利用卫星重力确定局部大地水准面及其在地球物理解释中的应用
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摘要
本文针对目前地面重力数据分布不均,而卫星重力数据的精度和分辨率不断提高这一现状,以湖南地区为例,分三个部分详细地研究了卫星重力在确定大地水准面以及在地球物理解释中的应用这两方面的内容,并对相关的原理和方法进行了介绍。其主要内容及结论如下：
1.比较研究了EGM08, EGM96, GGM02等几种地球重力位模型确定局部大地水准面的精度。首先分析了它们的阶方差；为得到各模型中长波分量和短波分量的精度,利用研究区域内GPS水准数据分别对所选模型120阶和360阶计算得到的大地水准面高进行了比较；又考虑到地形和实测重力数据缺失对大地水准面的影响,把研究区域粗略地划分为平原和山地丘陵两部分,并比较了两个地区内参考点上模型计算值的精度；最后利用最小二乘原理对模型计算值进行了拟合改正。研究结果表明,EGM08计算得到的研究区大地水准面是这几个模型中精度最高的。
2.在没有地面重力数据的情况下,利用目前Sandwell D T等公布的最新V18.1全球1'×1'重力异常作为局部重力异常数据,分别以360阶EGM96模型和EGM08模型作为参考场,利用“移去-恢复”法计算了研究区域1'×1'大地水准面,探讨了利用该卫星重力异常计算大地水准面的精度。结果表明,该卫星重力异常计算得到的大地水准面具有较高的精度；在今后的大地水准面计算中,可与实测地面重力数据相结合或者在地面重力空白区作为一种替代的重力数据。
3.利用第2部分使用的卫星重力计算了研究区的重力大地水准面和计算布格重力异常。由于两种数据对深部和浅部场源信息的不同敏感度,除对它们进行了综合分析之外,又用点质量模型法对重力大地水准面进行了长波分量分离处理,得到代表不同深度异常信息的剩余大地水准面；对计算布格重力异常进行了位场切割分离、向下延拓积分-迭代法以及视密度反演,得到代表不同深度的剩余重力异常和视密度异常。根据这些数据,结合其他的地球物理资料对研究区进行了详细的地球物理解释。结果证明了卫星重力在地球物理解释中的可行性。
In this paper, three case studies in the area of Hunan Province about the applications of satellite gravity in the determination of the geoid and the geophysical interpretation are presented in detail, due to the uneven distributions of the terrestrial gravimetric data and the dramatically development of the satellite gravimetric data in terms of accuracy and resolution. Meanwhile, the corresponding principles and methods are introduced. The main contents and conclusions are listed as follows:
1. The accuracies of the Geoids computed from several Geopotential Models (EGM08, EGM96, GGM02, etc) are compared. The analysis of their degree variances is presented firstly. In order to generating the accuracies of the long-medium and short medium components of the models, the Geoid Undulations computed by the models up to degree 120 and 360 are evaluated combing with the GPS Leveling Data in the research area. Considering the effect of the topography on the Geoid and the deficiency of the observed gravity data, the research area is divided into the flat part and the mountainous part roughly, and then the model values on the reference points are compared in each part. Finally, a Least Square Fitting (LSF) is used to correct and modify the model values. The Geoid computed from EGM08 is demonstrated to be the most precise one in the research area according to the results.
2. A new V18.1 Satellte Gravity Anomalies (SGA) which was recently published online by Sandwell D T, et al is used as the regional gravity data to compute the geoid of the research area with the "Remove-Restore" technique in the case of no observed terrestrial gravity data. The resolution of the geoid is 1'×1' which is the same as that of the SGA, the EGM96 and EGM08 global geopotential models up to degree and order of 360 are chosen to be the reference field respectively. The main purpose of this part is to discuss the accuracy of the geoid computed by the SGA and the results are showed as follows. The gravimetric geoid derived from the SGA can achieve to an accuracy of about 0.05m. It means that, in the future geoid modeling, the SGA can be used to combine with the terriestral gravity or to be a substitute one in the area with no terriestral data.
3. The satellite gravity mentioned in Part 2 is used to compute the gravimetric geoid (GG) and calculated Bouguer gravity anomalies (CBGA) over the research area. Both of them are synthetically analyzed because of their different sensitivities to the signals caused by deep and shallow anomalous sources. Moreover, the GG is separated into several residual gravimetric geoid (RGG) maps which reveal the anomalous features in different depth, by removing the long wavelength geoid features. In order to generating residual gravity anomalies (RGA) and apparent density anomalies (ADA) corresponding to strata of different depth, a cutting method for the potential field separation and apparent density inversion method are applied to process the CBGA. Then geophysical interpretation of the research area based on these data sets and other geophysical results is presented. The feasibility of satellite gravity in geophysical interpretation is demonstrated by the final results.
