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  • Erdgas
  • Erdöl
  • Erdölgeologie
  • petrology
  • Springer  (29)
  • American Association of Petroleum Geologists (AAPG)  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Submersible observations of Equatorial Atlantic mantle: The St. Paul Fracture Zone region (2000)
    Springer
    Marine geophysical researches 21 (2000), S. 529-560 
    Details
    ISSN: 1573-0581
    Keywords: Structure ; morphology ; petrology ; peridotite-basalt
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The St. Paul F.Z. is a large structural domain made up of multiple transform faults interrupted by several Intra-Transform Ridge (ITR) spreading segments. Two regions were studied in details by submersible: (1) The ITR short (〈20 km in length) segment near 0° 37′N–25° 27′W and 1° N–27° 42′W and (2) The St. Peter and St. Paul's Rocks (SPPR) massif located at 29° 25′W (¡3700 m depth). (1) The short ITR segments consist of a magma starved rift valley with recent volcanic activities at 4700 m depth. A geological profile made along the rift valley wall showed localized volcanics (basalts and dykes) which are believed to overlay and intrude the ultramafics. The geological setting and the high ultramafic/volcanic ratio suggest an extremely low magmatic supply and crustal-mantle uplift during lithospheric stretching and denudation. (2) The St. Peter and St. Paul's Rocks (SPPR) massif consists of a sigmoidal ridge within the active transform zone. The SPPR is divided into two different geological domains called the North and the South Ridges. The North Ridge consists of strongly tectonized fault scarps composed of banded and mylonitized peridotite, sporadic gabbros (3900–2500 m) and metabasalts (2700–1700 m). The South Ridge is less tectonized with undeformed, serpentinized spinel lherzolite (2000–1400 m) and basalts. Extensional motion and denudation accompanied by diapirism affected the South Ridge within a transform domain. Instead, the North Ridge was formed during an important strike-slip and faulting motion resulting in the uplifted portion of the St. Paul F.Z. transverse ridge. There is a regional compositional variation of the volcanics where E-MORBs and alkali basalts are produced on the SPPR massif and are comparable to the adjacent northern segments of the Mid-Atlantic Ridge. On the other hand, N and T- MORBs collected from the eastern part of the St. Paul F.Z. (25° 27′ W IRT) are similar to the volcanics from the southern segments of the MAR. The peridotites exposed in these provinces (SPPR and ITR) are similar in their REE and trace element distribution. Different degrees (3–15%) of partial melting of a mixed composite mantle consisting of spinel and amphibole bearing lherzolite veined with 5–40% clinopyroxenite gave rise to the observed MORBs and alkali basalts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004819701870
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  • 2
    Electronic Resource
    Electronic Resource
    Reference concentrations for heavy metals in mineral soils, oat, and orchard grass (Dáctylis glomeráta) from three agricultural regions in Norway (1996)
    Springer
    Water, air & soil pollution 89 (1996), S. 375-397 
    Details
    ISSN: 1573-2932
    Keywords: trace elements ; background values ; petrology ; alum shale ; soil parent material ; organic material ; soil pollution ; soil contamination ; arsenic ; plant uptake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Background values for heavy metals are necessary for the assessment of metal pollution of soils and plants. Samples of cultivated and uncultivated soils, oat grain, and seed heads of orchard grass (Dáctylis glomeráta) were collected from central, southeastern, and southwestern Norway. Total and easily extractable concentrations of As, Cd, Cr, Cu, Hg, Ni, Pb, and Zn were determined in soil samples and total concentrations in plant samples. Element distributions have been correlated with petrology of soil parent material, type of mineral deposit, soil depth, geographic area, and land use. Concentrations of heavy metals are generally within the lower part of the normal global range. The petrology of the soil parent material has the greatest influence on aqua regia extracted metal concentrations among the factors studied. DTPA extracted metals show less dependence on rock types. Presence of alum shale results in particularly high values for Cd in both soil extracts and in oat grain. Soil cultivation seems to influence the relative concentration of metals in the topsoil. The ratios of easily extractable to total concentrations of metals are primarily related to the organic matter content. Metal concentrations in oat grain can best be predicted by concentrations in DTPA extracts and soil pH among the factors studied. Seed heads of orchard grass are less affected by concentrations in the soil and appear therefore to be a poor indicator of heavy metals in soils.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00171643
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  • 3
    Electronic Resource
    Electronic Resource
    Volcanological and petrological evolution of Nyiragongo volcano, Virunga volcanic field, Zaire (1994)
    Springer
    Bulletin of volcanology 56 (1994), S. 47-61 
    Details
    ISSN: 1432-0819
