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  • Articles  (34)
  • sedimentology  (34)
  • Springer  (34)
  • Cambridge University Press
  • Frontiers Media
  • National Academy of Sciences
  • 2020-2022
  • 1980-1984  (3)
  • 1975-1979  (11)
  • 1970-1974  (20)
  • Mathematics  (34)
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  • Articles  (34)
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  • Springer  (34)
  • Cambridge University Press
  • Frontiers Media
  • National Academy of Sciences
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  • 2020-2022
  • 1980-1984  (3)
  • 1975-1979  (11)
  • 1970-1974  (20)
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  • 1
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    Mathematical geology 3 (1971), S. 227-238 
    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.
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  • 2
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    Mathematical geology 3 (1971), S. 281-295 
    ISSN: 1573-8868
    Keywords: analysis of variance ; autocorrelation ; simulation ; trend analysis ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is proposed that the variance in mapped geologic data should be formally considered to be composed of three components which arise on different geographic scales. The three components (regional, local, and residual) should be defined solely in terms of the parameters of the sample data set. A two-step analysis is required to separate three components. Applying autocorrelation criteria, trend-surface analysis has been used, in the first step, to remove the residual component and, in the second step, to separate regional and local components from the resulting noise-free data. This procedure has made it possible to quantify local components in stratigraphic thickness data from the East Midlands coalfield (central England) which can be identified in terms of the known geology.
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  • 3
    ISSN: 1573-8868
    Keywords: time-trend analysis ; carbonate petrology ; depositional environments ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Data from point counts of 376 thin sections from six stratigraphic sections in the Chickamauga Group carbonates (Middle Ordovician of northeastern Alabama) were smoothed by time-trend methods. The resulting curves were plotted against the stratigraphic sections to show depositional trends and to facilitate interpretation of depositional environments. The depositional environments in the lower third of the sequence studied were dominantly subtidal; in the middle portions they were interbedded subtidal, intertidal, and supratidal; in the lower upper third they were supratidal; and in the uppermost portions they were interbedded subtidal, intertidal, and supratidal. Time-trend methods proved to be useful in this study, for they are easy to use and eliminate much noise observed in the data, whereas preserving major trends. Correlation between outcrops was by means of two continuous bentonites; comparison of the time-trend curves show that they would have been useful for correlation if the bentonites had been absent, although small differences in the vertical positions of beds between localities (indicating lateral migration of environments) would not have been detected by time-trend methods.
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  • 4
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    Mathematical geology 8 (1976), S. 529-547 
    ISSN: 1573-8868
    Keywords: cycles ; Markov processes ; cluster analysis ; time-trend analysis ; coal petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An embedded Markov model is used to test microlithotype analyses of subsections of a wide range of Australian coal seams for the presence of nonrandom sequences of lithologies. The data for individual seams, transformed to give five states (four states if dirt bands are excluded),were summed into geologically and geographically distinct groupings. The results suggest that dirt bands form an essential part of the sequences and that partial or complete cyclicity is present in many seam groupings. The cyclicity is either asymmetric or partially symmetric with the vitrite +clarite content of the coal decreasing upwards within each cycle. A new cycle is marked either by a sharp reversion, or by a slightly gradational reversion, to a vitrite +clariterich lithology. This reversion may or may not be preceded by a dirt band. In virtually all groupings, a vitrite +clarite-rich lithology is the most likely type after a dirt band. The sequences are similar to those that have been described in European coals and it seems probable that the presence of intraseam, cyclic sequences is a normal, rather than an unusual condition, within coal seams. This cyclicity is a response to changes in the sedimentation balance. These changes are probably due in large part to processes originating within the peat-forming environment but processes external to this environment are also likely to produce cyclic sequences of coal lithologies.
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  • 5
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    Mathematical geology 6 (1974), S. 363-372 
    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.
