共查询到20条相似文献，搜索用时 359 毫秒
1.
V. Pawlowsky 《Mathematical Geology》1989,21(5):513-521
To avoid spurious spatial correlation when analyzing the spatial covariance structure of regionalized compositions, additive-log-ratio transformation can be used. Here, the additive-log-ratio cokriging estimator, derived in a natural way from this transformation, is shown to be invariant under permutation of components of the untransformed regionalized composition. It leads, as expected, to an exact interpolation. As original data, predicted values of the regionalized composition at unknown points add up to the same constant c and lie between 0 and c. 相似文献
2.
A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable. 相似文献
3.
Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. Here, these problems are illustrated, and a solution, based on the principle of working in coordinates using orthonormal logratio representations, is presented. This approach offers a tool for standard geostatistical studies. One of the advantages the method has is that it allows the usual inconsistencies with indicator kriging to be overcome through simplicial indicator kriging. A general way of modelling crossvariograms of coordinates, based on the matrix valued variation variogram, is discussed. In summary, the main aspects related to the modelling and analysis of regionalized compositions have had satisfactory solutions found for them. The proposed methodology is illustrated with public data from a survey concerning arsenic contamination in underground water in Bangladesh.
相似文献4.
Geochemical characterization of heavy metal contaminated area using multivariate factorial kriging 总被引：1，自引：0，他引：1
Joaquim C. B. Queiroz José R. Sturaro Augusto C. F. Saraiva Paulo M. Barbosa Landim 《Environmental Geology》2008,55(1):95-105
This paper describes a geostatistical method, known as factorial kriging analysis, which is well suited for analyzing multivariate
spatial information. The method involves multivariate variogram modeling, principal component analysis, and cokriging. It
uses several separate correlation structures, each corresponding to a specific spatial scale, and yields a set of regionalized
factors summarizing the main features of the data for each spatial scale. This method is applied to an area of high manganese-ore
mining activity in Amapá State, North Brazil. Two scales of spatial variation (0.33 and 2.0 km) are identified and interpreted.
The results indicate that, for the short-range structure, manganese, arsenic, iron, and cadmium are associated with human
activities due to the mining work, while for the long-range structure, the high aluminum, selenium, copper, and lead concentrations,
seem to be related to the natural environment. At each scale, the correlation structure is analyzed, and regionalized factors
are estimated by cokriging and then mapped. 相似文献
5.
《Applied Geochemistry》2000,15(7):1053-1067
This study examines the spatial variability of the factors obtained from the application of correspondence analysis to a hydrogeochemical data set. The goal was to synthesize the hydrogeochemical information using this multivariate statistical technique, by setting a series of factors which clarified the main properties of one aquifer. Then, a geostatistical framework to obtain a probabilistic assessment of groundwater quality was established. Experimental and theoretical semivariograms of the selected factors, considered as regionalized variables, were computed. These variographic information and factor values in the experimental sites were used in the ordinary kriging, which provides unbiased and linear estimates of the regionalized variables. These estimates were used to compile maps of the chosen factors, which explain their spatial distribution.The selected case study was the alluvial aquifer of Alto Guadalentı́n which is situated in southeast Spain, in the Internal Zones of Betic Cordilleras. These waters are chiefly SO4 and Cl types, but HCO3 facies are common in the central sector of the basin. High temperature, acid pH, problems of overexploitation and pollution by CO2-gas characterise these waters. Available groundwater quality monitoring data were used to calibrate the numerical model. The present study focused on setting the main physical and chemical attributes and establishing the spatial pattern of groundwater quality and the temporal changes in this pattern. 相似文献
6.
Peter K. Kitanidis 《Mathematical Geology》1985,17(2):195-208
The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging. 相似文献
7.
