The critical inclination problem — 30 years of progress

The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

Pleistocene mass-flow deposits of basaltic hyaloclastite on a shallow submarine shelf,South Iceland

A Pleistocene subaqueous, volcanic sequence in South Iceland consists of flows of basaltic hyaloclastite and lava with interbedded sedimentary diamictite units. Emplacement occurred on a distal submarine shelf in drowned valleys along the southern coast of Iceland. The higher sea level was caused by eustatic sea-level change, probably towards the end of a glaciation. This sequence, nearly 700 m thick, rests unconformably on eroded flatlying lavas and sedimentary rocks of likely Tertiary age. A Standard Depositional Unit, describing the flows of hyaloclastite, starts with compact columnar-jointed basalt overlain by cubejointed basalt, and/or pillow lava. This in turn is overlain by thick unstructured hyaloclastite containing aligned basalt lobes, and bedded hyaloclastite at the top. A similar lithofacies succession is valid for proximal to distal locations. The flows were produced by repeated voluminous extrusions of basaltic lava from subaquatic fissures on the Eastern Rift Zone of Iceland. The fissures are assumed to lie in the same general area as the 1783 Laki fissure which produced 12 km³ of basaltic lava. Due to very high extrusion rates, the effective water/melt ratio was low, preventing optimal fragmentation of the melt. The result was a heterogeneous mass of hyaloclastite and fluid melt which moved en masse downslope with the melt at the bottom of the flow and increasingly vesicular hyaloclastite fragments above. The upper and distal parts of the flow moved as low-concentration turbulent suspensions that deposited bedded hyaloclastite.     

High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle

Synthetic spinel harzburgite and lherzolite assemblages were equilibrated between 1040 and 1300° C and 0.3 to 2.7 GPa, under controlled oxygen fugacity (f _{O 2}). f _{O 2} was buffered with conventional and open double-capsule techniques, using the Fe−FeO, WC-WO₂-C, Ni−NiO, and Fe₃O₄−Fe₂O₃ buffers, and graphite, olivine, and PdAg alloys as sample containers. Experiments were carried out in a piston-cylinder apparatus under fluid-excess conditions. Within the P-T-X range of the experiments, the redox ratio Fe³⁺/ΣFe in spinel is a linear function of f _{O 2} (0.02 at IW, 0.1 at WCO, 0.25 at NNO, and 0.75 at MH). It is independent of temperature at given Δlog(f _{O 2}), but decreases slightly with increasing Cr content in spinel. The Fe³⁺/ΣFe ratio falls with increasing pressure at given Δlog(f _{O 2}), consistent with a pressure correction based on partial molar volume data. At a specific temperature, degree of melting and bulk composition, the Cr/(Cr+Al) ratio of a spinel rises with increasing f _{O 2}. A linear least-squares fit to the experimental data gives the semi-empirical oxygen barometer in terms of divergence from the fayalite-magnetite-quartz (FMQ) buffer:

Lead isotope and Pb-Pb model age determinations of ores from Central Europe and their metallogenetic interpretation