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  • 6
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    Mathematical geology 10 (1978), S. 225-241 
    ISSN: 1573-8868
    Keywords: factor analysis ; linear programming ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The problems involved in the factor analysis of data consisting of measurements of material quantity or proportion are discussed, and the inability of existing factor analysis solutions to properly model such data is pointed out. A new factor analysis solution using the linear programming technique is presented which properly analyzes mixture data. A numerical example is presented in which a body of suspended sediment grain-size distribution data is analyzed using the new factor analysis solution. FORTRAN-IV subroutines for computing this solution are included in an Appendix.
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  • 7
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    Mathematical geology 3 (1971), S. 15-41 
    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.
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  • 8
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    Mathematical geology 5 (1973), S. 91-110 
    ISSN: 1573-8868
    Keywords: Markov processes ; regression analysis ; time-trend analysis ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Cyclic characteristics of a sequence of Permian coal-measure sediments have been studied using Markov chain analysis on borehole data. Fining-upwards and oscillating sequences can be distinguished, and depositional regimes are proposed to explain the observed sequences. However, there is no clearly defined relationship of sequence type to tectonosedimentary environment. The relationship of the number of coal-defined and fining-upwards cycles to total thickness and mean cycle thickness is examined using linear regression. The relationships for coal-defined and fining-upwards cycles are essentially the same. Significant positive correlations are present between the number of cycles and total thickness and significant inverse relationships are present for the number of cycles and the mean cycle thickness.
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  • 9
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    Mathematical geology 8 (1976), S. 75-84 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; entropy ; facies analysis ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Criteria have been suggested for the optimal partitioning of a dendrogram into sample clusters. The implementation of these criteria by means of statistical and graphical measures is considered for two dendrograms. It is shown that the optimization of criteria is conditioned by research aims.
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  • 10
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    Mathematical geology 3 (1971), S. 239-263 
    ISSN: 1573-8868
    Keywords: simulation ; hydrology ; petroleum ; sedimentology ; high fluid pressures ; compaction ; primary migration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A mathematical model of sedimentation and compaction of fine-grained rocks such as shale has been constructed. Water is considered to flow upward or downward out of a compacting rock according to Darcy's law until the pore-water pressure within the rock is normal for the depth in question. The porosity decreases during compaction until a minimum porosity, determined by the difference between total vertical stress (overburden pressure) and pore-water pressure, is obtained. The model takes into account the dependence of permeability on porosity for a given rock type, and the dependence of water viscosity on salinity, temperature, and pressure. The derived equations have been computer programmed to obtain the time dependence of porosity, pressure, water velocity, permeability, and other factors within a compacting shale during (a) shale sedimentation, (b) a time lapse following shale deposition, (c) the deposition of normally pressured sediments over the shale, and (d) a second time lapse following deposition of the normally pressured unit. Solutions to these problems are given for the situation when the unit underlying the shale is normally pressured, and for the situation when the underlying unit is impermeable. The calculations show that a portion of a thick shale adjacent to a normally pressured unit may have a considerably reduced porosity and permeability, and act as a seal for the remainder of the shale. High fluid pressures may persist for many millions of years in thick shales with low permeability. The computations can be extended to cover more complicated cases of interbedded shales, sands, and other lithologies.
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  • 11
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    Mathematical geology 3 (1971), S. 43-50 
    ISSN: 1573-8868
    Keywords: dynamic programming ; sampling ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Increasing attention in recent years has been devoted to the application of statistical techniques in the analysis and interpretation of geologic and oceanographic data. Equally important, but less well explored, are methods for efficient experimental design. The theory of linear programming provides plans for optimal sampling of geologic and oceanographic phenomena. Of particular significance are solutions to problems of multivariate sampling. Often, a single field sample may be analyzed for a number of oxides, or a number of minerals, or a number of textural parameters. In general, these variables differ in the degree to which they are diagnostic of changes in the phenomenon of interest, and thus they must be known with different levels of precision if they are to be useful. Similarly, the variables differ in the ease with which they may be measured. If a sampling plan is to be most efficient, it must provide the requisite levels of precision for the minimum expenditure of time and effort. Sampling for a single variable may be optimized directly. Sampling for several variables simultaneously usually introduces special difficulties, but if the objective function can be generalized to hold for all variables, solutions can be determined even in this situation.
