利用空中球面边值问题确定似大地水准面

针对航空重力向下延拓计算过程中的不稳定性,提出了扰动位空中球面边值问题,以航空重力测量数据作为扰动位在空中球面上满足的边值条件,得到扰动位空中球面边值问题,在球外部即为经典的球外边值问题,但对于球内直到地面则没有封闭的解析形式,给出了空中球面球内到地面区域的级数解,对于认识空中重力测量数据向下延拓特征和实际应用具有参考意义。利用地面实测数据计算结果表明,对于1km航高的测量数据,一阶解可满足厘米级高程异常的解算精度。     

基于最小二乘配置法和奇异值截断法向下延拓航空重力数据的仿真研究

基于最小二乘配置法建立的航空重力异常与其相应地面重力异常的协方差函数,由于协方差矩阵严重病态,观测误差被放大从而影响向下延拓结果的稳定性和精度;引入基于 GCV 法选择正则化参数的奇异值截断法后,能抑制协方差矩阵的病态性对观测噪声的放大影响。 基于 EGM2008 重力场模型分别计算陆地和海域的航空重力异常作为基础数据,用本文方法向下延拓获取相应的地面重力异常,实验结果验证该方法的有效性。     

基于海空磁力测量数据的向下延拓方法比较

地磁场的向下延拓是实现磁场数据空间转换的主要手段,是多源海洋磁力测量数据融合和构建三维海洋磁空间背景场模型的关键技术。在分析频域位场向下延拓方法原理基础上,分别采用了4种向下延拓方法将300 m高度磁测数据延拓至200 m高度,并与同一海区200 m高度实测数据对比,以检验各延拓方法的计算效果,为构建三维海洋磁空间背景场模型提供参考。结果表明:Tikhonov正则化法延拓结果与实测数据最接近,积分迭代法容易放大实测数据中高频噪声,延拓误差最大,迭代Tikhonov正则化法与Landweber迭代法延拓结果等值线最光滑,各方法计算误差相差不大,均在4 nT左右,但各方法计算值缺乏局部细节信息,与实测数据仍存在一定差距。     

海空重力测量及应用技术研究进展与展望(四):数值模型构建与综合应用技术

分析总结了海空重力测量数据向上和向下延拓技术的研究现状及发展方向,简要论述了海空重力测量多源数据融合处理技术的研究动态及发展前景,分析讨论了海空重力测量数据应用于地球外部重力场赋值和大地水准面精化技术的研究进展及发展思路,为海空重力测量数值建模与数据综合应用技术的未来发展提供参考。     

GT-1M 海洋重力仪与KSS31M 海洋重力仪的对比

为了检验俄罗斯、加拿大合作生产的GT-1M海洋重力仪与德国KSS31M海洋重力仪的工作性能,验证GT-1M重力数据的可靠性,将GT-1M采集的3条重力剖面与KSS31M重力仪采集的重力测网进行了对比分析。结果显示:GT01剖面与26条KSS31M重力测线的交点差均值为0.31mGal,交点差均方根为2.51mGal;GT02剖面与11条KSS31M重力测线的,交点差均值为–0.78mGal,交点差均方根为1.97mGal;全部交点差均值为–0.01mGal,均方根(RMS)为2.32mGal。GT01剖面与KSS31M测网网格化切割的剖面的变化趋势一致,重力变化幅值基本吻合,相关系数为0.98;而GT02剖面位于KSS31测网边缘,网格化切割的KSS重力剖面不能反应真实的重力场,虽然GT02剖面变化趋势一致,但相关系数仅为0.94,在相位上也明显有误差。考虑到测网位于海底地形崎岖的深水区,而且两次测量时间间隔达3a,因此GT-1M重力仪测试的结果还是基本与KSS31M重力仪吻合的,数据是可靠的。该分析结果对今后的重力测量工作有参考价值。     

两种测高重力异常反演海底地形方法比较

针对基于测高重力异常反演海底地形理论众多、选取标准无法确定的情况,利用中国南海海域内的测高重力异常和船测水深数据研究比较了重力地质法(GGM)和SmithSandwell (SAS)法两种精度高、计算速度相对较快的海底地形反演理论。其中,GGM方法的密度差异常数Δρ由向下延拓技术确定为2.15 g·cm-3,SAS方法采用移去-恢复技术得到反演波段内重力异常和水深数据。结果表明:测线分布条件一定时,水深多在-1 000 m左右或反演区域岛礁、海山等复杂海底地形较多时选取SAS方法,水深主要在-3 000 m以深的区域或海底地形复杂程度不高时选取GGM方法则能获取更好的效果,其效果最优处与船测水深在检核点处的差值最优平均值能达-0.61 m,标准差可达14.67 m。     

