近区地形直接与间接影响的棱柱模型算法

doi:10.11947/j.AGCS.2018.20170369

测绘学报 ›› 2018, Vol. 47 ›› Issue (11): 1429-1436.doi: 10.11947/j.AGCS.2018.20170369

• 大地测量学与导航 • 下一篇

近区地形直接与间接影响的棱柱模型算法

马健^1,2,3, 魏子卿^1,3

1. 地理信息工程国家重点实验室, 陕西西安 710054;
2. 信息工程大学地理空间信息学院, 河南郑州 450001;
3. 西安测绘研究所, 陕西西安 710054

收稿日期:2017-06-29 修回日期:2018-02-01 出版日期:2018-11-20 发布日期:2018-11-29
作者简介:马健(1988-),女,博士,研究方向为物理大地测量。E-mail:majian_19881006@163.com
基金资助:
国家自然科学基金（41674025；41674082）；地理信息工程国家重点实验室开放研究基金（SKLGIE2016-M-1-5；SKLGIE2016-M-3-2）

Prism Algorithms for the Near-zone Direct and Indirect Topographic Effects

MA Jian^1,2,3, WEI Ziqing^1,3

1. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China;
2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China;
3. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China

Received:2017-06-29 Revised:2018-02-01 Online:2018-11-20 Published:2018-11-29
Supported by:
The National Natural Science Foundation of China (Nos. 41674025;41674082);The Open Research Foundation of State Key Laboratory of Geo-information Engineering (Nos. SKLGIE2016-M-1-5;SKLGIE2016-M-3-2)

摘要/Abstract

摘要： 基于Helmert第二压缩法进行边值解算时需要计算地形压缩对重力的直接影响和对（似）大地水准面的间接影响。计算近区直接、间接影响的传统积分算法仍是二重积分形式。该算法以网格中心点处的积分核作为网格积分核的平均值的计算模式在一定程度上引入了近似误差。另外，直接、间接影响的传统积分算法在中央区存在奇异性，需单独计算中央网格地形影响，因而增加了计算的复杂性。为此，本文推导了近区地形直接、间接影响的棱柱模型公式，一方面提高了地形影响的计算精度；另一方面中央区不存在奇异性，从而简化了计算过程。为避免棱柱模型存在的平面近似误差，可使用顾及地球曲率的棱柱模型算法计算地形影响。最后通过试验得出结论，在（似）大地水准面精度要求较高的应用中，应尽量使用顾及地球曲率的棱柱模型算法计算地形影响。

关键词: 近区直接影响, 近区间接影响, Helmert第二压缩法, 中央奇异性, 棱柱模型算法, 顾及地球曲率

Abstract: It is necessary to calculate the direct effect on gravity and the indirect effects on the geoid and quasi-geoid when reducing the topography based on Helmert's second condensation method for solving boundary value problems. The traditional integration algorithms for the near-zone direct and indirect topographic effects arein the double integral form and give some approximate errors when taking the integral kernel at the center of the grid as the average of the grid integral kernel. Furthermore, the traditional integral algorithms for the direct and indirect effects have singularity in the innermost area, which increases the computational complexity. In this paper, the prism formulae of the near-zone direct and indirect effects are deduced, which improves the calculation accuracy on the one hand and simplifies the computation process by removing the singularity in the innermost area on the other hand. To overcome the planar approximation error of the prism models, the curvature of the earth can be taken into account. Finally, experimental results show that the prism algorithm for the topographic effect considering the earth's curvature is recommended when a high-accuracy geoid/quasi-geoid is required.

Key words: near-zone direct effect, near-zone indirect effect, Helmert's second condensation method, innermost-zone singularity, prism algorithms, considering the earth's curvature

中图分类号:

P223

马健, 魏子卿. 近区地形直接与间接影响的棱柱模型算法[J]. 测绘学报, 2018, 47(11): 1429-1436.

MA Jian, WEI Ziqing. Prism Algorithms for the Near-zone Direct and Indirect Topographic Effects[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(11): 1429-1436.