Marzieh Shademan Khakestar Hossein Hassani Parvizz Moarefvand Hassan Madani 《Journal of the Geological Society of India》2016,87(1):97-104
Almost all collapses of rock slopes especially in open pit mines are related to discontinuities such as bedding planes, faults and major joints.Geostatistical assessments can be used for understanding the distribution of regionalized variables in any spatial study. In this paper3D spatial dispersion of the fault planes in the Gole Gohar open pit iron mine, located in Kerman province, south east of Iran, is modeled. Then, regionalized variable theory is used to analyze and interpret spatial distribution of the following geotechnical parameters: Geological strength index (GSI), Rock quality designation (RQD), Cohesion (C) and angle of internal friction (f). In order to define regionalized variable distribution, variogram functions were determined for identifying the regional behavior. Structural analysis of variograms showed that the mentioned parameters have spatial structures that make it possible to set up a geostatistical model to predict their values for each non-sampled block on the pit wall. Results showed that there is a relation between the low values of geotechnical parameters and the existence of discontinuities around the pit area. The role of discontinuities in the occurrence of collapses in the area was clearly demonstrated by comparing the estimated parameters models and the model of discontinuities dispersion. 相似文献
8.
J. A. Martín-Fernández R. A. Olea-Meneses V. Pawlowsky-Glahn 《Mathematical Geology》2001,33(8):889-909
The additive logratio (alr) transformation has been used in several case studies to predict regionalized compositions using standard geostatistical estimation methods such as ordinary kriging and ordinary cokriging. It is a simple method that allows application to transformed data all the body of knowledge available for geostatistical analysis of coregionalizations without a constant sum constraint. To compare the performance of methods, it is customary to use a univariate crossvalidation approach based on the leaving-one-out technique to evaluate the performance for each attribute separately. For multivariate observations this approach is difficult to interpret in terms of overall performance. Therefore, we propose using appropriate distances in real space and in the simplex, to improve the crossvalidation approach and, going a step forward, to adapt the concept of stress from multidimensional scaling to obtain a global measure of performance for each method. The Lyons West oil field of Kansas is used to illustrate the impactof using different distances in the performance of ordinary kriging versus ordinary cokriging. 相似文献
9.
岩土参数的空间变异性分析 总被引：4，自引：0，他引：4
岩土参数具有空间变异性和不确定性,本文将岩土参数视为具有随机性和结构性的区域化变量,利用区域化变量理论和地质统计方法分析上海地基土有代表性的抗剪强度指标的空间变异特性。结果表明该方法是可行的。 相似文献
10.
11.
Evaluation of Interpolation Accuracy of Neural Kriging with Application to Temperature-Distribution Analysis 总被引：8，自引：0，他引：8
An interpolation method based on a multilayer neural network (MNN), has been examined and tested for the data of irregular sample locations. The main advantage of MNN is in that it can deal with geoscience data with nonlinear behavior and extract characteristics from complex and noisy images. The training of MNN is used to modify connection weights between nodes located in different layers by a simulated annealing algorithm (one of the optimization algorithms of the network). In this process, three types of errors are considered: differences in values, semivariograms, and gradients between sample data and outputs from the trained network. The training is continued until the summation of these errors converges to an acceptably small value. Because the MNN trained by this learning criterion can estimate a value at an arbitrary location, this method is a form of kriging and termed Neural Kriging (NK). In order to evaluate the effectiveness of NK, a problem on restoration ability of a defined reference surface from randomly chosen discrete data was prepared. Two types of surfaces, whose semivariograms are expressed by isotropic spherical and geometric anisotropic gaussian models, were examined in this problem. Though the interpolation accuracy depended on the arrangement pattern of the sample locations for the same number of data, the interpolation errors of NK were shown to be smaller than both those of ordinary MNN and ordinal kriging. NK can also produce a contour map in consideration of gradient constraints. Furthermore, NK was applied to distribution analysis of subsurface temperatures using geothermal investigation loggings of the Hohi area in southwest Japan. In spite of the restricted quantity of sample data, the interpolation results revealed high temperature zones and convection patterns of hydrothermal fluids. NK is regarded as an interpolation method with high accuracy that can be used for regionalized variables with any structure of spatial correlation. 相似文献
12.
