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  • Articles  (27)
  • statistics  (23)
  • paleontology  (8)
  • Springer  (27)
  • American Meteorological Society
  • 1970-1974  (27)
  • Geosciences  (27)
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  • Articles  (27)
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  • Springer  (27)
  • American Meteorological Society
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  • 1
    Electronic Resource
    Electronic Resource
    Statistical considerations for grain-size analyses of tills (1971)
    Springer
    Mathematical geology 3 (1971), S. 227-238 
    Details
    ISSN: 1573-8868
    Keywords: classification ; data processing ; graphics ; mapping ; mathematics ; plotting ; sampling ; statistics ; sedimentology ; stratigraphy ; grain-size analysis ; textural analysis ; glacial geology ; Pleistocene stratigraphy ; till
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Relative percentages of sand, silt, and clay from samples of the same till unit are not identical because of different lithologies in the source areas, sorting in transport, random variation, and experimental error. Random variation and experimental error can be isolated from the other two as follows. For each particle-size class of each till unit, a standard population is determined by using a normally distributed, representative group of data. New measurements are compared with the standard population and, if they compare satisfactorily, the experimental error is not significant and random variation is within the expected range for the population. The outcome of the comparison depends on numerical criteria derived from a graphical method rather than on a more commonly used one-way analysis of variance with two treatments. If the number of samples and the standard deviation of the standard population are substituted in at-test equation, a family of hyperbolas is generated, each of which corresponds to a specific number of subsamples taken from each new sample. The axes of the graphs of the hyperbolas are the standard deviation of new measurements (horizontal axis) and the difference between the means of the new measurements and the standard population (vertical axis). The area between the two branches of each hyperbola corresponds to a satisfactory comparison between the new measurements and the standard population. Measurements from a new sample can be tested by plotting their standard deviation vs. difference in means on axes containing a hyperbola corresponding to the specific number of subsamples used. If the point lies between the branches of the hyperbola, the measurements are considered reliable. But if the point lies outside this region, the measurements are repeated. Because the critical segment of the hyperbola is approximately a straight line parallel to the horizontal axis, the test is simplified to a comparison between the means of the standard population and the means of the subsample. The minimum number of subsamples required to prove significant variation between samples caused by different lithologies in the source areas and sorting in transport can be determined directly from the graphical method. The minimum number of subsamples required is the maximum number to be run for economy of effort.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045793
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  • 2
    Electronic Resource
    Electronic Resource
    Statistical analysis of tectonic patterns in areal volcanism: The bunyaruguru volcanic field in West Uganda (1971)
    Springer
    Mathematical geology 3 (1971), S. 335-355 
    Details
    ISSN: 1573-8868
    Keywords: nearest neighbor analysis ; regression analysis ; statistics ; trend analysis ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A quantitative analysis was made of the spatial arrangement of 149explosion craters in the western rift of Uganda. A variety of methods demonstrate that the spatial pattern of the craters reveals significant structural patterns that have guided volcanism to the surface. It is shown that the east-west elements in the field affected location, and the main rift fault is resolved into two main components. Tentatively, a possible dextral transform fault is identified that affected the relative location of the two main zones of activity. Grouping techniques demonstrate that crater groups obey an exponential rank-size rule and allow a mapping of the craters into energy classes that reveals a concentric pattern of energy in the field. The effect of the topography on energy levels and crater size show that only topography greater than 11,000ft could have prevented all eruptive activity, but the smaller energies and craters are sensitive to height differences on the order of the height of the rift wall, about 1000ft. Total energy in each crater class size is roughly constant, and the field energy could create one or two single craters comparable in size to small central volcanoes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083356
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical classification applied to certain Jamaican eocene nummulitids (1971)
    Springer
    Mathematical geology 3 (1971), S. 297-311 
    Details
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; numerical taxonomy ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Eighty-eight specimens of Eocene nummulitids from the Yellow Limestone Formation of northwestern Jamaica are classified according to quantitative measurements of morphologic parameters that are generally considered to be taxonomically useful. The specimens are grouped into homogeneous classes by the computer screening of differently oriented data projections. By this method, the use of similarity coefficients and the question of a priori weighting of characters, for which numerical taxonomy has been heavily criticized, are both avoided. The stability of the classes thus obtained is validated by discriminant analysis. These techniques provide an objective view of phenetic differences among specimens and show how the measured characters produce those differences. Tightness of coiling and total number of whorls, prove to be the most useful features in discriminating between groups but seem to have taxonomic value only at the specific and not at the generic level. This suggests that the generaOperculinoides andNummulites are synonymous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045797
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  • 4
    Electronic Resource
    Electronic Resource
    A generalized set of discrete frequency distributions with Fortran program (1972)
