Triangulated spherical splines for geopotential reconstruction     

M. J. Lai  C. K. Shum  V. Baramidze  P. Wenston 《Journal of Geodesy》2009,83(8):695-708

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n _max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577.  相似文献   

Non-stationary covariance function modelling in 2D least-squares collocation   总被引：3，自引：3，他引：0  

N. Darbeheshti  W. E. Featherstone 《Journal of Geodesy》2009,83(6):495-508

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.  相似文献   

规则格网上双方向性插值DEM精度研究     

陈再辉 《测绘工程》2009,18(4):28-31

简要介绍双方向性插值方法的原理,并以线性插值和三次插值过程中的误差传播为基础,利用误差传播定律,推导出双方向性插值方法生成的DEM曲面平均高程误差值,并对线性插值和三次插值公式本身的精度进行分析。  相似文献   

双线性插值近似网格的栅格数据投影变换   总被引：1，自引：0，他引：1  

刘庆元  孟俊贞 《测绘工程》2009,18(5):15-17,21

在栅格数据投影变换常用算法的基础上,介绍一种新的基于双线性内插近似网格算法的栅格数据投影变换,并详细描述其算法过程,认真分析其特点,并证明该算法在大范围栅格数据投影变换中有显著优点。  相似文献   

凸包插值算法的改进与实现     

宫煦利  梅生强  王泽民  姚宜斌  黄石磊 《测绘信息与工程》2009,34(2):40-42

研究了凸包插值算法在n维欧拉空间构造Delaunay三角网的应用,提出了其三角剖分不惟一的重大缺陷,采用了限制区域生长法解决了这一缺陷。  相似文献   

提高对流层天顶总延迟解算精度的新方法探讨     

岳迎春  潘雄  明祖涛  俞艳 《测绘科学》2009,34(6)

对流层天顶总延迟的解算精度,直接影响长基线解算的精度和大气水汽含量的计算精度。文中提出克利金内插法解算天顶总延迟的新方法,并利用南极长城站和周边IGS跟踪站的GPS数据,通过高精度解算软件GAMIT/GLOBK,解算出长城站上空的对流层天顶总延迟,将其与利用内插方法解算的天顶总延迟进行了对比分析,得出:利用该内插方法获取的南极长城站在夏季的天顶总延迟的均方差可达0.2mm,这对今后GPS高精度定位和GPS气象学应用来说,具有重要意义。  相似文献   

海洋磁力测量中测线方向的选择方法     

边刚  刘雁春  于波  卞光浪  肖付民 《测绘学院学报》2009,(3)

采用测线间磁异常插值精度分析了测线方向对磁测的影响;探讨了测线方向的选择方法,结合我国不同海区磁异常分布特征给出了不同海区测量时测线方向的选择详细方案。结论表明:海洋磁力测量中,测线方向对磁异常插值精度的影响不大,但是为了获得更高的磁异常插值精度,测线方向应尽量沿磁异常梯度方向布设。给出的测线方向的选择方法和我国不同海区测线方向选择详细方案可供作业人员参考。  相似文献   

散乱数据插值的HASM方法   总被引：1，自引：0，他引：1  

宋敦江  岳天祥  龚云  杜正平 《地球信息科学学报》2007,9(3):45-51

本文运用高精度曲面建模(HASM)方法,研究了空间散乱数据插值算法,并以陕西咸阳彬县大佛寺煤矿区的实测数据为案例,使用交叉统计检验方法比较分析HASM方法与地理信息系统(GIS)领域中常用传统插值方法的空间插值结果。结果表明,HASM方法具有较高的精度。本文还分析了传统常用插值方法的一些统计结果,得出一些结论,这些结论对于使用常用传统GIS空间插值方法的研究者有很好的参考作用。  相似文献   

人口统计数据空间化的一种方法   总被引：11，自引：1，他引：10  

廖一兰  王劲峰  孟斌  李新虎 《地理学报》2007,62(10):1110-1119

人口空间分布信息在环境健康风险诊断、自然灾害损失评估和现场抽样调查比较等地理学和相关学科研究中占有重要的地位。目前随着对地观测技术和地理信息科学的飞速发展, 如何精确地进行人口数据空间化成为了研究的难点和热点。针对采用传统方法解决人口空间化问题所遇到的困难和不足, 设计了遗传规划(genetic programming, GP)、遗传算法(genetic algorithms, GA) 和GIS 相结合的方法, 以GIS 确定量化影响因子权重, 以GP 建立模型结构, 以GA 优化模型参数, 成功建立研究区-山西省和顺县的人口数据格网分布表面。实验证明与传统建模方法(如逐步回归分析模型和重力模型)相比, 所提方法建模过程更为智能化与自动化, 模型结构更为灵活多样, 而且数据拟合精度更高。  相似文献   

DEM内插方法与可视性分析结果的相似性研究   总被引：2，自引：0，他引：2  

韩富江  刘学军  潘胜玲 《地理与地理信息科学》2007,23(1):31-35

以实际采样的散点数据为原始数据,利用反距离权、样条函数、克里格、自然邻点内插、TIN内插5种内插方法生成规则格网DEM,并对其可视性分析结果进行对比分析和相关分析,揭示不同内插方法对可视性分析结果的影响规律和可视性分析对内插方法的敏感程度。结果表明,可视性分析对内插方法比较敏感,不同的内插方法会得到不同的可视性分析结果,其中相关程度最强的是样条函数内插和克里格内插、自然邻点内插和TIN内插。  相似文献