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  • 12
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    Mathematical geology 4 (1972), S. 103-113 
    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.
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  • 13
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    Mathematical geology 4 (1972), S. 219-234 
    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.
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  • 14
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    Mathematical geology 6 (1974), S. 107-115 
    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.
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  • 15
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    Mathematical geology 7 (1975), S. 63-73 
    ISSN: 1573-8868
    Keywords: crossassociation ; crosscorrelation ; proportions ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Simple correlation leads to misleading results when applied to the proportions of materials in mixtures, because of the constraint that the total of the proportions is less than one. A simple mainly graphical procedure to determine whether the proportions in mixtures are associated after allowing for the constraint is presented. No assumptions about the form of the underlying probability distributions are required. The technique is extended to problems where other constraints apply.
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  • 16
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    Mathematical geology 4 (1972), S. 249-261 
    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.
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  • 17
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    Mathematical geology 4 (1972), S. 277-290 
    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.
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  • 18
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    Mathematical geology 7 (1975), S. 117-128 
    ISSN: 1573-8868
    Keywords: data processing ; lognormal theory ; sampling ; simulation ; statistics ; transformations ; economic geology ; mining ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A logarithmic transformation may be used to improve the efficiency of estimates of the mean when observations follow the lognormal distribution. But if this transformation is applied to observations that follow another distribution, bias may be introduced. We consider some consequences of erroneously applying lognormal estimation theory and demonstrate that biased estimates may be obtained for certain classes of distributions. Illustrations of bias obtained in gold sampling are given.
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  • 19
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    Mathematical geology 8 (1976), S. 57-74 
    ISSN: 1573-8868
    Keywords: factor analysis ; principal components analysis ; oceanography ; sedimentology ; suspended sediment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Principal component analysis (PCA) was employed to investigate interrelationships among various characteristics of seawater and suspended sediments obtained from surface waters of two Asian marginal seas. On the basis of multivariate correlation analysis for the two marginal seas combined, three important factors were extracted and interpreted: (1) current-energy conditions, (2) the influence of rivers, and (3) biochemical conditions of seawater. A relationship between anisotropic mineral grains and combustible organic matter is suggested by the fact that suspended sediment, containing coarser anisotropic mineral grains, also contains larger amounts of combustible organic matter.
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  • 20
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    Mathematical geology 8 (1976), S. 267-282 
    ISSN: 1573-8868
    Keywords: decomposition ; statistics ; superpositions ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Some of the methods used in the resolution of mixed normal distributions are discussed under three headings: analytical, graphical, and numerical methods. Attention is given to their applicability in the analysis of grain-size data as derived from sieving. Comparisons are made by applying several methods to published data. It is concluded that the numerical methods offer most scope, especially the method of nonlinear least squares. Some analyses of beach sediments, using this method, are presented. The adoption of a convention for the number of individuals in the sample increases ease of interpretation.
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  • 21
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; ordination analysis ; grain size ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A multivariate statistical strategy for classifying paleoenvironments is effective for studying modern sedimentary processes in western Great South Bay and South Oyster Bay, New York. The 13 whole phi weight percent variables were tested for redundancy with R-mode cluster analysis. The samples were partitioned statistically into five environmentally significant facies using Q-mode cluster analysis: (A)sandy gravel, (B)sandy silt, (C)silty sand, (D)slightly gravelly sand, and (E)fine sand. An ordination depicted gradational relationships among the samples and the facies. It was used to evaluate the environmental and textural parameter gradients within the sample space. Interpretations obtained in this manner and by examination of the grain-size curves suggest that these sediments were deposited by waves and currents on beaches and in wave zones (facies C and E),shoal areas (facies B),and tidal channels (facies A and D).Tidal currents, wave action, and eelgrass control the distribution of sediments within the two bays.