    Springer
    Mathematical geology 4 (1972), S. 1-24 
    Details
    ISSN: 1573-8868
    Keywords: discrete frequency distributions ; statistics ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geologists unfamiliar with the application of probability theory to discrete data in other fields of research are usually acquainted with only three discrete theoretical frequency distributions: Poisson, binomial, and negative binomial distributions. In some situations these distributions may fail to adequately describe a set of experimental data. Other distributions such as the Poisson with zeros, Neyman type A, logarithmic with zeros, Poisson-binomial, and Thomas double Poisson together with the more common Poisson, binomial, and negative binomial form a generalized subset of discrete theoretical distributions, one of which should fit almost any experimental data set. A computer program is presented which allows testing of any combination of these distributions against observed discrete data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083189
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  • 5
    Electronic Resource
    Electronic Resource
    Geostatistical investigations of gabbro occurrences near Savantvadi, Ratnagiri district, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 147-153 
    Details
    ISSN: 1573-8868
    Keywords: classification ; statistical inference ; statistics ; geochemistry ; petrochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract This paper embodies petrographical and statistical investigations of three gabbro occurrences. The Mangaon and Kunkeri gabbros are similar in petrography and petrochemistry, whereas they are completely different from the Vajrat gabbro. Application of recently developed statistical tests help in classifying these gabbros by using three oxides, CaO, FeO, and K2O.This study shows that the evolution of the Mangaon and Kunkeri gabbros probably proceeded along different lines as compared to the Vajrat gabbro.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080299
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  • 6
    Electronic Resource
    Electronic Resource
    Multiple regression with correlated independent variables (1972)
    Springer
    Mathematical geology 4 (1972), S. 203-218 
    Details
    ISSN: 1573-8868
    Keywords: correlated independent variables ; regression analysis ; ridge trace ; statistics ; trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Multiple linear regression analysis may be used to describe the relation of one geologic variable to a number of other (independent) variables, and also may be used to fit a trend surface to geographically distributed variables. The leastsquares estimates of the regression coefficients differ unpredictably from the true coefficients if the independent variables are correlated. The estimates can be too large in absolute value, and may have the wrong sign. Also, the least-squares solution may be unstable in that replicate samples can give widely differing values of the regression coefficients. Ridgeregression analysis is a technique for removing the effect of correlations from the regression analysis. The procedure involves addition of a small constant K to the diagonal elements of the standardized covariance matrix. The estimates obtained are biased but have smaller sums of squared deviations between the coefficients and their estimates. The ridge trace, a plot of the coefficients versus K, helps determine the value of K that stabilizes the estimates. Correlations between geologic variables are common, and regression coefficients based on these data may be suspect. In trendsurface analysis, correlations between the geographic coordinates may differ widely, and extreme correlations may be introduced if higher order terms are used in the trend. Ridgeregression analysis serves to guide the geologist to a more reliable interpretation of the results of multiple regression if the independent variables are correlated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311718
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    General equations for volume and surface area of a logarithmically coiled shell (1972)
    Springer
    Mathematical geology 4 (1972), S. 307-316 
    Details
    ISSN: 1573-8868
    Keywords: mathematics ; paleoecology ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The equations of Moseley for the volume and surface area of a coiled shell have been rewritten in their most general forms. The general volume equation has been tested with 15 gastropods and found to give satisfactory results wherever there are no significant ontogenetic changes in the shell geometry. The equations provide a means for calculating the carbonate efficiency of a coiled shell. With this parameter analyzed into its component parts, it has been possible to understand the relationships between aspects of shell calcification and environmental factors that affect calcium carbonate availability. Preliminary studies indicate that it also may be possible to discriminate morphologically between terrestrial and aquatic gastropods, the various gastropod modes of life, and higher taxonomic categories. These equations offer possibilities for other studies concerned with the ecology, paleoecology, and evolution of coiled shells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114092
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  • 9
    Electronic Resource
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    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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  • 10
    Electronic Resource
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    Preliminary assessment of a nonlinear mapping algorithm in a geological context (1973)
    Springer
    Mathematical geology 5 (1973), S. 39-57 
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    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; dimensionality reduction ; mapping ; multivariate analysis ; principal-components analysis ; general geology ; geochemistry ; paleontology ; petrology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A new algorithm has been developed by J. W. Sammon for the nonlinear-point mapping of high-dimensional data in two dimensions such that the inherent structure of the data is approximately preserved. This paper describes results using several sets of geologic data including stratigraphic thickness, petrographic modal analysis, and morphological or geochemical measurements. Comparisons are made with hierarchical cluster analysis using dendrogram representation. Initial results are encouraging and suggest that the technique could have widespread geological applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114086
