共查询到20条相似文献，搜索用时 26 毫秒
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Abdullah Arik 《Mathematical Geology》2002,34(7):783-796
This paper presents a modified ordinary kriging technique referred to as the Area Influence Kriging (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
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动态Kriging方法 总被引：8，自引：0，他引：8
在空间Ｋｒｉｇｉｎｇ方法的基础上，考虑了地下水系统的状态变量在时间上的自相关关系，并建立了反应变量动态特征的动态Ｋｒｉｇｉｎｇ方法，并对该方法的应用范围和使用步骤进行了讨论。 相似文献
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Simplicial Indicator Kriging 总被引：2，自引：0，他引：2
Indicator kriging (IK) is a spatial interpolation technique devised for estimating a conditional cumulative distribution function at an unsampled location. The result is a discrete approximation, and its corresponding estimated probability density function can be viewed as a composition in the simplex. This fact suggested a compositional approach to IK which, by construction, avoids all its standard drawbacks (negative predictions, not-ordered or larger than one). Here, a simple algorithm to develop the procedure is presented. 相似文献
5.
This paper presents a modified ordinary kriging technique referred to as the “Area Influence Kriging” (AIK). The method is a simple and practical tool to use for more accurate prediction of global recoverable ore resources in any type of deposit. AIK performs well even in deposits with skewed grade distributions when the ordinary kriging (OK) results are unreasonably smooth. It is robust and globally unbiased like OK. The AIK method is not intended to replace OK, which is a better estimator of the average grade of the blocks. Rather it aims to complement OK with its excellent performance in predicting recoverable resources that have been the major pitfalls of OK in many resource estimation cases. The paper details the methodology of AIK with a couple of examples. It also reports the results from its application to a gold deposit. 相似文献
6.
Kriging with Inequality Constraints 总被引：1，自引：0，他引：1
A Gaussian random field with an unknown linear trend for the mean is considered. Methods for obtaining the distribution of the trend coefficients given exact data and inequality constraints are established. Moreover, the conditional distribution for the random field at any location is calculated so that predictions using e.g. the expectation, the mode, or the median can be evaluated and prediction error estimates using quantiles or variance can be obtained. Conditional simulation techniques are also provided. 相似文献
7.
Kriging without negative weights 总被引：1，自引：0，他引：1
Under a constant drift, the linear kriging estimator is considered as a weighted average ofn available sample values. Kriging weights are determined such that the estimator is unbiased and optimal. To meet these requirements, negative kriging weights are sometimes found. Use of negative weights can produce negative block grades, which makes no practical sense. In some applications, all kriging weights may be required to be nonnegative. In this paper, a derivation of a set of nonlinear equations with the nonnegative constraint is presented. A numerical algorithm also is developed for the solution of the new set of kriging equations. 相似文献
8.
The problem to predict a rotation (orientation) from corresponding geocoded data is discussed and a general solution by virtue of embedding the group of rotations in a real vector space is presented. It is referred to as kriging in embedding spaces as developed in part I of this contribution, and basically the same arguments apply and lead to equivalent results. However, the assumptions of isotropy have to be restated and reinterpreted. A one-to-one correspondence of reasonable isotropy assumptions for rotations represented as axes and for rotations represented by matrices does not seem to exist. 相似文献
9.
Kriging of water levels in the Souss aquifer,Morocco 总被引：2，自引：0，他引：2
Universal kriging is applied to water table data from the Souss aquifer in central Morocco. The procedure accounts for the spatial variability of the phenomenon to be mapped. With the use of measured elevations of the water table, an experimental variogram is constructed that characterizes the spatial variability of the measured water levels. Spherical and Gaussian variogram models are alternatively used to fit the experimental variogram. The models are used to develop contour maps of water table elevations and corresponding estimation variances. The estimation variances express the reliability of the kriged water table elevation maps. Universal kriging also provides a contour map of the expected elevation of the water table (drift). The differences between the expected and measured water table elevations are called residuals from the drift. Residuals from the drift are compared with residuals obtained by more traditional least-squares analysis. 相似文献
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Clayton V. Deutsch 《Mathematical Geosciences》1994,26(5):623-638
The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r(n),and presents a number of examples. 相似文献
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A. G. Journel 《Mathematical Geology》1977,9(6):563-586
In the last few years, an increasing number of practical studies using so-called kriging estimation procedures have been published. Various terms, such as universal kriging, lognormal kriging, ordinary kriging, etc., are used to define different estimation procedures, leaving a certain confusion about what kriging really is. The object of this paper is to show what is the common backbone of all these estimation procedures, thus justifying the common name of kriging procedures. The word kriging (in French krigeage) is a concise and convenient term to designate the classical procedure of selecting, within agiven class of possible estimators, the estimator with a minimum estimation variance (i.e., the estimator which leads to a minimum variance of the resulting estimation error). This estimation variance can be seen as a squared distance between the unknown value and its estimator; the process of minimization of this distance can then be seen as the projection of the unknown value onto the space within which the search for an estimator is carried out. 相似文献
13.
