共查询到20条相似文献，搜索用时 15 毫秒
1.
R. D. JACOBI 《《地质学报》英文版》2002,76(1):89-99
Semivariogram is applied to fracture data obtained from detailed scanline surveys of nine field sites in western New York, USA in order to investigate the spatial patterns of natural fractures. The length of the scanline is up to 36 m. How both fracture spacing and fracture length vary with distance is determined through semivariogram calculations. In this study, the authors developed a FORTRAN program to resample the fracture data from the scanline survey. By calculating experimental semivariogram, the authors found five different types of spatial patterns that can be described by linear, spherical, reversed spherical, polynomial I (for a<0) and polynomial II (for a>0) models, of which the last three are newly proposed in this study. The well-structured semivariograms of fracture spacing and length indicate that both the location of the fractures and the length distribution within their structure domains are not random. The results of this study also suggest that semivariograms can provide useful infor 相似文献
2.
A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a dataset of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners. We recommend a suitable contour plot to detect departures from isotropy. We then present a fully Bayesian analysis of the 1993 scallop data, demonstrating the range of inferential possibilities. 相似文献
3.
Multifractal modeling and spatial statistics 总被引：9，自引：0，他引：9
In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis. 相似文献
4.
Monte Carlo simulation was used to examine the error (statistical bias) introduced in estimating a sample semivariogram through application of oriented sampling patterns to variables which are correlated with fracture orientation. Sample semivariograms of the directional components of the water velocity were used to illustrate that oriented sampling schemes can provide biased data sets which result in error in the estimation of the semivariogram, particularly in the estimation of the sill (or variance). Three sampling patterns were used to analyze directional semivariograms of the components of the fluid velocity: sampling along lines parallel to the mean regional hydraulic gradient, sampling among lines perpendicular to the mean regional hydraulic gradient, and sampling along fracture segments. The first two sampling patterns were shown to introduce substantial error in the sills of the velocity variograms. It is argued that this error is due to the combination of unequal sampling of fractures with different orientations (i.e., sampling bias) and the systematic variation in the magnitude of the velocity components with orientation of the fracture. As a consequence, it is suggested that correction factors developed to correct fracture frequency statistics need to be extended to improve estimation of spatial moments of variables which are correlated with fracture orientation. 相似文献
5.
Clastic sediments may have a strong deterministic component to their permeability variation. This structure may be seen in the experimental semivariogram, but published geostatislical studies have not always exploited this feature during data analysis and covariance modeling. In this paper, we describe sedimentary organization, its importance for flow modeling, and how the semivariogram can be used for identification of structure. Clastic sedimentary structure occurs at several scales and is linked to the conditions of deposition. Lamination, bed, and bedset scales show repetitive and trend features that should be sampled carefully to assess the degree of organization and levels of heterogeneity. Interpretation of semivariograms is undertaken best with an appreciation of these geological units und how their features relate to the sampling program. Sampling at inappropriate intervals or with instruments having a large measurement volume, for example, may give misleading semivariograms. Flow simulations for models which include and ignore structure show that the repetitive features in permeability can change anisotropy and recovery performance significantly. If systematic variation is present, careful design of the permeability fields therefore is important particularly to preserve the structure effects. 相似文献
6.
Spatial data analytics provides new opportunities for automated detection of anomalous data for data quality control and subsurface segmentation to reduce uncertainty in spatial models. Solely data-driven anomaly detection methods do not fully integrate spatial concepts such as spatial continuity and data sparsity. Also, data-driven anomaly detection methods are challenged in integrating critical geoscience and engineering expertise knowledge. The proposed spatial anomaly detection method is based on the semivariogram spatial continuity model derived from sparsely sampled well data and geological interpretations. The method calculates the lag joint cumulative probability for each matched pair of spatial data, given their lag vector and the semivariogram under the assumption of bivariate Gaussian distribution. For each combination of paired spatial data, the associated head and tail Gaussian standardized values of a pair of spatial data are mapped to the joint probability density function informed from the lag vector and semivariogram. The paired data are classified as anomalous if the associated head and tail Gaussian standardized values fall within a low probability zone. The anomaly decision threshold can be decided based on a loss function quantifying the cost of overestimation or underestimation. The proposed spatial correlation anomaly detection method is able to integrate domain expertise knowledge through trend and correlogram models with sparse spatial data to identify anomalous samples, region, segmentation boundaries, or facies transition zones. This is a useful automation tool for identifying samples in big spatial data on which to focus professional attention.
