A flexible lag definition for experimental variogram calculation

Inferring the experimental variogram used in geostatistics commonly relies on the method-of-moments approach.Ideally,the available data-set used for calculating the experimental variogram should be drawn from a regular pattern.However,in practice the available data-set is typically sampled over a sparse pattern at irregularly spaced locations.Hence,some binning of the variogram cloud is required to obtain fair estimates of the experimental variogram.Grouping of the variogram data pairs as a result of conventional binning depends on parameters such as the main anisotropic directions and a regular definition of the lag vectors.These parameters are not based on the configuration of the variogram data pairs in the variogram cloud but on a segment of it that is arbitrarily predefined.Therefore,the conventional experimental variogram estimation approach is biased because of the strict configuration of the bins over the variogram cloud.In this paper,a new method of estimating experimental variograms is proposed.Lag vectors and their tolerances are decided in the proposed method from information in the variogram cloud：they are not influenced by any predefined directions.The proposed methodology is a well-founded,practicable and easy-to-automate approach for experimental variogram calculation using an irregularly sampled data-set.Comparison of results from the new method to those from the traditional approach is very encouraging.

VARIOGRAM无偏估计类探讨

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 。

Characterizing Landscape Spatial Heterogeneity in Multisensor Images with Variogram Models

Most evaluation of the consistency of multisensor images have focused on Normalized Difference Vegetation Index （NDVI） products for natural landscapes, often neglecting less vegetated urban landscapes. This gap has been filled through quantifying and evaluating spatial heterogeneity of urban and natural landscapes from QuickBird, Satellite pour l＇observation de la Terre （SPOT）, Ad- vanced Spacebome Thermal Emission and Reflection Radiometer （ASTER） and Landsat Thematic Mapper （TM） images with variogram analysis. Instead of a logarithmic relationship with pixel size observed in the corresponding aggregated images, the spatial variability decayed and the spatial structures decomposed more slowly and complexly with spatial resolution for real multisensor im- ages. As the spatial resolution increased, the proportion of spatial variability of the smaller spatial structure decreased quickly and only a larger spatial structure was observed at very coarse scales. Compared with visible band, greater spatial variability was observed in near infrared band for both densely and less densely vegetated landscapes. The influence of image size on spatial heterogeneity was highly dependent on whether the empirical sernivariogram reached its sill within the original image size. When the empirical semivariogram did not reach its sill at the original observation scale, spatial variability and mean characteristic length scale would increase with image size; otherwise they might decrease. This study could provide new insights into the knowledge of spatial heterogeneity in real multisen- sor images with consideration of their nominal spatial resolution, image size and spectral bands.

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

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.

ENHANCING GROUND RESOLUTION OF TM6 BASED ON MULTI-VARIATE REGRESSION MODEL AND SEMI-VARIOGRAM FUNCTION

It is well known that Landsat TM images are the most widely used remote sensing data in various fields.Usually,it has 7 different electromagnetic spectrum bands,among which the sixth one has much lower ground resolution compared with the other six bands.Nevertheless,it is useful in the study of rock spectrum reflection,geothermal resources exploration,etc.To improve the ground resolution of TM6 to the level as that of the other six bands is a problem .This paper presents an algorithm based on the combination of multivariate regression model with semivariogram function which can improve the ground resolution of TM6 by "fusing" the data of other six bands.It includes the following main steps: （1） testing the correlation between TM6 and one of TM15,7.If the correlation coefficient between TM6 and another one is greater than a given threshold value,then select the band to the regression analysis as an argument.（2） calculating the size of the template window within which some parameters needed by the regression model will be calculated; （3） replacing the original pixel values of TM6 by those obtained by regression analysis; （4） using image entropy as a measurement to evaluate the quality of the fused image of TM6.The basic mechanism of the algorithm is discussed and the V C ++ program for implementing this algorithm is also presented.A simple application example is given in the last part of this paper,showing the effectiveness of the algorithm.