    Keywords: Nyiragongo ; volcanology ; petrology ; melilitite ; nephelinite ; feldspathoid flotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Three major phases are distinguished during the growth of Nyiragongo, an active volcano at the western limit of the Virunga Range, Zaire. Lavas erupted during phase 1 are strongly undersaturated melilities characterized by the presence of kalsilite phenocrysts, perovskite, and the abundance of calcite in the matrix. Such lavas crop out mainly on the inner crater wall and progressively evolve toward more aphyric melilite nephelinites well represented on the flanks of the volcano. Adventive vents lying at the base of the cone developed along radial fracture systems and erupted olivine and/or clinopyroxene-rich melilitites or nephelinites. Stage 2 lavas are melilite-free nephelinites. Clinopyroxene is the main phenocryst and feldspathoids are abundant in the lavas exposed on the crater wall. These flows result from periodic overflowing of a magma column from an open crater. Extensive fissure flows which erupted from the base of the cone at the end of this stage are related to widespread draining out of magma which in turn induces the formation of the summit pit crater. Magmas erupted during stage 3 are relatively aphyric melilite nephelinites and the main volcanological characteristic is the permanent lava lake observed into the pit crater until the 1977 eruption. Fluctuations of the level of the lava lake was responsible for the development of the inner terraces. Periodic overflowing of the lava lake from the central pit formed the nepheline aggregate lava flows. Petrography and major element geochemistry allow the determination of the principal petrogenetic processes. Melilitites and nephelinites erupted from the summit crater are lavas derived, via clinopyroxene fractionation, from a more primitive melt. The abundance of feldspathoids in these lavas is in keeping with nepheline flotation. Aphyric melilite nephelinites covering the flanks and the extensive fissure flows have a homogencous chemical composition; rocks from the historical lava lake are slightly more evolved. All these lavas differentiated in a shallow reservoir. Lavas erupted from the parasitic vents are mainly olivine and/or clinopyroxene-phyric rocks. Rushayite and picrites from Muja cone are peculiar high-magnesium lavas resulting from the addition of olivine xenocrysts to melilitic or nephelinitic melts. Fluid and melt inclusions in olivine and clinopyroxene phenocrysts indicate a crystallization depth of 10–14 km. A model involving two reservoirs located at different depths and periodically connected is proposed to explain the petrography of the lavas; this hypothesis is in accordance with geophysical data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00279728
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  • 4
    Electronic Resource
    Electronic Resource
    Rhyolite volcanism in the Krafla central volcano, north-east Iceland (1994)
    Springer
    Bulletin of volcanology 56 (1994), S. 516-528 
    Details
    ISSN: 1432-0819
    Keywords: Key words Rhyolite ; petrology ; minimum melts near-solidus fractionation ; mixing ; Krafla ; Iceland
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract At the Krafla central volcano in north-east Iceland, two main phases of rhyolite volcanism are identified. The earlier phase (last interglacial) is related to the formation of a caldera, whereas the second phase (last glacial) is related to the emplacement of a ring dike. Subsequently, only minor amounts of rhyolite have been erupted. The volcanic products of Krafla are volumetrically bimodal. Geochemically, there is a series of basaltic to basalto-andesitic rocks and a cluster of rhyolitic rocks. Rocks of intermediate to silicic composition (icelandites and dacites) show clear signs of mixing. The rhyolites are Fe-rich (tholeiitic), and aphyric to slightly porphyritic (plagioclase, augite, pigeonite, fayalitic olivine and magnetite). They are minimum melts on the quartz–plagioclase cotectic plane in the granite system (Qz–Or–Ab–An). The rhyolites at Krafla were produced by near-solidus, rather than near-liquidus fractionation. They are interpreted as silicic minimum melts of hydrothermally altered crust, mainly of basaltic composition. They were primarily generated on the peripheries of an active basaltic magma chamber or intrusive domain, where sufficient volumes of crust were subjected to temperatures favorable for rhyolite genesis (850–950°  C). The silicic melts were extracted crystal-free from their source in response to crustal deformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004450050060
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  • 5
    Electronic Resource
    Electronic Resource
    Rhyolite volcanism in the Krafla central volcano, north-east Iceland (1994)
    Springer
    Bulletin of volcanology 56 (1994), S. 516-528 
    Details
    ISSN: 1432-0819
    Keywords: Rhyolite ; petrology ; minimum melts near-solidus fractionation ; mixing ; Krafla ; Iceland
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract At the Krafla central volcano in north-east Iceland, two main phases of rhyolite volcanism are identified. The earlier phase (last interglacial) is related to the formation of a caldera, whereas the second phase (last glacial) is related to the emplacement of a ring dike. Subsequently, only minor amounts of rhyolite have been erupted. The volcanic products of Krafla are volumetrically bimodal. Geochemically, there is a series of basaltic to basalto-andesitic rocks and a cluster of rhyolitic rocks. Rocks of intermediate to silicic composition (icelandites and dacites) show clear signs of mixing. The rhyolites are Fe-rich (tholeiitic), and aphyric to slightly porphyritic (plagioclase, augite, pigeonite, fayalitic olivine and magnetite). They are minimum melts on the quartz-plagioclase cotectic plane in the granite system (Qz-Or-Ab-An). The rhyolites at Krafla were produced by near-solidus, rather than nearliquidus fractionation. They are interpreted as silicic minimum melts of hydrothermally altered crust, mainly of basaltic composition. They were primarily generated on the peripheries of an active basaltic magma chamber or intrusive domain, where sufficient volumes of crust were subjected to temperatures favorable for rhyolite genesis (850–950° C). The silicic melts were extracted crystal-free from their source in response to crustal deformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00302832
