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  • Articles  (15)
  • factor analysis  (9)
  • mineralogy  (6)
  • Springer  (15)
  • American Meteorological Society
  • 1970-1974  (15)
  • Geosciences  (15)
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  • Articles  (15)
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Keywords
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  • Springer  (15)
  • American Meteorological Society
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  • 1
    Electronic Resource
    Electronic Resource
    An empirical discriminant method applied to sedimentary-rock classification from major-element geochemistry (1971)
    Springer
    Mathematical geology 3 (1971), S. 51-60 
    Details
    ISSN: 1573-8868
    Keywords: entropy ; principal components analysis ; geochemistry ; mineralogy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Classification of sandstones, greywackes, pelites, limestones, dolomites, and acid-igneous and basicigneous rocks, using a literature sample of 183 post-1920 analyses for the 11 major oxides has achieved an 80-percent success rate. The method is based on nonparametric estimation of a probability density function for each category to be classified, using the Bayes decision rule. The method is suitable for use with small training sets and gives much improved results over a linear discriminant function. Classification following data compression using principal components also has given satisfactory recognition rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047432
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  • 2
    Electronic Resource
    Electronic Resource
    An algorithm andFortran-iv program for large-scaleQ-mode factor analysis and calculation of factor scores (1971)
    Springer
    Mathematical geology 3 (1971), S. 61-77 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; principal components analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An algorithm andFortran-iv computer program,cabfac, forQ-mode factor analysis is described. The program will accept up to 1500 items and 50 variables on a moderate-size computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047433
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  • 3
    Electronic Resource
    Electronic Resource
    Computer program to analyze directional data, based on the methods of Fisher and Watson (1972)
    Springer
    Mathematical geology 4 (1972), S. 177-202 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; factor analysis ; mapping ; statistics ; petrology ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Based on the methods of Fisher and Watson,Fortran iv computer programs are presented for the following analyses of directional observations on the sphere: (1) to determine if points are randomly distributed; (2) to estimate the azimuth and inclination of the center (mean direction) of a cluster and to estimate the precision (closeness) with which points are clustered; (3) to determine if two or more clusters have the same mean direction; (4) to determine if two clusters have the same precision of clustering; and (5) to locate the pole of a greatcircle girdle of points. Limitations of these analyses for undirected directional observations on the hemisphere also are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311717
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  • 4
    Electronic Resource
    Electronic Resource
    Counting error in petrographic point-count analysis: A theoretical and experimental study (1971)
    Springer
    Mathematical geology 3 (1971), S. 15-41 
    Details
    ISSN: 1573-8868
    Keywords: modal analysis ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The binomial model, commonly used to estimate counting error in point-count analysis, misestimates this error when the observation points on a grid are positively or negatively correlated. A model, called the “cell model,” is proposed as an alternative to the binomial model for use in studies, especially with coarse-grained rocks, in which such correlation is known or thought to exist. In the new model the thin section is conceptually partitioned into a number of cells (six is recommended), and the assumption is made that the proportions in the individual cells are statistically independent and that their variance does not differ from cell to cell. Empirical relations obtained from a suite of 200 thin sections of limestones are in reasonable support of the prediction that large particle size adversely affects counting error estimates based on the binomial model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02047430
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  • 5
    Electronic Resource
    Electronic Resource
    Effect of trends on correlation in open and closed three-component systems (1972)
    Springer
    Mathematical geology 4 (1972), S. 317-330 
    Details
    ISSN: 1573-8868
    Keywords: linear correlation ; mapping ; trend analysis ; general geology ; mineralogy ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is well known among geologists that closure of an open-number system, as when stratigraphic rock thicknesses are converted to percentages, introduces correlations among the components even in the absence of correlations in the open system. In closed three-component systems the covariances are single-valued functions of the closed variances and are exactly predictable. If the open system has “inherent” correlation (point correlations) among its components the corresponding closed covariances reflect their presence in a predictable manner. If areal trends are present in the open system, the open covariances are themselves affected, but this “trend effect” can be completely removed to recover the initial point correlations among the components. Areal trends in open systems strongly influence the structure of the closed variance-covariance matrices, and the situation becomes increasingly complicated if the open system has both point correlations and areal trends. The paper considers the problems involved, and includes Monte Carlo runs to compare computed and predicted variances and covariances as data sets are followed from open systems with correlation but no trend to the closed equivalent of open systems with point correlations and trends.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114093
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  • 6
    Electronic Resource
    Electronic Resource
    Long-term growth of the oil industry in the United States (1973)
    Springer