Variogram Analyses of Soil Characters in Glacial Moraine Landscapes

The objective of this research is to analyze variogram analyses of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1：5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by geostatistics program for spatial soil variability analyses. The variogram models show that spatial soil variability ranges between 70-120 m （mean： 85 m）. Effective distances of sampling are calculated at around 50 m. The range values of soil characters are proportional with the range of elevation （range： 70 m, effective distance： 40 m）. The relief determines mainly the spatial variability of soil characters.

Imaging Analysis of Trabecular Bone Texture Based on the Initial Slope of Variogram of Ultra-Distal Radius Digital X-Ray Imaging: Effects on Bone Mineral Density and Age

Background: When applied to trabecular bone X-ray images, a method for analyzing trabecular bone texture based on the initial slope of variogram (ISV) was used to assess the trabecular bone health. Methodology: Data from more than two hundred subjects were retrospectively studied. For each subject, a DXA (GE Lunar Prodigy) scan of the forearm was performed, and bone mineral density (BMD) value was measured at the location of ultra-distal radius, X-ray digital image of the same forearm was taken on the same day, and ISV value over the same location of ultra-distal radius was calculated. Pearson’s correlation coefficients were calculated to examine the correlation between BMD and ISV of the trabecular bones located at the same ultra-distal radius. ISV values changed with subjects’ age were also reported. Results: The results show that ISV value was highly correlated with the DXA-measured BMD of the same trabecular bone located at the ultra-distal radius. The correlation coefficient between ISV and BMD with the 95% confident was 0.79 ± 0.09. They also demonstrated that the age-related changes in trabecular bone health and differentiated age patterns in males and females, respectively. The results showed that the decrease in BMD was accompanied by a decrease in the initial slope of variogram (ISV). Conclusions: This study suggests that ISV might be used to quantitatively evaluate trabecular health for osteoporosis and bone disease diagnosis.

Applications of variogram modeling to electrical resistivity data for the occurrence and distribution of saline groundwater in Domail Plain,northwestern Himalayan fold and thrust belt,Pakistan

This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical inversion and visualization techniques,it is possible to re-model and visualize the single dimension resistivity data into 2D and 3D space.The variogram models are utilized to extend the interpretation of the data and to distinguish individual lithologic units and the occurrence of saline water within the subsurface. The resistivity data has been calibrated with the lithological logs taken from the available boreholes. As such the alluvial system of the Domail Plain has formed during episodes of local tectonic activity with fluvial erosion and depositionyielding coarse sediments with high electrical resistivities near to the mountain ranges and finer sediments with medium to low electrical resistivities which tend to settle in the basin center. Thus a change is depositional setting happened from basin lacustrine environment to flash flooding during the Himalayan orogeny. The occurrence of rock salt in the northern mountains has imparted a great influence on the groundwater quality of the study area. The salt is dissolved by water which infiltrates into the subsurface through the water channels. Variogram aided gridding of resistivity data helps to identify the occurrence and distribution of saline water in the subsurface.

A Yield Mapping Procedure Based on Robust Fitting Paraboloid Cones on Moving Elliptical Neighborhoods and the Determination of Their Size Using a Robust Variogram

The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.

考虑地震事件内空间相关性的区域概率地震危险性分析

一次地震事件不同地点的地震动强度参数与结构响应参数之间是空间相关的,相关的地震效应将导致地震损失急剧集中与积累,从而造成灾难性事件,但是现有的区域尺度地震风险评估并没有考虑地震动的空间相关性。该文采用地统计学方法表征地震事件内地震动强度参数的空间相关性,提出了理论半变异函数的几何稳健估计方法,并采用加权最小二乘法实现对短距离空间相关性的准确高效评估。以新潟越冲地震为例,基于指数半变异函数模型,采用加权最小二乘法对几何稳健估计半变异函数值进行拟合,得到了PGA、PGV和0 s~10 s谱加速度的空间相关性函数,提出了变程b值的预测模型,结果表明:相比于短周期谱加速度,长周期谱加速度的空间相关性衰减速率更小,且在T=0.45 s处存在拐点。将所开发的空间相关性模型应用于区域概率地震危险性分析,采用Monte Carlo方法实现了空间相关随机场的区域地震动强度参数的模拟,改进了传统区域地震危险性分析的方法,发现绝大多数情况下考虑空间相关性的年超越概率大于未考虑空间相关性的年超越概率,表明考虑空间相关性对于建筑群落及基础设施风险评估、韧性城市建设等具有重要的指导意义。