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  • 11
    Electronic Resource
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    Fortran IV program for grey-level mapping of spatial data (1971)
    Springer
    Mathematical geology 3 (1971), S. 95-121 
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    ISSN: 1573-8868
    Keywords: data processing ; mapping plotting ; statistics ; general geology ; geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Afortran iv computer program for grey-level mapping of spatial data using a CDC 6600 is described. The program produces maps for irregularly distributed data in as many as 10 intensity levels which are displayed in grey tones by a lineprinter. Unlimited map size and unrestricted data input provide for as many as 5000 data points per 13-in.-wide strip of map. The program is easily modified for other installations. Examples are given of geochemical analyses of stream sediments in Northern Ireland.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045955
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  • 12
    Electronic Resource
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    Multivariate normality in morphometric analysis (1971)
    Springer
    Mathematical geology 3 (1971), S. 357-368 
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    ISSN: 1573-8868
    Keywords: multivariate analysis ; normality ; statistics ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Data on some living (salamanders and grasshoppers) and fossil (Devonian brachiopods) animals are analyzed by means of recently developed methods for the large-scale treatment of multivariate normality. Multivariate nonnormality was found to exist in all situations, even if the univariate deviations in the skewness and kurtosis statistics proved to be without significance for the most part. The effect of logarithmically transforming the data appears to be a mixed blessing. Apart from the fact that the investigator is removed one step from the biological relationships in his data by carrying out a transformation of them, the betterment in the multivariate interconnections with respect to normality tends to be slight, despite the general improvement in the univariate values. The relationship between sample size and the multivariate normality measures b1,p and b2,p are studied empirically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083357
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  • 13
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    Efficiency of regression techniques for ore valuation at Kolar Gold Fields, India (1972)
    Springer
    Mathematical geology 4 (1972), S. 25-34 
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    ISSN: 1573-8868
    Keywords: correlation ; lognormal distribution ; regression analysis ; statistics ; trend analysis ; mining ; ore valuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Kolar Gold Fields are some of the best known gold deposits in India. An example of ore valuation utilizing 49 ore blocks of the Oriental lode of the West Reefs, explored and developed in the Nundydroog mines, is given. In this reef system, there are large ore reserves of sulfidebearing quartz reefs, and the gold distribution is erratic both along strike and downdip. Ore valuation at present is based on the arithmetic mean of samples taken at peripheral positions of the blocks. Samples taken from internal portions of the blocks give a totally different picture of the value. To correct this discrepancy, normal regression and lognormal regression of internal block and total block values, over peripheral block values have been used to evaluate the deposits. The valuation efficiency criterion shows the logarithmic variance for distribution of ratios of unregressed and regressed block values with the corresponding arithmetic mean of internal stope values as observed inside the blocks. The studies have shown that the logarithmic variance is minimum if the logarithmic regression is used, thereby indicating maximum efficiency. Further, the undervaluation and overvaluation of low- and high-grade blocks is less for the logarithmic example. With help of the logarithmic regression equation an effective pay limit of 177.8 in.-dwt has been found for selective mining, for peripheral block values corresponding to the official pay limit of 240 in.-dwt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083190
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  • 14
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    Digital filtering as a tool for the study of some flysch deposits from the East Carpathians (Romania) (1972)
    Springer
    Mathematical geology 4 (1972), S. 103-113 
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    ISSN: 1573-8868
    Keywords: data processing ; graphics ; statistics ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Results from the application of digital filtering (simple and weighted averaging) to the analysis of sedimentary series are given. Two flysch sequences from the East Carpathians (Upper Eocene, Damacuşa Valley; and Lower Cretaceous, Sbrancani Valley) were studied. Individual components, affecting the conditions of deposition, were separated, and establishment of the geological significance of the components separated by digital filtering was investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080296
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  • 15
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    Ontogeny of a Miocene pelecypod (1973)
    Springer
    Mathematical geology 5 (1973), S. 73-90 
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    ISSN: 1573-8868
    Keywords: allometric equations ; correlation and regression ; principal-components analysis ; statistics ; allometric growth ; ontogeny ; paleontology ; relative growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Relative growth of the Miocene pelecypod Glycymeris parilis (Conrad) was examined using allometric equations and principal components. Different parts of the shell showed contrasting growth strategies that were dictated by functional morphology and basic shell geometry. Despite the divergent developmental strategies, 93 percent of the correlation matrix variance is accounted for by overall size increase. The remaining variance mainly represents growth of the teeth, which differed considerably from other variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114088