    Mathematical geology 5 (1973), S. 237-267 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; generalized logistic curve ; Gompertz curve ; petroleum ; regression analysis ; time series ; time-trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A number of growth models have been developed and used in an attempt to project the historical pattern of oil activities to some estimate of their upper limit. Techniques are outlined for the estimation of parameters of the logistic and Gompertz curves. Factor analysis indicated a close relationship between production and demand, whereas annual discoveries and discoveries classified by year of discovery tended to comprise unique factors which were indifferent to changes in time. The growth models projected relatively high values for ultimate demand and production in comparison to the figures for ultimate reserves. Inasmuch as these trends seemed to be occurring independently, some reconciliation of the results was necessary. Using the highest projections of estimates for reserves suggests that over 420 billion barrels of oil in place will eventually be discovered in the United States, with perhaps 200 billion barrels of this eventually to be proved in the form of reserves. Projections for production were higher, corresponding to a trend indicating high levels in demand for crude oil. The only credible long-term estimate of demand was given by a bounded exponential growth model, in which ultimate cumulative demand for crude oil would reach about 416 billion barrels. These figures imply that over 150 billion barrels of oil would be imported into the United States from 1970 to 2070. Provided the time pattern for one of the variables has been determined, then estimates of the other variables probably would be facilitated because of the high interrelationship between variables. Models are suggested in which accurate pivotal forecasting in the short term might be possible—assuming the particular future trend in some of the “independent” variables has been predetermined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111813
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  • 7
    Electronic Resource
    Electronic Resource
    Application of factor analysis to classification of engineering-geological environments (1974)
    Springer
    Mathematical geology 6 (1974), S. 17-31 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; factor analysis ; engineering geology ; soils
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The engineering-geological environment, as any other geological environment, can be described by a number of variables. A clustering of those variables or clustering of their quantities makes it possible to divide the environment into taxonomic types. It is also possible to determine factors which are functions of those variables and which characterize the environment or its parts. In this paper we have applied R-and Q-mode factor analysis to engineering-geological research, concentrating our attention on establishing criteria for subdividing an environment into various aspects by its engineering-geological characteristics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111924
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  • 8
    Electronic Resource
    Electronic Resource
    Quantitative discrimination between magmatic units of the singhbhum granite (1971)
    Springer
    Mathematical geology 3 (1971), S. 123-133 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; distance functions ; mineralogy ; petrology ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The weight-percent values of four mineralogic variables (quartz, K feldspar, color index, and muscovite) for 10 sets of granitic rocks (20–50 samples in each set) from magmatic units of the Singhbhum granite were used for (1) computation of the Mahalanobis' generalized distance functions (D 2) between all pairs of the 10 sets, (2) testing significance of the difference between the multivariate means, and (3) computation of the linear discriminant functions between all possible pairs of the sets. The 10 data sets are for six magmatic units which belong to three successive but closely related phases of emplacement. The multivariate means for all sets are significantly different except for those between two of the sets of phase I. Cluster analysis on the basis of theD 2 values enables the 10 sets to be placed into four distinct groups. Group A includes two subgroups, one of which consists of two sets representing typical members of phase I; the other subgroup includes two sets which are typical of phase II. Group B includes two sets which are typical of phase III. The other four sets do not group with the typical representatives of the three phases, probably because of certain special conditions of their emplacement. A separate series ofD 2 computation from the same data, but excluding the color index, was unsuccessful in making the four aberrant sets group with the typical members of the respective phases. Efficient LDF's could be determined for discrimination between most pairs of the 10 sets of granite rocks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045956
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  • 9
    Electronic Resource
    Electronic Resource
    Study of factors influencing variation in size characteristics of fluvioglacial sediments (1972)
    Springer
    Mathematical geology 4 (1972), S. 219-234 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Factor analysis using promax oblique rotation was used in a study of fluvioglacial sediments of Late Weichsilian (Wurm) age. The use of oblique rotation allowed a more realistic interpretation of the factors and understanding of relationships between sedimentsize classes. At the second-order level, two factors are operatable, one producing variations in the coarse-size range, the other in the fine-size range. The factors are uncorrelated and mutally unrelated. At the first-order level are six factors, four representing aspects of the second-order factor of coarse size and two representing the fine size. The factor producing the variation in the coarse size is the most important one. At the lowest level in the hierarchy scale are the individual size variables. Results show that the number of factors required to account for the variation in a sediment-size data set is a function of the scale at which the problem is examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311719
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  • 10
    Electronic Resource
    Electronic Resource
    Trend-surface analysis of distribution of some heavy minerals in shelf sediments off Mangalore, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 277-290 
    Details
    ISSN: 1573-8868
    Keywords: trend analysis ; mineralogy ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The mineralogy of the 0.062–0.125 and 0.125–0.25 mm fractions of 58 selected samples from a set of 78 samples collected at a spacing of 1–2 km in the inner shelf of Mangalore were studied. Trend-surface analysis of distribution of the heavy minerals, hornblende, muscovite, garnet, and sillimanite, were made to determine the various factors controlling the mineral-distribution patterns in the area. Parts of the area showing contrasting environments were analyzed separately to determine the relationship of the regional and local trends and the various factors controlling the trends. The linear, quadratic and cubic trends for hornblende, garnet, and sillimanite were controlled by the source, westerly river flow and southerly currents; for mica, the response to processes has been the main factor. The mineral distribution in this area is mainly the result of dynamic interaction of process and response elements and a process-response model is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114090
