Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1

Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they are layer specific and include uncertainty caused by using variance estimates.     

可持续发展评估指标、方法及应用研究

可持续发展评估指标及方法研究是可持续发展定量评估研究的基础,是实施可持续发展管理的依据,是生态经济学与可持续发展研究的前沿领域和热点问题之一. 在概括介绍可持续发展评估的工具--指标/指数的概念和功能、国际上代表性可持续发展研究机构指标选取的原则的基础上,全面分析归纳了可持续发展指标(体系)的类型及其框架模式. 详细介绍了联合国可持续发展委员会(UNCSD)、经济合作与发展组织(OECD)、世界保护同盟(IUCN)、世界银行等国际上代表性机构的可持续发展系统性指标体系的最新研究进展,并分析了这些系统性指标体系的优缺点. 深入分析了国际上典型的社会发展类、经济发展类、生态环境类可持续发展指标(指数)的研究、开发与实际评估应用的情况. 最后,总结了当前可持续发展指标(体系)研究的特点与趋势.     

Spatial and temporal variability of pore‐water pressures in residual soil slopes in a tropical climate

It is critical to understand and quantify the temporal and spatial variability in hillslope hydrological data in order to advance hillslope hydrological studies, evaluate distributed parameter hydrological models, analyse variability in hydrological response of slopes and design efficient field data sampling networks. The spatial and temporal variability of field‐measured pore‐water pressures in three residual soil slopes in Singapore was investigated using geostatistical methods. Parameters of the semivariograms, namely the range, sill and nugget effect, revealed interesting insights into the spatial structure of the temporal situation of pore‐water pressures in the slopes. While informative, mean estimates have been shown to be inadequate for modelling purposes, indicator semivariograms together with mean prediction by kriging provide a better form of model input. Results also indicate that significant temporal and spatial variability in pore‐water pressures exists in the slope profile and thereby induces variability in hydrological response of the slope. Spatial and temporal variability in pore‐water pressure decreases with increasing soil depth. The variability decreases during wet conditions as the slope approaches near saturation and the variability increases with high matric suction development following rainfall periods. Variability in pore‐water pressures is greatest at shallow depths and near the slope crest and is strongly influenced by the combined action of microclimate, vegetation and soil properties. Copyright © 2002 John Wiley & Sons, Ltd.     

Combining ordination techniques and geostatistics to determine the patterns of diatom distributions at Lake Lama, Central Siberia

The patterns of spatial variation of diatom assemblages from surface sediments in Lake Lama were quantified using a combined approach of ordination and geostatistics. The aims were (i) to estimate the amount of variation between diatom assemblages within the lake, (ii) to model the spatial variability of the diatom assemblages and their diversity, and (iii) to map the diatom distributions in the lake. A correspondence analysis (CA) separated the diatom assemblages into a planktonic and a periphytic group. Rheophilic taxa were found within the periphytic group. Variogram analysis showed that only the sample scores of the first CA axis and the Shannon diversity index were spatially structured. The range of spatial correlation was estimated to be 55 km for both variables. The diversity and, to a lesser extent, the sample scores had considerable small-scale variability of about 20 and 3%, respectively. Estimates of the first component of the CA and the Shannon index were derived using block-kriging. The maps of the estimates provided a basis for partitioning Lake Lama according to the spatial structures into an eastern and a western basin, a north–south connection between the basins, and a north–south directed tip at the far eastern end. It was shown that variation in diatom assemblages is mainly spatially structured at the catchment scale and that there is a considerable amount of variation at smaller scales. According to the modeled spatial distribution, the assemblages are most likely affected by the lake size, morphology, and the water and nutrient input introduced by rivers. This has to be taken into account when paleolimnological interpretations are drawn from records of complex lake systems like Lake Lama.     

锡铁山铅锌矿地质特征、矿床成因及找矿标志

通过找矿工作的实践，认为锡铁山铅锌矿床是由火山喷流沉积—后期热液叠加改造富集的块状硫化物多金属矿床。区域上NW—SE向早古生代形成的裂谷带，三级盆地内沉积的晚奥陶世滩间山群的大理岩与绿片岩系是表区找矿的最佳区段。而绢云绿泥斜长片岩、含碳质绢云绿泥片岩、白色大理岩、条带状大理岩是铅锌矿的最重要的找矿标志。     

深海岩芯高分辨率的古环境记录-以南海北部陆坡17940-2柱状样为例

本文将深海岩芯高分辩率记录的替代性指标分为沉积型和生物型两类。沉积型替代性指标主要包括沉积物的粒度，沉积速率，粘土矿物；生物型替代性指标主要包括有孔虫，氧同位素，古水温，有机碳通量。对比研究发现，17940—2柱状样沉积物的粒度、沉积速率、有孔虫，氧同位素，古水温，有机碳通量等指标记录海洋环境变化信息程度优于其它替代性指标；沉积型替代性指标与生物型替代性指标记录海洋环境变化信息不同步；海洋环境变化的突变与渐变影响替代性指标记录的同步性。     

Disjunctive Kriging with Hard and Imprecise Data

This paper presents a methodology for assessing local probability distributions by disjunctive kriging when the available data set contains some imprecise measurements, like noisy or soft information or interval constraints. The basic idea consists in replacing the set of imprecise data by a set of pseudohard data simulated from their posterior distribution; an iterative algorithm based on the Gibbs sampler is proposed to achieve such a simulation step. The whole procedure is repeated many times and the final result is the average of the disjunctive kriging estimates computed from each simulated data set. Being data-independent, the kriging weights need to be calculated only once, which enables fast computing. The simulation procedure requires encoding each datum as a pre-posterior distribution and assuming a Markov property to allow the updating of pre-posterior distributions into posterior ones. Although it suffers some imperfections, disjunctive kriging turns out to be a much more flexible approach than conditional expectation, because of the vast class of models that allows its computation, namely isofactorial models.     

动态指标层析法介绍

参数值是影响模拟结果正确可信的重要因素。介绍了一、二维模拟中参数值确定的动态指标层析法，以及作为其发展基础的由多种热指标确定古充的反演方法，简述了动态指标和热指标相结合的确定参数值层析方法。     

Dynamic stochastic estimation of physical variables

A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects.