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1.
Mathematical Geosciences - Modeling the semivariogram to characterize spatial continuity requires expert geostatistical knowledge and domain expertise about the spatial phenomenon of interest....  相似文献   

2.
In planning spatial sampling studies for the purpose of estimating the semivariogram, the number of data pairs separated by a given distance is sometimes used as a comparative index of the precision which can be expected from a given sampling design. Because spatial data are correlated, this index can be unreliable. An alternative index which partially corrects for this correlation, themaximum equivalent uncorrelated pairs, is proposed for comparing spatial designs. The index is developed under the assumption that the underlying stochastic process is Gaussian and is appropriate when the (population) semivariogram is to be estimated by the sample semivariogram.  相似文献   

3.
To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. Spatial decorrelation methods are usually based on the diagonalisation of the variance/covariance and semivariogram matrices of the set of attributes for a chosen family of lag spacings. These matrices are symmetric and there are several efficient methods for the approximate joint diagonalisation of a family of symmetric matrices. One of these is the uniformly weighted exhaustive diagonalisation with Gauss iterations (U-WEDGE) method. In contrast to the method of minimum/maximum autocorrelation factors (MAF), where a two structure linear model of coregionalisation is assumed, U-WEDGE can be applied directly to the set of experimental semivariogram matrices without having to place restrictions on the number of structures in the linear model of coregionalisation, thus removing one of the restrictions placed on the subsequent modelling of the spatial structure of the factors. We use an iron-ore data set to illustrate the method and present a comparison between the simulated attributes obtained from U-WEDGE and MAF with the full co-simulation of the attributes.  相似文献   

4.
A common assumption in geostatistics is that the underlying joint distribution of possible values of a geological attribute at different locations is stationary within a homogeneous domain. This joint distribution is commonly modeled as multi-Gaussian, with correlations defined by a stationary covariance function. This results in attribute maps that fail to reproduce local changes in the mean, in the variance and, particularly, in the spatial continuity. The proposed alternative is to build local distributions, variograms, and correlograms. These are inferred by weighting the samples depending on their distance to selected locations. The local distributions are locally transformed into Gaussian distributions embedding information on the local histogram. The distance weighted experimental variograms and correlograms are able to adapt to local changes in the direction and range of spatial continuity. The automatically fitted local variogram models and the local Gaussian transformation parameters are used in spatial estimation algorithms assuming local stationarity. The resulting maps are rich in nonstationary spatial features. The proposed process implies a higher computational effort than traditional stationary techniques, but if data availability allows for a reliable inference of the local distributions and statistics, a higher accuracy of estimates can be achieved.  相似文献   

5.
A class of multivariate nonparametric tests for spatial dependence, Multivariate Sequential Permutation Analyses (MSPA), is developed and applied to the analysis of spatial data. These tests allow the significance level (P value) of the spatial correlation to be computed for each lag class. MSPA is shown to be related to the variogram and other measures of spatial correlation. The interrelationships of these measures of spatial dependence are discussed and the measures are applied to synthetic and real data. The resulting plot of significance level vs. lag spacing, or P-gram, provides insight into the modeling of the semivariogram and the semimADogram. Although the test clearly rejects some models of correlation, the chief value of the test is to quantify the strength of spatial correlation, and to provide evidence that spatial correlation exists  相似文献   

6.
Geochemical maps are of great value in mineral exploration. Integrated geochemical anomaly maps provide comprehensive information about mapping assemblages of element concentrations to possible types of mineralization/ore, but vary depending on expert’s knowledge and experience. This paper aims to test the capability of deep neural networks to delineate integrated anomaly based on a case study of the Zhaojikou Pb-Zn deposit, Southeast China. Three hundred fifty two samples were collected, and ea...  相似文献   