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  • 6
    Electronic Resource
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    The origin of bathymetric highs at ridge-transform intersections: A multi-disciplinary case study at the Clipperton Fracture Zone (1994)
    Springer
    Marine geophysical researches 16 (1994), S. 1-50 
    Details
    ISSN: 1573-0581
    Keywords: transform fault ; Clipperton Fracture Zone ; mid-ocean ridge ; East Pacific Rise ; petrology ; multichannel seismic reflection ; sea floor photography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Bathmetric highs on the old crust proximal to ridge-transform intersections (RTIs), termed “intersection highs”, are common but poorly understood features at offsets of fast to intermediate rate spreading centers. We have combined new reflection seismic, photographic, and geochemical data with previously published Seabeam, SeaMARC I, and SeaMARC II data to address the nature of the intersection highs at the Clipperton Fracture Zone. The Clipperton Intersection Highs are both topped by a carapace of young lavas at least 100 m thick. These lavas, which were erupted on the intersection highs, are chemically similar to their adjacent ridge segments and different from the surrounding older crust. At least some of the erupted magma traveled directly from the adjacent ridge at a shallow crustal level. Ridge-related magma covers and intrudes at least the upper 500 m of the transform tectonized crust at the RTI. We suspect that additional magma enters the intersection highs from directly below, without passing through the ridge. The young oceanic crust near the western Clipperton RTI is not thin by regional comparison. The 1.4 m.y. old crust near the eastern Clipperton RTI thickens approaching the transform offset. If the thermal effects of the proximal ridge were negligible, the eastern intersection high crust would appear to be in isostatic equilibrium. We believe that thermal effects are significant, and that the intersection high region stands anomalously shallow for its crustal thickness. This is attributable to increased temperature in the mantle below the ridge-proximal crust. Although ridge magma is injected into the proximal old crust, plate boundary reorganization is not taking place. Intersection high formation has been an ongoing process at both of the Clipperton RTIs for at least the past 1 m.y., during which time the plate boundary configuration has not changed appreciably. We envision a constant interplay between the intruding ridge magma and the disrupting transform fault motion. In addition, we envision a nearly constant input of magma from below the high, as an extension of the magma supply to the ridge from the mantle. Because the proximal ridge profoundly affects the juxtaposed crust at the RTI, sea floor fabric along the aseismic extensions of this fast-slipping transform fault is primarily a record of processes at work at the RTI rather than a record of transform tectonism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01812444
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  • 7
    Electronic Resource
    Electronic Resource
    Analysis of spatial order in sandstones. I. Basic principles (1990)
    Springer
    Mathematical geology 22 (1990), S. 333-359 
    Details
    ISSN: 1573-8868
    Keywords: two-dimensional Fourier transform ; spatial analysis ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The spatial arrangement of sedimentary rock components is a fundamental property of sedimentary rocks. If we assume that the size, shape, and composition of sedimentary rock components (mineral grains, pores) carry useful petrologic information, there is no reason to assume that their spatial arrangement does not. Spatial arrangement has been discussed in terms of “texture” and “fabric,” but it has had little objective measurement or classification. This deficiency is primarily due to the difficulties associated with the quantification of spatial phenomena. However, using digital-imaging techniques it is possible to generate petrographic images from thin-sections and quantify the spatial arrangement of selected rock components using a two-dimensional (2D) Fourier transform. A Fourier transform creates a spectral representation of the image similar to an x-ray diffraction pattern. This paper presents the fundamental framework of 2D Fourier analysis in petrology. This type of analysis provides a means to quantify and analyze the spatial arrangement of rock components in an objective, mathematical framework. 2D Fourier power spectra can be used to characterize the type and degree of spatial order in an image, both in terms of the classical concepts of long-range and short-range order and in terms of spatial patterns characteristic of sedimentary rock. The clearly defined mathematical relationship between an image and its Fourier power spectrum provide the opportunity to define the 2D structure of an image in the same manner that x-ray diffraction patterns are used to map 3D structure in minerals. In addition, a 2D Fourier power spectrum is easily transformed into a radial power spectrum. Radial power spectra can be used to characterize the density of objects in an image. They also provide a valid means to compare and contrast images in a multivariate framework, regardless of the type of order. One of the most desirable properties of a Fourier transform is its reversibility. Using selected components of the power spectrum, the inverse transform can be used to build synthetic images, which highlight those petrologic components that most affect the power spectrum. The inverse transform provides the means to translate the results of analysis into meaningful petrologic characteristics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00889892