An idea to consider rock textures from a geostatistical viewpoint is suggested. Mineral grains are coded by indicator functions. Four metrics are shown of interest for petrographic applications. The simplest one is used to calculate covariograms of indicators for platinum-bearing gabbronorite from the Pansky rock massif (Kola Peninsula, Russia) with maximal range of 2 units. This is generalized in the concept of a minimal cluster of mineral grains for the given rock. The theory allows us to combine grain-by-grain and cluster-by-cluster considerations of rock texture. It may be used to classify monotonous lithological series using nuances of rock textures. 相似文献
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Kriging in a finite domain 总被引：2，自引：0，他引：2
Clayton V. Deutsch 《Mathematical Geology》1993,25(1):41-52
Adopting a random function model {Z(u),u study areaA} and using the normal equations (kriging) for estimation amounts to assume that the study areaA is embedded within a infinite domain. At first glance, this assumption has no inherent limitations since all locations outsideA are of no interest and simply not considered. However, there is an interesting and practically important consequence that is reflected in the kriging weights assigned to data contiguously aligned along finite strings; the weights assigned to the end points of a string are large since the end points inform the infinite half-space beyond the string. These large weights are inappropriate when the finite string has been created by either stratigraphic/geological limits or a finite search neighborhood. This problem will be demonstrated with numerical examples and some partial solutions will be proposed. 相似文献
15.
Kriging with strings of data 总被引：1，自引：0，他引：1
Clayton V. Deutsch 《Mathematical Geology》1994,26(5):623-638
The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r(n)
is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r(n),and presents a number of examples. 相似文献
16.
Kriging in a global neighborhood 总被引：1，自引：0，他引：1
The kriging estimator is usually computed in a moving neighborhood; only the data near the point to be estimated are used. This moving neighborhood approach creates discontinuities in mapping applications. An alternative approach is presented here, whereby all points are estimated using all the available data. To solve the resulting large linear system the kriging estimator is expressed in terms of the inverse of the covariance matrix. The covariance matrix has the advantage of being positive definite and the size of system which can be solved without encountering numerical instability is substantially increased. Because the kriging matrix does not change, the estimator can be written in terms of scalar products, thus avoiding the more time-consuming matrix multiplications of the standard approach. In the particular case of a covariance which is zero for distances greater than a fixed value (the range), the resulting banded structure of the covariance matrix is shown to lead to substantial computational savings in both run time and storage space. In this case the calculation time for the kriging variance is also substantially reduced. The present method is extended to the nonstationary case. 相似文献
17.
Clayton V. Deutsch 《Mathematical Geosciences》1993,25(1):41-52
Adopting a random function model {Z(u),u ε study areaA} and using the normal equations (kriging) for estimation amounts to assume that the study areaA is embedded within a infinite domain. At first glance, this assumption has no inherent limitations since all locations outsideA are of no interest and simply not considered. However, there is an interesting and practically important consequence that is reflected in the kriging weights assigned to data contiguously aligned along finite strings; the weights assigned to the end points of a string are large since the end points inform the infinite half-space beyond the string. These large weights are inappropriate when the finite string has been created by either stratigraphic/geological limits or a finite search neighborhood. This problem will be demonstrated with numerical examples and some partial solutions will be proposed. 相似文献
18.
The problem to predict a direction, axis, or orientation (rotation) from corresponding geocoded data is discussed and a general solution by virtue of embedding a sphere/hemisphere in a real vector space is presented. Its explicit justification in terms of mathematical assumptions concerning stationarity/homogeneity and isotropy is included. The data are modelled by a stationary random field, and the spatial correlation is represented by modified multivariate variograms and covariance functions. Various types of isotropy assumptions concerning invariance under translation/rotation of the data locations, the measurements, or a combination of both, can be distinguished and lead to different simplifications of the general cross-covariance function. Beyond spatial prediction a measure of confidence in the estimates is provided. 相似文献
19.
On Visualization for Assessing Kriging Outcomes 总被引：7，自引：0，他引：7
James R. Carr 《Mathematical Geology》2002,34(4):421-433
Extant opinion about kriging is that all weights should be positive. Visualizations rendered by converting kriged grids to digital images are presented to show that negative weights may be beneficial to some spatial problems. In particular, variogram models with zero-valued nuggets, already well known to minimize smoothing through kriging, result in a visual resolution substantially superior to that from kriging with a variogram model having a nonzero nugget value in application to satellite acquired data. Negative weights are more likely when using variogram models with zero-valued nuggets, but resultant visualizations often show a smoother transition between extreme data values. This is true even when a variogram model having a nugget value of zero is not optimum with respect to mean square error, as is demonstrated using a nitrate data set. An analogy to digital image processing is used to suggest that the influence of negative weights in kriging is similar to a high-boost kernel. 相似文献
20.
Block Kriging for Lognormal Spatial Processes 总被引：4，自引：0，他引：4
Noel Cressie 《Mathematical Geology》2006,38(4):413-443
Lognormal spatial data are common in mining and soil-science applications. Modeling the underlying spatial process as normal on the log scale is sensible; point kriging allows the whole region of interest to be mapped. However, mining and precision agriculture is carried out selectively and is based on block averages of the process on the original scale. Finding spatial predictions of the blocks assuming a lognormal spatial process has a long history in geostatistics. In this article, we make the case that a particular method for block prediction, overlooked in past times of low computing power, deserves to be reconsidered. In fact, for known mean, it is optimal. We also consider the predictor based on the “law” of permanence of lognormality. Mean squared prediction errors of both are derived and compared both theoretically and via simulation; the predictor based on the permanence-of-lognormality assumption is seen to be less efficient. Our methodology is applied to block kriging of phosphorus to guide precision-agriculture treatment of soil on Broom's Barn Farm, UK. 相似文献