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  • 16
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    The statistical zap versus the shotgun approach (1974)
    Springer
    Mathematical geology 6 (1974), S. 311-332 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02082354
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  • 17
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    Broken-line and complex frequency distributions (1971)
    Springer
    Mathematical geology 3 (1971), S. 135-155 
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    ISSN: 1573-8868
    Keywords: data processing ; plotting ; statistics ; geochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Broken straight lines on probability paper have been proposed as representing the cumulative probability distributions of SiO2, Na, and Cl in certain plutons. This corresponds to pairs of complementarily truncated normal or lognormal distributions. It is shown that alternative representations, such as pairs of overlapping complete normal or lognormal distributions, yield fits equally acceptable statistically if the sample selection is random. The method also yields a good description of distributions described as “complex.” Computer methods of optimizing the free parameters are used; significance testing is discussed in some detail. It is stressed that although significance testing is helpful, it can neither relieve the geochemist of the burden nor take from him the privilege of being independent, and forming his opinion on the total evidence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045957
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  • 18
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    Relationship between petroleum reservoir rocks and source rocks (1971)
    Springer
    Mathematical geology 3 (1971), S. 183-192 
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    ISSN: 1573-8868
    Keywords: dimensional analysis ; statistics ; petroleum ; primary migration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A substantial fraction of sandstones containing commercial quantities of oil are proposed to be in contact with source rocks which produce oil. For these situations the quantity of oil collected in a sandstone is proportional to the area of contact with a source rock of relatively low permeability, rather than to the total thickness of the potential source rock. It is inferred that source rocks along the upper or lower faces of a sandstone should produce more oil into the sandstone than source rocks lateral to the sandstone. Semiquantitative estimates of the thickness or width of required source rock are obtained. The arguments and results are based on published statistical studies and the assumption that a degree of geometrical similarity exists among sandstones.
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    URL: http://dx.doi.org/10.1007/BF02045960
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  • 19
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    Mathematical techniques for paleocurrent analysis: Treatment of directional data (1972)
    Springer
    Mathematical geology 4 (1972), S. 235-248 
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    ISSN: 1573-8868
    Keywords: directional data analysis ; new statistical tests ; sampling ; statistics ; orientation data ; paleocurrent analysis ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Statistical procedures for (1) sampling, (2) testing the existence of a preferred direction, and (3) testing homogeneity of twodimensional directional data, which have been developed by the authors for paleocurrent studies, are presented. It is well known that conventional methods of statistical analysis are not applicable to directional data (e.g., crossbedding and ripplemark directions, grain lineations, etc.) which are “circularly distributed” on a compass dial. A sampling technique for directional data has been developed using the circular measures of dispersion and approximate ANOVA of G. S. Watson. On the basis of a pilot survey, it is possible to compute the minimum sample size required for estimating, with a desired precision, the mean paleocurrent direction of a formation. The optimum allocation of sample size between and within outcrops also can be accomplished at a minimum cost. The procedure described for testing uniformity (or lack of preferred direction) is based on the arc lengths made by successive sample points and is simple to use if the sample size is moderate. A table of critical points and a numerical example are given after a description of the test procedure. Finally, the procedures for testing the homogeneity of directional data from several geological formations are described by (1) tests for equality of the resultant directions (polar vectors) and (2) tests for equality of dispersions. With these tests it is possible to determine whether the paleocurrent directions from different geological formations belong to significantly different populations.
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    URL: http://dx.doi.org/10.1007/BF02311720
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  • 20
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    Stratigraphic correlation of subsurface geologic data by computer (1972)
    Springer
    Mathematical geology 4 (1972), S. 331-343 
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    ISSN: 1573-8868
    Keywords: cross correlation ; mapping ; plotting ; statistics ; stratigraphy ; structure ; electric logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Manual, semiautomatic, and fully automatic procedures for correlating subsurface data are reviewed. Special emphasis is placed on the use of electric-log data, including that of the dipmeter log, in this discussion. The Holgate method is described for its use in “fine-tuning” or refining gross correlations. A procedure for creating a matrix map for empirically establishing correlation between sets of data is described, and idealized models are shown.
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    URL: http://dx.doi.org/10.1007/BF02114094
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  • 21
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    Foraminiferal associations of the Mid-Tertiary Edegem Sands at Terhagen, Belgium (1974)
    Springer
    Mathematical geology 6 (1974), S. 1-15 
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    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.
