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A Method to Integrate Geological Knowledge in variogram Modeling of Facies: A Case Study of a Fluvial Deltaic Reservoir

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International Journal of Geosciences 2018年第6期9卷 337-353页

作者： Margaret Akoth Oloo Congjiao Xie Faculty of Earth Resources Key Laboratory of Tectonics and Petroleum Resources China University of Geosciences Wuhan China

variograms are important tools in the spatial distribution of facies and petrophysical properties. Due to the scarcity of subsurface well data, both spatially and quantity wise, variograms representing the data tend to have a lot of uncertainties. In order to reduce uncertainty in variograms, well data can be supplemented with the geological knowledge of the reservoir. This has been demonstrated by various authors in previous works. In their paper “Methodology to Incorporate Geological Knowledge in variogram Modeling,” A. Bahar and M. Kelkar introduced a methodology to incorporate geological knowledge by studying the energy level of the depositional environment and grain texture. They used these two attributes to determine the relative distance of continuity of the lithofacies and incorporated it in the variogram modeling. In this paper, we introduce another attribute that determines the continuity of lithofacies;the accommodation or deposition space. For illustration purpose, two sets of facies models were constructed: The first using subsurface well data only and the second using well data and geological information of the reservoir. The two sets of models showed significant variation in the property distribution. The first set gave a more random appearance of the facies distribution while the second set gave a more realistic depiction of the depositional environment of the reservoir. We concluded that other than the grain size and the energy level of the depositional environment, another important determinant for continuity in variograms is the knowledge of the depositional space. Incorporating the knowledge of the depositional environment enabled a more accurate estimation of the variogram parameters. This resulted in an improvement in the accuracy of the model.

关键词： Geological Knowledge Depositional Environment Energy Level variogram

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variogram无偏估计类探讨

云南师范大学学报（自然科学版） 2000年第6期20卷 1-5页

作者：陈励云南师范大学数学系云南昆明650092

variogram是空间数据分析中的一个重要参数。本文给出了 variogram的一个无偏估计类。用之和传统估计作比较。

关键词： variogram 无偏估计类方差数理统计

Analysis of variograms with various sample sizes from a multispectral image

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International Journal of Agricultural and Biological Engineering 2009年第4期2卷 62-69页

作者： Huihui Zhang Yubin Lan Ronald E.Lacey Yanbo Huang W.Clint Hoffmann D.Martin G.C.Bora Department of Biological and Agricultural Engineering Texas A&M UniversityCollege StationTexasUSA USDA-ARS 2771 F&B RoadCollege StationTexasUSA USDA-ARS 141 Experiment Station RoadStonevilleMississippiUSA Department of Agriculture and Biosystems Engineering North Dakota State University FargoNorth DakotaUSA

variogram plays a crucial role in remote sensing application and *** is very important to estimate variogram reliably from sufficient *** this study,the analysis of variograms computed on various sample sizes of remotely sensed data was conducted.A 100×100-pixel subset was chosen randomly from an aerial multispectral image which contains three wavebands,Green,Red and near-infrared(NIR).Green,Red,NIR and Normalized Difference Vegetation Index(NDVI)datasets were imported into R software for spatial *** of these four full image datasets and sub-samples with simple random sampling method were *** this case,half size of the subset image data was enough to reliably estimate the variograms for NIR and Red *** map the variation on NDVI within the weed field,ground sampling interval should be smaller than 12 *** information will be particularly important for Kriging and also give a good guide of field sampling on the weed field in the future study.

