Model-free estimation from spatial samples: A reappraisal of classical sampling theory

A commonly held view among geostatisticians is that classical sampling theory is inapplicable to spatial sampling because spatial data are dependent, whereas classical sampling theory requires them to be independent. By comparing the assumptions and use of classical sampling theory with those of geostatistical theory, we conclude that this view is both false and unfortunate. In particular, estimates of spatial means based on classical sampling designs require fewer assumptions for their validity, and are therefore more robust, than those based on a geostatistical model.     

Bounding the required sample size for geologic site characterization

The proposed objective of limited sample geologic site characterization is to minimize the chance of unknown and unexpected extremes. This problem proves to be extremely difficult when the data are spatially correlated. A generalization of the classical one-sided nonparametric tolerance interval, based upon the statistical concept of associated random variables, establishes a rigorous, almost distribution-free, tool for computing the minimum required sample size for site characterization. An upper bound on the required number of samples follows from a heuristic measure for the quantity of information in a spatially dependent sample; the measure presented is the equivalent number of uncorrelated samples and is calculated using an estimated variogram. An empirical check of the upper and lower bounds, using more than 2 million simulations and seven real data sets produces a heuristic rule for quantifying the required number of samples.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

相关距离分析与勘察钻孔取样间距的合理确定

在场地岩土工程勘察中,为使所取土样之间满足数据独立性的要求,本文提出应使钻孔取样间距等于土的相关距离,这样能真实、准确地反映地基土的特性。根据Vanmarcke提出的随机场模型,结合数理统计和随机过程理论,采用递推平均法计算得到土的相关距离,其计算数据来自现场静力触探试验。     

基于克里金插值估算区域降水量的抽样方法对比分析——以甘肃省为例

降水数据的空间插值精度由降水的空间变异特征、插值方法和降水观测站分布决定的, 其中, 降水观测站及插值方法的选择尤为重要. 利用空间随机抽样、空间分层抽样和空间三明治抽样等空间抽样方案, 以甘肃省境内的气象站点为研究对象进行抽样分析, 在抽样结果的基础上进行区域降水量克里金插值, 并对比了插值结果精确度. 结果表明: 在较为丰富的先验知识的前提下, 空间三明治抽样所得的区域降水量插值结果的误差项ME(1.97)、MSE(0.0066)和RMSSE(1.0184)都是最优的, 空间分层抽样次之, 空间随机抽样最差. 与另外两种抽样方案相比, 空间三明治抽样是一种使区域误差最小, 适用范围更广, 精确度更高的抽样方法.     

An application of the deterministic variogram to design-based variance estimation

When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators.     

Universal cokriging under intrinsic coregionalization

Under the intrinsic coregionalization model if both primary and secondary measurements are available at all sample locations, the conventional geostatistical wisdom is that cokriging provides exactly the same solution as univariate kriging on the primary process alone. However, recent eamples have been given where nonzero secondary cokriging weights have accurred under this spatial dependence structure. This note identifies the conditions under which secondary information is useful under the assumption of intrinsic coregionalization. An illustration is given using a dataset of plutonium and americium concentrations collected from a region of the Nevada Test Site.     

Estimation of non-ergodic variograms and their sampling variance by design-based sampling strategies

Design-based sampling strategies based on classical sampling theory offer unprecedented potentials for estimation of non-ergodic variograms. Unbiased and uncorrelated estimates of the semivariance at the selected lags and of its sampling variance can be simply obtained. These estimates are robust against deviations from an assumed spatial autocorrelation model. The same holds for the variogram model parameters and their sampling (co)variances. Moreover, an objective measure for lack of fit of the fitted model can simply be derived. The estimators for two basic sampling designs, simple random sampling and stratified simple random sampling of pairs of points, are presented. The first has been tested in real world for estimating the non-ergodic variograms of three soil properties. The parameters of variogram models and their sampling (co)variances were estimated with 72 pairs of points distributed over six lags.     

利用采样定理与沉积速率确定旋回分析最佳采样间隔

旋回地层学方法近年来被成功应用于年代确定及重大地质事件天文影响因素的判别.采样是旋回分析中最重要的一步, 目前大多使用地球物理、地球化学替代性指标, 采样频率过高, 会大大增加测量和计算的工作量, 同时也会增加随机干扰或其他非气候因素的干扰; 采样频率过低, 可能识别不出其中所包含的米兰柯维奇旋回成分.为确定一个最佳的采样间隔, 通过对80~100 Ma理论日照量曲线及两个实测剖面3种采样间隔(密集采样间隔与约等于一个岁差周期沉积厚度四分之一和一半的采样间隔)数据分别进行谱估计并比较谱估计结果.发现在满足采样定理的前提下, 以一个岁差周期沉积厚度的约一半作为采样间隔, 既可以分析出全部的米兰柯维奇旋回信号, 又具有最少的工作量, 是旋回分析的最佳采样间隔.实际采样中需根据平均沉积速率来确定这个最佳采样间隔.      

Is a regional flood signal reproducible from lake sediments?

The evolution of flood activity with global warming remains uncertain. To better assess flood–climate relationships, lake sediments are increasingly being investigated because they could provide regional flood histories long enough to cover past climate changes. However, site‐specific sedimentary processes may bias flood reconstructions. The aim of this article is to investigate these effects through the reconstruction of two distinct flood records from independent, neighbouring sedimentary basins of the same lake (Lake Allos in the Mediterranean French Alps), i.e. under the same climate conditions. Understanding of sedimentary processes is crucial in order to adapt the sampling strategy and the flood‐intensity proxy to each sedimentary system and, thereby, reconstruct a complete and reliable flood history. Thanks to this detailed approach, the main trends of the regional flood variability can be reproduced; i.e. periods of high flood‐frequency, ranges of flood‐frequency values and timing of the most intense events. In detail, some differences appeared associated to the various stream capacities to erode and transport flood sediments to the lake system, implying variable sensitivity of sedimentary systems in recording floods. Comparing regional flood records based on independent sedimentary systems from similar environments could thus be a complementary approach to assessing past flood intensity. Such an approach could open particularly interesting perspectives because reconstructing the long‐term evolution of flood intensity is a key challenge in the geosciences.     

牙釉质生长结构及其高分辨率同位素分析

牙釉质同位素分析是重建古食谱、古环境及人类迁移行为的重要手段。以往牙釉质同位素分析在采样方式上多集中于釉质表层的均匀采样,其代表牙釉质生长过程中的平均信号。近年来,随着高分辨率仪器发展,研究者提出了两种新的采样方式,为研究人和动物的季节特性提供了详细信息:1)微钻系列采样法,即以牙齿形成时间为约束,在牙釉质表层等间距采样,以获取牙釉质生长期间的季节性信息。这是目前最常用的方法,但该方法样品损耗大且时间精度低;2)微区采样法,即以牙釉质生长结构的形成时间为时间约束,利用高空间分辨率仪器进行原位分析。该方法不仅样品损耗量小,而且能反映同位素组成在牙齿内部更细微、复杂的变化,但存在测试精密度和准确度低等问题。目前,微区采样法尚处于起步阶段,但在古环境及考古研究中已有重要意义和研究前景。