1.比较研究了EGM08, EGM96, GGM02等几种地球重力位模型确定局部大地水准面的精度。首先分析了它们的阶方差；为得到各模型中长波分量和短波分量的精度,利用研究区域内GPS水准数据分别对所选模型120阶和360阶计算得到的大地水准面高进行了比较；又考虑到地形和实测重力数据缺失对大地水准面的影响,把研究区域粗略地划分为平原和山地丘陵两部分,并比较了两个地区内参考点上模型计算值的精度；最后利用最小二乘原理对模型计算值进行了拟合改正。研究结果表明,EGM08计算得到的研究区大地水准面是这几个模型中精度最高的。
2.在没有地面重力数据的情况下,利用目前Sandwell D T等公布的最新V18.1全球1'×1'重力异常作为局部重力异常数据,分别以360阶EGM96模型和EGM08模型作为参考场,利用“移去-恢复”法计算了研究区域1'×1'大地水准面,探讨了利用该卫星重力异常计算大地水准面的精度。结果表明,该卫星重力异常计算得到的大地水准面具有较高的精度；在今后的大地水准面计算中,可与实测地面重力数据相结合或者在地面重力空白区作为一种替代的重力数据。
3.利用第2部分使用的卫星重力计算了研究区的重力大地水准面和计算布格重力异常。由于两种数据对深部和浅部场源信息的不同敏感度,除对它们进行了综合分析之外,又用点质量模型法对重力大地水准面进行了长波分量分离处理,得到代表不同深度异常信息的剩余大地水准面；对计算布格重力异常进行了位场切割分离、向下延拓积分-迭代法以及视密度反演,得到代表不同深度的剩余重力异常和视密度异常。根据这些数据,结合其他的地球物理资料对研究区进行了详细的地球物理解释。结果证明了卫星重力在地球物理解释中的可行性。
In this paper, three case studies in the area of Hunan Province about the applications of satellite gravity in the determination of the geoid and the geophysical interpretation are presented in detail, due to the uneven distributions of the terrestrial gravimetric data and the dramatically development of the satellite gravimetric data in terms of accuracy and resolution. Meanwhile, the corresponding principles and methods are introduced. The main contents and conclusions are listed as follows:
1. The accuracies of the Geoids computed from several Geopotential Models (EGM08, EGM96, GGM02, etc) are compared. The analysis of their degree variances is presented firstly. In order to generating the accuracies of the long-medium and short medium components of the models, the Geoid Undulations computed by the models up to degree 120 and 360 are evaluated combing with the GPS Leveling Data in the research area. Considering the effect of the topography on the Geoid and the deficiency of the observed gravity data, the research area is divided into the flat part and the mountainous part roughly, and then the model values on the reference points are compared in each part. Finally, a Least Square Fitting (LSF) is used to correct and modify the model values. The Geoid computed from EGM08 is demonstrated to be the most precise one in the research area according to the results.
2. A new V18.1 Satellte Gravity Anomalies (SGA) which was recently published online by Sandwell D T, et al is used as the regional gravity data to compute the geoid of the research area with the "Remove-Restore" technique in the case of no observed terrestrial gravity data. The resolution of the geoid is 1'×1' which is the same as that of the SGA, the EGM96 and EGM08 global geopotential models up to degree and order of 360 are chosen to be the reference field respectively. The main purpose of this part is to discuss the accuracy of the geoid computed by the SGA and the results are showed as follows. The gravimetric geoid derived from the SGA can achieve to an accuracy of about 0.05m. It means that, in the future geoid modeling, the SGA can be used to combine with the terriestral gravity or to be a substitute one in the area with no terriestral data.
3. The satellite gravity mentioned in Part 2 is used to compute the gravimetric geoid (GG) and calculated Bouguer gravity anomalies (CBGA) over the research area. Both of them are synthetically analyzed because of their different sensitivities to the signals caused by deep and shallow anomalous sources. Moreover, the GG is separated into several residual gravimetric geoid (RGG) maps which reveal the anomalous features in different depth, by removing the long wavelength geoid features. In order to generating residual gravity anomalies (RGA) and apparent density anomalies (ADA) corresponding to strata of different depth, a cutting method for the potential field separation and apparent density inversion method are applied to process the CBGA. Then geophysical interpretation of the research area based on these data sets and other geophysical results is presented. The feasibility of satellite gravity in geophysical interpretation is demonstrated by the final results.
