共查询到20条相似文献，搜索用时 15 毫秒
1.
Imprecise (fuzzy) information in geostatistics 总被引：2，自引：0，他引：2
A methodology based on fuzzy set theory for the utilization of imprecise data in geostatistics is presented. A common problem preventing a broader use of geostatistics has been the insufficient amount of accurate measurement data. In certain cases, additional but uncertain (soft) information is available and can be encoded as subjective probabilities, and then the soft kriging method can be applied (Journel, 1986). In other cases, a fuzzy encoding of soft information may be more realistic and simplify the numerical calculations. Imprecise (fuzzy) spatial information on the possible variogram is integrated into a single variogram which is used in a fuzzy kriging procedure. The overall uncertainty of prediction is represented by the estimation variance and the calculated membership function for each kriged point. The methodology is applied to the permeability prediction of a soil liner for hazardous waste containment. The available number of hard measurement data (20) was not enough for a classical geostatistical analysis. An additional 20 soft data made it possible to prepare kriged contour maps using the fuzzy geostatistical procedure.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987. 相似文献
2.
Kriging with imprecise (fuzzy) variograms. I: Theory 总被引：2，自引：0，他引：2
Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data. 相似文献
3.
Stochastic fractal (fGn and fBm) porosity and permeability fields are conditioned to given variogram, static (or hard), and multiwell pressure data within a Bayesian estimation framework. Because fGn distributions are normal/second-order stationary, it is shown that the Bayesian estimation methods based on the assumption of normal/second-order stationary distributions can be directly used to generate fGn porosity/permeability fields conditional to pressure data. However, because fBm is not second-order stationary, it is shown that such Bayesian estimation methods can be used with implementation of a pseudocovariance approach to generate fBm porosity/permeability fields conditional to multiwell pressure data. In addition, we provide methods to generate unconditional realizations of fBm/fGn fields honoring all variogram parameters. These unconditional realizations can then be conditioned to hard and pressure data observed at wells by using the randomized maximum likelihood method. Synthetic examples generated from one-, two-, and three-dimensional single-phase flow simulators are used to show the applicability of our methodology for generating realizations of fBm/fGn porosity and permeability fields conditioned to well-test pressure data and evaluating the uncertainty in reservoir performance predictions appropriately using these history-matched realizations. 相似文献
4.
Mauro A. E. Chaparro Marcos A. E. Chaparro Ana M. Sinito 《Environmental Earth Sciences》2012,66(5):1477-1485
In this contribution, a methodology is reported in order to build an interval fuzzy model for the pollution index PLI (a composite index using relevant heavy metal concentration) with magnetic parameters as input variables. In general, modelling based on fuzzy set theory is designed to mimic how the human brain tends to classify imprecise information or data. The “interval fuzzy model” reported here, based on fuzzy logic and arithmetic of fuzzy numbers, calculates an “estimation interval” and seems to be an adequate mathematical tool for this nonlinear problem. For this model, fuzzy c-means clustering is used to partition data, hence the membership functions and rules are built. In addition, interval arithmetic is used to obtain the fuzzy intervals. The studied sets are different examples of pollution by different anthropogenic sources, in two different study areas: (a) soil samples collected in Antarctica and (b) road-deposited sediments collected in Argentina. The datasets comprise magnetic and chemical variables, and for both cases, relevant variables were selected: magnetic concentration-dependent variables, magnetic features-dependent variables and one chemical variable. The model output gives an estimation interval; its width depends on the data density, for the measured values. The results show not only satisfactory agreement between the estimation interval and data, but also provide valued information from the rules analysis that allows understanding the magnetic behaviour of the studied variables under different conditions. 相似文献
5.