参考文献

[1] 管泽霖, 管铮, 黄谟涛, 等. 局部重力场逼近理论和方法[M]. 北京:测绘出版社, 1997. GUAN Zelin, GUAN Zheng, HUANG Motao, et al. Theory and Method of Regional Gravity Field Approximation[M]. Beijing:Surveying and Mapping Press, 1997.
[2] HEISKANNEN W A, MORITZ H. Physical Geodesy[J]. Bulletin Géodésique, 1967, 86(1):491-492.
[3] VANÍČEK P, HUANG J, NOVÁK P, et al. Determination of the Boundary Values for the Stokes-Helmert Problem[J]. Journal of Geodesy, 1999, 73(4):180-192.
[4] 李建成. 最新中国陆地数字高程基准模型:重力似大地水准面CNGG2011[J]. 测绘学报, 2012, 41(5):651-660. LI Jiancheng. The Recent Chinese Terrestrial Digital Height Datum Model:Gravimetric Quasi-geoid CNGG2011[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5):651-660.
[5] HUANG Jianliang, VÉRONNEAU M. Canadian Gravimetric Geoid Model 2010[J]. Journal of Geodesy, 2013, 87(8):771-790.
[6] WANG Y M, SALEH J, LI X, et al. The US Gravimetric Geoid of 2009(USGG2009):Model Development and Evaluation[J]. Journal of Geodesy, 2012, 86(3):165-180.
[7] 荣敏. Stokes-Helmert方法确定大地水准面的理论与实践[D]. 郑州:信息工程大学, 2015:43-68. RONG Min. Stokes-Helmert Method for Geoid Determination[D]. Zhengzhou:Information Engineering University, 2015:43-68.
[8] SJÖBERG L E. Topographic Effects by the Stokes-Helmert Method of Geoid and Quasi-geoid Determinations[J]. Journal of Geodesy, 2000, 74(2):255-268.
[9] SJÖBERG L E, NAHAVANDCHI H. On the Indirect Effect in the Stokes-Helmert Method of Geoid Determination[J]. Journal of Geodesy, 1999, 73(2):87-93.
[10] NAHAVANDCHI H. The Direct Topographical Correction in Gravimetric Geoid Determination by the Stokes-Helmert Method[J]. Journal of Geodesy, 2000, 74(6):488-496.
[11] NAHAVANDCHI H. Terrain Correction Computations by Spherical Harmonics and Integral Formulas[J]. Physics and Chemistry of the Earth, Part A:Solid Earth and Geodesy, 1999, 24(1):73-78.
[12] 罗志才, 陈永奇, 宁津生. 地形对确定高精度局部大地水准面的影响[J]. 武汉大学学报(信息科学版), 2003, 28(3):340-344. LUO Zhicai, CHEN Yongqi, NING Jinsheng. Effect of Terrain on the Determination of High Precise Local Gravimetric Geoid[J]. Geomatics and Information Science of Wuhan University, 2003, 28(3):340-344.
[13] 章传银, 晁定波, 丁剑, 等. 球近似下地球外空间任意类型场元的地形影响[J]. 测绘学报, 2009, 38(1):28-34. ZHANG Chuanyin, CHAO Dingbo, DING Jian, et al. Precision Topographical Effects for Any Kind of Field Quantities for Any Altitude[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(1):28-34.
[14] 郭春喜, 王惠民, 王斌. 全国高分辨率格网地形和均衡改正的确定[J]. 测绘学报, 2002, 31(3):201-205. GUO Chunxi, WANG Huimin, WANG Bin. Determination of High Resolution Grid Terrain and Isostatic Corrections in All China Area[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(3):201-205.
[15] 章传银, 晁定波, 丁剑, 等. 厘米级高程异常地形影响的算法及特征分析[J]. 测绘学报, 2006, 35(4):308-314. ZHANG Chuanyin, CHAO Dingbo, DING Jian, et al. Arithmetic and Characters Analysis of Terrain Effects for CM-order Precision Height Anomaly[J]. Acta Geodaetica et Cartographica Sinica, 2006, 35(4):308-314.
[16] 荣敏, 周巍. 球近似地形改正的研究分析[J]. 大地测量与地形动力学, 2015, 35(1):58-61. RONG Min, ZHOU Wei. Study on Topography Correction Based on Spherical Approximation[J]. Journal of Geodesy and Geodynamics, 2015, 35(1):58-61.
[17] 马健, 魏子卿, 武丽丽, 等. 有限范围的重力层间改正算法[J]. 测绘学报, 2017, 46(1):26-33. DOI:10.11947/j.AGCS.2017.20160173. MA Jian, WEI Ziqing, WU Lili, et al. The Bouguer Correction Algorithm for Gravity with Limited Range[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(1):26-33. DOI:10.11947/j.AGCS.2017.20160173.
[18] 魏子卿. 以地心参考椭球面为边界面的第二大地边值问题引论[J]. 测绘科学与工程, 2015, 35(1):1-6. WEI Ziqing. Introduction to the Second Geodetic Boundary-value Problem with the Geocentric Reference Ellipsoidal Surface as the Boundary[J]. Geomatics Science and Engineering, 2015, 35(1):1-6.
[19] WANG Y M. Precise Computation of the Direct and Indirect Topographic Effects of Helmert's 2nd Method of Condensation Using SRTM30 Digital Elevation Model[J]. Journal of Geodetic Science, 2011, 1(4):305-312.
[20] MAKHLOOF A A, ILK K H. Far-zone Effects for Different Topographic-compensation Models Based on a Spherical Harmonic Expansion of the Topography[J]. Journal of Geodesy, 2008, 82(10):613-635.
[21] NOVÁK P, VANÍČEK P, MARTINEC Z, et al. Effects of the Spherical Terrain on Gravity and the Geoid[J]. Journal of Geodesy, 2001, 75(9-10):491-504.
[22] MARTINEC Z, VANÍČEK P. The Indirect Effect of Topography in the Stokes-Helmert Technique for a Spherical Approximation of the Geoid[J]. Manuscript Geodaetica, 1994(19):213-219.
[23] NAGY D, GAPP G, BENEDEK J. The Gravitational Potential and Its Derivatives for the Prism[J]. Journal of Geodesy, 2000, 74(7-8):552-560.
[24] FORSBERG R. A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling[R]. Columbus:Ohio State University, 1984.
[25] 马健, 魏子卿, 沈忱, 等. 地形改正与地形直接影响的转化关系[J]. 测绘科学技术学报, 2017, 34(3):245-250. MA Jian, WEI Ziqing, SHEN Chen, et al. Transformation Relation Between the Topographic Correction and the Direct Topographic Effect[J]. Journal of Geomatics Science and Technology, 2017, 34(3):245-250.
[26] WICHIENCHAROEN C. The Indirect Effects on the Computation of Geoid Undulations[R].[S.l.]:NASA, 1982.
[27] MARTINEC Z. Boundary-value Problems for Gravimetric Determination of a Precise Geoid[M]. Berlin:Springer, 1998.