相似文献7.
Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90
2
or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs. 相似文献
8.
Spatial analyses of groundwater levels using universal kriging 总被引：6，自引：0，他引：6
For water levels, generally a non-stationary variable, the technique of universal kriging is applied in preference to ordinary
kriging as the interpolation method. Each set of data in every sector can fit different empirical semivariogram models since
they have different spatial structures. These models can be classified as circular, spherical, tetraspherical, pentaspherical,
exponential, gaussian, rational quadratic, hole effect, K-bessel, J-bessel and stable. This study aims to determine which
of these empirical semivariogram models will be best matched with the experimental models obtained from groundwater-table
values collected from Mustafakemalpasa left bank irrigation scheme in 2002. The model having the least error was selected
by comparing the observed water-table values with the values predicted by empirical semivariogram models. It was determined
that the rational quadratic empirical semivariogram model is the best fitted model for the studied irrigation area. 相似文献
9.
George Aim Skianis 《Earth Science Informatics》2012,5(1):13-21
Numerous efforts have been made to study how the spatial distribution of ground surface objects controls the image semivariogram.
The present paper is centered on how the histograms and semivariograms of the individual bands x and y influence the spatial variation of a simple spectral ratio u = arctan(x/y). The image histogram of each separate band is described by a proper distribution. The exponential model is used to describe
the semivariograms of x and y. Taking the first derivatives of the spectral ratio u for x and y and taking into account the mathematical behavior of the histograms of bands x and y, an approximate expression for the semivariogram γ
u
of the spectral ratio is derived. This mathematical expression shows how the spatial variation of the spectral ratio depends
on the standard deviations of the histograms, as well as the ranges of the semivariograms of x and y. Experimentation with multispectral images is then carried out and it shows that theoretical predictions agree, in qualitative
terms, with real data. The results and conclusions of this paper may be useful in assessing the efficiency of various spectral
band ratios and vegetation indices, which are often used in geological and environmental research (mapping of hydrothermal
zones and land cover types). 相似文献
10.
地质统计学是用于模拟土体固有空间变异性的方法之一,以变差函数为工具,采用Kriging插值提供未采样点处土工参数值的最优线性无偏估计。将地质统计学方法应用于宿-新（宿迁至新沂）高速公路某试验段内孔压静力触探（piezocone penetration test,CPTU）锥尖阻力qt空间变异性研究中,采用回归分析移除数据中的趋势项,从而获得具有弱平稳性的残差数据。指数型理论变差函数能够准确描述试验段内土体的连续空间变异性特征。根据估计结果,试验段内锥尖阻力qt残差的变程具有显著各向异性,在水平方向和竖直方向分别为4.05 m和1.2 m。采用普通Kriging插值结合趋势分析,绘制了qt在试验段的空间分布图和平面投影图,用于指导工程实践。结果表明,普通Kriging插值的估计结果能够与试验段内实测资料形成较好的对比,仅仅在部分极值变化和远离采样点的位置处估计值可靠性会降低。 相似文献
11.