7.
在Sklearn的Python语言代码基础上,开发了基于孤独森林和一类支持向量机的多元地球化学异常识别方法程序。选择吉林省和龙地区为实验区,从1∶5万水系沉积物资料中提取地球化学异常。把实验区已知矿点的空间分布位置作为"地真"数据,绘制两种机器学习算法的ROC曲线并计算AUC值,用来对比两种方法的多元地球化学异常识别效果。研究结果表明:两种机器学习算法都能够有效识别多元地球化学异常,所提取的多元地球化学异常与已知矿点具有显著的空间关联性;孤独森林算法在数据处理耗时和多元地球化学异常识别效果方面略优于一类支持向量机。  相似文献   

8.
There is a confusing situation in geostatistical literature: Some authors write variogram, and some authors write semivariogram. Based on a formula for the empirical variance that relates to pairwise differences, it is shown that the values depicted in a variogram are entire variances of observations at a given spatial separation (lag). Therefore, they should not be called semivariances, and the term semivariogram should also be avoided. To name a variogram value, we suggest the use of the term gammavariance instead of the misleading semivariance.  相似文献   

9.
Transition probability-based indicator geostatistics   总被引：30，自引：0，他引：30  
Traditionally, spatial continuity models for indicator variables are developed by empirical curvefitting to the sample indicator (cross-) variogram. However, geologic data may be too sparse to permit a purely empirical approach, particularly in application to the subsurface. Techniques for model synthesis that integrate hard data and conceptual models therefore are needed. Interpretability is crucial. Compared with the indicator (cross-) variogram or indicator (cross-) covariance, the transition probability is more interpretable. Information on proportion, mean length, and juxtapositioning directly relates to the transition probability: asymmetry can be considered. Furthermore, the transition probability elucidates order relation conditions and readily formulates the indicator (co)kriging equations.  相似文献   

10.
Semivariogram parameters are estimated by a weighted least-squares method and a jackknife kriging method. The weighted least-squares method is investigated by differing the lag increment and maximum lag used in the fit. The jackknife kriging method minimizes the variance of the jackknifing error as a function of semivariogram parameters. The effects of data sparsity and the presence of a trend are investigated by using 400-, 200-, and 100-point synthetic data sets. When the two methods yield significantly different results, more data may be needed to determine reliably the semivariogram parameters, or a trend may be present in the data.  相似文献   

11.
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap.  相似文献   

12.
Surface soil water content (SWC) is one of the key factors controlling wind erosion in Sistan plain, southeast of Iran. Knowledge of the spatial variability of surface SWC is then important to identify high-risk areas over the region. Sequential Gaussian simulation (SGSIM) is used to produce a series of equiprobable models of SWC spatial distribution across the study area. The simulated realizations are used to model the uncertainty attached to the surface SWC estimates through producing a probability map of not exceeding a specified critical threshold when soil becomes vulnerable to wind erosion. The results show that SGSIM is a suitable approach for modelling SWC uncertainty, generating realistic representations of the spatial distribution of SWC that honour the sample data and reproduce the sample semivariogram model. The uncertainty model obtained using SGSIM is compared with the model achieved through sequential indicator simulation (SISIM). According to accuracy plots, goodness statistics and probability interval width plots, SGSIM performs better for modelling local uncertainty than SISIM. Sequential simulation provided a probabilistic approach to assess the risk that SWC does not exceed a critical threshold that might cause soil vulnerability to wind erosion. The resulted risk map can be used in decision-making to delineate “vulnerable” areas where a treatment is needed.  相似文献   

