垂线偏差反演重力异常中央区效应计算模型
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摘要
为提高卫星测高反演重力场中央区效应的计算精度,以逆Vening-Meinesz公式为例,推导了包含4个网格的矩形中央区效应计算模型;基于"非奇异变换"思想,推导了中央区垂线偏差展开为泰勒级数式和二次多项式的非奇异变换法计算模型一和模型二。结果表明:矩形中央区积分法得到了与非奇异变换法模型一完全相同的中央区效应计算模型。设计了基于EGM2008模型数据的仿真计算,计算结果表明:该公式计算的重力异常中央区效应与将中央区视为圆域的传统方法算得的结果差值最大能够达到数个毫伽;与形式更为复杂的非奇异变换法算得的结果基本一致,说明在中央区效应计算中,使用矩形域中央区模型更为合理。
In order to improve the calculation accuracy of innermost area effect in using satellite altimetry to convert gravity field,and taking inverse Vening-M einesz formula for an example,the calculation model of singular transformation in the rectangle innermost area which includes four gridding is derived. The simulating calculation is designed based on EGM 2008 model.In conclusion the differences between the results gotten from the method used in this paper and traditional one,which take the innermost area as a circle,reach several m Gal;the results of singular and non-ingular transformation are almost equal,which means that taking the innermost area as a rectangle is more reasonable in innermost area effect calculation.
In order to improve the calculation accuracy of innermost area effect in using satellite altimetry to convert gravity field,and taking inverse Vening-M einesz formula for an example,the calculation model of singular transformation in the rectangle innermost area which includes four gridding is derived. The simulating calculation is designed based on EGM 2008 model.In conclusion the differences between the results gotten from the method used in this paper and traditional one,which take the innermost area as a circle,reach several m Gal;the results of singular and non-ingular transformation are almost equal,which means that taking the innermost area as a rectangle is more reasonable in innermost area effect calculation.
引文
[1]李建成,陈俊勇,宁津生,等.地球重力场逼近理论与中国2000似大地水准面的确定[M].武汉:武汉大学出版社,2003.
[2]翟国君,黄谟涛,谢锡君,等.卫星测高数据处理的理论与方法[M].北京:测绘出版社,2000.
[3]翟国君,黄谟涛,欧阳永忠,等.卫星测高原理及其应用[J].海洋测绘,2002,22(1):57-62.
[4]Hwang C.High precision gravity anomaly and sea surface height estimation from GEOS-3/SEASAT Satellite altimeter data[R].OSU Report No.399,Department of Geodetic Science and Surveying,The Ohio State University.1989.
[5]李建成,宁津生,陈俊勇,等,联合Topex/Poseidon,ERS2和Geosat卫星测高资料确定中国近海重力异常[J].测绘学报,2001 30(3):197-202.
[6]Molodensky M S,Eremeev V F,Yrukina M J.Methods for study of the external gravitational field and figure of the earth w orks of Central Research Institute of Geodesy Aerial Photography and Cartography[R].No.131,M oscow 1960.
[7]Hwang C.Inverse Vening Meinesz formula and deflection-geoid formula:applications to the predictions of gravity and geoid over the South China Sea[J].Journal of Geodesy,1998,72:304-312.
[8]Sandwell D T.A detailed view of the South Pacific Geoid from Satellite Altimetry[J].J Geodphys Res,198489(B2):1089-1104.
[9]Sandwell D T.Antarctic marine gravity field from high density satellite altimetry[J].Geophys J Int,1992,109:437-448.
[10]Hwang C.High Precision Gravity Anomaly and Sea Surface Height Estimation from Geos-3/Seasat Altimeter Data[R].Report No 399,Dept of Geod Sci and Surv,Ohio State University,Columbus 1989.
[11]边少锋.大地测量边值问题数值解法与地球重力场逼近[D].武汉:武汉测绘科技大学,1992.
[12]李厚朴,边少锋,纪兵.重力异常垂直梯度中央区效应的精密计算[J].海洋测绘,2012,32(1):1-4.
[13]李厚朴,边少锋.利用垂线偏差计算大地水准面中央区效应的改进方法[J].测绘学报,2011,40(6):730-735.
[14]章传银,郭春喜,陈俊勇,等.EGM2008地球重力场模型在中国大陆适用性分析[J].测绘学报,2009,38(4):283-289.
[2]翟国君,黄谟涛,谢锡君,等.卫星测高数据处理的理论与方法[M].北京:测绘出版社,2000.
[3]翟国君,黄谟涛,欧阳永忠,等.卫星测高原理及其应用[J].海洋测绘,2002,22(1):57-62.
[4]Hwang C.High precision gravity anomaly and sea surface height estimation from GEOS-3/SEASAT Satellite altimeter data[R].OSU Report No.399,Department of Geodetic Science and Surveying,The Ohio State University.1989.
[5]李建成,宁津生,陈俊勇,等,联合Topex/Poseidon,ERS2和Geosat卫星测高资料确定中国近海重力异常[J].测绘学报,2001 30(3):197-202.
[6]Molodensky M S,Eremeev V F,Yrukina M J.Methods for study of the external gravitational field and figure of the earth w orks of Central Research Institute of Geodesy Aerial Photography and Cartography[R].No.131,M oscow 1960.
[7]Hwang C.Inverse Vening Meinesz formula and deflection-geoid formula:applications to the predictions of gravity and geoid over the South China Sea[J].Journal of Geodesy,1998,72:304-312.
[8]Sandwell D T.A detailed view of the South Pacific Geoid from Satellite Altimetry[J].J Geodphys Res,198489(B2):1089-1104.
[9]Sandwell D T.Antarctic marine gravity field from high density satellite altimetry[J].Geophys J Int,1992,109:437-448.
[10]Hwang C.High Precision Gravity Anomaly and Sea Surface Height Estimation from Geos-3/Seasat Altimeter Data[R].Report No 399,Dept of Geod Sci and Surv,Ohio State University,Columbus 1989.
[11]边少锋.大地测量边值问题数值解法与地球重力场逼近[D].武汉:武汉测绘科技大学,1992.
[12]李厚朴,边少锋,纪兵.重力异常垂直梯度中央区效应的精密计算[J].海洋测绘,2012,32(1):1-4.
[13]李厚朴,边少锋.利用垂线偏差计算大地水准面中央区效应的改进方法[J].测绘学报,2011,40(6):730-735.
[14]章传银,郭春喜,陈俊勇,等.EGM2008地球重力场模型在中国大陆适用性分析[J].测绘学报,2009,38(4):283-289.