Saeed Soltani-Mohammadi 《Earth Science Informatics》2016,9(2):235-245
Using kriging has been accepted today as the most common method of estimating spatial data in such different fields as the geosciences. To be able to apply kriging methods, it is necessary that the data and variogram model parameters be precise. To utilize the imprecise (fuzzy) data and parameters, use is made of fuzzy kriging methods. Although it has been 30 years since different fuzzy kriging algorithms were proposed, its use has not become as common as other kriging methods (ordinary, simple, log, universal, etc.); lack of a comprehensive software that can perform, based on different fuzzy kriging algorithms, the related calculations in a 3D space can be the main reason. This paper describes an open-source software toolbox (developed in Matlab) for running different algorithms proposed for fuzzy kriging. It also presents, besides a short presentation of the fuzzy kriging method and introduction of the functions provided by the FuzzyKrig toolbox, 3 cases of the software application under the conditions where: 1) data are hard and variogram model parameters are fuzzy, 2) data are fuzzy and variogram model parameters are hard, and 3) both data and variogram model parameters are fuzzy. 相似文献
6.
概述了克里格法应用于北方某煤矿的储量计算结果,并将其与传统方法的计算结果进行比较,说明了该法的应用价值。 相似文献
7.
Probabilistic Fuzzy Logic Modeling: Quantifying Uncertainty of Mineral Prospectivity Models Using Monte Carlo Simulations 总被引：2，自引：0，他引：2
Significant uncertainties are associated with the definition of both the exploration targeting criteria and computational algorithms used to generate mineral prospectivity maps. In prospectivity modeling, the input and computational uncertainties are generally made implicit, by making a series of best-guess or best-fit decisions, on the basis of incomplete and imprecise information. The individual uncertainties are then compounded and propagated into the final prospectivity map as an implicit combined uncertainty which is impossible to directly analyze and use for decision making. This paper proposes a new approach to explicitly define uncertainties of individual targeting criteria and propagate them through a computational algorithm to evaluate the combined uncertainty of a prospectivity map. Applied to fuzzy logic prospectivity models, this approach involves replacing point estimates of fuzzy membership values by statistical distributions deemed representative of likely variability of the corresponding fuzzy membership values. Uncertainty is then propagated through a fuzzy logic inference system by applying Monte Carlo simulations. A final prospectivity map is represented by a grid of statistical distributions of fuzzy prospectivity. Such modeling of uncertainty in prospectivity analyses allows better definition of exploration target quality, as understanding of uncertainty is consistently captured, propagated and visualized in a transparent manner. The explicit uncertainty information of prospectivity maps can support further risk analysis and decision making. The proposed probabilistic fuzzy logic approach can be used in any area of geosciences to model uncertainty of complex fuzzy systems. 相似文献
8.
The variogram is a critical input to geostatistical studies: (1) it is a tool to investigate and quantify the spatial variability of the phenomenon under study, and (2) most geostatistical estimation or simulation algorithms require an analytical variogram model, which they will reproduce with statistical fluctuations. In the construction of numerical models, the variogram reflects some of our understanding of the geometry and continuity of the variable, and can have a very important impact on predictions from such numerical models. The principles of variogram modeling are developed and illustrated with a number of practical examples. A three-dimensional interpretation of the variogram is necessary to fully describe geologic continuity. Directional continuity must be described simultaneously to be consistent with principles of geological deposition and for a legitimate measure of spatial variability for geostatistical modeling algorithms. Interpretation principles are discussed in detail. Variograms are modeled with particular functions for reasons of mathematical consistency. Used correctly, such variogram models account for the experimental data, geological interpretation, and analogue information. The steps in this essential data integration exercise are described in detail through the introduction of a rigorous methodology. 相似文献
9.
Teacher''s Aide Variogram Interpretation and Modeling 总被引：13，自引：0，他引：13
The variogram is a critical input to geostatistical studies: (1) it is a tool to investigate and quantify the spatial variability of the phenomenon under study, and (2) most geostatistical estimation or simulation algorithms require an analytical variogram model, which they will reproduce with statistical fluctuations. In the construction of numerical models, the variogram reflects some of our understanding of the geometry and continuity of the variable, and can have a very important impact on predictions from such numerical models. The principles of variogram modeling are developed and illustrated with a number of practical examples. A three-dimensional interpretation of the variogram is necessary to fully describe geologic continuity. Directional continuity must be described simultaneously to be consistent with principles of geological deposition and for a legitimate measure of spatial variability for geostatistical modeling algorithms. Interpretation principles are discussed in detail. Variograms are modeled with particular functions for reasons of mathematical consistency. Used correctly, such variogram models account for the experimental data, geological interpretation, and analogue information. The steps in this essential data integration exercise are described in detail through the introduction of a rigorous methodology. 相似文献
10.