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  • 8
    Electronic Resource
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    Geology of Macdonald Seamount region, Austral Islands: Recent hotspot volcanism in the south Pacific (1989)
    Springer
    Marine geophysical researches 11 (1989), S. 101-112 
    Details
    ISSN: 1573-0581
    Keywords: volcanology ; hotspot ; Pacific ; Macdonald ; petrology ; Austral Islands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The southeastern extension of the Austral Islands volcanic chain terminates near 29°S, 140°W at the active Macdonald Seamount. The ‘hotspot’ region near Macdonald consists of at least five other volcanic edifices each more than 500 m high, included in an area about 50–100 km in diameter. On the basis of the sea-floor topography, the southeastern limit of the hotspot area is located about 20 km east of the base of Macdonald, where it is defined by the 3950 m isobath. At the edge of the hotspot area, there is a marked deepening of the seafloor from c.3900 m down to 4000–4300 m. The deeper sea-floor is faulted and heavily sedimented. The Macdonald volcano itself stands 3760 m above the surrounding seafloor, and has a basal diameter of 45 km. Its summit in January 1987 was 39 m below sea level, and it seems likely that Macdonald will emerge at the surface in the near future. Recent (March and November 1986) phreatic explosions on Macdonald Seamount erupted fragments of ultramafic and mafic plutonic blocks together with basic lapilli (volcaniclastic sand). The plutonic blocks have been variably altered and metamorphosed, and in some cases show signs of mineralisation (disseminated sulphides). The blocks presumably come from deeper levels in the volcanic system. The volcanics so far dredged from Macdonald consist of olivine and clinopyroxene cumulus-enriched basalts, evolved basalts, and mugearite. On the basis of incompatible element variations, simple crystal fractionation seems to be controlling the chemical evolution of Macdonald magmas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00285661
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  • 9
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    Some topological and combinatorial properties ofc-component (c + 4)-phase multisystem nets (1987)
    Springer
    Mathematical geology 19 (1987), S. 793-805 
    Details
    ISSN: 1573-8868
    Keywords: Multisystem net ; phase diagram ; petrology ; topology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Multisystem nets are topological analogs of real and potentially real phase diagrams which can be constructed given only the chemography of phases of interest. Combinatorial analysis of c-component (c + 4)-phase multisystems suggests the existence of [(c + 4)!/2] [2(c +4) − 2 (c + 4)] distinct nets. (c + 4)-phase multisystem nets are characterized by three different invariant point stability levels, four different reaction stability levels, and three invariant points along each univariant reaction. Invariant points at the intermediate stability level occur in two disjoint networks. Unlike (c + 3)-phase multisystems, in which all nets are related by transposition, (c + 4)-phase nets form distinct equivalence classes under transposition based on identities of those invariant points at the intermediate stability level. A position matrix is introduced to denote adjacency/connectivity relationships, and a relationship is suggested between the number of nets in each equivalence class under transposition and the number of ways of assigning stability levels to invariant points of an arbitrary position matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00893017
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  • 10
    Electronic Resource
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    Computerized vision for the geologist (1983)
    Springer
    Mathematical geology 15 (1983), S. 3-23 
    Details
    ISSN: 1573-8868
    Keywords: Geology ; petrology ; geological maps ; geological surveys ; image analysis ; image processing ; binary images ; component labels ; phase labels ; erosion ; dilatation ; logical operations ; spatial operations ; GIAPP ; Prospector ; CHARAN ; SIMSAG
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The digital computer can be a tireless friend and assistant to the geologist. The computer has no innate intelligence, but given adequate programs to analyze and interrelate the information on maps, photos, surveys, and other material, the computer can serve as an analytical tool and consultant. To the geologist's qualitative knowledge, theories, and models can be added the possibility of the computer's mathematically precise numerical answers, confirming or refuting the original ideas. In the interactive mode in particular, a dialogue between the geologist and the computer is established, where the geologist and the computer can complement each other's abilities. The basic principles of processing two-dimensional geological data, such as maps, charts, photos, and survey results, are discussed. Some comparisons are also made between the rule-based methods of Prospector, developed at Stanford Research Institute, and the more intuitively guided image-based procedures of GIAPP, developed on the equipment at the National Research Council of Canada, in collaboration with the Geological Survey of Canada and the University of Ottawa.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01030073
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  • 11
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    Morphologically based sampling designs for zoned orthopyroxenes (1979)
    Springer
    Mathematical geology 11 (1979), S. 627-642 
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    ISSN: 1573-8868