13.
The likelihood of Gaussian realizations, as generated by the Cholesky simulation method, is analyzed in terms of Mahalanobis distances and fluctuations in the variogram reproduction. For random sampling, the probability to observe a Gaussian realization vector can be expressed as a function of its Mahalanobis distance, and the maximum likelihood depends only on the vector size. The Mahalanobis distances are themselves distributed as a Chi-square distribution and they can be used to describe the likelihood of Gaussian realizations. Their expected value and variance are only determined by the size of the vector of independent random normal scores used to generate the realizations. When the vector size is small, the distribution of Mahalanobis distances is highly skewed and most realizations are close to the vector mean in agreement with the multi-Gaussian density model. As the vector size increases, the realizations sample a region increasingly far out on the tail of the multi-Gaussian distribution, due to the large increase in the size of the uncertainty space largely compensating for the low probability density. For a large vector size, realizations close to the vector mean are not observed anymore. Instead, Gaussian vectors with Mahalanobis distance in the neighborhood of the expected Mahalanobis distance have the maximum probability to be observed. The distribution of Mahalanobis distances becomes Gaussian shaped and the bulk of realizations appear more equiprobable. However, the ratio of their probabilities indicates that they still remain far from being equiprobable. On the other hand, it is observed that equiprobable realizations still display important fluctuations in their variogram reproduction. The variance level that is expected in the variogram reproduction, as well as the variance of the variogram fluctuations, is dependent on the Mahalanobis distance. Realizations with smaller Mahalanobis distances are, on average, smoother than realizations with larger Mahalanobis distances. Poor ergodic conditions tend to generate higher proportions of flatter variograms relative to the variogram model. Only equiprobable realizations with a Mahalanobis distance equal to the expected Mahalanobis distance have an expected variogram matching the variogram model. For large vector sizes, Cholesky simulated Gaussian vectors cannot be used to explore uncertainty in the neighborhood of the vector mean. Instead uncertainty is explored around the n-dimensional elliptical envelop corresponding to the expected Mahalanobis distance.  相似文献   

14.
数据驱动的证据权法被用来进行金矿潜力制作。为了确定秦岭~松潘金矿的潜力区,需利用地质、地球化学、地球物理等数据。数据采集、图形处理、空间分析都是在GIS平台上进行的。预测结果表明,证据权法在综合不同空间数据上是有效的,最终的预测图件圈出了最有利的矿化区,可用于进一步勘查研究。  相似文献   

15.
Separation of geochemical anomalies from background are one of the important steps in mineral exploration. The Khooni mineral district (Central Iran) has complex geochemical surface expression due to a complex geological background. This region was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods, spatial statistical methods and fractal and multi-fractal methods. In this article, two efficient methods, i.e. U-statistics and the fractal concentration-area for separation and detection of anomalous areas of the background were used. The U spatial statistic method is a weighted mean, which considers sampling point positions and their spatial relation in the estimation of anomaly location. Also, fractal and multi-fractal models have also been applied to separate anomalies from background values. In this paper, the concentration–area model (C–A) was suggested to separate the anomaly of background. For this purpose, about 256 stream sediment samples were collected and analyzed. Then anomaly maps of elements were generated based on U spatial statistics and the C-A fractal methods for Au, As and Sb elements. According to obtained results, the U-statistics method performed better than C-A method. Because the comparisons of the known deposits and occurrences against the anomalous area created using thresholds from U-statistics and C-A method show that the spatial U-statistics method hits all of 3 known deposits and occurrences, the C-A fractal method hits 1 and fails 2. In addition, the results showed that these methods with regard to spatial distribution and variability within neighboring samples, in addition to concentration value frequency distributions and correlation coefficients, have more accurate results than the traditional approaches.  相似文献   

