The stream function and Gauss' principle of least constraint: Two useful concepts for structural geology

To the extent that rock deformation can be approximated by a two-dimensional Newtonian model, a powerful stream-function simulation method is applicable. The significance of stream functions is that velocity, strain, stress and energy derived from the same stream function satisfy automatically three basic conditions of dynamics:

1. (1) the condition of continuity.

2. (2) the Navier-Stokes equations.

3. (3) conservation of energy.

Hence we state with Jaeger: “If a stream function can be found which satisfies the boundary conditions of a dynamic model the complete solution follows.” All pertinent bits of dynamic information are implied in the stream function from which they can be directly derived, guaranteed—so to speak—not to violate the basic conditions of dynamics. Stream functions useful in structural geology are solutions of: A double-polynomial solution of max. degree 14 is developed, in which the coefficients are related controlled by the ⁴ψ = 0 constraint, and their absolute values are determined by the boundary conditions of specific models and by the condition of maximum rate of energy dissipation or maximum rate of decline of potential energy. The polynomial stream function is applied to a collapsing viscous “nappe” consisting of a thin basal layer with low viscosity on which a thicker layer with high viscosity slides due to gravitational spreading. The velocity of forward movement depends upon absolute and relative values of the following parameters: viscosity, thickness, the aspect ratio and density. The velocity of a variety of nappes with different thicknesses, aspect ratios, viscosities and densities is determined.     

Synthetic seismograms from generalized ray tracing1

A new method of numerical computation of elastic wavefields in regions containing caustics is tested. The method is an extension of the asymptotic ray theory (ART). The essential features of the method consist of the application of expressions which are well defined at caustics and expressed in terms of ray tracing combined with complex ray tracing in caustic shadows. The method and an outline of the underlying theory are briefly presented, followed by a comparison with finite differences on a test model involving a caustic cusp. The comparison reveals the unexpectedly high degree of accuracy of the new method.     

Excess K-Ar ages of glauconite from the Upper Marine Molasse and evidence for glauconitization of mica

K-Ar age determinations along with optical investigations were used to examine whether glauconite from the Upper Marine Molasse (OMM) is of authigenic, allogenic or transformed origin. For this purpose 16 glauconite samples from 14 different localities were investigated from the Burdigalian Muschelsandstein collected along a traverse from Lake Constance to west of Geneva.Optical observations on washed grain concentrates reveal the presence of different alteration products of biotite, confirming earlier studies. Moreover, thin-section preparations of sample aliquots showed that the glauconite grains contain biotite-relics, which might account for the elevated absolute ages.The optical evidence is confirmed by individual mineral fractions, which show chlorite with biotite-»nucleii«, chlorite-lamellae, and »layered«-glauconites. All these observations point to glauconite genesis by transformation of biotite. The complete transformation from biotite via chlorite to glauconite apparently results in a chemically more stable state.The K-content of the samples varies from 5.6 to 7.0% K₂O, indicating mature but not highly evolved glauconite. 19 apparent K-Ar dates range from 17.7 to 34.9 Ma. In comparison with the biostratigraphy and the estimated Burdigalian age of about 18 Ma nearly all dates are too high. These strongly scattered dates are thus stratigraphically meaningless and seem to exclude an authigenic formation of these glauconites from faecal pellets. Furthermore, geologic arguments exclude an allogenic (= detrital) origin.Glauconite genesis in the Upper Marine Molasse must therefore be distinguished from both authigenic and allogenic formation mechanisms. A new term »meta-allogenic« is therefore used to describe glauconite growth by transformation of allogenic mica.

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Zusammenfassung Um zu prüfen, ob Glaukonite aus der Oberen Meeresmolasse (OMM) authigen, allothigen oder durch Umwandlung aus anderen Mineralien entstanden sind, wurden sie — nebst mineraloptischen und röntgenographischen Untersuchungen — mit der K-Ar-Methode datiert. Aus 14 verschiedenen Lokalitäten zwischen Bodensee und einigen Kilometern westlich von Genf wurden 16 Glaukonit-Proben aus dem burdigalen Muschelsandstein entnommen.Sedimentpetrologische Studien an Körner-Konzentraten offenbarten verschiedene Umwandlungsprodukte von Biotit. Zudem zeigten Aliquots von Dünnschliff-Präparaten, daß einzelne Körner unterschiedlich große Relikte von Biotit enthalten, die die zu hohen Alterswerte verursachen können.Die verschiedenen Mineralfraktionen bestätigen den Charakter von Übergangsstadien: Chlorit mit Biotit-Kernen, Chloritlamellen und »Schicht«-Glaukonit. Alle diese Beobachtungen deuten auf eine Glaukonitgenese aus der Umwandlung von Biotit. Die vollständige Umwandlung von Biotit über Chlorit zu Glaukonit scheint mit dem End-produkt einen chemisch stabileren Zustand anzustreben.Der K₂O-Gehalt aller Proben variert von 5.6 bis 7.0%. Dies weist auf »reifen«, aber nicht hochentwickelten Glaukonit hin. Die 19 K-Ar-»Alter« liegen zwischen 17.7 und 34.9 Ma. Im Vergleich mit der Biostratigraphie und dem geschätzten burdigalen Alter von ca. 18 Ma, sind diese Daten zu hoch und daher stratigraphisch bedeutungslos. Eine authigene Bildung von Glaukonit aus Kotpillen (faecal pellets) muß somit ausgeschlossen werden. Außerdem kommt aus geologischen Gründen eine detritische (allothigene) Herkunft ebenfalls nicht in Betracht.Für die Glaukonit-Genese in der Oberen Meeresmolasse muß daher ein anderer Bildungsprozess verantwortlich sein. Um die Umwandlung von eingeschwemmtem (= allothigenem) Biotit zu Glaukonit zu beschreiben, wurde der neue Term »meta-allothigen« eingeführt.

