756.
Wahr J,Molenaar M,Bryan F.1998.Time variability of the Earth’s gravity field:Hydrological and oceanic effects and their possible detection using GRACE[J].Journal of Geophysical Research,103(B12):30205-30209.
Wouters B,Schrama E J O.2007.Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics[J].Geophysical Research Letters,34(23):229-241.
Xi H,Zhang Z Z,Lu Y,et al.2016.The Performances of Different Filtering Methods on Ocean Mass Change Estimated from GRACE[J].Journal of Geodesy and Geodynamics(in Chinese),36(5):380-386.
Xu C J,Gong Z.2016.Review of post-processing methods on GRACEtime varied gravity data[J].Geomatics and Information Science of Wuhan University(in Chinese),41(4):503-510.
Zhan J G,Wang Y,Hao X G.2011.Improved method for removal of correlated errors in GRACE data[J].Acta Geodaetica et Cartographica Sinica(in Chinese),40(4):442-447.
Zhan J G,Wang Y,Shi H L,et al.2015.Removing correlative errors in GRACE data by the smoothness priors method[J].Chinese Journal Geophysics(in Chinese),58(4):1135-1144,doi:10.6038/cjg20150404.
Zhang Z Z,Chao B F,Lu Y,et al.2009.An effective filtering for GRACE time-variable gravity:Fan filter[J].Geophysical Research Letter,36(17):1397-1413.
Zhou X,Sun W K,Fu G Yu.2011.Gravity satellite GRACE detects coseismic gravity changes caused by 2010 Chile MW8.8 earthquake[J].Chinese Journal Geophysics(in Chinese),54(7):1745-1749,doi:10.3969/j.issn.0001-5733.2011.07.007.
冯伟.2013.区域陆地水与海平面变化的卫星重力监测研究[D].北京:中国科学院大学.
高春春,陆洋,张子占,等.2015.GRACE重力卫星探测南极冰盖质量平衡及其不确定性[J].地球物理学报,58(3):780-792,doi:10.6038/cjg20150308.
郭飞霄,苗岳旺,肖云,等.2017.采用点质量模型方法反演中国大陆及周边地区陆地水储量变化[J].武汉大学学报信息科学版,42(7):1002-1007.
郭飞霄,肖云,汪菲菲.2014.利用GRACE星间距离变率数据反演地球表层质量变化的Mascon方法[J].地球物理学进展,29(6):2494-2497,doi:10.6038/pg20140602.
鞠晓蕾,沈云中,陈秋杰.2016.GRACE时变重力场条带误差加权平均去相关滤波方法[J].大地测量与地球动力学,36(2):129-133.
廖梦思,章新平,黄煌,等.2016.利用GRACE卫星监测近10年洞庭湖流域水储量变化[J].地球物理学进展,31(1):61-68,doi:10.6038/pg20160107.
李琼,罗志才,钟波,等.2013.利用GRACE时变重力场探测2010年中国西南干旱陆地水储量变化[J].地球物理学报,56(6):1843-1849,doi:10.6038/cjg20130606.
李武东,常晓涛,朱广彬,等.2015.多通道奇异谱组合滤波反演水储量变化[J].测绘科学,40(12):16-21.
卢飞.2015.基于GRACE RL05数据的近十年全球质量变化分析[D].成都:西南交通大学.
卢飞,游为,范东明,等.2015.由GRACE RL05数据反演近10年中国大陆水储量及海水质量变化[J].测绘学报,44(2):160-167.
穆大鹏,郭金运,孙中昶,等.2014.基于主成分分析的GRACE重力场模型等效水高[J].地球物理学进展,29(4):1512-1517,doi:10.6038/pg20140405.
苏勇,于冰,游为,等.2017.基于重力卫星数据监测地表质量变化的三维点质量模型法.地球物理学报,60(1):50-60,doi:10.6038/cjg20170105.
郗慧,张子占,陆洋,等.2016.利用GRACE监测全球海水质量变化时滤波处理的影响分析[J].大地测量与地球动力学,36(5):380-386.
许才军,龚正.2016.GRACE时变重力数据的后处理方法研究进展[J].武汉大学学报信息科学版,41(4):503-510.
詹金刚,王勇,郝晓光.2011.GRACE时变重力位系数误差的改进去相关算法[J].测绘学报,40(4):0-441.
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