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  • geochemistry
  • kriging
  • petrology
  • Springer  (15)
  • American Chemical Society (ACS)
  • Periodicals Archive Online (PAO)
  • Wiley-Blackwell
  • 2020-2024
  • 2015-2019
  • 1980-1984  (12)
  • 1970-1974  (3)
  • 1965-1969
  • 1935-1939
  • 1925-1929
  • 1984  (12)
  • 1974  (3)
Collection
Keywords
Publisher
  • Springer  (15)
  • American Chemical Society (ACS)
  • Periodicals Archive Online (PAO)
  • Wiley-Blackwell
Years
  • 2020-2024
  • 2015-2019
  • 1980-1984  (12)
  • 1970-1974  (3)
  • 1965-1969
    • +
Year
  • 1
    Electronic Resource
    Electronic Resource
    Some problems of interpreting the correlations between the modal variables in granitic rocks (1974)
    Springer
    Mathematical geology 6 (1974), S. 245-258 
    Details
    ISSN: 1573-8868
    Keywords: correlation between proportions ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Correlation coefficients of modal variables from several suites of granitic rocks have been calculated and tested for significance using the Chayes-Kruskal and Chayes methods. The results show that although Chayes' remaining-space transformation does, in general, weaken the original proportion correlations, the positive and low-negative original proportion correlations tend to increase in absolute value because of a tendency of positive increment of the covariance by such transformation. However, no satisfactory procedure for choosing the variable to be transformed (V2)could be determined, and testing of the significance of remaining-space correlations is found to be highly problematic. It is shown also that the Vistelius-Sarmanov procedure of calculation of correlation coefficients from closed-table data does not effectively eliminate the closure effect. It is concluded that assigning statistical significance to the correlation coefficients between modal variables is, in general, unsatisfactory, except where the number of variables ⩾8,the sample size is large (say, ⩾30),and there is no negative element in the variance vector of the corresponding open variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082890
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  • 2
    Electronic Resource
    Electronic Resource
    Application of some correlation coefficient techniques to time-series analysis (1974)
    Springer
    Mathematical geology 6 (1974), S. 363-372 
    Details
    ISSN: 1573-8868
    Keywords: autocorrelation ; crosscorrelation ; time series ; geochemistry ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Application of the sliding correlation technique has permitted detailed stratigraphic correlation over entire basins. The main values of the technique are to (1) demonstrate correlation statistically, (2) extend the range of visual correlation, and (3) establish precise correlation where correlation is known to exist but is difficult to establish visually. The technique is especially valuable in aiding correlation of stratigraphic sequences such as varves and turbidites, which are characterized by monotonous repetition of two or more lithologic components. The moving correlation technique is a valuable aid in examining variations in degree of correlation between correlative sections, and in analysis of component associations within a single stratigraphic sequence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082357
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  • 3
    Electronic Resource
    Electronic Resource
    Robust kriging—A proposal (1984)
    Springer
    Mathematical geology 16 (1984), S. 3-18 
    Details
    ISSN: 1573-8868
    Keywords: Geostatistics ; kriging ; robust estimation ; time series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036237
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  • 4
    Electronic Resource
    Electronic Resource
    The statistical analysis of geochemical compositions (1984)
    Springer
    Mathematical geology 16 (1984), S. 531-564 
    Details
    ISSN: 1573-8868
    Keywords: Closure ; closed number system ; logistic ; logratio ; geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The analysis and interpretation of compositional data, such as major oxide compositions of rocks, has been traditionally plagued by the so-called constant-sum or closure problem. Particular difficulties have been the lack of a satisfactory, interpretable covariance structure and of rich, tractable, parametric classes of distributions on the simplex sample space. Consideration of logistic and logratio transformations between the simplex and Euclidan space has allowed the introduction of new concepts of covariance structure and of classes of logistic-normal distributions which have now opened up a substantial and meaningful array of statistical methodology for compositional data. From the motivation of a wide variety of practical geological problems we examine the range of possibilities with this new approach to the constant-sum problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029316
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  • 5
    Electronic Resource
    Electronic Resource
    Smoothing and interpolation by kriging and with splines (1984)
    Springer
