共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
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
3.
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
4.
Spatial declustering weights 总被引：1，自引：0，他引：1
G. Bourgault 《Mathematical Geology》1997,29(2):277-290
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for
estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy
(or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance.
The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data
clustering. 相似文献
5.
G. Bourgault 《Mathematical Geosciences》1997,29(2):277-290
Because of autocorrelation and spatial clustering, all data within a given dataset have not the same statistical weight for estimation of global statistics such mean, variance, or quantiles of the population distribution. A measure of redundancy (or nonredundancy) of any given regionalized random variable Z(uα)within any given set (of size N) of random variables is proposed. It is defined as the ratio of the determinant of the N X Ncorrelation matrix to the determinant of the (N - 1) X (N - 1)correlation matrix excluding random variable Z(uα).This ratio measures the increase in redundancy when adding the random variable Z(uα)to the (N - 1 )remainder. It can be used as declustering weight for any outcome (datum) z(uα). When the redundancy matrix is a kriging covariance matrix, the proposed ratio is the crossvalidation simple kriging variance. The covariance of the uniform scores of the clustered data is proposed as a redundancy measure robust with respect to data clustering. 相似文献
6.
Spatial prediction and ordinary kriging 总被引：11，自引：0，他引：11
Noel Cressie 《Mathematical Geology》1988,20(4):405-421
Suppose data {Z(s
i
):i=1, ..., n} are observed at spatial locations {s
i
:i=1, ..., n}. From these data, an unknownZ(s
0) is to be predicted at a known locations
0c, or, ifZ(s0) has a component of measurement error, then a smooth versionS(s
0) should be predicted. This article considers the assumptions needed to carry out the spatial prediction using ordinary kriging, and looks at how nugget effect, range, and sill of the variogram affect the predictor. It is concluded that certain commonly held interpretations of these variogram parameters should be modified.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987. 相似文献
7.
地质统计学是数学地质领域最为活跃而实用的分支,它是以区域化变量理论为基础,以变异函数为基本工具,研究那些在空间分布上既具有随机性又具有结构性的自然现象的科学。在第四纪研究中的很多特征(变量)均可看成区域化变量进行地质统计学分析。作者在讨论了经典概率论及数理统计方法简单地应用于第四纪研究可能出现的问题后,着重介绍了用于第四纪研究中的若干地质统计学方法及基本理论,同时,对地质统计学方法应用于第四纪研究中的前景进行了分析。 相似文献
8.
Marek Kacewicz 《Mathematical Geology》1991,23(1):111-118
This paper presents an approach to solve the kriging problem, defined in terms of projections, by using Gram-Schmidt orthogonalization. The Gram-Schmidt orthogonalization allows us to find an optimal approximationY* in then-dimensional subspaceH
n
of any vectorY element of a Hilbert spaceH. This approach requiresO(n
3) multiplication operations to obtain an orthogonal basis, andO(n
2) multiplications needed to calculate kriging solution for a given point. 相似文献
9.
Minimum energy geometries and electron density distributions, ϱ(r), for ∼40 polyatomic oxide molecules containing first and second row M-cations have been calculated at the Hartree-Fock level with a 6-311++G** basis set. The nature of the bonded interactions
in these molecules is examined in terms of the relative electronegativities, χ
M
, of the M-cations and the properties of the electron density distribution, ϱ(r
c
), evaluated at the bond critical points, r
c
, along each MO bond. As ϱ(r
c
) and the Laplacian of ϱ(r
c
) increase, χ
M
increases indicating an increase in the covalent character of the bonded interactions between M and O. The ratios of the curvatures of ϱ(r
c
) indicate that the NO bond is predominantly covalent, that the CO and SO bonds are of intermediate type and that the remaining
MO bonds are indicated to be predominantly ionic in character. A comparison of the critical point properties of ϱ(r
c
) and χ
M
indicates that the minimum energy MO bond length is an important determinate of the properties of ϱ(r
c
) and the character of the MO bonds.
On the other hand, values of the local energy density, H(r
c
), indicate that the LiO, BeO, NaO, MgO and AlO bonds are predominantly ionic and that the BO, CO, NO, SiO, PO and SO bonds
are predominantly covalent in character. The χ
M
-values provided by the properties of ϱ(r
c
) indicate that the covalent component of a bond increases with decreasing bond length, coordination number and increasing
bond strength. Each MO bond seems to represent a unique entity and to possess a distinct set of ϱ(r
c
) properties, the distinction being greater for the more electronegative cations.
The bonded radius of the oxide ion, r
b
(O), and the χ
M
-values determined from ϱ(r
c
) correlate with values determined from promolecule electron density distributions. In addition, r
b
(O) and χ
M
-values determined from experimental electron density distributions for crystals correlate with values determined from procrystal
electron density distributions. The number of critical points and bond paths are modeled rather faithfully by procrystal and
promolecule electron density distributions, despite the neglect of the binding forces in their constructions.
Received: October 15, 1996/Revised, accepted: February 10, 1997 相似文献
10.