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  • 11
    Electronic Resource
    Electronic Resource
    The statistical zap versus the shotgun approach (1974)
    Springer
    Mathematical geology 6 (1974), S. 311-332 
    Details
    ISSN: 1573-8868
    Keywords: canonical correlation ; cluster analysis ; correlation ; discriminant analysis ; factor analysis ; multivariate analysis ; numerical taxonomy ; principal coordinates ; regression analysis ; statistics ; allometry ; eurypterids ; integration and coordination ; ontogeny ; paleontology ; relative growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Multivariate analysis is used in the search for one or more types of structure. The statistical zap applies a single method to determine one preselected type of structure. Several zaps suffice to ascertain several types of structure. The statistical shotgun represents an alternative approach. Here, a series of methods is applied to the data with the intent of ascertaining all possible types of structure that may exist. If strong structure is present, an appropriate zap will probably reveal it, and a variety of techniques will determine the same general structure. If only the main structure is required, the zap is adequate. In this situation, the shotgun will display a basic consistency which is at least reassuring. However, zaps may fail to detect a more subtle secondary structure of geological interest which will be displayed by the shotgun. For weakly structured data, a zap will only determine one type of structure but the shotgun reveals all. Study of the ontogeny of Parastylonurus myops(Clarke), a Lower Silurian eurypterid from New York (USA) shows the virtues of the statistical shotgun.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082354
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  • 12
    Electronic Resource
    Electronic Resource
    Factor analysis: How it copes with complex geological problems (1973)
    Springer
    Mathematical geology 5 (1973), S. 351-363 
    Details
    ISSN: 1573-8868
    Keywords: classification ; factor analysis ; mapping ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Factor analysis utilizing textural data from 81 bottom samples was used to analyze the surficial sediments covering a 40,000-sq km area, which is one input data point per 500 km. On the other hand, the surficial geology of the area studied is complex as some map units are only 1 km wide in places. Under these circumstances it is interesting to determine that factor analysis nonetheless aims toward a reasonable geological solution. If the premise is accepted that factor analysis provides a solution “best-fitted” to the data, the geologist has carried his research one step further and is left with the problem of interpreting the results of factor analysis correctly. In this experiment, the interpretation of the factors representing the gravel and the mud is relatively simple, although the two factors representing sands are more difficult to explain. The proper interpretation of factors leads naturally to an inquiry on the optimum number of factors to use, but this problem can be solved objectively by considering the factor loadings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111986
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  • 13
    Electronic Resource
    Electronic Resource
    Foraminiferal associations of the Mid-Tertiary Edegem Sands at Terhagen, Belgium (1974)
    Springer
    Mathematical geology 6 (1974), S. 1-15 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; paleoecology ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A factor-analytic approach (varimax rotated factors) was used in studying the benthonic foraminiferal associations of the Mid-Tertiary Edegem Sands at Terhagen (near Antwerpen) Belgium. The fauna can be described by two groups. The lower and upper part of the stratigraphic section are characterized by one group and the middle transitional part by a second group. The results can be correlated with the number of the planktonic forms and with the fossil richness of the sediment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111923
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  • 14
    Electronic Resource
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    A geomathematic investigation of syntexis in a Gabbroic formation (1973)
    Springer
    Mathematical geology 5 (1973), S. 321-339 
    Details
    ISSN: 1573-8868
    Keywords: factor analysis ; Fourier analysis ; mapping ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Mathematical methods were employed in an investigation of syntexis in the “Gabbro di Sondalo,” a mafic igneous formation in the Central Alps (Italy). A set of 100 specimens was selected according to sampling criteria and analyzed by X-ray fluorescence for eight elements; Q-mode and R-mode factor analysis then was applied to these data. Results of the computations indicate that the general trend of differentiation is related to the syntexis of gneissic wall rocks (“Gneiss del Monte Tonale”) in the mafic melt. Ca and Mg are abundant in the gabbro, and Si and K in the gneiss; the independent variation trend of Fe and Ti may be related to a differentiation episode due to a magmatic phase. Spatial representation of multivariate data on differentiation also was performed on the main elements and a picture of the trend of syntexis was mapped.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111984
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  • 15
    Electronic Resource
    Electronic Resource
    Operator error in petrographic point-count analysis: A theoretical approach (1972)
    Springer
    Mathematical geology 4 (1972), S. 35-43 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Operator error in petrographic point-count analysis introduces bias into the estimates of proportion in a thin section. A correction for this bias, leading to an unbiased estimator of the true proportion in that thin section, is here proposed. Operator error also affects the confidence interval, and in this situation, too, an adjustment is possible. The approach proposed requires that the probabilities associated with operator error, categorized into A-type and B-type errors, are known or assumed. The A-type operator error tends to underestimate the true proportion in a thin section, whereas the B-type operator error tends to overestimate it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083191
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