    Keywords: sampling ; crystal morphology ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Compositional data of orthopyroxene crystals obtained by the electron microprobe may be biased unless zoning morphologies are taken into account in the sampling design. Statistical models (predictive or interpretative) based on such data are open to question because the input data, such as correlations, are spurious. In an attempt to propose sampling designs two established crystal zoning morphologies are considered which are (a) the concentric shell-type and (b) sectoral zonations. These zonational types lend themselves well to statistical population modeling and graphical interpretation provided assumptions of chemical invariance hold or are approximated by a stratified sampling design. The statistical designs may be regarded as limiting cases in the sense that relaxations of certain assumptions lead to other population models. Hypersthene crystals from a central portion of the mafic norite formation at the Strathcona Mine, Sudbury irruptive, are examined for zonation. It appears that the trace elements have a different zoning morphology than the major elements of hypersthene.
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    URL: http://dx.doi.org/10.1007/BF01031888
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  • 12
    Electronic Resource
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    Principal components analysis of three-way tables (1979)
    Springer
    Mathematical geology 11 (1979), S. 611-626 
    Details
    ISSN: 1573-8868
    Keywords: principal components analysis ; factor analysis ; organic geochemistry ; paleoecology ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A three-mode principal components method allows visualization of the structural or taxonomic relationships within three-way data tables. The fundamental model includes three sets of eigenvectors and a “core matrix” relating the principal components of each mode. Formal relationships between the method and the usual principal components formulation allow calculation of “loadings” and “scores” for each mode; taken with the core matrix, these provide a number of points of view in graphical analysis of three-mode data. The model compares favorably with alternative formulations in terms of simplicity of computation, generality, and symmetry of operation among the modes. An organic geochemical example illustrates the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031887
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  • 13
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    Cooling of a convecting intrusive sheet (1978)
    Springer
    Mathematical geology 10 (1978), S. 301-310 
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    ISSN: 1573-8868
    Keywords: Layered intrusions ; petrology ; thermal histories
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The complete description of the cooling of a layered intrusive sheet is mathematically complex since even the simplest conceivable model involves a moving boundary—the floor or base of the convecting portion of the intrusion for which the boundary conditions are second-order equations including partial derivatives. Numerical solutions for reasonable thermal parameters and initial conditions demonstrate that for most situations between 90 and 100% of the heat loss of the liquid region is through the roof. In certain circumstances the layered series—the crystallized position of the intrusion—actually supplies heat to the convecting region in the late stages of cooling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02048493
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  • 14
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    Mineral variation in anorthositic, troctolitic, and adamellitic rocks of the Barth Island layered structure in the Nain anorthosite complex, Labrador (1976)
    Springer
    Mathematical geology 8 (1976), S. 561-574 
    Details
    ISSN: 1573-8868
    Keywords: regression analysis ; trend analysis ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The Barth Island layered structure is an oval, 6 by 9 km body, consisting of rhythmically layered adamellitic rock in the center which grades outward through jotunite into troctolite. Farther outward the sequence repeats itself in reversed order, strongly reduced in magnitude and finer grained; the adamellitic zone is followed by jotunite which grades into coarse-grained leuconorite and into anorthosite of the Nain complex. The Barth Island structure, having an inverted conical base topped by a hemispherical depression, seems to represent a distorted sequence of rock layers with troctolite at the bottom, grading upward into adamellitic rocks which grade into anorthosite at the top. Trend-surface analysis demonstrates the regional variation of plagioclase and orthopyroxene compositions in the troctolite—adamellite sequence of the central part of the structure. The fits for the second- and third-degree surfaces are good and significant at the 99 percent level. The regression line for compositional variation in coexisting plagioclase and orthopyroxene in all analyzed rocks has a correlation coefficient of r2 = 0.78. The difference between the trends in the troctolite—adamellite sequence and the anorthosite—adamellite sequence is insignificant. The regression curve for compositional variation in coexisting orthopyroxene and olivine has a correlation coefficient of r2 = 0.98. The curve shows good correlation with the experimentally established partitioning curve of Medaris, which indicates that equilibrium conditions prevailed during formation of the olivine—ortho-pyroxene pairs. The results suggest that the troctolite—adamellite sequence and the anorthosite—adamellite sequence are products of fractional crystallization, possibly from the same parental magma.
