共查询到20条相似文献，搜索用时 62 毫秒
1.
Noel Cressie 《Mathematical Geology》1987,19(5):425-449
Fitting trend and error covariance structure iteratively leads to bias in the estimated error variogram. Use of generalized increments overcomes this bias. Certain generalized increments yield difference equations in the variogram which permit graphical checking of the model. These equations extend to the case where errors are intrinsic random functions of order k, k=1, 2, ..., and an unbiased nonparametric graphical approach for investigating the generalized covariance function is developed. Hence, parametric models for the generalized covariance produced by BLUEPACK-3D or other methods may be assessed. Methods are illustrated on a set of coal ash data and a set of soil pH data. 相似文献
2.
Roussos Dimitrakopoulos 《Mathematical Geology》1990,22(3):361-380
Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rn; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada. 相似文献
3.
Roussos Dimitrakopoulos 《Mathematical Geosciences》1990,22(3):361-380
Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rn; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada. 相似文献
4.
Pilar García-Soidán Raquel Menezes Óscar Rubiños-López 《Environmental Earth Sciences》2012,66(2):615-624
The use of kriging for construction of prediction or risk maps requires estimating the dependence structure of the random
process, which can be addressed through the approximation of the covariance function. The nonparametric estimators used for
the latter aim are not necessarily valid to solve the kriging system, since the positive-definiteness condition of the covariance
estimator typically fails. The usage of a parametric covariance instead may be attractive at first because of its simplicity,
although it may be affected by misspecification. An alternative is suggested in this paper to obtain a valid covariance from
a nonparametric estimator through the Fourier series tool, which involves two issues: estimation of the Fourier coefficients
and selection of the truncation point to determine the number of terms in the Fourier expansion. Numerical studies for simulated
data have been conducted to illustrate the performance of this approach. In addition, an application to a real environmental
data set is included, related to the presence of nitrate in groundwater in Beja District (Portugal), so that pollution maps
of the region are generated by solving the kriging equations with the use of the Fourier series estimates of the covariance. 相似文献
5.
Chunsheng Ma 《Mathematical Geosciences》2012,44(6):765-778
This paper presents the characterization of the covariance matrix function of a Gaussian or second-order elliptically contoured vector random field on the sphere which is stationary, isotropic, and mean square continuous. This characterization involves an infinite sum of the products of positive definite matrices and Gegenbauer??s polynomials, and may not be available for other non-Gaussian vector random fields on spheres such as a ?? 2 or log-Gaussian vector random field. We also offer two simple but efficient constructing approaches, and derive some parametric covariance matrix structures on spheres. 相似文献
6.
This paper is concerned with vector random fields on spheres with second-order increments, which are intrinsically stationary and mean square continuous and have isotropic variogram matrix functions. A characterization of the continuous and isotropic variogram matrix function on a sphere is derived, in terms of an infinite sum of the products of positive definite matrices and ultraspherical polynomials. It is valid for Gaussian or elliptically contoured vector random fields, but may not be valid for other non-Gaussian vector random fields on spheres such as a χ 2, log-Gaussian, or skew-Gaussian vector random field. Some parametric variogram matrix models are derived on spheres via different constructional approaches. A simulation study is conducted to illustrate the implementation of the proposed model in estimation and cokriging, whose performance is compared with that using the linear model of coregionalization. 相似文献
7.
Spatio-Temporal Covariance Functions Generated by Mixtures 总被引：2，自引：0，他引：2
Chunsheng Ma 《Mathematical Geology》2002,34(8):965-975
Spatio-temporal covariance functions are introduced in this paper by using two approaches: (1) positive power mixture of purely spatial and purely temporal covariances, and (2) scale mixture of purely spatial and purely temporal covariances. Various parametric and nonparametric families of nonseparable spatio-temporal covariance functions are obtained with appropriate selections of the mixing function and covariances being mixed. 相似文献
8.
A procedure is proposed that employs first-moment estimation (kriging), cross-validation, and response surface analysis to estimate parameters of a generalized covariance function. Results from application of this procedure to two data sets are given. 相似文献
9.
Based on historical and observational data of wet-and-low water resource changes, this article used the rescaled range (R/S) analysis principle and method to calculate the H index and establish the relation formula of R(i)/S(i) and i. Based on {x i }, and by using the least squares method, a new time series calculation method was proposed which endows the Brownian motion equation with forecasting abilities. This is a new attempt to forecast trend changes of water resources. Utilizing the time series data of water resources in Jinhua City, China, and the Brownian motion equation, aforecast was made of future trends in wet-and-low water resource changes. Satisfactory validation results were obtained, which indicate that this is an effective method for forecasting water resource changes. 相似文献
10.
