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  • Articles  (22)
  • stratigraphy  (13)
  • factor analysis  (9)
  • Springer  (22)
  • American Meteorological Society
  • 1970-1974  (22)
  • Geosciences  (22)
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  • Articles  (22)
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  • Springer  (22)
  • American Meteorological Society
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  • 1
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    Springer
    International journal of earth sciences 62 (1973), S. 918-938 
    ISSN: 1437-3262
    Keywords: Calc-silicate rock ; tectonics ; stratigraphy ; facies ; Damara Orogen (South West Africa)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Description / Table of Contents: Abstract The behaviour during rock deformation of diagenetically formed layers, lenses, nodules (concretions) and diffuse concentrations of calc-silicate rock is described from parts of the Damara belt. Depending on their relative solubility and/or competency and on the angle between bedding and cleavage planes the layers and lenses may either more or less retain their shape or be cut up into spindle-shaped bodies (boudinage due to shortening). Nodules are deformed to ellipsoides, while diffuse concentrations of calc-silicate rock are transformed into a number of spindles. All spindles and ellipsoides which are formed during the formation of the cleavage are strictly orientated parallel to the cleavage planes. It is therefore obvious that the spindleshape of these bodies is a consequence of rock deformation. Thus, in areas in which a cleavage is suspected to lie parallel to a distinct bedding, the occurrence of spindles may confirm the existence of this cleavage. The non-statistical occurrence of calc-silicate rock bodies within the Khomas Series may render possible a first subdivision of this up to 6000 m thick succession.
    Abstract: Résumé Ce travail décrit le comportement de couches, lentilles et nodules de cornéennes à silicates calcaires, et de concentrations diffuses du même matériau, parallèles à la stratification, au cours de la déformation de roches dans une partie de l'orogène de Damara. Suivant leur solubilité relative et leur rigidité, et selon l'angle entre la stratification et la schistosité, les couches et les lentilles peuvent subsister telles quelles ou être débitées en corps fusiformes (boudinage de raccourcissement). Les nodules prennent la forme d'ellipsoides ou de fuseaux, et les concentrations de cornéennes à silicates calcaires se résolvent en une multiplicité de corps fusiformes. Tous les corps fusiformes formés pendant le développement de la schistosité sont orientés strictement suivant la schistosité. Il est clair que la forme en fuseau des cornéennes à silicates calcaires est le résultat de la déformation des roches. Dans les régions où l'on la soupçonne parallèle au changement évident du matériau, cette schistosité peut se déduire de l'existence de fuseaux. - La distribution irrégulière des cornéennes à silicates calcaires dans la série de Khomas permet de subdiviser cette série, épaisse de 6000 mètres, restée jusqu'à présent indivisée.
    Notes: Zusammenfassung Beschrieben wird das Verhalten von frühdiagenetisch gebildeten schichtparallelen Kalksilikatfels-Lagen, -Linsen, -Knollen und diffusen Ansammlungen während der Gesteinsdeformation in Teilen des Damara-Orogens. In Abhängigkeit von ihrer relativen Löslichkeit und/oder Kompetenz sowie vom Winkel zwischen Schichtung und Schieferung können Lagen und Linsen als solche erhalten bleiben oder in spindelförmige Körper zerlegt werden (Verkürzungsboudinage). Knollen werden zu Ellipsoiden oder Spindeln deformiert und diffuse Kalksilikatfels-Ansammlungen in eine Vielzahl von Spindeln aufgelöst. Alle im Zusammenhang mit der Anlage der Schieferung gebildeten Spindeln und Ellipsoïde sind streng in der Schieferung orientiert. Es wird deutlich, daß die Spindelform der Kalksilikatfels-Körper ein Produkt der Gesteinsdeformation ist. In Gebieten, in denen der Verdacht besteht, daß parallel zu einem deutlichen Materialwechsel eine Schieferung verläuft, kann aus der Existenz von Spindeln auf das Vorhandensein dieser Schieferung geschlossen werden. Die ungleichmäßige Verteilung von Kalksilikatfels-Körpern innerhalb der Khomas-Serie ermöglicht eine Unterteilung dieser bisher ungegliederten, bis zu 6000 m mächtigen Gesteinsfolge.
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  • 2
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    Mathematical geology 3 (1971), S. 61-77 
    ISSN: 1573-8868
    Keywords: factor analysis ; principal components analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An algorithm andFortran-iv computer program,cabfac, forQ-mode factor analysis is described. The program will accept up to 1500 items and 50 variables on a moderate-size computer.
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  • 3
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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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  • 4
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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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  • 5
    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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  • 6
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    Mathematical geology 4 (1972), S. 61-72 
    ISSN: 1573-8868
    Keywords: data processing ; data recording ; data files ; lithology ; petroleum ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Well-data files maintained by petroleum companies and service companies are important sources of data for exploration geologists. To make these data readily accessible and useful for computer studies, three preliminary steps are necessary: (1) systematic data gathering and recording, (2) storage for ready retrieval, and (3) preparation of analysis programs. One important source of geologic data is lithologic descriptions of well cuttings and cores. The practical lithologic data-recording form described here is used routinely at the well site and in the laboratory. It is designed in an 80-column format and uses codes for lithologic characteristics, porosity, and hydrocarbon shows, and forms part of an integrated well-data file. This datarecording form has the advantages that descriptions are made according to a standardized format convenient to use at the well site, and the data are subsequently available in raw form relatively free from interpretive bias. A library of analysis and display programs can be assembled for utilization of the data.