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    URL: http://dx.doi.org/10.1007/BF01042994
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  • 15
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    Principal components analysis using the hypothetical closed array (1976)
    Springer
    Mathematical geology 8 (1976), S. 25-36 
    Details
    ISSN: 1573-8868
    Keywords: principal components analysis ; closure correlations ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The application of R-mode principal components analysis to a set of closed chemical data is described using previously published chemical analyses of rocks from Gough Island. Different measures of similarity have been used and the results compared by calculating the correlation coefficients between each of the elements of the extracted eigenvectors and each of the original variables. These correlations provide a convenient measure of the contribution of each variable to each of the principal components. The choice of similarity measure (variance-covariance or correlation coefficient)should reflect the nature of the data and the view of the investigator as to which is the proper weighting of the variables—according to their sample variance or equally. If the data are appropriate for principal components analysis, then the Chayes and Kruskal concept of the hypothetical open and closed arrays and the expected closure correlations would seem to be useful in defining the structure to be expected in the absence of significant departures from randomness. If the data are not multivariate normally distributed, then it is possible that the principal components will not be independent. This may result in significant nonzero covariances between various pairs of principal components.
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    URL: http://dx.doi.org/10.1007/BF01039682
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  • 16
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    The use of correspondence analysis in the metallogenic study of ultrabasic and basic complexes (1976)
    Springer
    Mathematical geology 8 (1976), S. 669-681 
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    ISSN: 1573-8868
    Keywords: classification ; factor analysis ; economic geology ; mineralization ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological descriptions of unmineralized and mineralized ultrabasic and basic complexes were collected on a world-wide basis from published literature in the framework of the research project “Basimine.”Its aim is the discovery of controls governing the existence of mineralization in certain complexes and subsequently the development of working hypotheses for nickel prospection. Files were created containing geological and petrological data for each complex. In order to gain an understanding into the relationship existing between variables and complexes, correspondence analysis was applied to various data sets taken from the files. The results indicated criteria, either favorable or unfavorable, for the presence of mineralization in the complexes, and pointed out certain unmineralized complexes which could well be mineralized due to their position as regards known ore deposits in the plan of the factorial axes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01031098
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    Electronic Resource
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    On the need, design, and prospects for an electronic information system serving igneous petrology (1975)
    Springer
    Mathematical geology 7 (1975), S. 363-371 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract An information system is needed to restore access to published information, now so voluminous that suitable levels of familiarity with it cannot be maintained by conventional nonelectronic scholarly devices. The services of the system should be available to petrologists via mail or remote terminal, and should provide, as requested, either retrieval or reduction of data contained in its base. The base should contain chemical, geological, mineralogical, and petrographic information about specimens for which full descriptions have been published. Provisional plans for construction of such a base are briefly reviewed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02080495
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  • 18
    Electronic Resource
    Electronic Resource
    Analysis of geological events (1975)
    Springer
    Mathematical geology 7 (1975), S. 295-321 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; data structure ; independent events ; paleontology ; petrology ; regional mapping ; stratigraphy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geological events, such as emplacement of granite or growth of slaty cleavage, may be ordered into a sequence by two methods. One is to assign each event a place in a time scale, such as years before the present, which amounts to assigning events an age designation from the set of real numbers. In ordering such a list, the algebra of real numbers applies. A second method is to determine the time relations of events in pairs, such as a fold is of type (S1, S2) or granite intrudes conglomerate. These binary relations between events may be used to order events into a sequence using the transitive properties of the relation “older than.” It is shown, however, that the binary relations between events do not follow the familiar rules for the algebra of real or integral numbers and it is necessary to erect a new system of relations called the “algebra of events.” The fundamental relation is “older than or equivalent to” and this may be used to define the relations “older than”, “younger than”, “equivalent to”, “incomparable to”, and “covers.” The essential difference from the algebra of integers is that the reflexive relation (“equal to”) is replaced by two such relations (“equivalent to” and “incomparable to”) in the algebra of events. A number of binary relations between events may be assembled into an event matrix which is basically a truth table for the relation “older than.” This may be ordered and stacked by operations termed ORDER and STACK. The relationship of each event to every other event may be determined by simple inspection of an ordered, stacked matrix, and from this a geological history may be assembled. If there are contradictions in the field data, ordering into a proper sequence is impossible and may be detected. If there are ambiguities in the field data, there are several different orders that are proper sequences so that the event matrix may be ordered. However, the ambiguities occur as voids in the stacked matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02081703
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  • 19
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    Some problems of interpreting the correlations between the modal variables in granitic rocks (1974)
    Springer
    Mathematical geology 6 (1974), S. 245-258 
    Details
    ISSN: 1573-8868
    Keywords: correlation between proportions ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Correlation coefficients of modal variables from several suites of granitic rocks have been calculated and tested for significance using the Chayes-Kruskal and Chayes methods. The results show that although Chayes' remaining-space transformation does, in general, weaken the original proportion correlations, the positive and low-negative original proportion correlations tend to increase in absolute value because of a tendency of positive increment of the covariance by such transformation. However, no satisfactory procedure for choosing the variable to be transformed (V2)could be determined, and testing of the significance of remaining-space correlations is found to be highly problematic. It is shown also that the Vistelius-Sarmanov procedure of calculation of correlation coefficients from closed-table data does not effectively eliminate the closure effect. It is concluded that assigning statistical significance to the correlation coefficients between modal variables is, in general, unsatisfactory, except where the number of variables ⩾8,the sample size is large (say, ⩾30),and there is no negative element in the variance vector of the corresponding open variables.