引文
[1]管泽霖,管铮,黄谟涛,等.局部重力场逼近理论和方法.北京：测绘出版社,1997
[2]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.武汉：武汉大学出版社,2003
[3]黄谟涛,翟国君,管铮等.海洋重力场测定及其应用.北京：测绘出版社,2005
[4]Rapp R H, Wang Y M, Pavlis N K. The Ohio State 1991 geopotential and seasurface topography harmonic coefficient models. OSU Report No.410, Department of Geodetic Science and Survey, The Ohio State University,1991
[5]Lemoine F G, Kenyon S C, Factor J K, et al. The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96. NASA Goddard Space Flight Center, Greenbelt, Maryland,1998
[6]Reigber C, Schmidt R, Flechtner F, et al. An Earth gravity field model complete to degree and order 150 from GRACE:EIGEN-GRACE02S. Journal of Geodynamics,2005,39(l):1-10
[7]Tapley B, Ries J, Bettadpur S, et al. GGM02-An Improved Earth Gravity Field Model from GRACE. Journal of Geodesy,2005,79(8):467-478
[8]Forste C, Schmidt R, Stubenvoll R, et al. The GeoForschungsZentrum Potsdam/Groupe de Recherche de Geodesie Spatiale satellite-only and combined gravity field models:EIGEN-GL04SL and EIGEN-GL04C. Journal of Geodesy, 2008,82(6):331-346
[9]Pavlis N K, Holmes S A, Kenyon S C, et al. An Earth Gravitational Model to Degree2160:EGM2008. presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18,2008
[10]Kotsakis C, Katsambalos K, Ampatzidis D, et al. Evaluation of EGM08 in Greece using GPS and leveling heights. Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation. Chania, Greece, June 23-27,2008
[11]宁津生,李建成,晁定波,等.WDM94 360阶地球重力场模型研究.武汉测绘科技大学学报,1994,19(4)：283-291
[12]管泽霖,李建成,晁定波,等.WDM94中国重力大地水准面研究.武汉测绘科技大学学报,1994,19(4)：292-297
[13]夏哲仁,林丽,石磐.360阶地球重力场模型DQM94A及其精度分析.地球物 理学报,1995,38(6)：788-795
[14]Colombo O L. Numerical methods for harmonic analysis on the sphere. OSU Report No.310. Department of Geodetic Science and Survey, The Ohio State University,1981
[15]Sideris M G A fast Fourier transform method of computing terrain corrections. Manuscripta Geodaetica,1985,10:66-73
[16]Forsberg R. Gravity field terrain effect computation by FFT. Bulletin Geodesique, 1985,59:342-360
[17]Schwartz K R, Sideris M G, Forsberg R. The use of FFT techniques in physical geodesy. Geophysical Journal International,1990,100:485-514
[18]Strang Van Hees G Stokes formula using fast Fourier transform techniques. Manuscripta Geodaetica,1990,15:235-239
[19]Forsberg R, Sideris M G. Geoid computation by the multi-banding spherical FFT approach. Manuscripta Geodaetica,1993,18:82-90
[20]Haagmans R, de Min E, van Gelderen M. Fast evaluation of convolution integrals on the sphere using 1DFFT, and a comparison with existing methods for Stokes integral. Manuscripta Geodaetica,1993,18:227-241
[21]Sideris M G, Li Y C. Gravity field convolutions without windowing and edge effects. Bulletin Geodesique,1993,67:107-118
[22]Li Y C, Sideris M G. Improved gravimetric terrain correction. Geophysical Journal International,1994,119:740-752
[23]Tsoulis D. Terrain correction computation for a densely sampled DTM in the Bavarian Alps. Journal of Geodesy,2001,75:291-307
[24]Tsoulis D. Terrain modeling in forward gravimetric problems:a case study on local terrain effects. Journal of Applied Geophysics,2003,54:145-160
[25]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.武汉大学学报·信息科学版,2003,28(3)：340-344
[26]Sideris M G, She B B. A new, high-resolution geoid for Canada and part of the U.S by the 1D-FFT method. Bulletin Geodesique,1995,69:92-108
[27]Tziavos I N, Andritsanos V D. Recent Geoid Computations For the Hellenic Area. Phys. Chem. Earth,1999,24:91-96
[28]Featherstone W E, Kirby J F, Kearsley A H W, et al. The AUSGeoid98 geoid model of Australia:data treatment, computations and comparisons with GPS-leveling data. Journal of Geodesy,2001,75:313-330