含水层渗透性空间分布的指示克立格估值 总被引：3，自引：0，他引：3
详细介绍了指示克立格估值计算的理论和方法。以指示变异函数为基本工具分析了华北某地区第四系含水层渗透性空间分布的结构特征,结果表明该地区含水层渗透性存在明显的各向异性特征。水平方向上,X轴方向的相关性较Y轴方向的好,Z轴的相关性最差。用指示克立格法对未采样点处进行估值,估值结果显示含水层渗透性由山前向滨海逐渐变低,在垂直方向上,渗透性变化不明显,浅部比深部略好;同时给出了估计精度,并认为对估计精度不高的区域可通过增加适当的工程加以控制。最后用交叉验证法对估值结果进行了检验,证明建立的指示变异函数模型合理且估值效果较好。这一实际应用表明指示克立格法可以很好地描述第四系含水层渗透性的空间分布规律。 相似文献
11.
Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body 总被引：3，自引：0，他引：3
Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited. 相似文献
12.
13.
I. C. Lemmer 《Mathematical Geosciences》1986,18(7):605-623
The theory of mononodal variography developed in the preceeding paper is checked against a simulated deposit consisting of 60,500 grade values, called Stanford II. In the case of this deposit at least, assumptions underlying the concept of mononodal variography are borne out accurately. In particular, a linear relationship does exist indeed between indicator and grade variogram values of Stanford II at corresponding lags. Furthermore, such grade-indicator plots, and the information deduced from them, are robust under reduction of data at the mononodal cutoff. The method thus has predictive potential for grade variograms of highly variant deposits. Forecasting a grade variogram from the associated mononodal indicator variogram and grade-indicator plot is illustrated. Agreement with the experimental variogram is shown to be excellent. 相似文献
14.
Changik Han Jiyang Wang Mingguo Zheng Ende Wang Jianming Xia GwangSu Li Sunchol Choe 《Earth Science Informatics》2016,9(2):197-213
A critical step for kriging in geostatistics is estimation of the variogram. Traditional variogram modeling comprise of the experimental variogram calculation, appropriate variogram model selection and model parameter determination. Selecting of the variogram model and fitting of model parameters is the most controversial aspect of geostatistics. Shapes of valid variogram models are finite, and sometimes, the optimal shape of the model can not be fitted, leading to reduced estimation accuracy. In this paper, a new method is presented to automatically construct a model shape and fit model parameters to experimental variograms using Support Vector Regression (SVR) and Multi-Gene Genetic Programming (MGGP). The proposed method does not require the selection of a variogram model and can directly provide the model shape and parameters of the optimal variogram. The validity of the proposed method is demonstrated in a number of cases. 相似文献
15.
I. C. Lemmer 《Mathematical Geology》1986,18(7):605-623
The theory of mononodal variography developed in the preceeding paper is checked against a simulated deposit consisting of 60,500 grade values, called Stanford II. In the case of this deposit at least, assumptions underlying the concept of mononodal variography are borne out accurately. In particular, a linear relationship does exist indeed between indicator and grade variogram values of Stanford II at corresponding lags. Furthermore, such grade-indicator plots, and the information deduced from them, are robust under reduction of data at the mononodal cutoff. The method thus has predictive potential for grade variograms of highly variant deposits. Forecasting a grade variogram from the associated mononodal indicator variogram and grade-indicator plot is illustrated. Agreement with the experimental variogram is shown to be excellent.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished). 相似文献
16.
