反演地表质量变化的附有空间约束的三维加速度点质量模型法
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摘要
重力卫星可以在相同误差尺度下对全球质量变化进行连续重复观测,并在近十余年来取得了巨大成功,探索重力卫星数据精化处理方法和相关应用研究具有重要意义.本文基于三维加速度点质量模型法的基本原理,进一步发展建立了时变重力场模型球谐位系数的变化和地面点质量变化的关系,可有效考虑地表质量变化导致的负荷形变的影响;引入等权形式、线性形式、指数形式和高斯形式的空间约束方法处理南北条带噪声和向下延拓导致的病态问题,并与零阶Tikhonov正则化方法进行对比分析.采用模拟数据和一个月的实测GRACE时变重力场模型计算全球质量变化,对三维加速度点质量模型法和几种空间约束方法进行对比分析验证.计算结果表明,对于3°等面积的全球格网质量点,高斯和指数形式空间约束方法的最优相关距离约为500km,等权和线性形式空间约束方法的最优相关距离约为600km,各方法均可有效处理条带噪声的影响,四种空间约束方法的计算效果优于零阶Tikhonov正则化方法,本文的相关方法为进一步利用三维加速度点质量模型法监测全球质量变化提供了借鉴.
Global mass distribution could be continuously and repeatedly detected by gravity satellites at the same error scale,and great success has been achieved in related work in the past decades.It is valuable to continue studying the refinement methods and related applications of gravity satellite data.In this study,the relationship between the spherical harmonic coefficient variation of time-variable gravity field models and the mass change on the Earth′s surface is developed,which is based on the basic principle of three-dimensional acceleration point-massmodeling approach(3 D-PMA).The effect of the load deformation caused by the change of the Earth′s surface mass distribution can be effectively considered in this method.The uniform-type,linear-type,exponential-type and Gaussian-type spatial constraint methods are introduced to smooth the north-south strip noise and to stabilize the ill-posed problems caused by downward continuation,and at the same time,the four spatial constraint methods are compared with zero-order Tikhonov regularization method.In order to compare and validate the three-dimensional acceleration pointmass modeling approach and four spatial constraint methods,the global mass distribution is computed by simulation data and one-month GRACE time-variable gravity solution(CSR-RL05 version data).The calculation results show that the optimal distance of exponential-type,Gaussian-type and uniform-type,linear-type spatial constraint methods is about 500 km and 600 km when 3-degree equal-area grid is used to arrange mass point on the Earth′s surface.The influence of north-south strip noise can be effectively constrained by the spatial constraint methods,and four spatial constraint methods are better than zero-order Tikhonov regularization method.In general,it has provided reference for further use of gravity satellite data to monitor global mass change with relevant methods investigated in this paper.
Global mass distribution could be continuously and repeatedly detected by gravity satellites at the same error scale,and great success has been achieved in related work in the past decades.It is valuable to continue studying the refinement methods and related applications of gravity satellite data.In this study,the relationship between the spherical harmonic coefficient variation of time-variable gravity field models and the mass change on the Earth′s surface is developed,which is based on the basic principle of three-dimensional acceleration point-massmodeling approach(3 D-PMA).The effect of the load deformation caused by the change of the Earth′s surface mass distribution can be effectively considered in this method.The uniform-type,linear-type,exponential-type and Gaussian-type spatial constraint methods are introduced to smooth the north-south strip noise and to stabilize the ill-posed problems caused by downward continuation,and at the same time,the four spatial constraint methods are compared with zero-order Tikhonov regularization method.In order to compare and validate the three-dimensional acceleration pointmass modeling approach and four spatial constraint methods,the global mass distribution is computed by simulation data and one-month GRACE time-variable gravity solution(CSR-RL05 version data).The calculation results show that the optimal distance of exponential-type,Gaussian-type and uniform-type,linear-type spatial constraint methods is about 500 km and 600 km when 3-degree equal-area grid is used to arrange mass point on the Earth′s surface.The influence of north-south strip noise can be effectively constrained by the spatial constraint methods,and four spatial constraint methods are better than zero-order Tikhonov regularization method.In general,it has provided reference for further use of gravity satellite data to monitor global mass change with relevant methods investigated in this paper.
