卫星测高与船载重力测量数据融合的点质量拟合法
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摘要
以拟合方差最小为准则,通过点质量法拟合船载重力测量数据,得到点质量大小、埋深等参数。回避点质量法数值求解的不稳定性问题,借鉴移去-恢复技术的思路,利用该参数计算船载重力测量点上的重力异常,并将其在测线上的重力异常中扣除,计算出船载重力残差值。以点质量大小、埋深等参数计算卫星测高重力格网点上重力异常,同样得到测高重力残差值。采用加权最小曲率格网化方法,将船载重力残差值与测高重力残差值格网化,进而恢复由点质量大小、埋深等参数计算格网点处的重力异常,实现卫星测高与船载重力测量数据融合。经国际船载重力测量数据检核,融合后的模型较国际船载重力测量数据的平均偏差在1~2mGal(1Gal=1×10~(-2) m/s~2),标准差约为4mGal。本文的研究方法可为陆地、海岸带区域的多种重力数据的融合、航空重力及卫星重力的向下延拓等问题提供参考。
Using the point mass fit method,the position,size and other parameters of the point mass source are inversed by fitting the shipborne gravity anomaly data with the minimum variance between the point mass model and observed value.Avoiding the instability posed by the point mass method,the shipborne residual gravity anomalies are calculated by using these parameters based on the idea of remove-restore technique.Shipborne gravity residuals can be obtained by minusing the gravity anomaly in the track line.The altimetric residual gravity data are also obtained by using the similar method.Weighted the two residual gravity anomaly by the minimum curvature gridding method,and restored the model gravity anomaly calculated by the point mass size,depth and other parameters,then realized the satellite altimetry and shipborne gravity data fusion.The mean bias is 1~2 mGal and the root mean square is about 4 mGal,which is verified by the international shipborne gravity measurement data.The proposed method can be used as a reference for processing the various gravity data fusion in coastal zone and for satellite gravity downward continuation problem.
Using the point mass fit method,the position,size and other parameters of the point mass source are inversed by fitting the shipborne gravity anomaly data with the minimum variance between the point mass model and observed value.Avoiding the instability posed by the point mass method,the shipborne residual gravity anomalies are calculated by using these parameters based on the idea of remove-restore technique.Shipborne gravity residuals can be obtained by minusing the gravity anomaly in the track line.The altimetric residual gravity data are also obtained by using the similar method.Weighted the two residual gravity anomaly by the minimum curvature gridding method,and restored the model gravity anomaly calculated by the point mass size,depth and other parameters,then realized the satellite altimetry and shipborne gravity data fusion.The mean bias is 1~2 mGal and the root mean square is about 4 mGal,which is verified by the international shipborne gravity measurement data.The proposed method can be used as a reference for processing the various gravity data fusion in coastal zone and for satellite gravity downward continuation problem.
引文
[1]黄谟涛,欧阳永忠,翟国君,等.海域多源重力数据融合处理的解析方法[J].武汉大学学报(信息科学版),2013,38(11):1261-1265.HUANG Motao,OUYANG Yongzhong,ZHAI Guojun,et al.Analytical Methods of Multi-source Gravity Data Fusion Processing in the Sea Area[J].Geomatics and Information Science of Wuhan University,2013,38(11):1261-1265.
[2]吴怿昊,罗志才,周波阳.基于泊松小波径向基函数融合多源数据的局部重力场建模[J].地球物理学报,2016,59(3):852-864.WU Yihao,LUO Zhicai,ZHOU Boyang.Regional Gravity Modeling Based on Heterogeneous Data Sets by Using Poisson Wavelets Radial Basis Functions[J].Chinese Journal of Geophysics,2016,59(3):852-864.
[3]黄谟涛,欧阳永忠,刘敏,等.融合海域多源重力数据的正则化点质量方法[J].武汉大学学报(信息科学版),2015,40(2):170-175.HUANG Motao,OUYANG Yongzhong,LIU Min,et al.Regularization of Point-mass Model for Multi-source Gravity Data Fusion Processing[J].Geomatics and Information Science of Wuhan University,2015,40(2):170-175.
[4]吴健生,刘苗.基于小波的位场数据融合[J].同济大学学报(自然科学版).2008,36(8):1133-1137.WU Jiansheng,LIU Miao.Potential Field Data Fusion Based on Wavelet Multi-resolution Decomposition[J].Journal of Tongji University(Natural Science),2008,36(8):1133-1137.
[5]SUNKEL H.The Generation of a Mass Point Model from Surface Gravity Data[M].Ohio:Ohio State University,1983.