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  • 22
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    Mathematical geology 8 (1976), S. 635-647 
    ISSN: 1573-8868
    Keywords: principal-components analysis ; geomorphology ; oceanography ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Analysis of channel cross sections is hindered by lack of parameters to describe the shape of the cross section. In the situation of a sample of cross sections taken across tidal inlets, if the cross section is expressed as an observation vector, principal-component analysis can be used to derive eigenvectors for the data set. By neglecting eigenvectors that explain little variance, mathematical representation of the original data set is simplified by transformation to the eigenvector space. For 408 cross sections each represented by a 60-component vector, three eigenvectors explain 97.5 percent of the total variance in the data set. The three-dimensional representation simplifies the task of analyzing cross-sectional shape. The physical form of the first three eigenvectors have considerable resemblance to classical types of variation noted in inlet-channel studies. The method is applicable directly to analysis of other fluvial and estuarine channels.
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    Mathematical geology 12 (1980), S. 69-77 
    ISSN: 1573-8868
    Keywords: dynamic clustering ; classification ; geochemical data ; sedimentology
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    Topics: Geosciences , Mathematics
    Notes: Abstract The purpose of typological factor analysis is to detect, within a multidimensional sample, the existence of subsets characterized by different maximal elongation directions. The method which has been successfully applied in the field of pattern recognition can be considered from two points of view: (1) an automatic classification or “dynamic clustering” technique: and (2) a form of factor analysis. Using this form of analysis nuclei of affine varieties (points, axes, planes, etc) are identified. Different case studies were analyzed in order to establish the advantages of the method compared to other methods. Geochemical analyses of rock samples; that is, rhyolites, mafic, and intermediate rocks of the Normetal (Abitibi) area were subjected to typological factor analysis for the purpose of classification of geological deposits and detection of geochemical anomalies. The method was also applied to the classification of sediments from the Barataria Bay area in Louisiana.
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  • 24
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    Mathematical geology 13 (1981), S. 303-320 
    ISSN: 1573-8868
    Keywords: sedimentology ; outline shape ; Fourier analysis
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    Topics: Geosciences , Mathematics
    Notes: Abstract Sedimentologists, among others, have been accustomed to the analysis of the shape of sedimentary particles. Recently such shapes have been subjected to more quantitative analysis, almost completely removing the subjective element so long inherent in the various indices. However, these quantitative analyses themselves are not free from qualitative bias, partly displayed in the choice of appropriate technique, and to some extent in the intermediate steps of the data collection and analysis. Various numerical methods are introduced within the framework of a typology based on whether the analysis is performed on the grain considered as an outline, or as a planar surface. Nine desirable properties are suggested, as a yardstick against which to evaluate the descriptors. In all these techniques the object is to examine a discrete approximation of single items, in two dimensions only. Some of the methods are nevertheless applicable to three dimensions.
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    Mathematical geology 16 (1984), S. 217-236 
    ISSN: 1573-8868
    Keywords: nonlinear regression ; discriminant analysis ; decomposition of mixtures ; pattern recognition ; geochemistry ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The decomposition problem—the assignment of sample observations to component populations—is studied in a spatial context. The observations are spatially located and the assignment to component populations takes into account the value of each observation as well as the values of neighboring observations. Both parameter estimation and assignment rules use a new method that integrates a standard multivariate decomposition algorithm with nonlinear regression. The method is illustrated and tested with artificial data. The distribution of the trace component Cr2O3 in recent Lake Michigan sediments is, then, analyzed by the method. It yields a pattern of component populations that is correlated with the Lake's bottom structure and depositional environments.
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    Mathematical geology 3 (1971), S. 265-279 
    ISSN: 1573-8868
    Keywords: simulation ; mathematical models ; sedimentology ; stratigraphy
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    Notes: Abstract To study sedimentary phenomena, we introduce random-genetic models in which genetic hypotheses and structural random elements occur for the main part. Starting from geologic hypotheses we choose principal factors which may be random functions or random variables. These factors are: depth, nature of the facies, sedimentation rate, and subsidence. Equations of evolution link the factors. Depth is a Markov process, but generally the resultant sequence does not make a Markov chain or Markov process. Three examples of such models are given with the results of simulations.