Estimating spatial distributions of heterogeneous subsurface characteristics by regionalized classification of electrofacies 总被引：1，自引：0，他引：1
Regionalized classification of electrofacies utilizes the statistical relationships between laboratory determined hydrologic properties and field-measured geophysical properties to estimate spatial distributions of porosity, permeability, and diagenetic characteristics. The method, illustrated with an application to the St. Peter Sandstone in the Michigan basin, combines techniques for multivariate analysis and spatial estimation. Core plug and borehole geophysical data are clustered into electrofacies that reflect the hydrologic properties and diagenetic characteristics of the formation. Electrofacies characteristics then are used to assign a class membership probability at locations where only geophysical data are available. Three-dimensional estimation of electrofacies occurrence is done by kriging datasets containing the probability of electrofacies membership at borehole locations. The discretization and kriging geometry allow three-dimensional estimation of hydrologic parameters for a large region that incorporates meter-scale heterogeneity. Finally, permeability and porosity are estimated at each grid location by probability-weighting. Because the electrofacies carry information about both the hydrologic and lithologic properties, the resulting spatial distributions provide an understanding of both the present-day flow characteristics and the extent of processes that control them.Managed by Martin Marietta Energy Systems. Inc., under contract DE-AC05-84OR21400 with the U.S. Department of Energy); Publication No. 4371, Environmental Sciences Division, ORNL. 相似文献
17.
The reliability of using fractal dimension (D) as a quantitative parameter to describe geological variables is dependent mainly
on the accuracy of estimated D values from observed data. Two widely used methods for the estimation of fractal dimensions
are based on fitting a fractal model to experimental variograms or power-spectra on a log-log plot. The purpose of this paper
is to study the uncertainty in the fractal dimension estimated by these two methods. The results indicate that both spectrum
and variogram methods result in biased estimates of the D value. Fractal dimension calculated by these two methods for the
same data will be different unless the bias is properly corrected. The spectral method results in overestimated D values.
The variogram method has a critical fractal dimension, below which overestimation occurs and above which underestimation occurs.
On the bases of 36,000 simulated realizations we propose empirical formulae to correct for biases in the spectral and variogram
estimated fractal dimension. Pitfalls in estimating fractal dimension from data contaminated by white noise or data having
several fractal components have been identified and illustrated by simulated examples. 相似文献
18.
Geostatistics has traditionally used a probabilistic framework, one in which expected values or ensemble averages are of primary importance. The less familiar deterministic framework views geostatistical problems in terms of spatial integrals. This paper outlines the two frameworks and examines the issue of which spatial continuity measure, the covarianceC (h) or the variogram (h), is appropriate for each framework. AlthoughC (h) and (h) were defined originally in terms of spatial integrals, the convenience of probabilistic notation made the expected value definitions more common. These now classical expected value definitions entail a linear relationship betweenC (h) and (h); the spatial integral definitions do not. In a probabilistic framework, where available sample information is extrapolated to domains other than the one which was sampled, the expected value definitions are appropriate; furthermore, within a probabilistic framework, reasons exist for preferring the variogram to the covariance function. In a deterministic framework, where available sample information is interpolated within the same domain, the spatial integral definitions are appropriate and no reasons are known for preferring the variogram. A case study on a Wiener-Levy process demonstrates differences between the two frameworks and shows that, for most estimation problems, the deterministic viewpoint is more appropriate. Several case studies on real data sets reveal that the sample covariance function reflects the character of spatial continuity better than the sample variogram. From both theoretical and practical considerations, clearly for most geostatistical problems, direct estimation of the covariance is better than the traditional variogram approach.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987. 相似文献
19.
The landslide hazard is one of the geological hazards in mountainous zone. Its occurrence is controlled by many factors. To assess the risk level of landslide in Shiwangmiao accurately, intuitionistic fuzzy sets-Topsis model is introduced at first; secondly, the decisive matrix about the intuitionistic fuzzy sets is established, and the index weight coefficients considering the uncertainty of assessment indices are determined by using the Entropy weight method, then the weighed decisive matrix is obtained. Finally, degree of membership at different levels about the landslide is determined based on the ranking sequence of degree of membership, the risk level corresponding to the maximum degree of membership is final assessment level. The conclusions are drawn that accurate rate of risk estimation about landslide hazards is very high based on the intuitionistic fuzzy sets model in comparison with the current specifications, and the method is feasible for the risk assessment of landslide hazards, so it provides a new method and thoughts to assess the risk level of landslide in future.
相似文献20.
Statistical characterization and stochastic modeling of pore networks in relation to fluid flow 总被引：18，自引：0，他引：18
R. D. Hazlett 《Mathematical Geology》1997,29(6):801-822