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  • Articles  (20)
  • sedimentology  (20)
  • 1970-1974  (20)
  • 1935-1939
  • Mathematics  (20)
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  • Articles  (20)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    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
    Electronic Resource
    Electronic Resource
    Springer
    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
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    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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