关键词： variogram multispectral image geostatistics

Research on the reconstruction method of porous media using multiple-point geostatistics

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Science China(Physics,Mechanics & Astronomy) 2010年第9期53卷 122-134页

作者： ZHANG Ting 1,2,3, LI DaoLun 1,2 , LU DeTang 1,2 & YANG JiaQing 1,2 1 Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China 2 Research Center of Oil and Natural Gas, University of Science and Technology of China, Hefei 230027, China 3 The 28th Research Institute, China Electronics Technology Group Corporation, Nanjing, 210007, China Department of Modern Mechanics University of Science and Technology of China Hefei China Research Center of Oil and Natural Gas University of Science and Technology of China Hefei China The 28th Research Institute China Electronics Technology Group Corporation Nanjing China

The pore structural characteristics have been the key to the studies on the mechanisms of fluids flow in porous media. With the development of experimental technology, the modern high-resolution equipments are capable of capturing pore structure images with a resolution of microns. But so far only 3D volume data of millimeter-scale rock samples can be obtained losslessly. It is necessary to explore the way of virtually reconstructing larger volume digital samples of porous media with the representative structural characteristics of the pore space. This paper proposes a reconstruction method of porous media using the structural characteristics captured by the data templates of multiple-point geostatistics. In this method, the probability of each structural characteristic of a pore space is acquired first, and then these characteristics are reproduced according to the probabilities to present the real structural characteristics in the reconstructed images. Our experimental results have shown that: (i) the deviation of LBM computed permeability respectively on the virtually reconstructed sandstone and the original sample is less than 1.2%; (ii) the reconstructed sandstone and the original sample have similar structural characteristics demonstrated by the variogram curves.

关键词： porous media reconstruction multiple-point geostatistics pore space training image variogram data template

ESTIMATION OF WATER TABLE ELEVATION BY UNIVERSAL COKRIGING

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Journal of Hydrodynamics 2005年第2期17卷 154-163页

作者： CHENJia-jun TIANKai-ming GUOQiao-yu StateKeyJointLaboratoryofEnvironmentalSimulationandPollutionControl InstituteofEnvironmentalSciencesBeijingNormalUniversityBeijing100875China ChinaUniversityofGeosciences Beijing100083China StateKeyJointLaboratoryofEnvironmentalSimulationandPollutionControl.InstituteofEnvironmentalSciences BeijingNormalUniversityBeijing100875China

When water resource or quality problems associated with phreatic water in geological settings are studied, information about water table elevations is often crucial. In those cases where the water table is a subdued replica of the ground surface, universal cokriging can be used to estimate water table elevations at un-sampled locations on the basis of water table and ground surface elevation measurements obtained at well locations. In this paper, universal cokriging, with ground surface elevation considered as a co-variate, was used to estimate water table elevations. Universal cokriging equations were derived, an iterative method for obtaining experimental variograms was established, and a case study of an initial groundwater flow simulation in the Xiuwu County, Henan Province, China, was presented. In the case study, the initial groundwater flow regime was represented both by universal cokriging with the ground surface elevation serving as a covariate and by universal kriging without the inclusion of ground surface elevation as a covariate. A comparison of the results from these two approaches shows that groundwater levels of phreatic water at locations without measurements in regions with unconsolidated porous media can be estimated more accurately by universal cokriging.

关键词： water table estimation universal cokriging covariate ground surface elevation variogram

DESIGN OF GROUNDWATER LEVEL MONITORING NETWORK WITH ORDINARY KRIGING

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Journal of Hydrodynamics 2008年第3期20卷 339-346页

作者： YANG Feng-guang CAO Shu-you LIU Xing-nian YANG Ke-jun State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University Chengdu 610065China

The primary network of groundwater level observation wells aims at realizing a regional groundwater management policy. It may give a regional picture of groundwater level with emphasis on the natural situation. Observation data from the primary network can be used to estimate the actual state of groundwater system. Since the cost of the installation and maintenance of a groundwater monitoring network is extremely high, the assessment of effectiveness of the network becomes very necessary. Groundwater level monitoring networks are the examples of discontinuous sampling on variables presenting spatial continuity and highly skewed frequency distributions. Anywhere in the aquifer, ordinary kriging provides estimates of the variable sampled and a standard error of the estimate. In this article, the average Kriging standard deviation was used as a criterion for the determination of network density,and the GIS-based approach was analysized. A case study of groundwater level network simulation in the Chaiwopu Basin, Xinjiang Uygur Autonomous Region, China, was presented. In the case study, the initial phreatic water observation wells were 18, a comparison of the three variogram parameters of the three defferent variogram models shows that the Gaussian model is the best. Finally, a network with 55 wells was constructed.