The paper presents lead isotope data from 211 samples from Phanerozoic lead-bearing ore occurrences in Central Europe, particularly from the Southern part of the former German Democratic Republic. The data are interpreted in terms of Amov's dynamic model of continuous lead isotope evolution. The relationships between thoro-genic and urano-genic model ages and the source of lead in different regional units are discussed. We observed differences in lead isotope evolution in the Hercynian internides and externides. Within the Moldanubian and Saxothuringian zones we distinguish five main lead-bearing ore associations: (1) Cambrian, stratiform base metal (Hermsdorf-Waldsassen; ²⁰⁶Pb/ ²⁰⁴Pb=17.50–17.70), (2) Devonian, vein type Sb-bearing, metamorphogene (neumühle-Hartmannsdorf; 17.80–18.00), (3) Upper Carboniferous-Permian, polymetallic, including tin, vein type (Kutna hora-Freiberg-Altenberg; 18.00–18.20), (4) Triassic (-Jurassic), Pb–Ba, vein type (Stibro-Halsbrücke; 18.20–18.60), (5) Cenozoic, polymetallic, vein type, riftogene (Roztoky-Banska tiavnica; 18.80–19.10). Pb isotope characteristics from ores of the Montagne Noire and the Brioude-Massiac district correspond to this subdivision. Ore associations from the Rheno-Hercynian zone display higher ²⁰⁷Pb/²⁰⁴Pb ratios which can be explained by more evolved and less metamorphosed source rocks. Mineralizations of the eastern Harz (Straßberg-Neudorf) belong to the Permian association, those from the western Harz (Clausthal-Bad Grund) to the Triassic-Jurassic. Because of Pb isotope agreement the stratabound Rammelsberg and the vein bound Ramsbeck-I mineralization are presumed to be isogenetic. Pb isotope identity of distinct mineralizations in the basement zone (Halsbrücke-Bad Grund) and in the Triassic sediments (Gorny Slask-Mechernich-Bleiglanzbänke) suggests a strong genetic coherence. Pb isotope conformity between the Upper Carboniferous-Permian-Triassic ore associations and Hercynian postkinematic granitoids, and lamprophyric rocks, also favours a close relationship. Pb isotope and other data indicate crustal sources. As the age of the ore associations decreases, crustal influences generally increase, apart from the Roztoky mineralization.     

Littoral '92

Reports

Littoral '92     

A layered basic intrusion,deformed and metamorphosed in granulite faciès of the Sri Lanka basement

A layered basic intrusion has been found in the Central Granulite Belt of the Sri Lanka continental basement. It intruded parallel to bedding, before all or early during deformation of neighbouring metasediments. Deformation, affecting metasediments and the intrusion alike, includes flattening to c. 1/20 of the original thickness and NNW-stretching to c. 20 times the original length. The intrusion is now 170–300 m thick. Most of the deformation was acquired under granulite facies metamorphism. The intrusion was then folded, still at high T, by a large F₄-synform with an axis parallel to str₁ and a steep axial plane. A steep axial plane cleavage and minor folds are related to this big fold. Stretching continued along its axis. Late during formation of this fold a granite intruded, mainly following S₄ cleavage planes. The intrusion shows a homogeneous gabbroic series at the bottom, followed upwards by a differentiated and layered series. A thin sequence of ultramafic rocks occurs near the middle. This indicates multiple melt-injection. More homogeneous partly biotite-bearing amphibolites form the top of the succession. Magmatic layering is well preserved, but no magmatic minerals or grain fabrics have escaped deformation or metamorphism. Static annealing under granulite facies conditions outlasted all deformation and was accompanied and followed by the beginning of cooling. Hornblende-Plagioclase coronas formed round garnets at this stage. Geochemical work, carried out by STOSCH (1991) on our samples, confirms the cumulate nature of the rocks.

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Zusammenfassung Eine geschichtete Basische Intrusion wurde im Central Granulite Belt der tiefen, kontinentalen Kruste Sri Lankas entdeckt. Sie intrudierte parallel zur Schichtung in benachbarte Sedimente, vor aller oder sehr früh in deren Deformation. Die Deformation, die Sedimente und die Intrusion in gleicher Weise betraf, führte zu Plättung auf das ca. 1/20 der Ausgangsdicke und zu NNW-Streckung auf das ca. 20fache der Ausgangslänge. Heute ist die Intrusion 170–300 m dick. Der Hauptteil der Deformation wurde unter Granulit-Fazies-Bedingungen erworben. Noch bei hoher T wurde die Intrusion durch eine große F₄-Falte gefaltet. Deren Achse liegt parallel der Streckungsrichtung, stri, ihre Achsenebene ist steil. Eine steile, Achsenebenen-parallele S₄-Schieferung und kleinere Falten entstanden mit ihr. Während der Bildung dieser Falte hielt die Streckung parallel ihrer Achse an. Spät während ihrer Bildung intrudierte ein Granit. Er folgt im wesentlichen S₄. Die Intrusion beginnt unten mit einer homogenen, gabbroiden Serie. Nach oben folgt eine differenzierte, geschichtete. Ein dünnes Paket ultramafischer Lagen erscheint nahe der Mitte. Es weist auf multiple Schmelz-Zufuhr hin. Homogenere Amphibolite, teils mit Biotit, bilden den obersten Teil. Magmatischer Lagenbau ist gut erhalten, lokal mit Gradierung. Magmatische Minerale oder Korngefüge haben Deformation und Metamorphose nicht überlebt. Statische Temperung unter Granulit-Fazies-Bedingungen überdauerte alle Deformation. Sie beginnt und dauert an bei bereits sinkender T. Hornblende-Plagioklas-Koronas bilden sich in diesem statischen Endstadium. STOSCH (1991) untersuchte unsere Proben von der Intrusion geochemisch. Er bestätigte die Kumulatnatur der Gesteine.

