A variance of geostatisticians

Different individuals will take different approaches to the analysis and interpretation of data. This study attempted to quantify the effect of such individual differences on the quality of geostatistical spatial estimates. Identical spatial data sets were sent to 12 investigators, who independently analyzed the data and produced spatial interpolations. The results varied considerably. Differences in the interpolations could be attributed to differences in choice of methodology, differences in data interpretation, and, in a few cases, errors in procedure. The potential differences in economic and societal costs between decisions based on good vs. bad interpolations warrant a systematic approach to the identification and testing of interpolation methods.Although the research described in this article has been supported by the U.S. Environmental Protection Agency, it has not been subjected to Agency review and no official endorsement should be inferred.     

General polygonal variogram functions: Evaluation of estimation variance integrals

The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a general polygonal function the requisite integrals may be easily computed by a closed form representation of simple integrals. This paper provides the integration formulas for two-dimensional variogram functions whose domain is represented as a finite collection of rectangles. The integration formulas essential for a fully developed polygonal approach to an extensive statistical evaluation of geostatistical quantities are presented.     

Definition of kriging in terms of fuzzy logic

In this paper, we have basically attempted to solve two problems: (i) the restricted kriging problem as stated by Matheron, and (ii) the defining of Matheron's kriging problem within the framework of fuzzy logic in order to interpret the Lagrange multiplier, which is a function of kriging variance and is a dual variable with respect to which the generalized Lagrange function F(X, ) is minimized.on leave from Department of Geology, Indian Institute of Technology, Kharagphur 721302, West Bengal, India.     

Small-scale distribution characteristics of Munida spp. populations (Decapoda: Anomura) off the Catalan coasts (western Mediterranean)

The small-scale distribution characteristics of three species of the anomuran genus Munida, namely Munida rutllanti, Munida intermedia and Munida tenuimana, have been studied on the lower shelf and upper-middle continental slope near the coasts of Tarragona and the Ebro delta region in the western Mediterranean. The differential bathymetric distribution showed that a fair degree of overlap exists between M. rutllanti and M. intermedia, with the former being mainly found at shallower depths. The size population structure of the three species showed that polymodality, as indicative of a longer life-span and of a higher degree of population structuring was more evident in the deeper-living species, whereas unimodality, as an indication of a recruitment dependent population, was more evident in the shallowest-occurring species. Geostatistics have been applied to determine the degree of spatial variability occurring in M. intermedia abundance, the better-sampled species. The Mantel test has been used to assess the significance of the overlap between the three species distributions as well as the relation between certain population parameters. A discussion on the population characteristics of M. rutllanti is made in relation with its expansion along the western Mediterranean in the last decades.     

采煤沉陷湖人工湿地对周边土地价格的溢出效应研究——以徐州市九里湖湿地为例

采煤沉陷湖由采煤地表沉陷经常年积水而形成,把采煤沉陷湖改造为人工湿地是近年来中国尝试的一种生态修复途径。由于采煤沉陷湖人工湿地对区域微观环境改良作用明显,从而对周边土地价格产生溢出效应。以平原高潜水位地区采煤沉陷湖人工湿地——九里湖湿地为研究案例,以商业和住宅用地为研究对象,分别采集九里湖湿地生态修复前后相同评估基准日的区域地价样点数据,通过Kriging空间插值生成价格曲面,以地统计和GIS栅格计算的方法测度了九里湖湿地对周边土地价格的溢出效应。研究表明,越接近九里湖湿地,土地价格涨幅越高,且明显高于九里湖湿地所在区域土地价格的平均涨幅,显示出九里湖湿地对周边土地价格产生了明显的溢出效应。经进一步测算得出,九里湖湿地对周边商业、住宅用地价格的溢出效应影响范围分别为21.07 km²和20.76 km²,影响强度分别为135.76元/m²、182.39元/m²。把溢出效应影响范围和城市规划用地进行套合,通过栅格计算得出,研究期间九里湖湿地对周边商业、住宅用地价格的溢出效应价值分别为20 225.64万元、20 507.09万元,其溢出效应的价值总量（ΔSE）为40 732.73万元。     

Sequential indicator conditional simulation and indicator kriging applied to discrimination of dolomitization in GER 63-channel imaging spectrometer data