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    URL: http://dx.doi.org/10.1007/BF02111923
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  • 22
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    Statistical techniques and their application in palynology (1973)
    Springer
    Mathematical geology 5 (1973), S. 297-311 
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    ISSN: 1573-8868
    Keywords: statistics ; general geology ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The basic principals of hypothesis testing are reviewed, including the development of the hypothesis, the statistical assumptions made, and the test of the hypothesis. The appropriate experimental design and sampling technique for evaluation of hypotheses posed are discussed. Because the analysis of variance involving the F-test should be used in a wide variety of geological experiments, emphasis is placed on this analysis. Many geological experiments result in the measurement of one or more factors on a continuous scale, whereas others are recorded in a discrete fashion. This necessitates the use of a covariance analysis to evaluate the effect of discrete and continuous factors in the same model. Orthogonal comparisons are discussed as they are used to evaluate specific hypotheses following the general test of hypothesis in the analysis of variance or covariance. All procedures discussed are illustrated using actual palynofloral data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111816
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    Electronic Resource
    Electronic Resource
    Grouped regression analysis—A sedimentologic example (1973)
    Springer
    Mathematical geology 5 (1973), S. 377-388 
    Details
    ISSN: 1573-8868
    Keywords: analysis of variance ; regression analysis ; statistics ; sedimentation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When sample data are divided into groups, and observations consist of the independent variable xand associated dependent variable y,a logical form of analysis is “grouped regression.” This statistical technique allows testing of the relationship between the two variables and assessment of how the relationship is affected by the grouping. A sedimentologic example illustrates the usefulness of such a technique in classifying environments of deposition based on the size of quartz grains and the quartz content.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111988
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    Electronic Resource
    Electronic Resource
    Estimation of components of variance for partially cross-classified data in a factorial arrangement of treatments (1974)
    Springer
    Mathematical geology 6 (1974), S. 117-133 
    Details
    ISSN: 1573-8868
    Keywords: statistics ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A procedure is presented for obtaining estimates of components of variance for the main effects and interaction in a two-way factorial arrangement of treatments with only partially cross-classified data (sometimes referred to as unbalanced data in a two-way crossed classification model with interaction). The procedure entails the use of two hierarchical analyses of variance in which each main effect is first treated as classes and then as subclasses. The estimation of the variance component for each main effect results from the solution of two simultaneous equations with values used obtained directly from the hierarchical analyses. The interaction component of variance can be obtained from the variance components for main effects. An example is presented for the purpose of illustrating the procedure. Interpretation of the interaction variance component estimated by the method is limited due to the absence of some of the subclasses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080151
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    Electronic Resource
    Electronic Resource
    Analytical comparison of two methods of assay weighting using vein assays from Butte, Montana (1974)
    Springer
    Mathematical geology 6 (1974), S. 219-233 
    Details
    ISSN: 1573-8868
    Keywords: sampling ; simulation ; statistics ; assay weighting ; economic geology ; geochemistry ; mining ; ore-reserve calculations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Weighting of vein assays is desirable where assays represent variable vein widths and variable distances along the vein. The method of weighting used is important in ore-reserve calculations and other investigations. Two possible methods are considered here. The first method, commonly applied in mining, assumes in effect linear variation of assay-width products between assay points. The second method, developed in this paper, assumes linear variation of assays and widths separately. The weighted average assay in an interval dby the second method (aw1, 2)is given by the expression $$a_{w1,2} = V/[(w_1 + w_2 )/2]$$ where $$\begin{gathered} v = (1/3)(\Delta a)(\Delta w)d + (1/2)(\Delta a)w_1 d + (1/2)(\Delta w)a_1 d + a_1 w_1 d \hfill \\ \Delta a = a_2 - a_1 {\text{,}}\Delta w = w_2 - w_1 \hfill \\ \end{gathered} $$ a1, w1 are assay and width at point 1, a2, w2 are assay and width at point 2,and dis the distance between points 1and 2.Statistical testing of the two methods, using 8,913 pairs of copper assay-width data from the Belmont mine area at Butte, suggests the following: within major veins or within veins which show near-linear width variations, the second method may be used with the expectation that the average grade calculated will more closely represent the actual average grade than if the first method were used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082888
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  • 26
    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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  • 27
    Electronic Resource
    Electronic Resource
    On the resolution of mixed frequency distributions into normal components (1972)
    Springer
    Mathematical geology 4 (1972), S. 55-60 
    Details
    ISSN: 1573-8868
    Keywords: frequency distribution ; regression analysis ; statistics ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The resolution of mixed frequency distributions into normal components may be accomplished graphically on probability paper. By means of nonlinear regression, a method for such a resolution in the probability net is given and exemplified. It is based on the observed cumulative frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083193
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