引文
Baur O,Sneeuw N.2011.Assessing Greenland ice mass loss by means of point-mass modeling:a viable methodology.Journal of Geodesy,85(9):607-615,doi:10.1007/s00190-011-0463-1.
Baur O.2013.Greenland mass variation from time-variable gravity in the absence of GRACE.Geophysical Research Letters,40(16):4289-4293,doi:10.1002/grl.50881.
Chen T Y,Shen Y Z,Chen Q J.2016.Mass flux solution in the Tibetan plateau using Mascon modeling.Remote Sensing,8(5):439,doi:10.3390/rs8050439.
Dahle C,Flechtner F,Gruber C,et al.2013.GFZ GRACE level-2processing standards document for level-2product release 0005,Revised Edition,January 2013,doi:10.2312/GFZ.b103-1202-25.
Duan X J,Guo J Y,Shum C K,et al.2009.On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions.Journal of Geodesy,83(11):1095-1106,doi:10.1007/s00190-009-0327-0.
Farrell W.1972.Deformation of the earth by surface loads.Reviews of Geophysics,10(3):761-797,doi:10.1029/RG010i003p00761.
Han S C,Shum C K,Braun A.2005a.High-resolution continental water storage recovery from low-low satellite-to-satellite tracking.Journal of Geodynamics,39(1):11-28,doi:10.1016/j.jog.2004.08.002.
Han S C,Shum C K,Jekeli C,et al.2005b.Improved estimation of terrestrial water storage changes from GRACE.Geophysical Research Letters,32(7):L07302,doi:10.1029/2005GL022382.
Hansen P C.1992.Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review,34(4):561-580,doi:10.1137/1034115.
Ilk K H.1983.Ein Beitrag zur Dynamik ausgedehnter K9rper:Gravitationswechselwirkung[Ph.D.thesis].München:Deutsche Geodtische Kommission bei der Bayerischen Akademie der Wissenschaften.
Klees R,Revtova E A,Gunter B C,et al.2008.The design of an optimal filter for monthly GRACE gravity models.Geophysical Journal International,175(2):417-432,doi:10.1111/j.1365-246X.2008.03922.x.
Kusche J,Klees R.2002.Regularization of gravity field estimation from satellite gravity gradients.Journal of Geodesy,76(6-7):359-368,doi:10.1007/s00190-002-0257-6.
Luthcke S B,Zwally H J,Abdalati W,et al.2006.Recent Greenland ice mass loss by drainage system from satellite gravity observations.Science,314(5803):1286-1289,doi:10.1126/science.1130776.
Mayer-Gürr T.2006.Gravitationsfeldbestimmung aus der Analyse kurzer Bahnb9gen am Beispiel der Satellitenmissionen CHAMPund GRACE[Ph.D.thesis].Bonn:University of Bonn.
Mayer-Gürr T,Behzadpour S,Ellmer M,et al.2016.ITSG-Grace2016-Monthly and daily gravity field solutions from GRACE.GFZ Data Services.http:∥doi.org/10.5880/icgem.2016.007.
Ramillien G L,Seoane L,Frappart F,et al.2012.Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies over South America.Surveys in Geophysics,33(5):887-905,doi:10.1007/s10712-012-9177-z.
Ran J,Ditmar P,Klees R,et al.2017.Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACEmonthly solutions using an improved mascon approach.Journal of Geodesy,92(3):299-319,doi:10.1007/s00190-017-1063-5.
Rowlands D D,Luthcke S B,Klosko S M,et al.2005.Resolving mass flux at high spatial and temporal resolution using GRACEintersatellite measurements.GeophysicalResearchLetters,32(4):L04310,doi:10.1029/2004GL021908.
Rowlands D D,Luthcke S B,McCarthy J J,et al.2010.Global mass flux solutions from GRACE:a comparison of parameter estimation strategies-mass concentrations versus Stokes coefficients.Journal of Geophysical Research:Solid Earth,115(B1):B01403,doi:10.1029/2009JB006546.
Save H,Bettadpur S,Tapley B D.2016.High-resolution CSRGRACE RL05 mascons.Journal of Geophysical Research:Solid Earth,121(10):7547-7569,doi:10.1002/2016JB013007.
Sheard B S,Heinzel G,Danzmann K,et al.2012.Intersatellite laser ranging instrument for the GRACE follow-on mission.Journal of Geodesy,86(12):1083-1095,doi:10.1007/s00190-012-0566-3.