A method for determining the reversibility of a Markov sequence 总被引：1，自引：0，他引：1
This paper describes, given a tally matrix with strictly positive entries, a method to determine whether the associated Markov process is reversible, and (for reversible Markov processes) methods to compute the reversibility matrix from the tally matrix. If the tally matrixN is symmetric, then it is shown that the Markov process must be reversible and the reversibility matrixC equalss (R
–1NR–1), whereR is the diagonal matrix whosei
th diagonal entry is the sum of the entries of thei
th row ofN (for everyi) ands denotes the sum of all the entries ofN. Because a symmetric tally matrix is of special importance in applications, a 2 test is proposed for determining, in the presence of experimental errors, whether such a matrix is symmetric. 相似文献
11.
The impact of using an incorrect covariance function on kriging predictors is investigated. Results of Stein (1988) show that the impact on the kriging predictor from not using the correct covariance function is asymptotically negligible as the number of observations increases if the covariance function used is compatible with the actual covariance function on the region of interestR. The definition and some properties of compatibility of covariance functions are given. The compatibility of generalized covariances also is defined. Compatibility supports the intuitively sensible concept that usually only the behavior near the origin of the covariance function is critical for purposes of kriging. However, the commonly used spherical covariance function is an exception: observations at a distance near the range of a spherical covariance function can have a nonnegligible effect on kriging predictors for three-dimensional processes. Finally, a comparison is made with the perturbation approach of Diamond and Armstrong (1984) and some observations of Warnes (1986) are clarified. 相似文献
12.
Multivariate Intrinsic Random Functions for Cokriging 总被引：2，自引：0，他引：2
In multivariate geostatistics, suppose that we relax the usual second-order-stationarity assumptions and assume that the component
processes are intrinsic random functions of general orders. In this article, we introduce a generalized cross-covariance function
to describe the spatial cross-dependencies in multivariate intrinsic random functions. A nonparametric method is then proposed
for its estimation. Based on this class of generalized cross-covariance functions, we give cokriging equations for multivariate
intrinsic random functions in the presence of measurement error. A simulation is presented that demonstrates the accuracy
of the proposed nonparametric estimation method. Finally, an application is given to a dataset of plutonium and americium
concentrations collected from a region of the Nevada Test Site used for atomic-bomb testing. 相似文献
13.
Computationally efficient restricted maximum likelihood estimation of generalized covariance functions 总被引：1，自引：0，他引：1
Dale L. Zimmerman 《Mathematical Geology》1989,21(7):655-672
Computational aspects of the estimation of generalized covariance functions by the method of restricted maximum likelihood (REML) are considered in detail. In general, REML estimation is computationally intensive, but significant computational savings are available in important special cases. The approach taken here restricts attention to data whose spatial configuration is a regular lattice, but makes no restrictions on the number of parameters involved in the generalized covariance nor (with the exception of one result) on the nature of the generalized covariance function's dependence on those parameters. Thus, this approach complements the recent work of L. G. Barendregt (1987), who considered computational aspects of REML estimation in the context of arbitrary spatial data configurations, but restricted attention to generalized covariances which are linear functions of only two parameters. 相似文献
14.
Smoothing and interpolation by kriging and with splines 总被引：1，自引：0，他引：1
G. S. Watson 《Mathematical Geology》1984,16(6):601-615
Let scalar measurements at distinct points x1, , xn
be y1, , yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem. 相似文献
15.
黄锦江 《中国地球化学学报》1993,12(4):373-380
On the basis of the previous quantitative modeling of trace element behavior in magmatic pro-cesses such as fractional crystallization ,batch melting and magma mixing,the author has shown the covariance relationship between compatible and incompatible elements. The discussion of the covariance relationship among trace elements indicates that the covariance relationship can be used to study the petrogenesis of igneous rocks and that the relationship be-tween compatible and incompatible elements are most important in distinguishing equilibrium process(melting and crystallization )from other magmatic processes, i.e.,the former shows a hyperbola trend on C1^i vs .C1^i diagrams,and however, the fractional process gives an exponent curve and magma mixing presents a straight line .On the other hand ,log C1^i vs .C1^i diagrams are also discussed here. Alkaline rocks from Zijinshan, Lin County, Shanxi Province are taken for example in our study ,indicating that the rocks were derived from batch melting of the upper mantle. 相似文献
16.