[29]Kuroishi Y. An improved gravimetric geoid for Japan, JGEOID98, and relationships to marine gravity data. Journal of Geodesy,2001,74:745-755
[30]Smith D A, Small H J. The CARIB97 high-resolution geoid height model for the Caribbean Sea. Journal of Geodesy,1999,73:1-9
[31]Smith D A, Milbert D G. The GEOID96 high-resolution geoid height model fot United States. Journal of Geodesy,1999,73:219-236
[32]Smith D A, Roman D R. GEOID99 and G99SSS:1-arc-minute geoid models for the United States. Journal of Geodesy,2001,75:469-490
[33]Corchete V, Chourak M, Khattach D. The high-resolution gravimetric geoid of Iberia:IGG2005. Geophysical Journal International,2005,162:676-684
[34]Corchete V, Flores D, Oviedo F. The first high-resolution gravimetric geoid for the Bolivian tableland:BOLGEO. Physics of the earth and planetary interiors, 2006,157:250-256
[35]Corchete V, Chourak M, Khattach D, et al. The high-resolution gravimetric geoid of Morocco:MORGEO. Journal of African Earth Sciences,2007,48:267-272
[36]Vanicek P, Christou N T. Geoid and its geophysical interpretations. Florida:CRC Press,1994
[37]Bowin C. Depth of principle mass anomalies contributing to the earth's geoid undulation and gravity anomalies. Marine Geodesy.1983,7:61-101
[38]Bowin C, Scheer E, Smith W. Depth estimates from ratios of gravity, geoid, and gravity gradient anomalies. Geophysics.1986,51:123-136
[39]张赤军.由地面、卫星重力资料研究岩石层密度.地球物理学报,1988,31(6)：664-671
[40]方剑.利用卫星重力数据计算地球内部密度异常.地球物理学进展,1994,9(3)：60-65
[41]方剑,许厚泽.中国及邻区大地水准面异常的场源深度探讨.地球物理学报,2002,45(1)：42-48
[42]方剑,许厚泽.中国及邻区岩石层大地水准面正演模拟.地壳形变与地震.2000,20(4)：10-17
[43]方剑.青藏高原及邻区大地水准面异常场源结构.地学前缘,2001,8(4)：449-452
[44]陆洋,许厚泽.青藏地区大地水准面形态及其与构造动力学的关系.地球物理学报,1996,39(2)：203-210
[45]Featherstone W E. On the use of the Geoid in Geophysics:A Case Study over the
North-West Shelf of Australia. Exploration Geophysics,1997,28(1):52-57
[46]Kamguia J, Nouayou R, Tabod C T, et al. Geophysical signature of geological units inferred from the analysis of geoid maps in Cameroon and its surroundings. Journal of African Earth Sciences,2008,52:1-8
[47]王谦身,安玉林.南黄海西部及邻域重力场与深部构造.科学通报,1999,44(22)：2448-2453
[48]周国藩,陈建国,张健.青藏高原卫星重力场及所反映的壳幔结构和深部构造特征.地球科学—中国地质大学学报,1996,21(2)：191-197
[49]滕吉文,王谦身,王光杰等.喜马拉雅“东构造结”地区的特异重力场与深部地壳结构.地球物理学报,2006,49(4)：1045-1052
[50]Braitenberg C, Wienecke S, Wang Y. Basement structure from the satellite-derived gravity field:South China Ridge. Journal of Geophysical Research,2006, 111:B05407
[51]Braitenberg C, Ebbing J. The GRACE-satellite gravity and geoid fields in analyzing large-scale, cratonic or intracratonic basins. Geophysical Prospecting, 2009,57:559-571
[52]Braitenberg C, Ebbing J. New insight into the basement structure of the West Siberian Basin from forward and inverse modeling of GRACE satellite gravity data. Journal of Geophysical Research,2009,114:B06402
[53]Shin Y, Xu H, Braitenberg C, et al. Moho undulations beneath Tibet from GRACE-integrated gravity data. Geophysical Journal International,2007, 170:971-985
[54]Delikaraoglou D, Blais J, Kanasewich E, et al. Satellite altimetry:Utilization for resource exploration. Geoscience and Remote Sensing Symposium,1989
[55]Hackney R, Bousquet R, Goetze H, et al. Geophysical and petrological applications of new-generation satellite-derived gravity data:What can and needs to be done?. Proc. The 3rd International GOCE User Workshop, ESA-ESRIN, Frascati, Italy,6-8 November,2006
[56]海斯卡宁,莫里茨著.物理大地测量.卢福康,胡国理译,北京：测绘出版社,1979
[57]Sjoberg L. On the quasigeoid to geoid separation. Manuscripata Geodaetica,1995, 20:182-192
[58]Omang O, Forsberg R. How to handle topography in practical geoid determination:three examples. Journal of Geodesy,2000,74:458-466
[59]楼海.重力方法在地壳结构研究中的应用：[博士论文].北京：中国地震局地球物理研究所,2001
[60]张正禄,邓勇,罗长林,等.利用GPS精化区域似大地水准面.大地测量与地球动力学,2006,26(4)：14-17
