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  • Articles  (14)
  • mathematics  (8)
  • discriminant analysis  (6)
  • 1970-1974  (14)
  • Geosciences  (14)
  • Architecture, Civil Engineering, Surveying
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  • Articles  (14)
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  • Geosciences  (14)
  • Architecture, Civil Engineering, Surveying
  • Mathematics  (14)
  • 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
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Automatic contouring of geological maps to detect target areas for mineral exploration (1974)
    Springer
    Mathematical geology 6 (1974), S. 373-395 
    Details
    ISSN: 1573-8868
    Keywords: contouring ; discriminant analysis ; logistic model ; regression analysis ; geological maps ; mineral exploration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Various statistical methods for predicting mineral potential from geological maps are reviewed. It is pointed out that, if the features are coded in more detail for relatively small cells, several new problems arise because of the dichotomous nature of the resulting variables. The objective of this paper is to present a method for the automatic contouring of both discovered and undiscovered deposits of a given type in terms of the geological framework. It is based on the assumption that the probability of occurrence of a deposit is fully determined by a combination of functions of the mappable geological attributes in a region. Application of the logistic model is proposed for the situation in which relatively few deposits of a given type are known to exist in the study region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02082358
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  • 5
    Electronic Resource
    Electronic Resource
    A piecewise exponential model for seismic well-logging data (1974)
    Springer
    Mathematical geology 6 (1974), S. 33-45 
    Details
    ISSN: 1573-8868
    Keywords: inversion of data ; mathematics ; numerical analysis ; regression analysis ; geophysics ; petroleum ; well logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conventional methods of analyzing sonic log data do not always yield accurate information on each velocity segment of a well. It is shown here that the velocity-depth parameters and the sections of approximately constant velocity may be more precisely defined by using an exponential spline to model the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111925
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  • 6
    Electronic Resource
    Electronic Resource
    Quasifunctional equations for Ste. Genevieve Limestone facies and lithology (1974)
    Springer
    Mathematical geology 6 (1974), S. 107-115 
    Details
    ISSN: 1573-8868
    Keywords: functional equations ; mathematics ; numerical analysis ; rock description ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Equations describing ten microfacies of Ste. Genevieve Limestone established previously on qualitative analysis of petrographic features are derived here in terms of measured lithic parameters. Mean values of each lithic parameter for each facies comprise independent variables with eigenvalues from discriminant analysis serving as coefficients for quasifunctional equations. This provides a unique quantitative expression for each qualitative microfacies, the dependent variable. Although these equations are not truly functional equations, they do provide explicit description of Ste. Genevieve Limestone facies. Quasifunctional equations form a necessary first step toward establishment of true functional equations describing unit lithology as functions of depositional parameters. Functional equations for lithic units offer a potential for an ultimate unification of classifications for all geologic materials. An immediate value of these quasifunctional equations resides in their explicit description and identification of subjective lithic classifications (facies), their utilization in comparative studies of lithic components in one or more stratigraphie units, their facility for an objective and automated digital reduction and graphic presentation of data, and their invitation for more careful examination and critical evaluation of natural relationships.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080150
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  • 7
    Electronic Resource
    Electronic Resource
    Multivariate discriminant analysis of bioclastic turbidites (1972)
    Springer
    Mathematical geology 4 (1972), S. 249-261 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; discriminant analysis ; principal-components analysis ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A piston core from the southern Blake Basin penetrated nine distinct bioclastic carbonate turbidites separated by pelagic terrigenous clay units. X-ray diffraction analysis of the carbonate mineralogy of the graded, laminated, and homogenous units of the individual turbidite units indicated a general loss of unstable carbonates in the homogenous unit beyond that contained in the lower two units. Univariate and multivariate statistical tests were employed to determine the significance of the changes and to determine if different units of a turbidite sequence could be consistently grouped by statistical methods. Principal components, discriminant function, and cluster analysis were used in the multivariate tests. The graded and laminated units were closely related in mineralogy with little significant differences. The mineralogy of the homogenous units was significantly different than that of the other two units except in one example. Cluster analysis generated five groupings of the samples with the end members consisting of graded and laminated units at one end and homogenous units at the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02311721
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  • 8
    Electronic Resource
    Electronic Resource
    A statistical prediction technique for deriving contour maps from geophysical data (1973)
    Springer
    Mathematical geology 5 (1973), S. 179-189 
    Details
    ISSN: 1573-8868
    Keywords: contouring ; data processing ; mapping ; mathematics ; plotting ; general geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A technique for preparing contour maps is presented which has particular applicability for geophysical data. This technique derives from the assumption that each measured value is a sample from a statistical distribution which is taken to be valid in the area around that sample location. This distribution may be specified in the manner which best defines the relationship between the data and its spatial environment. Extending this principle to cover all areas to be mapped, and not just those measured, it is possible to predict values over a grid array of locations and hence to produce a contour map. Inherent in this simple procedure is: (i) the ability to adjust to the nature of the data being contoured; (ii) the elimination of edge effects; (iii) visual indication of the relative accuracy with which contours are located, at all points of the map; (iv) the automatic downgrading of data values which are in error; (v) the ability to contour combinations of measured data values without compounding errors; and (vi) a relatively simple extension to data spatially distributed in three dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111894
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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Use of discriminant analysis for classification of strata in sedimentary successions (1973)
    Springer
    Mathematical geology 5 (1973), S. 163-177 
    Details
    ISSN: 1573-8868
    Keywords: classification ; discriminant analysis ; geochemistry ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The technique of instrumental neutron activation analysis (INAA) has been used to analyze chip samples of geological material for 12 elements. Discriminant analysis has been used to classify the unknown chip samples to the correct stratum in a sedimentary succession.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111893
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