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    URL: http://dx.doi.org/10.1007/BF02082890
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  • 20
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    Preliminary assessment of a nonlinear mapping algorithm in a geological context (1973)
    Springer
    Mathematical geology 5 (1973), S. 39-57 
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    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; dimensionality reduction ; mapping ; multivariate analysis ; principal-components analysis ; general geology ; geochemistry ; paleontology ; petrology ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A new algorithm has been developed by J. W. Sammon for the nonlinear-point mapping of high-dimensional data in two dimensions such that the inherent structure of the data is approximately preserved. This paper describes results using several sets of geologic data including stratigraphic thickness, petrographic modal analysis, and morphological or geochemical measurements. Comparisons are made with hierarchical cluster analysis using dendrogram representation. Initial results are encouraging and suggest that the technique could have widespread geological applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114086
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    Thoughts on use of principal component analysis in petrogenetic problems (1973)
    Springer
    Mathematical geology 5 (1973), S. 341-350 
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    ISSN: 1573-8868
    Keywords: principal components analysis ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111985
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  • 22
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    Estimation of parameters in petrologic materials balance equations (1973)
    Springer
    Mathematical geology 5 (1973), S. 225-236 
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    ISSN: 1573-8868
    Keywords: estimation ; materials balance ; mathematics ; mixing equations ; geochemistry ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A rigorous treatment of the least-squares estimation of the parameters in petrologic materials balance equations is developed to take into account the uncertainties inherent in the chemical analyses. The choice of the optimal estimation procedure for a particular problem is dependent upon the extent of the petrogenetic understanding of the exact nature of the materials balance involved. Some of the complications entailed in obtaining least-squares estimates are illustrated by the examples of magmatic differentiation and metamorphic reactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111812
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  • 23
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    A geomathematic investigation of syntexis in a Gabbroic formation (1973)
    Springer
    Mathematical geology 5 (1973), S. 321-339 
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    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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    URL: http://dx.doi.org/10.1007/BF02111984
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    Ideal granite and its properties. I. The stochastic model (1972)
    Springer
    Mathematical geology 4 (1972), S. 89-102 
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    ISSN: 1573-8868
    Keywords: crystallization ; stochastic model ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Investigation of granitic rocks in the search for hidden ore deposits, restoration of their history, and understanding their special properties requires comparison of intrusive bodies. Comparisons are best made to some standard. The conception of an ideal magmatic granite as a standard is introduced in this paper. Investigation indicates that sequences of quartz grains potassium feldspars, and plagioclases of an ideal magmatic granite have definite mathematical properties.
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    URL: http://dx.doi.org/10.1007/BF02080295
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    Computer program to analyze directional data, based on the methods of Fisher and Watson (1972)
    Springer
    Mathematical geology 4 (1972), S. 177-202 
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    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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    URL: http://dx.doi.org/10.1007/BF02311717
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    Effect of trends on correlation in open and closed three-component systems (1972)
    Springer
    Mathematical geology 4 (1972), S. 317-330 
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    ISSN: 1573-8868
    Keywords: linear correlation ; mapping ; trend analysis ; general geology ; mineralogy ; petrology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract It is well known among geologists that closure of an open-number system, as when stratigraphic rock thicknesses are converted to percentages, introduces correlations among the components even in the absence of correlations in the open system. In closed three-component systems the covariances are single-valued functions of the closed variances and are exactly predictable. If the open system has “inherent” correlation (point correlations) among its components the corresponding closed covariances reflect their presence in a predictable manner. If areal trends are present in the open system, the open covariances are themselves affected, but this “trend effect” can be completely removed to recover the initial point correlations among the components. Areal trends in open systems strongly influence the structure of the closed variance-covariance matrices, and the situation becomes increasingly complicated if the open system has both point correlations and areal trends. The paper considers the problems involved, and includes Monte Carlo runs to compare computed and predicted variances and covariances as data sets are followed from open systems with correlation but no trend to the closed equivalent of open systems with point correlations and trends.