河流床面粗糙程度的度量方法研究

【目的】河流床面的粗糙程度是河流动力学中重要的研究内容。【方法】用统计分析法来量化河流床面的粗糙程度,在不考虑河床宏观起伏的前提下,用非均匀天然沙人工铺制初始粗糙床面,并逐渐增大流量使床面粗化,粗化完成后依托激光扫描技术获得试验床面的精确数字高程。基于统计理论探究在不同来水条件下,粗化后河流床面表层的结构特性并利用床面高程统计参数及变异函数满足的理论模型建立新的床面粗糙程度度量方法。【结果】结果显示:曼宁糙率n与中值粒径的拟合关系一般,相关系数为0.649。n与标准差、众数及偏度拟合关系良好,与峰度拟合关系相对较差。n与三种变异函数球状模型典型参数都呈现出较好的相关性,剖面平均变异函数块金值与基台值和n的拟合关系优秀,相关系数均在0.89以上。【结论】结果表明:代表粒径法在某些时刻是可以用于表述床面粗糙特性的,高程数据的标准差随水流强度的增加而严格增大的特性和其众数随水流结构的增大而严格减小的特性使它们成为量化床面粗糙程度的优良指标。偏度和峰度的单调趋势使其作为床面粗糙程度的衡量指标也成为可能。块金值与基台值可以作为床面粗糙程度的表征指标。此次研究用统计法探讨了度量河流床面粗糙程度的方法,对粗糙程度的度量有一定启示。

Down-scaling LUCC based on the histo-variogram

In remote sensing applications,accurate extraction of land type area after classification is very impor-tant.But for images of land use/cover change(LUCC) obtained from the special spatial resolution re-mote sensing data,it will be of great significance to obtain the land type area information with higher resolution by making use of spatial distribution characteristcs information of the land type itself first and further scaling-down in a given scale threshold on the basis of the existing spatial resolution data.An explicit expression of the relationship between the measurement scale,global fractal dimension and the land type area corresponding to different measurement scales is obtained on the research basis of the authors' histo-variogram using the standardized area index(SAI).A good attempt has been made to obtain the land type area information with higher resolution by merely using the spatial distribution characteristcs information of the land type in the image itself and further scaling-down in a given scale threshold on the basis of the existing spatial resolution data.

Analysis of variograms with various sample sizes from a multispectral image

Variogram plays a crucial role in remote sensing application and geostatistics.It is very important to estimate variogram reliably from sufficient data.In 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 analysis.Variograms of these four full image datasets and sub-samples with simple random sampling method were investigated.In this case,half size of the subset image data was enough to reliably estimate the variograms for NIR and Red wavebands.To map the variation on NDVI within the weed field,ground sampling interval should be smaller than 12 m.The information will be particularly important for Kriging and also give a good guide of field sampling on the weed field in the future study.