    Mathematical geology 16 (1984), S. 601-615 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; splines ; interpolation ; smoothing ; prediction ; Green's function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029320
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  • 6
    Electronic Resource
    Electronic Resource
    Cokriging of aquifer transmissivities from field measurements of transmissivity and specific capacity (1984)
    Springer
    Mathematical geology 16 (1984), S. 19-35 
    Details
    ISSN: 1573-8868
    Keywords: groundwater ; geostatistics ; cokriging ; kriging ; transmissivity ; specific capacity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper presents a new application of the cokriging technique for constructing maps of aquifer transmissivity from field measurements of transmissivity and specific capacity. The technique is illustrated using data from Yolo Basin, California. Cokriging is well-suited for estimating undersampled variables. To improve the accuracy of the estimation, cokriging considers the spatial auto-correlation of the variable to be estimated and the spatial cross-correlation between the variable to be estimated and other, better-sampled variables. Consequently, in regions that lack data of the variable to be estimated, accurate estimation can still be made on the basis of auto- and cross-correlation. In addition, estimation variances can be obtained with a little additional computation effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01036238
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  • 7
    Electronic Resource
    Electronic Resource
    A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California (1984)
    Springer
    Mathematical geology 16 (1984), S. 125-137 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; cokriging ; hydrology ; groundwater
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032212
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  • 8
    Electronic Resource
    Electronic Resource
    Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels (1984)
    Springer
    Mathematical geology 16 (1984), S. 499-521 
    Details
    ISSN: 1573-8868
    Keywords: Spatial variability ; nonintrinsic ; nonstationary ; drift ; kriging ; residuals ; groundwater levels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A method for obtaining pointwise or spatially averaged estimates of a nonintrinsic function is introduced based on residual kriging. The method relies on a stepwise iterative regression process for simultaneously estimating the global drift and residual semivariogram. Estimates of the function are then obtained by solving a modified set of simple kriging equations written for the residuals. The modification consists of replacing the true variogram in the kriging equations by the variogram of the residual estimates as obtained from the iterative regression process. The method is illustrated by considering groundwater levels in an Arizona aquifer. The results are compared with those obtained for the aquifer by the generalized covariance package BLUEPACK-3D.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01886329
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  • 9
    Electronic Resource
    Electronic Resource
    Kriging in a global neighborhood (1984)
    Springer
    Mathematical geology 16 (1984), S. 249-265 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; moving neighborhood ; global neighborhood ; geostatistics ; automatic contouring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032690
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  • 10
    Electronic Resource
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    Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till (1984)
    Springer
    Mathematical geology 16 (1984), S. 283-301 
    Details
    ISSN: 1573-8868
    Keywords: Bayesian classifiers ; classification ; cluster analysis ; cluster validity ; fuzzyc means ; fuzzyc varieties ; fuzzy covariances ; geochemical prospecting ; glacial till ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract To evaluate the provenance of glacial till, the trace element content of magnetite was used. Magnetite was present in all known rock types and all till samples in the area investigated. By using fuzzy-set theory it was possible to group samples of magnetite taken from bedrock into relatively homogeneous and geologically meaningful groups and also, by fuzzy classification, to relate the till samples to the rocks in such a way that the relative contribution of each rock type to the till is estimated. Each rock and till sample is assigned a membership value between 0 and 1 for each rock type. The membership values, for a certain rock type in the till, are then interpolated by kriging onto maps. Magnetites from skarns associated with sulfide ores especially are rather distinct, and so a map of such membership values for till unveils all known ore deposits some 1–5 km “downstream”in the general direction of the ice flow. Other anomalies show up which cannot be related to hitherto known ores or mineralizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01032692
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