Jorge Kazuo Yamamoto 《Mathematical Geology》2000,32(4):489-509
This paper presents an interpolation variance as an alternative to the measure of the reliability of ordinary kriging estimates. Contrary to the traditional kriging variance, the interpolation variance is data-values dependent, variogram dependent, and a measure of local accuracy. Natural phenomena are not homogeneous; therefore, local variability as expressed through data values must be recognized for a correct assessment of uncertainty. The interpolation variance is simply the weighted average of the squared differences between data values and the retained estimate. Ordinary kriging or simple kriging variances are the expected values of interpolation variances; therefore, these traditional homoscedastic estimation variances cannot properly measure local data dispersion. More precisely, the interpolation variance is an estimate of the local conditional variance, when the ordinary kriging weights are interpreted as conditional probabilities associated to the n neighboring data. This interpretation is valid if, and only if, all ordinary kriging weights are positive or constrained to be such. Extensive tests illustrate that the interpolation variance is a useful alternative to the traditional kriging variance. 相似文献
11.
A number of criteria based on kriging variance calculations may be used for infill sampling design in geologic site characterization. Searching for the best new sample locations from a set of candidate locations can result in excessive computation time if these criteria and the naive rekriging are used. The relative updated kriging estimate and variance for universal kriging estimation are demonstrated as a simple kriging estimate and variance, respectively. The updated kriging variance is demonstrated as the multiplication of two kriging variances. Using these updated kriging variance equations can increase the computational speed for selecting the best new sample locations. The application results for oil rock thickness in an oilfield indicate that minimizing the average relative updated kriging variance is a useful alternative to the other criteria based on kriging variance in optimal infill sampling design for geologic site characterization. 相似文献
12.
Geostatistical estimations of the hydraulic conductivity field (K) in the Carrizo aquifer, Texas, are performed over three regional domains of increasing extent: 1) the domain corresponding
to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the 10 counties
encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain).
Two different approaches are used: 1) an indirect approach where transmissivity (T) is estimated first and K is retrieved through division of the T estimate by the screen length of the wells, and; 2) a direct approach where K data are kriged directly. Due to preferential well screen emplacement, and scarcity of sampling in the deeper portions of
the formation (> 1 km), the available data set is biased toward high values of hydraulic conductivities. Kriging combined
with linear regression, simple kriging with varying local means, kriging with an external drift, and cokriging allow the incorporation
of specific capacity as secondary information. Prediction performances (assessed through cross-validation) differ according
to the chosen approach, the considered variable (log-transformed or back-transformed), and the scale of interest. For the
indirect approach, kriging of log T with varying local means yields the best estimates for both log-transformed and back-transformed variables in the model domain.
For larger regional scales (County and Texas domains), cokriging performs generally better than other kriging procedures when
estimating both (log T)∗ and T∗. Among procedures using the direct approach, the best prediction performances are obtained using kriging of log K with an external drift. Overall, geostatistical estimation of the hydraulic conductivity field at regional scales is rendered
difficult by both preferential well location and preferential emplacement of well screens in the most productive portions
of the aquifer. Such bias creates unrealistic hydraulic conductivity values, in particular, in sparsely sampled areas. 相似文献
13.
G. V. Gibbs K. M. Rosso D. F. Cox M. B. Boisen Jr. 《Physics and Chemistry of Minerals》2003,30(5):317-320
The average strength, s, of the bonded interactions comprising a cation containing oxide anion coordination polyhedron and the value of the electron
density, ρ(r
c
), at the bond-critical points are inversely correlated with bond length. In each case, the observed bond lengths, R, were modeled with power-law expressions defined in terms of s/r and ρ(r
c
)/r, respectively, where r is the Periodic Table row number of the cation involved in the bonded interaction. On the basis of the close connection between
bond strength and the value of the electron density at the bond-critical point, we conclude that bond strength is a direct
measure of bond type; the greater its value, the greater the localization of electron density in the binding region and the
greater the shared–electron covalent character of the bonded interaction.
Received: 15 October 2002 / Accepted: 17 February 2003
Present address:G. V. Gibbs in care of M. Spackman Department of Chemistry, University of New England, Armidale 2351, Australia
Acknowledgements The NSF is thanked for supporting this study with grant EAR–9627458. The paper was written while GVG was a Visiting NSF Scholar
at The University of Arizona. The faculty and graduate students of the Department of Geosciences and Bob Downs and Marelina
Stimpf in particular are thanked for making the visit great fun. 相似文献
14.
Under the intrinsic coregionalization model if both primary and secondary measurements are available at all sample locations, the conventional geostatistical wisdom is that cokriging provides exactly the same solution as univariate kriging on the primary process alone. However, recent eamples have been given where nonzero secondary cokriging weights have accurred under this spatial dependence structure. This note identifies the conditions under which secondary information is useful under the assumption of intrinsic coregionalization. An illustration is given using a dataset of plutonium and americium concentrations collected from a region of the Nevada Test Site. 相似文献
15.