三维地质统计学矿产资源量估算变异函数影响因素与参数敏感性研究

随着数字矿山建设不断深入和三维地质信息化技术不断发展,三维地质统计学方法在矿产资源量估算领域的应用越发广泛。变异函数是三维地质统计学矿产资源量估算方法的核心,其分析过程受诸多因素影响,参数控制复杂且敏感性各异。因此,度量这些因素对实验变异函数的影响并解析理论变异函数各参数的敏感性,对于获取更为合理的理论变异函数参数、提高资源量估算精度具有重要意义。以安徽省安庆—贵池矿集区某大型铁铜矿床为例,基于数学统计方法对影响实验变异函数的诸多因素进行系统分析,并运用Sobol′敏感性分析与控制变量方法深入解析和对比了理论变异函数相关参数的敏感性。研究结果表明:(1)实验变异函数稳健性受数据分布以及滞后距影响最为强烈;(2)理论变异函数模型中块金值是最为关键的参数,对交叉验证结果影响最为显著,变程次之;(3)理论变异函数模型参数值的调整可参考交叉验证结果,但同时还需参考地质勘查手段和矿体特征等要素进行综合评判。研究成果可为三维地质统计学矿产资源量估算过程中变异函数的合理确定提供参考和依据,并为相关方法的实践应用与推广提供帮助。

基于SADIE和SPPA的柳蝙蛾小尺度空间格局分析

【目的】柳蝙蛾是一种多食性的森林害虫,在我国东北地区对水曲柳危害严重。在小尺度上研究柳蝙蛾的空间格局,可为精准管理提供基础信息。【方法】本文将柳蝙蛾蛀孔数及其寄主树木水曲柳胸径作为标记的空间点过程的标记,使用基于距离指数的空间分析(SADIE)来分析标记空间格局和空间关联性。使用L函数来检验水曲柳分布的空间随机性,使用标记条件均值函数来度量标记与点之间的独立性,使用标记变异函数和Stoyan标记相关函数来度量标记的空间相关性。每个样方划分成2种不同密度的小样方来利用SADIE研究水曲柳分布与蛀孔的空间关联性。【结果】两个样地中柳蝙蛾蛀孔均呈显著的聚集分布。样地G1的斑块和间隙分别处于样地的两端,而样地G2的斑块和间隙混杂在一起。样地G1中,在4.0~4.8 m和14.5~16.0 m距离上存在显著的蛀孔数少的树与其他蛀孔少的树互为邻居的格局。样地G2中,在8.5~9.0 m距离上存在上述格局。标记变异函数分析表明,两个样地中的空间自相关性均不显著。水曲柳的空间格局及其胸径的空间格局均与柳蝙蛾蛀孔的空间格局成强烈的关联性,表明这两个因素均影响柳蝙蛾蛀孔空间格局的形成。SADIE分析及L函数分析均表明水曲柳的空间格局为聚集性。标记条件均值函数分析表明,标记(蛀孔数)不依赖于点(水曲柳位置)。【结论】柳蝙蛾蛀孔在水曲柳林中的空间分布呈聚集性。水曲柳的空间格局及其胸径的空间格局均影响柳蝙蛾蛀孔的空间格局。

Abandoned land identification in karst mountain area based on time series SAR characteristics at geo-parcels scale

Mapping abandoned land is very important for accurate agricultural management.However,in karst mountainous areas,continuous high-resolution optical images are difficult to obtain in rainy weather,and the land is fragmented,which poses a great challenge for remote sensing monitoring of agriculture activities.In this study,a new method for identifying abandoned land is proposed:firstly,a few Google Earth images are used to transform arable land into accurate vectorized geo-parcels;secondly,a time-series data set was constructed using Sentinel-1A Alpha parameters for 2020 on each farmland geoparcel;thirdly,the semi-variation function(SVF)was used to analyze the spatial-temporal characteristics,then identify abandoned land.The results show:(1)On the basis of accurate spatial information and boundary of farmland land,the SAR time-series dataset reflects the structure and time-series response.abandoned land with an accuracy of 80.25%.The problem of remote sensing monitoring in rainy regions and complex surface areas is well-resolved.(2)The spatial heterogeneity of abandoned land is more obvious than that of cultivated land within geoparcels.The step size for significant changes in the SVF of abandoned land is shorter than that of cultivated land.(3)The SVF time sequence curve presented a strong peak feature when farmland was abandoned.This reveals that the internal spatial structure of abandoned land is more disordered and complex.It showed that time-series variations of spatial structure within cultivated land have broader applications in remote sensing monitoring of agriculture in complex imaging environments.