Simulation of geological surfaces using fractals 总被引：2，自引：0，他引：2
Methods suggested in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is introduced here which is a generalization of the subdivision method used in fractals. This method is based on the construction of a fractal plane-to-line functionf(x, y, R, e, u), where(x, y) is in[a, b]×[c, d], R is the autocorrelation function,e is the resolution limit, andu is a random real function on [–1, 1]. The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in bothx andy directions is smaller than a prespecified resolution. If thex coordinate of theith quadrilateral is in[a
i
,b
i
] and they coordinate is in[c
i
,d
i
], the growth of this quadrilateral is a function of(b
i
–a
i
) and(d
i
–c
i
); the quadrilateral could grow toward the positive or negativez axis with equal probability forming four new quadrilaterals having a common vertex.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987. 相似文献
17.
Raymond G. Vugrinovich 《Mathematical Geology》1981,13(5):443-454
A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n – 1)/2 slope estimators, which may be calculated by inserting pairs of points (X
i, Yi)and (X
j, Yj)into the slope formula S
i = (Y
i – Yj)/(X
i – Xj),1 i < j n Once S
m is determined, outliers may be detected by calculating the residuals given by Ri = Yi – SmXi where 1 i n, and chosing the median Rm. Outliers are defined as points for which |Ri – Rm| > k (median {|R
i – Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques. 相似文献
18.
Role of coal type and rank on methane sorption characteristics of Bowen Basin, Australia coals 总被引：5，自引：0，他引：5
The effect of coal composition, particularly the organic fraction, upon gas sorption has been investigated for Bowen Basin and Sydney Basin, Australia coals. Maceral composition influences on gas retention and release were investigated using isorank pairs of hand-picked bright and dull coal in the rank range of high volatile bituminous (0.78% Ro max) to anthracite (3.01% Ro max). Adsorption isotherm results of dry coals indicated that Langmuir volume (VL) for bright and dull coal types followed discrete, second-order polynomial trends with increasing rank. Bright coals had a minimum VL at 1.72% Ro max and dull coals had a minimum VL at 1.17% Ro max. At low rank, VL was greater in bright coal by about 10 cm3/g, but as rank increased, the bright and dull trends converged and crossed at 1.65% Ro max. At ranks higher than 1.65% Ro max, both bright and dull coals followed similar trends. These competing trends mean that the importance of maceral composition on VL varies according to rank. In high volatile bituminous coals, increases in vitrinite content are associated with increases in adsorption capacity. At ranks higher than medium to low volatile bituminous, changes in maceral composition may exert relatively little influence on adsorption capacity. The Langmuir pressure (PL) showed a strong relationship of decreasing PL with increasing rank, which was not related to coal type. It is suggested that the observed trend is related to a decrease in the heterogeneity of the pore surfaces, and subsequent increased coverage by the adsorbate, as coal rank increases. Desorption rate studies on crushed samples show that dull coals desorb more rapidly than bright coals and that desorption rate is also a function of rank. Coals of lower rank have higher effective diffusivities. Mineral matter was found to have no influence on desorption rate of these finely crushed samples. The evolution of the coal pore structure with changing rank is implicated in diffusion rate differences. 相似文献
19.
Richard Arthur Reyment 《Mathematical Geology》1969,1(2):185-197
A method of analysis of covariance structure proposed by A. P. Dempster complements, in some respects, a recently suggested procedure by the author. The method is based on the comparison of ratios of generalized statistical distances and distancelike quantities. An analysis of septivariate data on the foraminiferTextilina mexicana (Cushman) shows general differences in covariance structure in which the sample rest linear discriminators also differ. This difference in covariance structure is thought to be genetic in origin. Two species of Middle Devonian brachiopods,Martinia inflata (Schnur) andUncites gryphus von Schlotheim), also show differences in covariance structure—the former slightly, the latter strongly. This is further analyzed forUncites by the author's methods and good agreement between the two approaches obtained. 相似文献
20.
Richard Arthur Reyment 《Mathematical Geosciences》1969,1(2):185-197
A method of analysis of covariance structure proposed by A. P. Dempster complements, in some respects, a recently suggested procedure by the author. The method is based on the comparison of ratios of generalized statistical distances and distancelike quantities. An analysis of septivariate data on the foraminiferTextilina mexicana (Cushman) shows general differences in covariance structure in which the sample rest linear discriminators also differ. This difference in covariance structure is thought to be genetic in origin. Two species of Middle Devonian brachiopods,Martinia inflata (Schnur) andUncites gryphus von Schlotheim), also show differences in covariance structure—the former slightly, the latter strongly. This is further analyzed forUncites by the author's methods and good agreement between the two approaches obtained. 相似文献