The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging. 相似文献
13.
Geostatistical analysis of spatial random functions frequently uses sample variograms computed from increments of samples of a regionalized random variable. This paper addresses the theory of computing variograms not from increments but from spatial variances. The objective is to extract information about the point support space from the average or larger support data. The variance is understood as a parametric and second moment average feature of a population. However, it is well known that when the population is for a stationary random function, spatial variance within a region is a function of the size and geometry of the region and not a function of location. Spatial variance is conceptualized as an estimation variance between two physical regions or a region and itself. If such a spatial variance could be measured within several sizes of windows, such variances allow the computation of the sample variogram. The approach is extended to covariances between attributes that lead to the cross-variogram. The case of nonpoint sample support of the blocks or elements composing each window is also included. A numerical example illustrates the application of this conceptualization. 相似文献
14.
Guocheng Pan 《Mathematical Geology》1993,25(5):603-631
This paper presents a regionalized method for the estimation of a favorability function through generalization of all relevant variables (explanatory and target) into random functions. The new method allows the use of cross-covariance functions in addition to ordinary covariances for extracting spatial joint information, which is virtually overlooked in the conventional analyses. The optimal weights for a favorability equation are derived from solving a generalized eigen-system established by the maximization of covariances between a favorability function and the principal components of a set of pre-selected target variables. Various correlation coefficients may be computed to assist in interpretation of the favorability estimates. Both favorability functions and correlation coefficients may be estimated for a point or a block. The regionalized favorability theory can be compared to cokriging in that both use the sample-sample covariances to account for the sample-sample relations and the point-sample covariances to account for the point-sample configurations. The new technique is demonstrated on a test case study, which involves the integration of geochemical, airborne-geophysical, and structural data sets for the target selection of hydrothermal gold-silver deposits. 相似文献
15.
Data-driven topo-climatic mapping with machine learning methods 总被引：1，自引：1，他引：0
Automatic environmental monitoring networks enforced by wireless communication technologies provide large and ever increasing volumes of data nowadays. The use of this information in natural hazard research is an important issue. Particularly useful for risk assessment and decision making are the spatial maps of hazard-related parameters produced from point observations and available auxiliary information. The purpose of this article is to present and explore the appropriate tools to process large amounts of available data and produce predictions at fine spatial scales. These are the algorithms of machine learning, which are aimed at non-parametric robust modelling of non-linear dependencies from empirical data. The computational efficiency of the data-driven methods allows producing the prediction maps in real time which makes them superior to physical models for the operational use in risk assessment and mitigation. Particularly, this situation encounters in spatial prediction of climatic variables (topo-climatic mapping). In complex topographies of the mountainous regions, the meteorological processes are highly influenced by the relief. The article shows how these relations, possibly regionalized and non-linear, can be modelled from data using the information from digital elevation models. The particular illustration of the developed methodology concerns the mapping of temperatures (including the situations of Föhn and temperature inversion) given the measurements taken from the Swiss meteorological monitoring network. The range of the methods used in the study includes data-driven feature selection, support vector algorithms and artificial neural networks. 相似文献
16.
Juan L. Fernández Martínez César O. Menéndez Pérez Luis M. Pedruelo González José P. Fernández Alvarez Pablo Cienfuegos Suárez 《Mathematical Geology》2003,35(8):953-969
In this article we present a geostatistical approach to the transmission tomographic inverse problem, which is based on consideration of the inverse problem variables (velocity and traveltime errors) as regionalized variables (R.V.). Their structural analysis provides us with a new method to study the geophysical anisotropy of the rock, an important source of a priori information in order to design the anisotropic corrections. The underlying idea is that the geophysical structure can be deduced from the spatial structure of the regionalized variables which result from solving the tomographic problem with an isotropic algorithm. Also, the application of the structural analysis technique to the anisotropic corrected velocity field allows us to characterize the reliability of these corrections (model quality analysis). Geostatistical formalism also provides us with different techniques (parametric and non-parametric) to estimate and even simulate the velocity in the areas where this field has been considered anomalous based on field studies and on geophysical and statistical criteria. The kriging acts as a low-pass smoothing filter for the anomalous model parameters (velocities), but is not a substitute for an adequate filtering of the outliers before the inversion. This methodology opens the possibility of considering the inverse problem variables as stochastic processes, an important feature in cases where the tomogram is to be used as a tool of assessment to quantify the rock heterogeneities. 相似文献
17.