近区地形直接与间接影响的棱柱模型算法

Prism Algorithms for the Near-zone Direct and Indirect Topographic Effects

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	赵鸿彬, 谷延超, 范东明, 邱春洪, 宿春鹏, 方伟浩. 联合卫星测高、GRACE与温盐数据分析红海海平面变化季节性特征[J]. 测绘学报, 2019, 48(9): 1119-1128.
[2]	马健, 魏子卿, 任红飞. 低阶修正的Hotine截断核函数的频谱分析与应用[J]. 测绘学报, 2019, 48(5): 537-546.
[3]	马健, 魏子卿, 任红飞. 确定似大地水准面的Hotine-Helmert边值解算模型[J]. 测绘学报, 2019, 48(2): 153-160.
[4]	瞿庆亮, 常晓涛, 于胜文, 朱广彬. 利用先验重力场模型求定GOCE卫星重力梯度仪校准参数[J]. 测绘学报, 2019, 48(2): 176-184.
[5]	梁磊, 于锦海, 万晓云. 椭球谐和球谐系数之间一个简单的转换关系[J]. 测绘学报, 2019, 48(2): 185-190.
[6]	朱传东, 刘金钊, 王同庆, 陈兆辉, 张品, 张双喜. GRACE离散时变重力场的大尺度动态变化模型构建分析[J]. 测绘学报, 2018, 47(12): 1581-1590.
[7]	田家磊, 李新星, 吴晓平, 邢志斌. 超高阶重力场模型最小二乘快速实现[J]. 测绘学报, 2018, 47(11): 1437-1445.
[8]	黄谟涛, 刘敏, 吴太旗, 陆秀平, 邓凯亮, 翟国君, 欧阳永忠, 陈欣. 海空重力测量关键技术指标体系论证与评估[J]. 测绘学报, 2018, 47(11): 1537-1548.
[9]	柯宝贵, 张利明, 章传银, 党亚民. 卫星测高与船载重力测量数据融合的点质量拟合法[J]. 测绘学报, 2018, 47(7): 924-929.
[10]	李圳, 章传银, 柯宝贵, 刘阳, 李婉秋, 尹财. 顾及GRACE季节影响的华北平原水储量变化反演[J]. 测绘学报, 2018, 47(7): 940-949.
[11]	党亚民, 杨强, 梁诗明, 王伟. 川滇区域活动块体运动与应变特征地震影响分析[J]. 测绘学报, 2018, 47(5): 559-566.
[12]	蒋涛, 肖学年, 党亚民, 章传银, 刘站科. 航空重力向上延拓的外部精度评估[J]. 测绘学报, 2018, 47(5): 567-574.
[13]	邢志斌, 李姗姗. 我国陆海统一似大地水准面构建的三维重力矢量法[J]. 测绘学报, 2018, 47(5): 575-583.
[14]	梁伟, 徐新禹, 李建成, 朱广彬. 联合EGM2008模型重力异常和GOCE观测数据构建超高阶地球重力场模型SGG-UGM-1[J]. 测绘学报, 2018, 47(4): 425-434.
[15]	何思源, 谷延超, 范东明, 赵鸿彬, 郑蓉. 利用GPS垂直位移反演云南省陆地水储量变化[J]. 测绘学报, 2018, 47(3): 332-340.