16.
Soil erosion is one of most widespread process of degradation. The erodibility of a soil is a measure of its susceptibility to erosion and depends on many soil properties. Soil erodibility factor varies greatly over space and is commonly estimated using the revised universal soil loss equation. Neglecting information about estimation uncertainty may lead to improper decision-making. One geostatistical approach to spatial analysis is sequential Gaussian simulation, which draws alternative, equally probable, joint realizations of a regionalised variable. Differences between the realizations provide a measure of spatial uncertainty and allow us to carry out an error analysis. The objective of this paper was to assess the model output error of soil erodibility resulting from the uncertainties in the input attributes (texture and organic matter). The study area covers about 30 km2 (Calabria, southern Italy). Topsoil samples were collected at 175 locations within the study area in 2006 and the main chemical and physical soil properties were determined. As soil textural size fractions are compositional data, the additive-logratio (alr) transformation was used to remove the non-negativity and constant-sum constraints on compositional variables. A Monte Carlo analysis was performed, which consisted of drawing a large number (500) of identically distributed input attributes from the multivariable joint probability distribution function. We incorporated spatial cross-correlation information through joint sequential Gaussian simulation, because model inputs were spatially correlated. The erodibility model was then estimated for each set of the 500 joint realisations of the input variables and the ensemble of the model outputs was used to infer the erodibility probability distribution function. This approach has also allowed for delineating the areas characterised by greater uncertainty and then to suggest efficient supplementary sampling strategies for further improving the precision of K value predictions.  相似文献   

17.
Stability is a key issue in any mining or tunnelling activity. Joint frequency constitutes an important input into stability analyses. Three techniques are used herein to quantify the local and spatial joint frequency uncertainty, or possible joint frequencies given joint frequency data, at unsampled locations. Rock quality designation is estimated from the predicted joint frequencies. The first method is based on kriging with subsequent Poisson sampling. The second method transforms the data to near-Gaussian variables and uses the turning band method to generate a range of possible joint frequencies. The third method assumes that the data are Poisson distributed and models the log-intensity of these data with a spatially smooth Gaussian prior distribution. Intensities are obtained and Poisson variables are generated to examine the expected joint frequency and associated variability. The joint frequency data is from an iron ore in the northern part of Norway. The methods are tested at unsampled locations and validated at sampled locations. All three methods perform quite well when predicting sampled points. The probability that the joint frequency exceeds 5 joints per metre is also estimated to illustrate a more realistic utilisation. The obtained probability map highlights zones in the ore where stability problems have occurred. It is therefore concluded that the methods work and that more emphasis should have been placed on these kinds of analyses when the mine was planned. By using simulation instead of estimation, it is possible to obtain a clear picture of possible joint frequency values or ranges, i.e. the uncertainty.  相似文献   

18.
刘岳 《地质与勘探》2019,55(6):1416-1425
地球化学异常通常是直接按某个阈值将整个研究区划分为高异常区或低异常区,这可能导致一些重要异常信息的丢失或决策判断失误。从统计学角度分析,推断未采样点处可能取得结果的概率,或者刻画估计值大于或小于某一地球化学异常阈值的概率分布,更符合勘查地球化学找矿活动的实际需要。针对确定性地球化学场建模方法的局限性,本研究通过集成地统计随机模拟和局部奇异性理论实现地球化学异常识别及其不确定性度量。通过奇异性指数-分位数分析,刻画奇异性指数在频率域中的分布模式,实现地球化学异常阈值分割。采用局部不确定性和空间不确定性算法模拟地球化学异常不确定性传播过程,并以新疆西天山地区为研究区,开展铜异常识别及其不确定性评价应用研究。  相似文献   

19.
地球化学负异常及其找矿意义   总被引：7，自引：0，他引：7  
地球化学负异常的存在具有普遍性。完整的地球化学异常场应包括正异常场和负异常场。负异常按其规模和找矿意义可分为区域、矿床和矿体３个不同层次。区域负异常，可以指明区域找矿方向，圈定找矿靶区；矿床负异常指出矿床可能存在的地段；矿体负异常具体圈定矿体存在的空间位置。负异常与正异常的综合研究，有助于深化对矿床成因的认识，扩大找矿信息，提高找矿效果。  相似文献   

20.
Fitting the Linear Model of Coregionalization by Generalized Least Squares   总被引：2，自引：0，他引：2  
In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS1), (ii) calculated using the fourth-order moments with the theoretical sills (GLS2), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS3). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS1 and theoretical GLS2 are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS1 can be recommended for future studies using the LMC.  相似文献   

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