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[9]BRIGGS I C.Machine Contouring Using Minimum Curvature[J].Geophysics,1974,39(1):39-48.
[10]庞振兴,张传定,叶修松.Surfer8.0在重力异常数据格网化中的应用[J].海洋测绘,2008,28(1):43-45,51.PANG Zhenxing,ZHANG Chuanding,YE Xiusong.Application Surfer8.0in the Gridding of Gravity Anomaly Data[J].Hydrographic Surveying and Charting,2008,28(1):43-45,51.
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[13]黄谟涛.海洋重力测量半系统差检验、调整及精度计算[J].海洋通报,1990,9(4):81-86.HUANG Motao.Examination,Adjustment and Precision Estimation of Half-systematic Error in Marine Gravity Surveying[J].Marine Science Bulletin,1990,9(4):81-86.
[14]黄谟涛.海洋重力测线网平差[J].测绘学报,1993,22(2):103-110.HUANG Motao.Marine Gravity Survey Line Network Adjustment[J].Acta Geodaetica et Cartographica Sinica,1993,22(2):103-110.
[15]李明叁,刘雁春,黄谟涛,等.海洋测线网系统误差确定的3种模型[J].测绘学院学报,2002,19(3):157-161.LI Mingsan,LIU Yanchun,HUANG Motao,et al.Three Models for Determination of Survey-line Systematic Errors in Marine Survey Net[J].Journal of Institute of Surveying and Mapping,2002,19(3):157-161.
[16]刘雁春,李明叁,黄谟涛.海洋测线网系统误差调整的秩亏网平差模型[J].武汉大学学报(信息科学版),2012,26(6):533-538.LIU Yanchun,LI Mingsan,HUANG Motao.The Rankdefect Adjustment Model for Survey-line Systematic Errors in Marine Survey Net[J].Geomatics and Information Science of Wuhan University,2012,26(6):533-538.
[17]柯宝贵,章传银,郭春喜,等.船载重力测量数据不同测区系统偏差纠正方法研究[J].武汉大学学报(信息科学版),2015,40(3):417-421.KE Baogui,ZHANG Chuanyin,GUO Chunxi,et al.Research on the System Error Correction for Shipborne Gravimetric Data of Different Region in China Offshore[J].Geomatics and Information Science of Wuhan University,2015,40(3):417-421.
[18]HWANG C,PARSONS B.Gravity Anomalies Derived from Seasat,Geosat,ERS-1and TOPEX/Poseidon Altimetry and Ship Gravity:A Case Study over the Reykjanes Ridge[J].Geophysical Journal International,1995,122(2):551-568.
[19]WESSL P,WATTS A B.On the Accuracy of Marine Gravity Measurements[J].Journal of Geophysical Research,1988,93(B1):393-413.
[20]SANDWELL D T,MLLER R D,SMITH W H F,et al.New Global Marine Gravity Model from Cryosat-2and Jason-1 Reveals Buried Tectonic Structure[J].Science,2014,346(6):65-67.
[21]ANDERSEN O B,KNUDSEN P,BERRY P A M.The DNSC08GRA Global Marine Gravity Field from Double Retracked Satellite Altimetry[J].Journal of Geodesy,2010,84(3):191-199.
[2]吴怿昊,罗志才,周波阳.基于泊松小波径向基函数融合多源数据的局部重力场建模[J].地球物理学报,2016,59(3):852-864.WU Yihao,LUO Zhicai,ZHOU Boyang.Regional Gravity Modeling Based on Heterogeneous Data Sets by Using Poisson Wavelets Radial Basis Functions[J].Chinese Journal of Geophysics,2016,59(3):852-864.
[3]黄谟涛,欧阳永忠,刘敏,等.融合海域多源重力数据的正则化点质量方法[J].武汉大学学报(信息科学版),2015,40(2):170-175.HUANG Motao,OUYANG Yongzhong,LIU Min,et al.Regularization of Point-mass Model for Multi-source Gravity Data Fusion Processing[J].Geomatics and Information Science of Wuhan University,2015,40(2):170-175.
[4]吴健生,刘苗.基于小波的位场数据融合[J].同济大学学报(自然科学版).2008,36(8):1133-1137.WU Jiansheng,LIU Miao.Potential Field Data Fusion Based on Wavelet Multi-resolution Decomposition[J].Journal of Tongji University(Natural Science),2008,36(8):1133-1137.
[5]SUNKEL H.The Generation of a Mass Point Model from Surface Gravity Data[M].Ohio:Ohio State University,1983.
