Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a membrane to a thin steel plate), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.On leave from the Department of Physical Geography and Cartography, Comenius University, Mlynská dolina, Bratislava, Czechoslovakia.On leave from the Institute of Physics, Dúbravská cesta 9, Bratislava, Czechoslovakia.     

GIS中直线元内插点精度及对误差带的影响

基于误差传播定律，考虑参数r误差影响，推导了线元内插点的精度计算公式，讨论内插点精度对线元误差带的影响，并对影响的结果进行了分析，得到了一些有益的结论。     

地学自由曲面径向基函数网络重建的详细算法

径向基函数(RadialBasisFunction,简称RBF)神经网络是一种理想的地学离散数据网格化工具,能够适应各种不同分布形式和边界条件的数据,收敛速度较快,可以逼近任何复杂曲面。这里详细介绍了RBF神经网络的算法。适当径向基函数的形式和偏差系数是使用RBF神经网络作地学曲面重建的关键。大量的实际数据验证结果表明,当选用Gauss型径向基函数时,一般可获得比较理想的网格化效果,同时具备"曲面平滑"和"拟合度高"的特点。     

基于体素模型的三维显示技术

针对矿产资源勘探数据的特点,研究了适合地质体信息三维可视化的体绘制模型和空间插值算法。基于IDL软件平台,开发了三维数据可视化软件;该软件能够快速、准确地将地质体的物性特征展示出来。最后,以内蒙古某金属矿床钻孔资料为例,对建立的三维可视化方法技术进行了应用检验,取得了较好的应用效果。     

Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based Research in Cancer Control and Epidermiology, from the National Cancer Institute. The author thank the anonymous reviewers and the editor for their helpful comments.     

气象资料三维化技术中的插值问题

通过对不同源气象资料及数字地理信息资料的插值，实现了不同气象资料与地理信息资料分辨率的协调；从而将多种信息叠加到一起，实现了多源资料的二维、三维仿真显示。这对于模拟真实的大气空间结构、理解地形及植被对大气运动的影响、辨识各种天气系统及多种信息的融合等有积极意义。     

时间序列转折突变点检测的线性函数方法

根据转折突变的定义，在引入线性半截多项式的前提下，提出检测时间序列转折突变点的一种新方法。此方法不仅能找出时间序列中存在的多个转折突变点，而且使得检测到的突变点通过统计显著性检验。应用此方法对北半球1851—1990年年平均气温距平及其11年滑动平均序列，1901—1999年昆明5月降水及其11年滑动平均的降水序列分别进行了检测。发现北半球年平均气温距平在1879、1889、1939和1973年附近出现了年际转折突变，在1878、1888和1941年以及1972年出现了年代际尺度的转折突变；昆明5月雨量不存在年际转折突变点，但昆明5月雨量在1918、1966以及1978年附近出现了年代际尺度转折突变。     

Palaeolimnology of Lake Piene-Kuuppalanlampi (Kurkijoki, Karelian Republic, Russia): isolation history, lake ecosystem development and long-term agricultural impact

The post-glacial history of Lake Pieni-Kuuppalanlampi, western Lake Ladoga region, was studied by means of stratigraphic pollen and diatom analyses. Diatoms were analysed to track the isolation history of the basin and the limnological effects of the early land-use phases indicated by pollen analysis. Chrysophycean stomatocysts and Isoëtes spores were also employed in the limnological reconstructions. Sediment dating was provided by six conventional radiocarbon dates.The lower part of the 370-cm long sediment sequence represents early Holocene, large lake conditions: the (freshwater) Yoldia and Ancylus stages of the Baltic basin, with a short-term lagoonal or isolation phase at the end of Yoldia. The basin was isolated due to Ancylus lake regression at 9785 cal B.P. For the small-lake sequence (0–250 cm) we used diatom inferences (WA-method) for hindcasting water chemistry. The post-isolation limnology of Pieni-Kuuppalanlampi reflects the development of vegetation on its small hill-top catchment. In its early development, the lake was mesotrophic, but became more acidic (pH about 6) and oligotrophic after the decline of temperate hardwood trees and the spread of spruce to the area after around 5000 B.P. The lake ecosystem appears to have reacted sensitively to agricultural land-use in the catchment from AD 400–800 onwards: inferred total phosphorus levels and pH both rise during these periods.     

地图投影的最小二乘二元多项式拟合的误差估计

探讨了在地图投影的最小二乘二元多项式拟合中参考点的分布对拟合误差的影响,提出了一种基于矩阵的秩亏的方法来判断参考点是否在指定次数的二元多项式空间的代数曲线上,并导出在极小范数最小二乘意义下的拟合多项式的误差估计式,公式表明拟合误差和参考点的最小二乘误差无关。     

3-D structural reconstruction of Moho in the Tangshan earthquake area by using inversion of curved interface

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