Shen Y Z,Xu P L,Li B F.2012.Bias-corrected regularized solution to inverse ill-posed models.Journal of Geodesy,86(8):597-608,doi:10.1007/s00190-012-0542-y.
Su Y,Yu B,You W,et al.2017.Surface mass distribution from gravity satellite observations by using three-dimensional pointmass modeling approach.Chinese Journal of Geophysics(in Chinese),60(1):50-60,doi:10.6038/cjg20170105.
Swenson S,Wahr J.2006.Post-processing removal of correlated errors in GRACE data.Geophysical Research Letters,33(8):L08402,doi:10.1029/2005GL025285.
Tangdamrongsub N,Hwang C,Shum C K,et al.2012.Regional surface mass anomalies from GRACE KBR measurements:Application of L-curve regularization and a priori hydrological knowledge.Journal of Geophysical Research:Solid Earth,117(B11):B11406,doi:10.1029/2012JB009310.
Tapley B D,Bettadpur S,Watkins M,et al.2004.The gravity recovery and climate experiment:Mission overview and early results.Geophysical Research Letters,31(9):L09607,doi:10.1029/2004GL019920.
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.Journal of Geophysical Research:Solid Earth,103(B12):30205-30229,doi:10.1029/98JB02844.
Wahr J,Swenson S,Zlotnicki V,et al.2004.Time-variable gravity from GRACE:First results.Geophysical Research Letters,31(11):L11501,doi:10.1029/2004GL019779.
Wessel P,Smith W F,Scharroo R,et al.2013.Generic mapping tools:improved version released.EOS,94(45):409-410.
Xu P L,Shen Y Z,Fukuda Y,et al.2006.Variance component estimation in linear inverse ill-posed models.Journal of Geodesy,80(2):69-81,doi:10.1007/s00190-006-0032-1.
Zhan J G,Wang Y,Shi H L,et al.2015.Removing correlative errors in GRACE data by the smoothness priors method.Chinese Journal of 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.Geophysical Research Letters,36(17):L17311,doi:10.1029/2009GL039459.
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.
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.地球物理学报,58(4):1135-1144,doi:10.6038/cjg20150404.
Baur O.2013.Greenland mass variation from time-variable gravity in the absence of GRACE.Geophysical Research Letters,40(16):4289-4293,doi:10.1002/grl.50881.
Chen T Y,Shen Y Z,Chen Q J.2016.Mass flux solution in the Tibetan plateau using Mascon modeling.Remote Sensing,8(5):439,doi:10.3390/rs8050439.
Dahle C,Flechtner F,Gruber C,et al.2013.GFZ GRACE level-2processing standards document for level-2product release 0005,Revised Edition,January 2013,doi:10.2312/GFZ.b103-1202-25.
Duan X J,Guo J Y,Shum C K,et al.2009.On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions.Journal of Geodesy,83(11):1095-1106,doi:10.1007/s00190-009-0327-0.
Farrell W.1972.Deformation of the earth by surface loads.Reviews of Geophysics,10(3):761-797,doi:10.1029/RG010i003p00761.
Han S C,Shum C K,Braun A.2005a.High-resolution continental water storage recovery from low-low satellite-to-satellite tracking.Journal of Geodynamics,39(1):11-28,doi:10.1016/j.jog.2004.08.002.
Han S C,Shum C K,Jekeli C,et al.2005b.Improved estimation of terrestrial water storage changes from GRACE.Geophysical Research Letters,32(7):L07302,doi:10.1029/2005GL022382.
Hansen P C.1992.Analysis of discrete ill-posed problems by means of the L-curve.SIAM Review,34(4):561-580,doi:10.1137/1034115.
Ilk K H.1983.Ein Beitrag zur Dynamik ausgedehnter K9rper:Gravitationswechselwirkung[Ph.D.thesis].München:Deutsche Geodtische Kommission bei der Bayerischen Akademie der Wissenschaften.
Klees R,Revtova E A,Gunter B C,et al.2008.The design of an optimal filter for monthly GRACE gravity models.Geophysical Journal International,175(2):417-432,doi:10.1111/j.1365-246X.2008.03922.x.
Kusche J,Klees R.2002.Regularization of gravity field estimation from satellite gravity gradients.Journal of Geodesy,76(6-7):359-368,doi:10.1007/s00190-002-0257-6.