Laboratory reflectance spectra of synthetic mixtures of the carbonate minerals calcite and dolomite were measured in the visible and near-infrared wavelength region (0.4–2.5 m) using a high-spectral resolution laboratory spectrometer. The instrument measured reflectivity with an accuracy of 0.001 m, allowing detailed resolution of the carbonate spectrum. The spectra of calcite and dolomite could be characterized by the presence of a strong absorption band centered at 2.3465 m for pure calcite and at 2.3039 m for pure dolomite. Nine mixtures of intermediate composition were analyzed demonstrating that the position of the carbonate absorption band is semilinearly related to the calcite content of the sample. Theoretically, this model allows mapping of dolomitization from high-spectral resolution remotely sensed imagery, GER 63-channel imaging spectrometer data from southern Spain were used to attempt such a mapping. First, pixels of vegetation were removed. For the remaining pixels, the wavelength center of the carbonate absorption band was detected and converted to a category of calcite fraction. The percentage of calcite for the remaining pixels was estimated using direct indicator kriging (IK) and sequential conditional indicator simulation, assuming that the calcite content could be represented as a category variable (SCIS category variable) and as a continuous variable (SCIS continuous variable). Four realizations of an SCIS (category variable) showed that on the average, 60 percent of the data was simulated in the same class and over 90 percent of the data within one class difference. A comparison with field samples showed that IK estimates of calcite content were within 20 percent accurate. The SCIS (continuous variable) does not perform as well with differences between –45% and +26% calcite; however, simulation reproduces the spatial variability better.     

Estimating hydraulic conductivity from specific capacity for Hawaii aquifers,USA

Site-specific relationships between specific capacity and hydraulic parameters (transmissivity and hydraulic conductivity) were investigated for volcanic rocks in Maui, Hawaii, USA. Details about well construction were commonly ignored in previous studies. To improve on such efforts, specific-capacity values were normalized by the open interval of the well. Correcting specific capacity for turbulent head losses using step-drawdown tests and including aquifer penetration length improved the correlation between specific capacity and hydraulic conductivity and reduced uncertainty in the prediction of hydraulic parameters. The relationships provide estimates of aquifer parameters with correlation coefficients between 0.81 and 0.99. The relationships for Maui can probably be extended to other Hawaii islands, given the similarity of aquifer formations and a reasonable fit to step-drawdown data from Oahu. Hydraulic conductivity was estimated from 1,257 specific-capacity values in the Hawaii’s well database. Hydraulic-conductivity estimates for dike-free volcanic rocks are consistent on different islands. For all islands, the estimates range from 3 to 8,200 m/d, with a geometric-mean and median value of 272 and 291 m/d, respectively. A geostatistical approach was applied to Maui and Oahu to generate island-wide hydraulic-conductivity maps to facilitate groundwater management efforts.     

Fast FILTERSIM Simulation with Score-based Distance

FILTERSIM is a pattern-based multiple-point geostatistical algorithm for modeling both continuous and categorical variables. It first groups all the patterns from a training image into a set of pattern classes using their filter scores. At each simulation location, FILTERSIM identifies the training pattern class closest to the local conditioning data event, then samples a training pattern from that prototype class and pastes it onto the simulation grid. In the original FILTERSIM algorithm, the selection of the closest pattern class is based on the pixel-wise distance between the prototype of each training pattern class and the local conditioning data event. Hence, FILTERSIM is computationally intensive for 3D simulations, especially with a large and pattern-rich training image. In this paper, a novel approach is proposed to accelerate the simulation process by replacing that pixel-wise distance calculation with a filter score comparison, which is the difference between the filter score of local conditioning data event and that of each pattern prototype. This score-based distance calculation significantly reduces the CPU consumption due to the tremendous data dimension reduction. The results show that this new score based-distance calculation can speed up FILTERSIM simulation by a factor up to 10 in 3D applications.     

A Distance-based Prior Model Parameterization for Constraining Solutions of Spatial Inverse Problems

Spatial inverse problems in the Earth Sciences are often ill-posed, requiring the specification of a prior model to constrain the nature of the inverse solutions. Otherwise, inverted model realizations lack geological realism. In spatial modeling, such prior model determines the spatial variability of the inverse solution, for example as constrained by a variogram, a Boolean model, or a training image-based model. In many cases, particularly in subsurface modeling, one lacks the amount of data to fully determine the nature of the spatial variability. For example, many different training images could be proposed for a given study area. Such alternative training images or scenarios relate to the different possible geological concepts each exhibiting a distinctive geological architecture. Many inverse methods rely on priors that represent a single subjectively chosen geological concept (a single variogram within a multi-Gaussian model or a single training image). This paper proposes a novel and practical parameterization of the prior model allowing several discrete choices of geological architectures within the prior. This method does not attempt to parameterize the possibly complex architectures by a set of model parameters. Instead, a large set of prior model realizations is provided in advance, by means of Monte Carlo simulation, where the training image is randomized. The parameterization is achieved by defining a metric space which accommodates this large set of model realizations. This metric space is equipped with a “similarity distance” function or a distance function that measures the similarity of geometry between any two model realizations relevant to the problem at hand. Through examples, inverse solutions can be efficiently found in this metric space using a simple stochastic search method.