[6]吴晓平.局部重力场的点质量模型[J].测绘学报,1984,13(4):249-258.WU Xiaoping.Point-mass Model of Local Gravity Field[J].Acta Geodaetica et Cartographica Sinica,1984,13(4):249-258.
[7]陆仲连.地球重力场理论与方法[M].北京:解放军出版社,1996.LU Zhonglian.Theory and Method of Earth’s Gravity Field[M].Beijing:Liberation Army Press,1996.
[8]高新兵,李姗姗,李海,等.点质量模型与最小二乘配置在多源重力数据融合中的应用[J].大地测量与地球动力学,2013,33(1):145-149.GAO Xinbing,LI Shanshan,LI Hai,et al.Application of Point Mass Model and Least Square Collocation in Multisource Gravity Data Fusion[J].Journal of Geodesy and Geodynamics,2013,33(1):145-149.
[9]BRIGGS I C.Machine Contouring Using Minimum Curvature[J].Geophysics,1974,39(1):39-48.
[10]庞振兴,张传定,叶修松.Surfer8.0在重力异常数据格网化中的应用[J].海洋测绘,2008,28(1):43-45,51.PANG Zhenxing,ZHANG Chuanding,YE Xiusong.Application Surfer8.0in the Gridding of Gravity Anomaly Data[J].Hydrographic Surveying and Charting,2008,28(1):43-45,51.
[11]王万银,邱之云.一种稳定的位场数据最小曲率网格化方法研究[J].地球物理学进展,2011,26(6):2003-2010.WANG Wanyin,QIU Zhiyun.The Research to a Stable Minimum Curvature Gridding Method in Potential Data Processing[J].Progress in Geophysics,2011,26(6):2003-2010.
[12]骆遥,吴美平.位场向下延拓的最小曲率方法[J].地球物理学报,2016,59(1):240-251.LUO Yao,WU Meiping.Minimum Curvature Method for Downward Continuation of Potential Field Data[J].Chinese Journal of Geophysics,2016,59(1):240-251.
[13]黄谟涛.海洋重力测量半系统差检验、调整及精度计算[J].海洋通报,1990,9(4):81-86.HUANG Motao.Examination,Adjustment and Precision Estimation of Half-systematic Error in Marine Gravity Surveying[J].Marine Science Bulletin,1990,9(4):81-86.
[14]黄谟涛.海洋重力测线网平差[J].测绘学报,1993,22(2):103-110.HUANG Motao.Marine Gravity Survey Line Network Adjustment[J].Acta Geodaetica et Cartographica Sinica,1993,22(2):103-110.
[15]李明叁,刘雁春,黄谟涛,等.海洋测线网系统误差确定的3种模型[J].测绘学院学报,2002,19(3):157-161.LI Mingsan,LIU Yanchun,HUANG Motao,et al.Three Models for Determination of Survey-line Systematic Errors in Marine Survey Net[J].Journal of Institute of Surveying and Mapping,2002,19(3):157-161.
[16]刘雁春,李明叁,黄谟涛.海洋测线网系统误差调整的秩亏网平差模型[J].武汉大学学报(信息科学版),2012,26(6):533-538.LIU Yanchun,LI Mingsan,HUANG Motao.The Rankdefect Adjustment Model for Survey-line Systematic Errors in Marine Survey Net[J].Geomatics and Information Science of Wuhan University,2012,26(6):533-538.
[17]柯宝贵,章传银,郭春喜,等.船载重力测量数据不同测区系统偏差纠正方法研究[J].武汉大学学报(信息科学版),2015,40(3):417-421.KE Baogui,ZHANG Chuanyin,GUO Chunxi,et al.Research on the System Error Correction for Shipborne Gravimetric Data of Different Region in China Offshore[J].Geomatics and Information Science of Wuhan University,2015,40(3):417-421.
[18]HWANG C,PARSONS B.Gravity Anomalies Derived from Seasat,Geosat,ERS-1and TOPEX/Poseidon Altimetry and Ship Gravity:A Case Study over the Reykjanes Ridge[J].Geophysical Journal International,1995,122(2):551-568.
[19]WESSL P,WATTS A B.On the Accuracy of Marine Gravity Measurements[J].Journal of Geophysical Research,1988,93(B1):393-413.
[20]SANDWELL D T,MLLER R D,SMITH W H F,et al.New Global Marine Gravity Model from Cryosat-2and Jason-1 Reveals Buried Tectonic Structure[J].Science,2014,346(6):65-67.
[21]ANDERSEN O B,KNUDSEN P,BERRY P A M.The DNSC08GRA Global Marine Gravity Field from Double Retracked Satellite Altimetry[J].Journal of Geodesy,2010,84(3):191-199.