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    Mathematical geology 4 (1972), S. 235-248 
    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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    Mathematical geology 5 (1973), S. 59-72 
    ISSN: 1573-8868
    Keywords: data processing ; dimensionless diagrams ; mathematics ; hydrology ; sediment transport mechanisms ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Methods for calculating constant terminal-settling velocities (vs)of spheres are examined for their validity and limitations of usefulness. A different approach is given which accurately predicts vs for spheres over a wide range of hydraulic conditions based on past experimental work. The theory behind this approach is given along with the listing of a fortran program which directs the calculations of vs.The practical limits of the author's method are stated, and tables of vs may be generated from the program for common mineral densities over a range of sizes useful to sedimentologists.
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    Mathematical geology 5 (1973), S. 351-363 
    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.
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    Mathematical geology 6 (1974), S. 333-352 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; multivariate analysis ; ordination ; numerical taxonomy ; paleoecology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A multivariate analytical strategy is proposed for aiding the investigator in extracting maximum information from environmental data. Data are carefully coded and scaled and are tested for redundancy using R-mode cluster analysis. The samples are partitioned into environmental classes using Q-mode cluster analysis. Q-mode ordination facilitates interpretations, which usually can be verified by comparison with field relationships. Discriminant analysis serves as an identification procedure for extending the classification to unknown samples. The strategy is demonstrated by application to Cape Hatteras microorganism distributions and Devonian sedimentary facies.
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    Mathematical geology 6 (1974), S. 353-362 
    ISSN: 1573-8868
    Keywords: data processing ; paleocurrent directions ; basin analysis ; orientation statistics ; computer graphics ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Basin analysis for paleocurrent directions commonly makes use of hundreds of cross-bedding dip and strike measurements taken on structurally tilted sedimentary beds which may be parts of plunging folds. For regional interpretations the desired forms of data are vector means and rose diagrams of dip directions after reduction to the assumed horizontal plane of deposition. Three FORTRAN computer programs have been integrated to perform the data reduction from raw field measurements to graphic plotted rose diagrams. Program PLUNGR rotates the raw field data back to the original horizontal plane of deposition. Output from PLUNGR is a deck of punched cards suitable for input into the second and third programs, with provision for various regroupings of data. VECMEN computes vector mean and other statistics on data groups defined by inserted control cards. Program ROSE, with a variety of options, plots a rose diagram of dip direction azimuths on a CalComp plotter.
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    Mathematical geology 4 (1972), S. 35-43 
    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.
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    Mathematical geology 8 (1976), S. 649-655 
    ISSN: 1573-8868
    Keywords: topology ; catastrophe theory ; volcanology ; sedimentology ; structure ; morphogenesis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Catastrophe theory is a recently developed branch of topology which has a number of practical applications, principally because of its ability to model situations which include discontinuities or singularities, where the methods of differential calculus break down. Some examples of its possible use in geology are presented, in fields as diverse as volcanology, sedimentology, and structural geology, and wider applications, in modeling spatial or temporal discontinuities in other fields, are suggested.
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    Mathematical geology 9 (1977), S. 113-122 
    ISSN: 1573-8868
    Keywords: statistics ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A theory of pebble erosion is presented, based on the assumption that the rate of erosion at a point on the surface is a function Vof the curvature there. It is proved that for physically reasonable functions V,the sphere is the only shape of pebble which can maintain its proportions as it wears away. An argument is given which leads to a particular form for the function Vand a few qualitative consequences of this form are indicated. The surface of the pebble at time tmay be described using spherical polar coordinates θ, Φ by the radius function r (θ, Φ, t). This function is given by a highly nonlinear partial differential equation. However, in the case of the erosion of a deformed sphere, when terms which are of second order or higher in the deformation are neglected, the equation becomes linear and is a version of the diffusion equation. The stability of the spherical shape against deformations of the various harmonic types is then easily analyzed.
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