[61]Luo Z C, Chen YQ. Evaluation of Geo-potential Models EGM96, WDM94 and GPM98CR in Hong Kong and ShenZhen. Journal of Geospatial Engineering, 2002,49(1):21-30
[62]曾元武,杨沾吉,张天纪.EGM96,WDM94和GPM98CR高阶地球重力场模型表示深圳局部重力场的比较与评价.测绘学报,2002,31(4)：289-291
[63]罗佳,施闯,邹贤才,等.现有SST重力场模型的比较研究.武汉大学学报信息科学版,2006,31(7)：594-598
[64]罗佳,姜卫平,汪海洪,等.中国区域SST卫星重力场模型精度分析.武汉大学学报·信息科学版,2006,31(3)：199-203
[65]Rapp R H, Wang Y M. Geoid Undulation Differences between Geopotential Models. Surveys in Geophysics,1993,14:373-380
[66]周旭华,吴斌,彭碧波,等.利用CHAMP科学轨道数据和星载加速度计数据反演地球重力场.武汉大学学报·信息科学版,2006,31(2)：172-175
[67]周旭华,许厚泽,吴斌,等.用GRACE卫星跟踪数据反演地球重力场.地球物理学报,2006,49(3)：718-723
[68]Chen Y Q, Luo Z C. Precise Hong Kong Geoid HKGEOID-2000. Journal of Geospatial Engineering,2003,5(2):35-41
[69]宁津生,罗志才,杨沾吉,等.深圳市1km高分辨率厘米级高精度大地水准面的确定.测绘学报,2003,32(2)：102-107
[70]Sandwell D T, Smith W H F. Global marine gravity from retracked Geosat and ERS-1 altimetry:Ridge segmentation versus spreading rate. Journal of Geophysical Research,2009,114, B01411
[71]张全德,郭春喜,王斌,等.华东、华中区域似大地水准面精化.地理信息世界,2007,5：21-26
[72]张全德,郭春喜,王斌.浙闽赣区域似大地水准面精化.测绘科学,2007,31(1)：11-13
[73]Rapp R H. Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. Journal of Geodesy,1997,71:282-289
[74]Kotsakis C, Katsambalos K, Ampatzidis D, et al. Evaluation of EGM08 in Greece
using GPS and leveling heights. Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation, Chania, Greece, June 23-27,2008
[75]Nahavandchi H. Two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential, topographic corrections and the height anomaly-geoidal height difference. Journal of Geodesy,2002, 76:345-352
[76]Li X, Goetze H J. Ellipsoid, geoid, gravity, geodesy, and geophysics. Geophysics, 2001,66:1660-1668
[77]程方道,刘东甲,姚汝信.划分重力区域场和局部场的研究.物探化探计算技术,1987,9(1)：1-9
[78]文百红,程方道.用于划分磁异常的新方法——插值切割法.中南矿冶学院学报,1990,21(3)：229-235
[79]段本春,徐世浙,阎汉杰,等.划分磁异常场的差值切割法在研究火成岩体分布中的应用.石油地球物理勘探,1998,33(1)：125-131
[80]段本春,范典高.利用插值切割法研究磁性基底局部起伏特征.石油物探,1999,38(4)：89-95
[81]徐世浙,张研,文百红,等.切割法在陆东地区磁异常解释中的应用.石油物探,2006,45(3)：316-318
[82]杨金玉,徐世浙,余海龙等.视密度反演在东海及邻区重力异常解释中的应用.地球物理学报,2008,51(6)：1909-1916
[83]徐世浙,余海龙,李海侠等.基于位场分离与延拓的视密度反演.地球物理学报,2009,52(6)：1592-1598
[84]徐世浙,王华军,余海龙等.普光气田重力异常的视密度反演.地球物理学报,2009,52(9)：2357-2363
[85]段本春,徐世浙.磁(重力)异常局部场与区域场分离处理中的扩边方法研究.物探化探计算技术,1997,19(4)：298-304
[86]徐世浙.位场延拓的积分-迭代法.地球物理学报,2006,49(4)：1176-1182
[87]徐世浙.迭代法与FFT法位场向下延拓效果的比较.地球物理学报,2007,50(1)：285-289
[88]Xu S Z, Yang J Y, Yang C F, et al. The iteration method for downward continuation of a potential field from a horizontal plane. Geophysical Prospecting, 2007,55:883-889
[89]刘东甲,洪天求,贾志海,等.位场向下延拓的波数域迭代法及其收敛性.地球物理学报,2009,52(6)：1599-1605
[90]Nagy D. The gravitational attraction of a right rectangular prism. Geophysics, 1966,31:362-371
[91]Li X, Chouteau M. Three-Dimensional gravity modeling in all space. Surveys in Geophysics,1998,19:339-368
[92]Bhattacharyya B K, Leu L K. Spectral analysis of gravity and magnetic anomalies due to rectangular prismatic bodies. Geophysics,1977,42(1):41-50
[93]肖鹏飞,陈生昌.稳定的频率域变深度视密度反演方法.地球物理学进展,2008,23(4)：1254-1260
[94]曾华霖.重力场与重力勘探.北京：地质出版社,2005
[95]饶家荣,王纪恒,曹一中.湖南深部构造.湖南地质,1993,7(增刊)：1-100
[96]朱自强.湖南地区中生代以来深部地球动力学演化的有限元数值模拟及成矿作用特征研究[博士论文].长沙：中南大学,2004
[97]谢湘雄.湖南大地构造单元划分及其地球物理场特征.湖南地质,1992,11(4)：334-342
[98]谢湘雄,顾剑虹.试论湖南省莫霍面形态及地壳厚度特征.湖南地质,1990,9(2)：10-18
[99]谢湘雄.试论湖南地壳均衡特征.湖南地质,1995,14(3)：179-183
[100]谢湘雄,顾剑虹.地壳均很假说与湘西北地壳均衡失调探讨.物探与化探,2002,26(3)：171-174
[101]杨宗仁.地壳重力均衡的定量研究—以湖南地区为例.地壳形变与地震,1986,6(4)：285-291
[102]Zhang C Y. A general formula and its inverse formula for gravimetric transformations by use of convolution and deconvolution techniques. Journal of Geodesy,1995,70:51-64
[103]叶学齐.湖北的地质与地质构造.华中师范大学学报,1985,20(3)：368-372
[104]Skeel D. Ambiguity in gravity interpretation. Geophysics,1947,12:43-56