Luthcke S B,Zwally H J,Abdalati W,et al.2006.Recent Greenland ice mass loss by drainage system from satellite gravity observations.Science,314(5803):1286-1289,doi:10.1126/science.1130776.
Mayer-Gürr T.2006.Gravitationsfeldbestimmung aus der Analyse kurzer Bahnb9gen am Beispiel der Satellitenmissionen CHAMPund GRACE[Ph.D.thesis].Bonn:University of Bonn.
Mayer-Gürr T,Behzadpour S,Ellmer M,et al.2016.ITSG-Grace2016-Monthly and daily gravity field solutions from GRACE.GFZ Data Services.http:∥doi.org/10.5880/icgem.2016.007.
Ramillien G L,Seoane L,Frappart F,et al.2012.Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies over South America.Surveys in Geophysics,33(5):887-905,doi:10.1007/s10712-012-9177-z.
Ran J,Ditmar P,Klees R,et al.2017.Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACEmonthly solutions using an improved mascon approach.Journal of Geodesy,92(3):299-319,doi:10.1007/s00190-017-1063-5.
Rowlands D D,Luthcke S B,Klosko S M,et al.2005.Resolving mass flux at high spatial and temporal resolution using GRACEintersatellite measurements.GeophysicalResearchLetters,32(4):L04310,doi:10.1029/2004GL021908.
Rowlands D D,Luthcke S B,McCarthy J J,et al.2010.Global mass flux solutions from GRACE:a comparison of parameter estimation strategies-mass concentrations versus Stokes coefficients.Journal of Geophysical Research:Solid Earth,115(B1):B01403,doi:10.1029/2009JB006546.
Save H,Bettadpur S,Tapley B D.2016.High-resolution CSRGRACE RL05 mascons.Journal of Geophysical Research:Solid Earth,121(10):7547-7569,doi:10.1002/2016JB013007.
Sheard B S,Heinzel G,Danzmann K,et al.2012.Intersatellite laser ranging instrument for the GRACE follow-on mission.Journal of Geodesy,86(12):1083-1095,doi:10.1007/s00190-012-0566-3.
Shen Y Z,Xu P L,Li B F.2012.Bias-corrected regularized solution to inverse ill-posed models.Journal of Geodesy,86(8):597-608,doi:10.1007/s00190-012-0542-y.
Su Y,Yu B,You W,et al.2017.Surface mass distribution from gravity satellite observations by using three-dimensional pointmass modeling approach.Chinese Journal of Geophysics(in Chinese),60(1):50-60,doi:10.6038/cjg20170105.
Swenson S,Wahr J.2006.Post-processing removal of correlated errors in GRACE data.Geophysical Research Letters,33(8):L08402,doi:10.1029/2005GL025285.
Tangdamrongsub N,Hwang C,Shum C K,et al.2012.Regional surface mass anomalies from GRACE KBR measurements:Application of L-curve regularization and a priori hydrological knowledge.Journal of Geophysical Research:Solid Earth,117(B11):B11406,doi:10.1029/2012JB009310.
Tapley B D,Bettadpur S,Watkins M,et al.2004.The gravity recovery and climate experiment:Mission overview and early results.Geophysical Research Letters,31(9):L09607,doi:10.1029/2004GL019920.
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.Journal of Geophysical Research:Solid Earth,103(B12):30205-30229,doi:10.1029/98JB02844.
Wahr J,Swenson S,Zlotnicki V,et al.2004.Time-variable gravity from GRACE:First results.Geophysical Research Letters,31(11):L11501,doi:10.1029/2004GL019779.
Wessel P,Smith W F,Scharroo R,et al.2013.Generic mapping tools:improved version released.EOS,94(45):409-410.
Xu P L,Shen Y Z,Fukuda Y,et al.2006.Variance component estimation in linear inverse ill-posed models.Journal of Geodesy,80(2):69-81,doi:10.1007/s00190-006-0032-1.
Zhan J G,Wang Y,Shi H L,et al.2015.Removing correlative errors in GRACE data by the smoothness priors method.Chinese Journal of 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.Geophysical Research Letters,36(17):L17311,doi:10.1029/2009GL039459.
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.
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.地球物理学报,58(4):1135-1144,doi:10.6038/cjg20150404.