关键词： ordinary Kriging variogram sill nugget effect range groundwater monitoring network

Spatial heterogeneity of plant species on the windward slope of active sand dunes in a semi-arid region of China

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Journal of Arid Land 2013年第1期5卷 80-88页

作者： DeMing JIANG ChunPing MIAO XueHua LI XiaoLan LI ALAMUSA QuanLai ZHOU Institute of Applied Ecology Chinese Academy of Sciences Shenyang 110016 China Graduate University of Chinese Academy of Sciences Beijing 100049 China Xinjiang Academy of Agricultural and Reclamation Sciences Shihezi 832000 China

Species richness and abundance are two important species diversity variables that have attracted particular attention because of their significance in determining present and future species composition conditions. This paper aims to explain the qualitative and quantitative relationships between species diversity pattern and grain size （i.e. size of the sampling unit）, and species diversity pattern and sampling area, and to analyze species diversity variability on active sand dunes in the Horqin Sandy Land, northeastern Inner Mongolia, China. A 50 mx50 m sampling plot was selected on the windward slope, where the dominant species was annual herb Agriophyllum squarrosum. Species composition and abundance at five grain sizes were recorded, and the species-area curves were produced for thirteen grain sizes. The range of values for species abundance tended to increase with in- creasing grain size in the study area, whereas, generally, species richness did not follow this rule because of poor species richness on the windward slope of active sand dunes. However, the homogeneity of species richness in- creased significantly. With the increase in sampling area, species abundance increased linearly, but richness in- creased logarithmically. Furthermore, variograms showed that species diversity on the windward slope of active sand dunes was weakly anisotropic and the distribution pattern was random, according to the Moran Coefficient. The results also showed that species richness was low, with a random distribution pattern. This conflicts with the results of previous studies that showed spatial aggregation in lower richness in a sampling area within a community and inferred that the physical processes play a more important role in species diversity than distribution pattern on active sand dunes. Further research into different diversity patterns and mechanisms between active sand dunes and interdune lowlands should be conducted to better understand biodiversity conservation in

关键词： abundance richness grain size species-area curve variogram Horqin Sandy Land

3D Property Modeling of Void Ratio by Cokriging

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Journal of China University of Geosciences 2008年第4期19卷 410-415页

作者：姚凌青潘懋成秋明 State Key Laboratory of Geological Processes and Mineral Resources China University of Geosciences Key Laboratory of Orogenic Belts and Crustal Evolution Ministry of Education Peking University Department of Earth and Space Science and Engineering York University

Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also analyzed. To map the spatial distribution of void ratio in the area based on these types of point, observation data interpolation is often needed. Owing to the variance of sampling density along the horizontal and vertical directions, special consideration is required to handle anisotropy of estimator. 3D property modeling aims at predicting the overall distribution of property values from limited samples, and geostatistical method can be employed naturally here because they help to minimize the mean square error of estimation. To construct 3D property model of void ratio, cokriging was used considering its mutual correlation with water content, which is another important soil parameter. Moreover, K-D tree was adopted to organize the samples to accelerate neighbor query in 3D space during the above modeling process. At last, spatial configuration of void ratio distribution in an engineering body was modeled through 3D visualization, which provides important information for civil engineering purpose.

关键词： property modeling cokriging variogram anisotropy K-D tree

Sampling Geostatistical Structures in Extremal Framework

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Open Journal of Statistics 2023年第1期13卷 46-60页

作者： Fabrice Ouoba Hay Yoba Talkibing Diakarya Barro Université de Fada N’Gourma Fada N’Gourma Burkina Faso Université Joseph Ki-Zerbo Ouagadougou Burkina Faso Université Thomas Sankara Ouagadougou Burkina Faso

Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.

关键词： Extremal Index Extremogram variogram Copulas Stationary Process Extreme Values