[2]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.武汉：武汉大学出版社,2003
[3]黄谟涛,翟国君,管铮等.海洋重力场测定及其应用.北京：测绘出版社,2005
[4]Rapp R H, Wang Y M, Pavlis N K. The Ohio State 1991 geopotential and seasurface topography harmonic coefficient models. OSU Report No.410, Department of Geodetic Science and Survey, The Ohio State University,1991
[5]Lemoine F G, Kenyon S C, Factor J K, et al. The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96. NASA Goddard Space Flight Center, Greenbelt, Maryland,1998
[6]Reigber C, Schmidt R, Flechtner F, et al. An Earth gravity field model complete to degree and order 150 from GRACE:EIGEN-GRACE02S. Journal of Geodynamics,2005,39(l):1-10
[7]Tapley B, Ries J, Bettadpur S, et al. GGM02-An Improved Earth Gravity Field Model from GRACE. Journal of Geodesy,2005,79(8):467-478
[8]Forste C, Schmidt R, Stubenvoll R, et al. The GeoForschungsZentrum Potsdam/Groupe de Recherche de Geodesie Spatiale satellite-only and combined gravity field models:EIGEN-GL04SL and EIGEN-GL04C. Journal of Geodesy, 2008,82(6):331-346
[9]Pavlis N K, Holmes S A, Kenyon S C, et al. An Earth Gravitational Model to Degree2160:EGM2008. presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18,2008
[10]Kotsakis C, Katsambalos K, Ampatzidis D, et al. Evaluation of EGM08 in Greece using GPS and leveling heights. Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation. Chania, Greece, June 23-27,2008
[11]宁津生,李建成,晁定波,等.WDM94 360阶地球重力场模型研究.武汉测绘科技大学学报,1994,19(4)：283-291
[12]管泽霖,李建成,晁定波,等.WDM94中国重力大地水准面研究.武汉测绘科技大学学报,1994,19(4)：292-297
[13]夏哲仁,林丽,石磐.360阶地球重力场模型DQM94A及其精度分析.地球物 理学报,1995,38(6)：788-795
[14]Colombo O L. Numerical methods for harmonic analysis on the sphere. OSU Report No.310. Department of Geodetic Science and Survey, The Ohio State University,1981
[15]Sideris M G A fast Fourier transform method of computing terrain corrections. Manuscripta Geodaetica,1985,10:66-73
[16]Forsberg R. Gravity field terrain effect computation by FFT. Bulletin Geodesique, 1985,59:342-360
[17]Schwartz K R, Sideris M G, Forsberg R. The use of FFT techniques in physical geodesy. Geophysical Journal International,1990,100:485-514
[18]Strang Van Hees G Stokes formula using fast Fourier transform techniques. Manuscripta Geodaetica,1990,15:235-239
[19]Forsberg R, Sideris M G. Geoid computation by the multi-banding spherical FFT approach. Manuscripta Geodaetica,1993,18:82-90
[20]Haagmans R, de Min E, van Gelderen M. Fast evaluation of convolution integrals on the sphere using 1DFFT, and a comparison with existing methods for Stokes integral. Manuscripta Geodaetica,1993,18:227-241
[21]Sideris M G, Li Y C. Gravity field convolutions without windowing and edge effects. Bulletin Geodesique,1993,67:107-118
[22]Li Y C, Sideris M G. Improved gravimetric terrain correction. Geophysical Journal International,1994,119:740-752
[23]Tsoulis D. Terrain correction computation for a densely sampled DTM in the Bavarian Alps. Journal of Geodesy,2001,75:291-307
[24]Tsoulis D. Terrain modeling in forward gravimetric problems:a case study on local terrain effects. Journal of Applied Geophysics,2003,54:145-160
[25]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.武汉大学学报·信息科学版,2003,28(3)：340-344
[26]Sideris M G, She B B. A new, high-resolution geoid for Canada and part of the U.S by the 1D-FFT method. Bulletin Geodesique,1995,69:92-108
[27]Tziavos I N, Andritsanos V D. Recent Geoid Computations For the Hellenic Area. Phys. Chem. Earth,1999,24:91-96
[28]Featherstone W E, Kirby J F, Kearsley A H W, et al. The AUSGeoid98 geoid model of Australia:data treatment, computations and comparisons with GPS-leveling data. Journal of Geodesy,2001,75:313-330