A good fining of the structural junction that describes the variability of a spatial phenomenon is an essential stage in the building of an accurate estimator by kriging. The technique of the integral of the semivariogram (ISV) makes it possible to find this structural function while overcoming the problem of grouping together the pairs of experimental points into classes of distances when the data are not sampled on a regular grid. The ISV is particularly useful when the dispersion of the values of the classical Semivariogram (SV) makes it difficult to fit a model. Since the ISV is composed of a large number of values, it is more continuous than a SV and therefore easier to fit analytically. In fact, when the general shape of the SV is known, the ISV method proves its worth in finding the parameters that best fit a given variogram model. The analytical models of ISV which will be used, are the integral expressions of the traditional analytical SV. In this paper and on the basis of hydrogeological examples, we propose a method to adjust all the parameters of each model. The first derivative of a filled ISV, used in the kriging equations, appears to be systematically the best SV for a cross-validation on the data. This is why we think that the ISV technique should be used when the strong spatial variability of a parameter spreads out the values of the experimental SV. 相似文献
12.
Zekai Sen 《Mathematical Geology》1989,21(8):891-903
The cumulative semivariogram approach is proposed for modeling regionalized variables in the geological sciences. This semivariogram is defined as the successive summation of half-squared differences which are ranked according to the ascending order of distances extracted from all possible pairs of sample locations within a region. This procedure is useful especially when sampling points are irregularly distributed within the study area. Cumulative semivariograms possess all of the objective properties of classical semivariograms. Classical semivariogram models are evaluated on the basis of the cumulative semivariogram methodology. Model parameter estimation procedures are simplified with the use of arithmetic, semilogarithmic, or double-logarithmic papers. Plots of cumulative semivariogram values vs. corresponding distances may scatter along a straight line on one of these papers, which facilitates model identification as well as parameter estimation. Straight lines are fitted to the cumulative semivariogram scatter diagram by classical linear regression analysis. Finally, applications of the methodology are presented for some groundwater data recorded in the sedimentary basins of the Kingdom of Saudi Arabia. 相似文献
13.
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
14.
Pierre Goovaerts 《Mathematical Geosciences》2008,40(1):101-128
This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the point-support model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a naïve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports. 相似文献
15.
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
16.
Goovaerts P 《Mathematical Geology》2008,40(1):101-128
This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the pointsupport model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a na?ve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports. 相似文献
17.
Compensating for estimation smoothing in kriging 总被引：2，自引：0，他引：2
Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator—compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-ft2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well—better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. 相似文献
18.
Estimation of semivariogram parameters and evaluation of the effects of data sparsity 总被引：1，自引：0，他引：1
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
19.
《Geomechanics and Geoengineering》2013,8(4):307-316
The purpose of this study is to develop a geostatistical model to evaluate the spatial and depth variability of Standard Penetration Test (SPT) data from Bangalore, India. The database consists of 766 boreholes spread over a 220 km2 area, with several SPT values (N) in each of them. The geostatistical analysis is done for N corrected (N corrected) values. The N corrected value has been corrected for different parameters such as overburden stress, size of the bore hole, type of sampler, hammer energy and length of the connecting rod. The knowledge of the semivariogram of the SPT data is used with kriging theory to estimate the values at points in the subsurface of Bangalore where field measurements are not available. The model is used to compute the variance of estimated data. The model predicts reasonably well the SPT data. The geostatistical model provides valuable results that can be used for seismic hazard analysis, site response and liquefaction studies for the development of microzonation maps. The predicted N values from the developed model can also be used to estimate the subsurface information, allowable bearing pressure of soils and elastic modulus of soils. 相似文献
20.
The postprocessing algorithm introduced by Yao for imposing the spectral amplitudes of a target covariance model is shown to be efficient in correcting the smoothing effect of estimation maps, whether obtained by kriging or any other interpolation technique. As opposed to stochastic simulation, Yao's algorithm yields a unique map starting from an original, typically smooth, estimation map. Most importantly it is shown that reproduction of a covariance/semivariogram model (global accuracy) is necessarily obtained at the cost of local accuracy reduction and increase in conditional bias. When working on one location at a time, kriging remains the most accurate (in the least squared error sense) estimator. However, kriging estimates should only be listed, not mapped, since they do not reflect the correct (target) spatial autocorrelation. This mismatch in spatial autocorrelation can be corrected via stochastic simulation, or can be imposed a posteriori via Yao's algorithm. 相似文献