增加近岸船载重力测量数据覆盖的推估方法研究

针对海洋区域离岸距离5～30km的范围内船载重力测量数据覆盖空白的现状,基于已有测线数据,对其进行不同空间距离采样形成对应的采样序列。利用动态时间规整算法计算其与初始测线数据的相关系数,依据相关系数与采样距离之间的关系,确定了最优重采样空间距离新方法。以最优重采样空间距离对测线数据进行重采样,利用拉格朗日插值算法,沿测线方向将测线数据向陆地推估。经过不同测线的内外部检核,结果表明船载重力测量向陆地方向扩展的保守距离约为5～10km,减少了船载重力测量数据在近岸海域覆盖空白的面积。本研究成果可为建立陆海一致垂直基准工作提供更全面的基础数据,技术方法可为航空重力、地磁等测线数据的精细处理及应用提供参考。     

台湾地区重力场特征及莫霍面反演

台湾地区空间重力异常幅值在-240~340mGal之间变化,布格重力异常幅值在-140~380mGal之间变化,重力异常及圈闭走向呈现北东、北北东向。将小波分析方法引入台湾地区的重力异常数据处理,经过分析比对,台湾地区布格重力异常小波分析三阶逼近结果代表莫霍面起伏形态,利用重力数据反演了深部界面莫霍面,研究区莫霍面深度为12~32km,莫霍面展布呈现北东走向,台湾岛区莫霍面深,在24~31km之间变化,由西北往东南为厚-薄-厚分布,台湾东部海区莫霍面深度浅,在12~17km之间变化,台湾岛属于陆壳结构,靠近菲律宾海的台湾岛外海地区,属于海洋性地壳结构。     

虚拟压缩恢复法应用于航空重力向下延拓的适用性问题

为了求解不规则边界面的大地测量边值问题,我国学者提出了虚拟压缩恢复法,并尝试将其应用于航空重力测量数据的向下延拓解算。在对虚拟压缩恢复法进行模型化分析基础上,从理论上证明了在求解地球内部Bjerhammar球上的虚拟重力异常时,虚拟压缩恢复法与基于逆Poisson积分的逐步迭代解是完全等价的,利用数值计算验证了两种解算结果的一致性,同时通过数值仿真计算,分析探讨了数据观测噪声对虚拟压缩恢复法解算结果的影响。检验结果表明,虚拟压缩恢复法应用于航空重力向下延拓计算,一方面可能增加边缘效应的影响,另一方面同样存在数据误差累积放大问题,因此其适用性有待做进一步的研究。     

重力异常的视密度反演推断扬子与华北块体在南黄海地区的地质界线

通过对南黄海及周边船载测量重力数据、现代卫星测高重力数据、陆地测量重力数据以及地球重力模型等多来源重力数据进行整理和融合,对南黄海地区布格重力异常特征进行了分析。利用基于切割法和插值迭代法的大深度位场向下延拓技术的视密度反演法对南黄海布格重力进行处理和解释,结合山东和朝鲜半岛的地质信息,推断了扬子块体和中朝块体在南黄海海域的界限。中朝和扬子块体在海上的分界位置为千里岩北缘断裂,向NE延伸到125°E后,折向NNW向并在36°N附近再次转为NE向进入朝鲜半岛并经过洪城南侧继续以NE向延伸。扬子的北缘为苏鲁造山带,穿过黄海与京畿造山带相接,苏鲁超高压变质带对应洪城杂岩。     

经验模分解在动态重力测量数据处理中的应用

在动态重力测量中,测量结果会受到各种因素的影响,尤其是载体的动态运动会引起重力测量结果的波动。针对这一问题,研究了经验模分解的方法在动态重力测量中的应用,并利用捷联式重力仪SGA-WZ02的实测数据对经验模分解的方法进行了验证。实验结果表明,通过经验模分解能够消除载体运动对重力测量的影响,重复测线的数据表明了通过经验模分解处理之后重力异常的重复性从0.881m Gal提高到了0.611m Gal。     

Heterogeneous Gravity Data Fusion and Gravimetric Quasigeoid Computation in the Coastal Area of China

ABSTRACT

Different types of gravity observations are available over coastal areas. The main challenge for coastal geoid determination is the proper fusion of heterogeneous gravity data including land, shipborne, airborne, and altimetry-derived gravity data. This paper describes the gravity data fusion and the computation of the gravimetric quasigeoid in the coastal area of mainland China. An iterative procedure of the weighted least-squares prediction based on rectangular harmonic functions is used for merging the land, altimetric, shipborne, and airborne gravity data. Applying the analytical continuation method in Molodensky's theoretic frame, the merged gravity data are then used to determine the gravimetric quasigeoid model by using the generalized Stokes' integral in a remove-compute-restore fashion. The gravimetric quasigeoid model is compared with the height anomalies determined at 662 GPS leveling points over the coastal region of mainland China, where both the geodetic height and the normal height are known. The standard deviations of the differences in the coastal provinces range from 1.8 to 4.4 cm. For the entire computation area, the mean and standard deviation of the differences are 27.9 and 3.9 cm, respectively.     