[29]Kuroishi Y. An improved gravimetric geoid for Japan, JGEOID98, and relationships to marine gravity data. Journal of Geodesy,2001,74:745-755
[30]Smith D A, Small H J. The CARIB97 high-resolution geoid height model for the Caribbean Sea. Journal of Geodesy,1999,73:1-9
[31]Smith D A, Milbert D G. The GEOID96 high-resolution geoid height model fot United States. Journal of Geodesy,1999,73:219-236
[32]Smith D A, Roman D R. GEOID99 and G99SSS:1-arc-minute geoid models for the United States. Journal of Geodesy,2001,75:469-490
[33]Corchete V, Chourak M, Khattach D. The high-resolution gravimetric geoid of Iberia:IGG2005. Geophysical Journal International,2005,162:676-684
[34]Corchete V, Flores D, Oviedo F. The first high-resolution gravimetric geoid for the Bolivian tableland:BOLGEO. Physics of the earth and planetary interiors, 2006,157:250-256
[35]Corchete V, Chourak M, Khattach D, et al. The high-resolution gravimetric geoid of Morocco:MORGEO. Journal of African Earth Sciences,2007,48:267-272
[36]Vanicek P, Christou N T. Geoid and its geophysical interpretations. Florida:CRC Press,1994
[37]Bowin C. Depth of principle mass anomalies contributing to the earth's geoid undulation and gravity anomalies. Marine Geodesy.1983,7:61-101
[38]Bowin C, Scheer E, Smith W. Depth estimates from ratios of gravity, geoid, and gravity gradient anomalies. Geophysics.1986,51:123-136
[39]张赤军.由地面、卫星重力资料研究岩石层密度.地球物理学报,1988,31(6)：664-671
[40]方剑.利用卫星重力数据计算地球内部密度异常.地球物理学进展,1994,9(3)：60-65
[41]方剑,许厚泽.中国及邻区大地水准面异常的场源深度探讨.地球物理学报,2002,45(1)：42-48
[42]方剑,许厚泽.中国及邻区岩石层大地水准面正演模拟.地壳形变与地震.2000,20(4)：10-17
[43]方剑.青藏高原及邻区大地水准面异常场源结构.地学前缘,2001,8(4)：449-452
[44]陆洋,许厚泽.青藏地区大地水准面形态及其与构造动力学的关系.地球物理学报,1996,39(2)：203-210
[45]Featherstone W E. On the use of the Geoid in Geophysics:A Case Study over the
North-West Shelf of Australia. Exploration Geophysics,1997,28(1):52-57
[46]Kamguia J, Nouayou R, Tabod C T, et al. Geophysical signature of geological units inferred from the analysis of geoid maps in Cameroon and its surroundings. Journal of African Earth Sciences,2008,52:1-8
[47]王谦身,安玉林.南黄海西部及邻域重力场与深部构造.科学通报,1999,44(22)：2448-2453
[48]周国藩,陈建国,张健.青藏高原卫星重力场及所反映的壳幔结构和深部构造特征.地球科学—中国地质大学学报,1996,21(2)：191-197
[49]滕吉文,王谦身,王光杰等.喜马拉雅“东构造结”地区的特异重力场与深部地壳结构.地球物理学报,2006,49(4)：1045-1052
[50]Braitenberg C, Wienecke S, Wang Y. Basement structure from the satellite-derived gravity field:South China Ridge. Journal of Geophysical Research,2006, 111:B05407
[51]Braitenberg C, Ebbing J. The GRACE-satellite gravity and geoid fields in analyzing large-scale, cratonic or intracratonic basins. Geophysical Prospecting, 2009,57:559-571
[52]Braitenberg C, Ebbing J. New insight into the basement structure of the West Siberian Basin from forward and inverse modeling of GRACE satellite gravity data. Journal of Geophysical Research,2009,114:B06402
[53]Shin Y, Xu H, Braitenberg C, et al. Moho undulations beneath Tibet from GRACE-integrated gravity data. Geophysical Journal International,2007, 170:971-985
[54]Delikaraoglou D, Blais J, Kanasewich E, et al. Satellite altimetry:Utilization for resource exploration. Geoscience and Remote Sensing Symposium,1989
[55]Hackney R, Bousquet R, Goetze H, et al. Geophysical and petrological applications of new-generation satellite-derived gravity data:What can and needs to be done?. Proc. The 3rd International GOCE User Workshop, ESA-ESRIN, Frascati, Italy,6-8 November,2006
[56]海斯卡宁,莫里茨著.物理大地测量.卢福康,胡国理译,北京：测绘出版社,1979
[57]Sjoberg L. On the quasigeoid to geoid separation. Manuscripata Geodaetica,1995, 20:182-192
[58]Omang O, Forsberg R. How to handle topography in practical geoid determination:three examples. Journal of Geodesy,2000,74:458-466
[59]楼海.重力方法在地壳结构研究中的应用：[博士论文].北京：中国地震局地球物理研究所,2001
[60]张正禄,邓勇,罗长林,等.利用GPS精化区域似大地水准面.大地测量与地球动力学,2006,26(4)：14-17
