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

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。     

散乱数据插值的HASM方法

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。     

人口统计数据空间化的一种方法

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。     

AVHRR 1B定位数据经验插值模型的误差分析

确定像元地理坐标是几何纠正及卫星数据应用的基础。经验插值方法常用于计算高分辨率辐射计AVHRR1B定位数据,研究插值模型的定位误差具有重要意义。该文分析了AVHRR像元空间位置和像元大小,利用AVHRR扫描线的圆心角θ表示像元的位置,建立了像元位置θ和像元大小Δθ的表达模型;根据分段线性插值模型,计算插值后的像元位置θafter和像元大小Δθafter,获得分段线性插值模型的像元位置和大小的误差模型。     

When do we need a trend model in kriging?

Under usual estimation practice with local search windows for data and for interpolation situations, universal kriging and ordinary kriging yield the same estimates, using a data set with apparent trend, for both the unknown attribute and its trend component. Modeling the trend matters only in extrapolation situations. Because conditions of the case study presented arise most frequently in practice, the simpler ordinary kriging is the preferred option.     

Fractal reconstruction of sea-floor topography

Sea-floor bathymetric profiles exhibit features at many different scales of length; this suggests that they could be described as fractals. An algorithm interpolating a fractal line between points has been used to reconstruct bathymetric profiles from a few data points. In general, this fractal line has the same Fourier amplitude spectrum as real bathymetry, and, if the parameters of the interpolation are suitably chosen, it has a very similar appearance. The success of this fractal reconstruction algorithm for the sea-floor raises the possibility that it could be used to extrapolate, from data collected at one scale, the properties of the sea-floor at finer scales, and that similar techniques could be used to interpolate a surface between bathymetric profiles. The fractal character is a sign that the processes that shape the sea-floor are scale invariant and suggests that the renormalization group technique could be used to model these processes.     

Uncertainty in Coal Property Valuation in West Virginia: A Case Study

Interpolated grids of coal bed thickness are being considered for use in a proposed method for taxation of coal in the state of West Virginia (United States). To assess the origin and magnitude of possible inaccuracies in calculated coal tonnage, we used conditional simulation to generate equiprobable realizations of net coal thickness for two coals on a 7 min topographic quadrangle, and a third coal in a second quadrangle. Coals differed in average thickness and proportion of original coal that had been removed by erosion; all three coals crop out in the study area. Coal tonnage was calculated for each realization and for each interpolated grid for actual and artificial property parcels, and differences were summarized as graphs of percent difference between tonnage calculated from the grid and average tonnage from simulations. Coal in individual parcels was considered minable for valuation purposes if average thickness in each parcel exceeded 30 inches. Results of this study show that over 75% of the parcels are classified correctly as minable or unminable based on interpolation grids of coal bed thickness. Although between 80 and 90% of the tonnages differ by less than 20% between interpolated values and simulated values, a nonlinear conditional bias might exist in estimation of coal tonnage from interpolated thickness, such that tonnage is underestimated where coal is thin, and overestimated where coal is thick. The largest percent differences occur for parcels that are small in area, although because of the small quantities of coal in question, bias is small on an absolute scale for these parcels. For a given parcel size, maximum apparent overestimation of coal tonnage occurs in parcels with an average coal bed thickness near the minable cutoff of 30 in. Conditional bias in tonnage for parcels having a coal thickness exceeding the cutoff by 10 in. or more is constant for two of the three coals studied, and increases slightly with average thickness for the third coal.     

Archaeomagnetic secular variation in the UK during the past 4000 years and its application to archaeomagnetic dating

This paper examines the limitations and deficiencies of the current British archaeomagnetic calibration curve and applies several mathematical approaches in an attempt to produce an improved secular variation curve for the UK for use in archaeomagnetic dating. The dataset compiled is the most complete available in the UK, incorporating published results, PhD theses and unpublished laboratory reports. It comprises 620 archaeomagnetic (directional) data and 238 direct observations of the geomagnetic field, and includes all relevant information available about the site, the archaeomagnetic direction and the archaeological age. A thorough examination of the data was performed to assess their quality and reliability. Various techniques were employed in order to use the data to construct a secular variation (SV) record: moving window with averaging and median, as well as Bayesian statistical modelling. The SV reference curve obtained for the past 4000 years is very similar to that from France, most differences occurring during the early medieval period (or Dark Ages). Two examples of dating of archaeological structures, medieval and pre-Roman, are presented based on the new SV curve for the UK and the implications for archaeomagnetic dating are discussed.     

地统计学分析技术及其在气象中的适用性

首先论述了地统计学的一些特点，然后从变异函数和Kriging插值两个方面介绍了地统计学的分析技术，最后讨论了地统计学在气象研究中的适用性。