Spatial orthogonality of the principal components computed from coregionalized variables 总被引：6，自引：0，他引：6
P. Goovaerts 《Mathematical Geology》1993,25(3):281-302
Within the frame of the linear model of coregionalization, this paper sets up equations relating the variogram matrix of the principal components extracted from the variance-covariance matrix to the diagonal variogram matrices of the regionalized factors. The spatial orthogonality of the principal components is investigated in three situations: the intrinsic correlation, two basic structures with independent nugget components, three basic structures with independent nugget components and uncorrelated subsets of variables. Two examples point out that the correlation between the principal components may be nonnegligible at short distances, especially if the correlation structure changes according to the spatial scale considered. For one of the two case studies, an orthogonal varimax rotation of the first principal components is found to greatly reduce the spatial correlation between some of them. 相似文献
18.
Koike Katsuaki 《地球科学》2011,36(2):209-226
Sample data in the Earth and environmental sciences are limited in quantity and sampling location and therefore, sophisticated spatial modeling techniques are indispensable for accurate imaging of complicated structures and properties of geomaterials. This paper presents several effective methods that are grouped into two categories depending on the nature of regionalized data used. Type I data originate from plural populations and type II data satisfy the prerequisite of stationarity and have distinct spatial correlations. For the type I data, three methods are shown to be effective and demonstrated to produce plausible results: (1) a spline-based method, (2) a combination of a spline-based method with a stochastic simulation, and (3) a neural network method. Geostatistics proves to be a powerful tool for type II data. Three new approaches of geostatistics are presented with case studies: an application to directional data such as fracture, multi-scale modeling that incorporates a scaling law, and space-time joint analysis for multivariate data. Methods for improving the contribution of such spatial modeling to Earth and environmental sciences are also discussed and future important problems to be solved are summarized. 相似文献
19.
Determining whether a reaction can be written between a set of minerals within error is an example of the more general problem of determining whether a set of compositions are coplanar within error. Generally if the compositions are of minerals, ‘within error’ should allow the minerals to maintain stoichiometry. The problem is addressed via the addition of a ‘bogus’ composition to the set, and calculating the reaction coefficients for a reaction between the compositions in this augmented set. A reaction can be written if a confidence interval on the reaction coefficient of ‘bogus’ includes zero. The reaction coefficients can be solved for directly when the problem is posed in terms of least squares with equality constraints. The confidence interval is determined with a bootstrap method, allowing the result to depend on the scatter of the data around the solution of the least squares problem, not on the data uncertainties 相似文献
20.
Arnon Karnieli Dr. 《GeoJournal》1990,22(4):391-398
The classical methods for interpolating and spatial averaging of precipitation fields fail to quantify the accuracy of the estimate. On the other hand, kriging is an interpolation method for predicting values of regionalized variables at points (punctual kriging) or average values over an area (block kriging).This paper demonstrates the use of the kriging method for mapping and evaluating precipitation data for the State of Arizona. Using 158 rain gauge stations with 30 years or more of record, the precipitation over the state has been modeled as a realization of a two dimensional random field taking into consideration the spatial variability conditions.Three data sets have been used: (1) the mean annual precipitation over the state; (2) the mean summer rainy season; and (3) the mean winter rainy season. Validation of the empirical semi-variogram for a constant drift case indicated that the exponential model was appropriate for all the data sets. In addition to a global kriging analysis, the data have been examined under an anisotropic assumption which reflects the topographic structure of the state. 相似文献