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    URL: http://dx.doi.org/10.1007/BF02114093
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  • 27
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    Operator error in petrographic point-count analysis: A theoretical approach (1972)
    Springer
    Mathematical geology 4 (1972), S. 35-43 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Operator error in petrographic point-count analysis introduces bias into the estimates of proportion in a thin section. A correction for this bias, leading to an unbiased estimator of the true proportion in that thin section, is here proposed. Operator error also affects the confidence interval, and in this situation, too, an adjustment is possible. The approach proposed requires that the probabilities associated with operator error, categorized into A-type and B-type errors, are known or assumed. The A-type operator error tends to underestimate the true proportion in a thin section, whereas the B-type operator error tends to overestimate it.
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    URL: http://dx.doi.org/10.1007/BF02083191
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  • 28
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    Counting error in petrographic point-count analysis: A theoretical and experimental study (1971)
    Springer
    Mathematical geology 3 (1971), S. 15-41 
    Details
    ISSN: 1573-8868
    Keywords: modal analysis ; sampling ; statistics ; mineralogy ; petrology ; sedimentology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The binomial model, commonly used to estimate counting error in point-count analysis, misestimates this error when the observation points on a grid are positively or negatively correlated. A model, called the “cell model,” is proposed as an alternative to the binomial model for use in studies, especially with coarse-grained rocks, in which such correlation is known or thought to exist. In the new model the thin section is conceptually partitioned into a number of cells (six is recommended), and the assumption is made that the proportions in the individual cells are statistically independent and that their variance does not differ from cell to cell. Empirical relations obtained from a suite of 200 thin sections of limestones are in reasonable support of the prediction that large particle size adversely affects counting error estimates based on the binomial model.
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    URL: http://dx.doi.org/10.1007/BF02047430
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    Quantitative discrimination between magmatic units of the singhbhum granite (1971)
    Springer
    Mathematical geology 3 (1971), S. 123-133 
    Details
    ISSN: 1573-8868
    Keywords: cluster analysis ; distance functions ; mineralogy ; petrology ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The weight-percent values of four mineralogic variables (quartz, K feldspar, color index, and muscovite) for 10 sets of granitic rocks (20–50 samples in each set) from magmatic units of the Singhbhum granite were used for (1) computation of the Mahalanobis' generalized distance functions (D 2) between all pairs of the 10 sets, (2) testing significance of the difference between the multivariate means, and (3) computation of the linear discriminant functions between all possible pairs of the sets. The 10 data sets are for six magmatic units which belong to three successive but closely related phases of emplacement. The multivariate means for all sets are significantly different except for those between two of the sets of phase I. Cluster analysis on the basis of theD 2 values enables the 10 sets to be placed into four distinct groups. Group A includes two subgroups, one of which consists of two sets representing typical members of phase I; the other subgroup includes two sets which are typical of phase II. Group B includes two sets which are typical of phase III. The other four sets do not group with the typical representatives of the three phases, probably because of certain special conditions of their emplacement. A separate series ofD 2 computation from the same data, but excluding the color index, was unsuccessful in making the four aberrant sets group with the typical members of the respective phases. Efficient LDF's could be determined for discrimination between most pairs of the 10 sets of granite rocks.
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    URL: http://dx.doi.org/10.1007/BF02045956
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    Journal cover
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    AAPG Bulletin / Bulletin American Association of Petroleum Geologists
    American Association of Petroleum Geologists (AAPG) | GeoScienceWorld
    Online: 1.1917 – (GFZ only)
    Print: 34(12).1950 – 93(4).2009 (Location: A17, Kompaktmagazin, 9/7 - 10/6)
    Details
    Formerly as: The American Association of Petroleum Geologists Bulletin; Bulletin of the American Association of Petroleum Geologists; Bulletin of the Southwestern Association of Petroleum Geologists  (1917–1980)
    Publisher: American Association of Petroleum Geologists (AAPG) , GeoScienceWorld
    Print ISSN: 0016-7606 , 0149-1423
    Electronic ISSN: 1943-2674
    Topics: Geosciences
    Keywords: GeoScienceWorld ; petrology ; Erdöl ; Erdölgeologie ; Erdölgewinnung ; Erdgas ; Erdgasgeologie
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