Triangulated spherical splines for geopotential reconstruction

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.     

凸包插值算法的改进与实现

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。     

FPGA在时间测量中的应用

利用现场可编程门阵列(FPGA)的内部资源，在FPGA中实现了高精度时间间隔测量系统的设计。     

Non-stationary covariance function modelling in 2D least-squares collocation

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.     

海洋磁力测量中测线方向的选择方法

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普通Kriging插值算法研究

地统计学是进行空间变异分析的有力工具.文章说明了地统计学的基本原理及其实现算法,并应用该算法对研究区域的草句白浆土有效磷的空间变异特征进行了分析,通过计算得出的地统计学参数说明了土壤有效磷具有中等空间相关性,并生成了该养分的空间分布图.     

提高对流层天顶总延迟解算精度的新方法探讨

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。     

规则格网上双方向性插值DEM精度研究

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。     

基于GIS的近海剩余环境容量计算模型

探讨一种基于GIS 克里格插值方法的剩余环境容量计算方法, 通过GIS 地统计分析插值模型将水质模拟问题转化为数学统计问题, 充分利用水质水体、沉积物监测数据, 采用克里格插值法对污染物浓度和水深在局部海域内进行插值, 将研究区域离散为一个个的均匀栅格单元, 比较每个单元污染物浓度与水质目标之间的差值, 从而估算得到研究海域的剩余环境容量。通过2009 年8 月锦州湾剩余环境容量的计算实例表明, 基于GIS 的剩余环境容量初步计算方法在资料缺乏地区是十分简便、有效的, 这为海域开发利用区环境管理与规划提供了参考。     

多波束海底地形数据空值区域的插值填补方法分析

由于边界误差剔除、测线布设过于稀疏等因素影响,利用多波束数据生成高分辨率DEM时,常常会存在一些水深空值单元或区域。为了对这些数据空值区域进行可靠填补,在考虑地形特征及空值单元大小的情况下,利用IDW、Spline、Kriging、TIN四种插值方法对某区域多波束海底DEM空值区域进行直接内插填补试验,结果表明插值算法的选取不仅受地形类型限制,而且与空值区域的大小也密切相关。