Comparative performance of indicator algorithms for modeling conditional probability distribution functions 总被引：1，自引：0，他引：1
P. Goovaerts 《Mathematical Geology》1994,26(3):389-411
This paper compares the performance of four algorithms (full indicator cokriging. adjacent cutoffs indicator cokriging, multiple indicator kriging, median indicator kriging) for modeling conditional cumulative distribution functions (ccdf).The latter three algorithms are approximations to the theoretically better full indicator cokriging in the sense that they disregard cross-covariances between some indicator variables or they consider that all covariances are proportional to the same function. Comparative performance is assessed using a reference soil data set that includes 2649 locations at which both topsoil copper and cobalt were measured. For all practical purposes, indicator cokriging does not perform better than the other simpler algorithms which involve less variogram modeling effort and smaller computational cost. Furthermore, the number of order relation deviations is found to be higher for cokriging algorithms, especially when constraints on the kriging weights are applied. 相似文献
16.
Spatial and scaling modelling for geochemical anomaly separation 总被引：1，自引：0，他引：1
Qiuming Cheng 《Journal of Geochemical Exploration》1999,65(3):447
A spatial and scaling approach with a user-friendly windows program is introduced which can be used to assist exploration geologists and geochemists in geochemical data analysis and anomaly separation. It can also be used for image enhancement and classification. Statistics are calculated and optimized within a variable-sized moving window centred at an arbitrary sample location. The moving window has both variable size and shape determined by three parameters: r (size), β (ratio of long and short axes), and θ (orientation). It calculates five optimal indexes for each sample location: the optimal statistic U(r0,β0,θ0), optimal size r0, shape indexes β0 and θ0, and scaling index α (singularity exponent). These indexes characterize the entities present in an image from different angles and, therefore, can be analyzed by means of multivariate techniques to assist in image enhancement and classification. The user-friendly program prepared can be used in conjunction with GIS (Geographic Information System) software such as ArcView to implement the spatial and scaling method. It has been applied to the stream sediment geochemical data set (923 grid samples) for gold mineral exploration in the Habahe map sheet, Altay Shan, Xinjiang, northwestern China. The spatial and scaling method provides better results than the ordinary moving average method. 相似文献
17.
Gui Zhen Men 《Mathematical Geology》1991,23(1):71-76
Hundreds of samples and 17 variables collected from coalfields of major coal-bearing strata over China except for Tibet and Taiwan, were used in this study. The dry, ash-free basis volatile matter (V
r) and caking index (G
(RI)) were chosen by means of correlation analysis and stepwise discriminatory analysis as major indices of a new classification. By means of the optimum section, the boundary value of the axis of ordinate (G
(RI)) and axis of abscissas (V
r) can be determined in the classification system. Thus, aV
r –G
(RI) classification scheme diagram was formed and bituminous coal was divided into nine classes. Use of correspondence analysis reduced dimensions of sample-expressive space without losing initial information. The trend on the factor surface of samples shows that the classification obtained from correspondence analysis conforms to theV
r –G
(RI) classification result and further verified the dependability of classification by two indices. At the same time, a certain relationship between the properties of a great variety of coal and their attributes can be explained. Hence, bituminous coal classification becomes more scientific, reasonable, and practical than before. 相似文献
18.
Typically, datasets originated from mining exploration sites, industrially polluted and hazardous waste sites are correlated spatially over the region under investigation. Ordinary kriging (OK) is a well-established geostatistical tool used for predicting variables, such as precious metal contents, biomass, species counts, and environmental pollutants at unsampled spatial locations based on data collected from the neighboring sampled locations at these sites. One of the assumptions required to perform OK is that the mean of the characteristic of concern is constant for the entire region under consideration (e.g., there is no spatial trend present in the contaminant distribution across the site). This assumption may be violated by dalasets obtained from environmental applications. The occurrence of spatial trend in a dataset collected from a polluted site is an indication of the presence of two or more statistical populations (strata) with significantly different mean concentrations. Use of OK in these situations can result in inaccurate kriging estimates with higher SDs which, in turn, can lead to incorrect decisions regarding all subsequent environmental monitoring and remediation activities. A univariate and a multivariate approach have been described to identify spatial trend that may be present at the site. The trend then is removed by subtracting the respective means from the corresponding populations. The results of OK before and after trend removal are being compared. Using a real dataset, it is shown that standard deviations (SDs) of the kriging estimates obtained after trend removal are uniformly smaller than the corresponding SDs of the estimates obtained without the trend removal. 相似文献
19.
Geological data frequently have a heavy-tailed normal-in-the-middle distribution, which gives rise to grade distributions that appear to be normal except for the occurrence of a few outliers. This same situation also applies to log-transformed data to which lognormal kriging is to be applied. For such data, linear kriging is nonrobust in that (1)kriged estimates tend to infinity as the outliers do, and (2)it is also not minimum mean squared error. The more general nonlinear method of disjunctive kriging is even more nonrobust, computationally more laborious, and in the end need not produce better practical answers. We propose a robust kriging method for such nearly normal data based on linear kriging of an editing of the data. It is little more laborious than conventional linear kriging and, used in conjunction with a robust estimator of the variogram, provides good protection against the effects of data outliers. The method is also applicable to time series analysis. 相似文献