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  • 7
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    Mathematical geology 4 (1972), S. 177-202 
    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.
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  • 8
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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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  • 9
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    Mathematical geology 5 (1973), S. 39-57 
    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.
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  • 10
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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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  • 11
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    Mathematical geology 5 (1973), S. 237-267 
    ISSN: 1573-8868
    Keywords: factor analysis ; generalized logistic curve ; Gompertz curve ; petroleum ; regression analysis ; time series ; time-trend analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A number of growth models have been developed and used in an attempt to project the historical pattern of oil activities to some estimate of their upper limit. Techniques are outlined for the estimation of parameters of the logistic and Gompertz curves. Factor analysis indicated a close relationship between production and demand, whereas annual discoveries and discoveries classified by year of discovery tended to comprise unique factors which were indifferent to changes in time. The growth models projected relatively high values for ultimate demand and production in comparison to the figures for ultimate reserves. Inasmuch as these trends seemed to be occurring independently, some reconciliation of the results was necessary. Using the highest projections of estimates for reserves suggests that over 420 billion barrels of oil in place will eventually be discovered in the United States, with perhaps 200 billion barrels of this eventually to be proved in the form of reserves. Projections for production were higher, corresponding to a trend indicating high levels in demand for crude oil. The only credible long-term estimate of demand was given by a bounded exponential growth model, in which ultimate cumulative demand for crude oil would reach about 416 billion barrels. These figures imply that over 150 billion barrels of oil would be imported into the United States from 1970 to 2070. Provided the time pattern for one of the variables has been determined, then estimates of the other variables probably would be facilitated because of the high interrelationship between variables. Models are suggested in which accurate pivotal forecasting in the short term might be possible—assuming the particular future trend in some of the “independent” variables has been predetermined.
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  • 12
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    Mathematical geology 6 (1974), S. 17-31 
    ISSN: 1573-8868
    Keywords: cluster analysis ; factor analysis ; engineering geology ; soils
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The engineering-geological environment, as any other geological environment, can be described by a number of variables. A clustering of those variables or clustering of their quantities makes it possible to divide the environment into taxonomic types. It is also possible to determine factors which are functions of those variables and which characterize the environment or its parts. In this paper we have applied R-and Q-mode factor analysis to engineering-geological research, concentrating our attention on establishing criteria for subdividing an environment into various aspects by its engineering-geological characteristics.
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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 6 (1974), S. 311-332 
    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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  • 16
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    Mathematical geology 3 (1971), S. 171-181 
    ISSN: 1573-8868
    Keywords: Fourier analysis ; graphics ; mapping ; spatial filtering ; trend analysis ; stratigraphy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Z-trend maps are a simplified lineprinter version of spatially filtered maps designed to give a quick visual appraisal of trends. The printout shows a “yes-no” configuration by a printed character or a blank so that the map has a conspicuous pattern. This pattern reflects the presence, position, and trend of the desired features. If a reasonable symbol density ratio is used the results can be visually pleasing thus enhancing trend recognition. Z-trending can be adapted to any map with stationary properties but is most easily applied to data that have been filtered with a bandpass operator.
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  • 17
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    Mathematical geology 3 (1971), S. 265-279 
    ISSN: 1573-8868
    Keywords: simulation ; mathematical models ; sedimentology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    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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  • 18
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    Mathematical geology 3 (1971), S. 79-86 
    ISSN: 1573-8868
    Keywords: data processing ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The development of a standardized system for conveniently coding lithologic-log data for use in the digital computer has long been needed. The technique suggested involves a reduction of the original written alphanumeric log to a numeric log by use of computer programs. This numeric log can then be retrieved as a written log, interrogated for pertinent information, or analyzed statistically.
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  • 19
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    Mathematical geology 4 (1972), S. 331-343 
    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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  • 20
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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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  • 21
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    Mathematical geology 6 (1974), S. 1-15 
    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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  • 22
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    Mathematical geology 5 (1973), S. 321-339 
    ISSN: 1573-8868
    Keywords: factor analysis ; Fourier analysis ; mapping ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Mathematical methods were employed in an investigation of syntexis in the “Gabbro di Sondalo,” a mafic igneous formation in the Central Alps (Italy). A set of 100 specimens was selected according to sampling criteria and analyzed by X-ray fluorescence for eight elements; Q-mode and R-mode factor analysis then was applied to these data. Results of the computations indicate that the general trend of differentiation is related to the syntexis of gneissic wall rocks (“Gneiss del Monte Tonale”) in the mafic melt. Ca and Mg are abundant in the gabbro, and Si and K in the gneiss; the independent variation trend of Fe and Ti may be related to a differentiation episode due to a magmatic phase. Spatial representation of multivariate data on differentiation also was performed on the main elements and a picture of the trend of syntexis was mapped.
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