[61]Luo Z C, Chen YQ. Evaluation of Geo-potential Models EGM96, WDM94 and GPM98CR in Hong Kong and ShenZhen. Journal of Geospatial Engineering, 2002,49(1):21-30
[62]曾元武,杨沾吉,张天纪.EGM96,WDM94和GPM98CR高阶地球重力场模型表示深圳局部重力场的比较与评价.测绘学报,2002,31(4)：289-291
[63]罗佳,施闯,邹贤才,等.现有SST重力场模型的比较研究.武汉大学学报信息科学版,2006,31(7)：594-598
[64]罗佳,姜卫平,汪海洪,等.中国区域SST卫星重力场模型精度分析.武汉大学学报·信息科学版,2006,31(3)：199-203
[65]Rapp R H, Wang Y M. Geoid Undulation Differences between Geopotential Models. Surveys in Geophysics,1993,14:373-380
[66]周旭华,吴斌,彭碧波,等.利用CHAMP科学轨道数据和星载加速度计数据反演地球重力场.武汉大学学报·信息科学版,2006,31(2)：172-175
[67]周旭华,许厚泽,吴斌,等.用GRACE卫星跟踪数据反演地球重力场.地球物理学报,2006,49(3)：718-723
[68]Chen Y Q, Luo Z C. Precise Hong Kong Geoid HKGEOID-2000. Journal of Geospatial Engineering,2003,5(2):35-41
[69]宁津生,罗志才,杨沾吉,等.深圳市1km高分辨率厘米级高精度大地水准面的确定.测绘学报,2003,32(2)：102-107
[70]Sandwell D T, Smith W H F. Global marine gravity from retracked Geosat and ERS-1 altimetry:Ridge segmentation versus spreading rate. Journal of Geophysical Research,2009,114, B01411
[71]张全德,郭春喜,王斌,等.华东、华中区域似大地水准面精化.地理信息世界,2007,5：21-26
[72]张全德,郭春喜,王斌.浙闽赣区域似大地水准面精化.测绘科学,2007,31(1)：11-13
[73]Rapp R H. Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference. Journal of Geodesy,1997,71:282-289
[74]Kotsakis C, Katsambalos K, Ampatzidis D, et al. Evaluation of EGM08 in Greece
using GPS and leveling heights. Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation, Chania, Greece, June 23-27,2008
[75]Nahavandchi H. Two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential, topographic corrections and the height anomaly-geoidal height difference. Journal of Geodesy,2002, 76:345-352
[76]Li X, Goetze H J. Ellipsoid, geoid, gravity, geodesy, and geophysics. Geophysics, 2001,66:1660-1668
[77]程方道,刘东甲,姚汝信.划分重力区域场和局部场的研究.物探化探计算技术,1987,9(1)：1-9
[78]文百红,程方道.用于划分磁异常的新方法——插值切割法.中南矿冶学院学报,1990,21(3)：229-235
[79]段本春,徐世浙,阎汉杰,等.划分磁异常场的差值切割法在研究火成岩体分布中的应用.石油地球物理勘探,1998,33(1)：125-131
[80]段本春,范典高.利用插值切割法研究磁性基底局部起伏特征.石油物探,1999,38(4)：89-95
[81]徐世浙,张研,文百红,等.切割法在陆东地区磁异常解释中的应用.石油物探,2006,45(3)：316-318
[82]杨金玉,徐世浙,余海龙等.视密度反演在东海及邻区重力异常解释中的应用.地球物理学报,2008,51(6)：1909-1916
[83]徐世浙,余海龙,李海侠等.基于位场分离与延拓的视密度反演.地球物理学报,2009,52(6)：1592-1598
[84]徐世浙,王华军,余海龙等.普光气田重力异常的视密度反演.地球物理学报,2009,52(9)：2357-2363
[85]段本春,徐世浙.磁(重力)异常局部场与区域场分离处理中的扩边方法研究.物探化探计算技术,1997,19(4)：298-304
[86]徐世浙.位场延拓的积分-迭代法.地球物理学报,2006,49(4)：1176-1182
[87]徐世浙.迭代法与FFT法位场向下延拓效果的比较.地球物理学报,2007,50(1)：285-289
[88]Xu S Z, Yang J Y, Yang C F, et al. The iteration method for downward continuation of a potential field from a horizontal plane. Geophysical Prospecting, 2007,55:883-889
[89]刘东甲,洪天求,贾志海,等.位场向下延拓的波数域迭代法及其收敛性.地球物理学报,2009,52(6)：1599-1605
[90]Nagy D. The gravitational attraction of a right rectangular prism. Geophysics, 1966,31:362-371
[91]Li X, Chouteau M. Three-Dimensional gravity modeling in all space. Surveys in Geophysics,1998,19:339-368
[92]Bhattacharyya B K, Leu L K. Spectral analysis of gravity and magnetic anomalies due to rectangular prismatic bodies. Geophysics,1977,42(1):41-50
[93]肖鹏飞,陈生昌.稳定的频率域变深度视密度反演方法.地球物理学进展,2008,23(4)：1254-1260
[94]曾华霖.重力场与重力勘探.北京：地质出版社,2005
[95]饶家荣,王纪恒,曹一中.湖南深部构造.湖南地质,1993,7(增刊)：1-100
[96]朱自强.湖南地区中生代以来深部地球动力学演化的有限元数值模拟及成矿作用特征研究[博士论文].长沙：中南大学,2004
[97]谢湘雄.湖南大地构造单元划分及其地球物理场特征.湖南地质,1992,11(4)：334-342
[98]谢湘雄,顾剑虹.试论湖南省莫霍面形态及地壳厚度特征.湖南地质,1990,9(2)：10-18
[99]谢湘雄.试论湖南地壳均衡特征.湖南地质,1995,14(3)：179-183
[100]谢湘雄,顾剑虹.地壳均很假说与湘西北地壳均衡失调探讨.物探与化探,2002,26(3)：171-174
[101]杨宗仁.地壳重力均衡的定量研究—以湖南地区为例.地壳形变与地震,1986,6(4)：285-291
[102]Zhang C Y. A general formula and its inverse formula for gravimetric transformations by use of convolution and deconvolution techniques. Journal of Geodesy,1995,70:51-64
[103]叶学齐.湖北的地质与地质构造.华中师范大学学报,1985,20(3)：368-372
[104]Skeel D. Ambiguity in gravity interpretation. Geophysics,1947,12:43-56