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Résumé Afin de rechercher si les glauconites de la OMM (= molasse marine supérieure) sont authigènes, allothigènes ou proviennent de la transformation d'autres minéraux, on les a datées par la méthode K-Ar, conjointement à une étude optique et röntgenographique. 14 localités, situées depuis de lac de Constance jusqu'à quelques kilomètres à l'ouest de Genève, ont fourni 16 échantillons de glauconite du Muschelsandstein burdigalien.L'étude optique des grains, effectuée sur des concentrés, a révélé divers produits de transformation de la biotite. En outre, les examens en coupes minces ont montré, dans les grains de glauconite, des restes de biotite d'importance variable. Ces restes de biotite peuvent être responsables de valeurs trop élevées obtenues dans les mesures d'âge.L'examen des diverses fractions minérales permet de préciser les stades de transformation: chlorite avec noyaux de biotite, lamelles de chlorite et glauconite »stratifiées«. Toutes ces observations indiquent une genèse de la glauconite par transformation de la biotite. La transformation complète de la biotite en chlorite puis en glauconite semble ainsi correspondre à un état chimique plus stable.La teneur en K₂O de tous les échantillons varie entre 5,6 et 7,0%, indiquant une glauconite »mature«, mais pas très évoluée. Les 19 »âges« K-Ar sont compris entre 17,7 et 34,9 Ma. Comparés à la biostratigraphie et à l'âge burdigalien, estimé à environ 18 Ma, ces résultats sont nettement trop élevés et ne présentent donc aucune valeur stratigraphique. Il faut ainsi exclure une formation authigène de la glauconite à partir de pelotes fécales. De plus, une origine détritique (= allothigène) ne peut être envisagée pour des raisons géologiques.En conséquence, c'est bien un processus différent qui est responsable de la genése de la glauconite dans la OMM. Le terme nouveau »méta-allogénique« est proposé pour indiquer la transformation de la biotite détritique en glauconite.

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- , , , (OMM) , , /. 14- 16 . - . , . : , « ». , . , , . K₂O 5,6 7,0%. / 17,7 34,9 . , 18 . (faecal pellets) . , ., . , «-».

     

Mineral equilibria in the six-component seawater system,Na-K-Mg-Ca-SO4-Cl-H2O at 25°C. II: Compositions of the saturated solutions

Using the solubility model developed by Harvie and Weare (1980), the stable mineral-solution assemblages for the six-component system Na-K-Mg-Ca-SO₄-Cl-H₂O and its constituent 5-, 4- and 3-component systems at 25°C have been defined. Invariant point maps have been constructed showing the connections by univariant lines. The solubility volumes for all 20 minerals considered are also illustrated. Of the 37 invariant points, only 3 have solutions which are Ca-rich; the remaining 34 can be plotted in the reciprocal system Na-K-Mg-SO₄-Cl, which is similar to the seawater system, except that the restriction of halite saturation has been removed. Application of these results and implications for the evolution of major brine types are briefly discussed.     

Paleomagnetism of red beds of Early Devonian age from Central Iran

Paleomagnetic results are reported from 13 sites of red beds of Early Devonian age from Central Iran. Detailed paleomagnetic analyses were carried out. Two types of partial progressive demagnetization were applied, one using alternating magnetic fields, the other heating. These procedures resulted in the detection of the characteristic remanences with a mean direction with D = 24.2°, I = 1.3° (α₉₅ = 10.1°). The paleomagnetic pole is located at 51.3°N, 163.7°W. If one shifts the Iranian landmass to its most likely position in the Gondwana configuration, then the position of the paleomagnetic pole coincides with the alternative polar wander path [14,15] which crossed South America in early Middle Paleozoic times.