Oceanic gravity by analytical inversion of Hotine's formula

An analytical inversion of the Hotine formula is developed using fast Fourier transform techniques. Detailed mathematical derivations are used to explain the concepts behind the inverse transformation. Three modifications of the analytical inversion of the Hotine formula are compared and tested using both synthetic data from the OSU91A geopotential model and real GEOSAT altimetry data from the Exact Repeat Mission. The stability of this inverse Hotine approach is investigated using simulated data, and numerical tests are done to quantify the stability of this approach. The approach seems to be numerically stable without employing any stabilization technique. Estimated gravity information from GEOSTAT altimetry data is compared to marine gravity data from shipboard measurements in the Orphan Knoll area. The standard deviations and mean values of the differences between satellite and marine gravity disturbances are 8.2 and 2.9 mGal for the planar approximation, 9.2 and 3.7 mGal for the spherical approximation, and 9.5 and 1.9 mGal for the Molodenskii‐like approximation, respectively, indicating that latitude‐dependent errors affect the latter two approximations. Such errors could be eliminated by performing the calculations by the rigorous one‐dimensional fast Fourier transform (FFT) technique, and any data noise could be filtered out by utilizing covariance knowledge about the input geoid undulations and their errors. Simulation studies also showed that the accuracy of the techniques (for all approximations) can reach a root‐mean‐square (RMS) level of only a few mGal when proper treatment of FFT edge effects is employed and a rather wide area of results is disregarded around the edges.     

多型航空重力仪同机测试及其数据分析

介绍了运8飞机加装4型5套航空重力仪开展同机测试的整体情况,对5套重力仪所获取的重复线和测网成果数据进行了对比分析。试验结果表明,俄罗斯GT-1A航空重力仪具有最佳的综合性能技术指标,平差前测量精度为±2.45mGal;美国TAGS航空重力仪为其次,平差前测量精度为±3.9mGal;SII型船载海空重力仪可改造升级为航空重力仪,并具有与TAGS同等的综合性能技术指标;国内自主研发的SGA-WZ01捷联航空重力仪具有最佳的重复线测量精度,测网精度接近于GT-1A航空重力仪水平,平差前测量精度为±2.96mGal,另一款自主研制的GDP-1重力仪首次成功实现了航空重力测量功能,平差前测量精度为±4.52mGal。     

RTM Gravity Forward-Modeling Using Topography/Bathymetry Data to Improve High-Degree Global Geopotential Models in the Coastal Zone

We apply the residual terrain modeling (RTM) technique for gravity forward-modeling to successfully improve high-resolution global gravity fields at short spatial scales in coastal zones. The RTM scheme is combined with the concept of rock-equivalent topography, allowing to use a single uniform constant mass-density in the RTM forward-modeling, both at land and sea. SRTM30_PLUS bathymetry is merged with higher-resolution SRTM V4.1 land topography, and expanded into spherical harmonics to degree 2160, yielding a new and consistent high-degree RTM reference surface. The forward-modeling performance is demonstrated in coastal zones of Greece and Canada using ground-truth vertical deflections, gravity from land and shipborne gravimetry, and geoid heights from GPS/leveling, with improvements originating from bathymetry clearly identified. We demonstrate that the SRTM30_PLUS bathymetry carries information on gravity field structures at spatial scales less than 5 arc minutes, which can be used to augment EGM2008 in (rugged) coastal zones, both over land and marine areas. This may be of value (i) to partially reduce the signal omission error in EGM2008/GOCE-based height transfer in areas devoid of dense gravity data, (ii) to fill the gap between land gravity and shipborne gravity along rugged coastlines, and (iii) for the development of next-generation altimetric gravity fields.     

重力异常延拓计算积分半径的选择及远区效应

基于球谐展开和两分量模型,推导了基于Poisson积分方程的重力异常延拓的远区效应截断误差的函数表达;研究了近区半径、移去重力场阶次、延拓高度与远区效应截断误差之间的相互关系.数值分析表明,当延拓高度为1 000m时,移去360阶的重力场模型,积分半径大于0.5°能保证远区效应截断误差可以忽略;当移去2160阶的重力场...     

Airborne Gravimetry Survey for the Marine Area of the United Arab Emirates

The Military Survey Department (MSD) of the United Arab Emirates (UAE) undertook an airborne gravity survey project for the marine area of the country in 2009, especially to strengthen the marine and coastal geoid in the near-shore regions. For the airborne gravity survey, 5 km spacing coast-parallel flight lines were planned and surveyed. These lines were supplemented by cross-lines in order to assess the quality of the airborne gravity surveys. The flight lines were extended 10 km, spacing lines further offshore. A Beech King Air 350 aircraft was used for the surveys, collecting data at a typical flight speed of 170 knots and a typical flight elevation of 900–1500 m, depending on weather conditions and topography. Gravity was measured with a ZLS-modified LaCoste and Romberg gravimeter (S-99), augmented with a Honeywell strap-down inertial navigation system unit. The estimated accuracy for the airborne gravity data is better than 2.0 mGal r.m.s., as judged from the airborne track crossovers. The new airborne gravimetry data changed the UAE coastal geoid by up to 30 cm in some regions, highlighting the importance of airborne gravity coastal surveys.     

Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.