Sampling Geostatistical Structures in Extremal Framework

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.

基于地统计学的重庆市桉树云斑天牛幼虫空间分布特征研究

利用重庆市18个区/县98个桉树林样点天牛的危害调查结果,应用地统计学方法进行云斑天牛的空间分布情况研究。结果表明:在局部视野下,3类不同受害程度桉树林云斑天牛种群数量及空间分布特征差异明显;轻度、中度和重度桉树林天牛幼虫种群空间分布最适拟合模型分别为高斯模型、球型模型和球型模型,3类受害林的天牛幼虫种群分布均属于聚集型;天牛幼虫数量在轻度、中度与重度受害林中的空间自相关性存在较大差异,但均具有明显的空间依赖性,空间依赖范围分别为3.18、6.40、31.75 m;空间分布图显示,天牛幼虫的种群空间分布特征为明显的聚集型。在大尺度视野下,这些区/县间的桉树云斑天牛幼虫种群数量差异显著;各调查区/县的天牛危害以中度和重度为主,且具有明显的天牛高风险危害和扩散中心特征。交通道路及林分中树木分布格局是影响丘陵山地桉树云斑天牛种群分布特征的关键因素。

基于GIS的环巢湖地区土壤养分空间变异特征研究

为探究环巢湖地区土壤养分的空间自相关性及其变异规律,在研究区域共采集8073个土壤样品,基于GIS技术并使用地统计方法和Moran′s I指数法对土壤pH、有机质、全氮、碱解氮、有效磷、速效钾和缓效钾进行了系统分析。结果表明:土壤pH、有机质、全氮、碱解氮、有效磷、速效钾和缓效钾的均值分别为6.07、19.97 g·kg^(-1)、1.16 g·kg^(-1)、112.95 mg·kg^(-1)、18.21 mg·kg^(-1)、130.88 mg·kg^(-1)和378.58 mg·kg^(-1),除有效磷为强变异外,其他养分均为中等程度变异;pH、全氮、有效磷、速效钾和缓效钾半变异函数最佳拟合模型为指数模型,有机质和碱解氮为高斯模型;pH和速效钾为中等空间自相关性,其他养分空间自相关性均较弱,表明养分空间变异主要受人为活动等随机性因素影响;各养分均为极显著空间正相关,其空间相关性大小依次为有效磷>速效钾>pH>缓效钾>全氮>有机质>碱解氮,且有效磷的空间自相关性显著大于其他养分。总体上看,环巢湖地区养分分布较为分散,南北方向有逐渐上升或下降的趋势,且养分高低值聚集区域也有明显的南北分布。

基于空间统计的珠三角地区土地利用生态风险时空特征

[目的]揭示珠三角地区土地利用生态风险的空间结构模式和时空变化规律,为促进土地资源可持续利用和保障区域生态安全提供参考依据。[方法]基于景观指数构建土地利用生态风险评价模型,测算2000年、2010年、2020年珠三角地区多种尺度下的土地利用生态风险,利用半变异函数确定最适宜的研究尺度,运用空间自相关和GIS空间分析方法分析了适宜尺度下土地利用生态风险的时空特征。[结果](1)3 km样方尺度是最佳研究尺度,小流域尺度也较合适;两个尺度下土地利用生态风险空间变异均以结构性因素影响为主,即存在较强的空间自相关性。(2)研究区土地利用生态风险总体上具较强的正空间集聚特征,但集聚程度趋于减弱;大多单元局部空间集聚特征相对稳定,以高—高集聚和低—低集聚为主,低—高和高—低集聚区零星分布且变化不大。(3)区域土地利用生态风险总体呈略微下降趋势,以低风险和较低风险等级区为主且面积逐渐增加,中风险等级以上面积减小。[结论]珠三角地区土地利用生态风险整体上呈现正空间集聚特征,且土地利用生态风险水平逐渐降低,研究结果可为区域国土空间优化利用和生态风险管控提供决策参考。