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Résumé Une intrusion basique litée a été découverte dans la ceinture centrale granulitique du socle continental du Sri Lanka. L'intrusion s'est effectuée parallèlement à la stratification, avant la déformation des métasédiments encaissants ou tout au début de celleci. La déformation, qui affecte à la fois les métasédiments et l'intrusion, comporte un aplatissement jusqu'à ± 1/20 de l'épaisseur d'origine, et un allongement de ± 20 fois en direction NNW. L'intrusion présente actuellement une épaisseur de 170 à 300 m. La plus grande part de la déformation a été acquise dans les conditions du faciès des granulites. L'intrusion a ensuite été plissée, toujours à haute T, en un large synforme F₄ dont l'axe est parallèle à l'allongement stri et dont le plan axial est vertical. Ce grand pli est accompagné d'une schistosité S₄ plan-axiale redressée et de plis secondaires. L'allongement s'est poursuivi parallèlement à son axe. A la fin de la formation de ce pli, un granite s'est intrudé, qui suit en gros S₄. L'intrusion comporte à sa base une série gabbroïque homogène, suivie vers le haut par une série litée et différenciée. Elle contient, vers son milieu, une intercalation mince de roches ultramafiques. Ceci implique des injections répétées de magma. Le sommet est formé d'amphibolites homogènes partiellement biotitiques. Le litage magmatique est bien conservé, mais aucun minéral ou fabrique magmatique n'a échappé à la déformation et au métamorphisme. Un recuit statique dans les conditions granulitiques a suivi la déformation; il a été accompagné et suivi par le début du refroidissement. A ce stade, des couronnes à hornblende-plagioclase se sont formées autour des grenats. Une étude géochimique, effectuée en 1991 par Stosch sur nos échantillons confirme le caractère de cumulat des roches.

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- . , . , , 1/20 20- NNW . 170–300 . . F₄, str₁, . , S₄, . . . S₄. , , . . , , . coxpa . , .. . , . . . . STOSCH (1991) .

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List of abbreviations ss sedimentary bedding - s₁ first cleavage, plane of first flattening - str₁ Direction of first stretching; although L is usually used for lineations of different kind, including stretching, we use this term to point out that extension is proved in each case - F₂ second folds = first folds folding s₁ - s₂ second cleavage or plane of flattening - F₃ third folds - s₃ third cleavage or plane of flattening - F₄ fourth folds, folding s_1,2,3 and F_1,2,3 - s₄ fourth cleavage or plane of flattening - str₄ direction of fourth stretching - F_5,6 fifth and sixth folds - gf(m) granulite facies (metamorphism) - af(m) amphibolite facies (metamorphism) - KNa-f KNa-feldspar - pg plagioclase - f feldspar - opx orthopyroxene - cpx clinopyroxene - px pyroxene - hb hornblende - bi biotite - cc calcite - do dolomite - qz quartz - mt magnetite     

The structural state of the former lower continental crust in Calabria (S. Italy)

In the Northern Serre (S. Italy), a continuous section through a former lower continental crust is exposed (Schenk 1984, 1985). These granulite facies rocks have not been penetratively deformed during their uplift to higher crustal levels. Therefore, they allow to study the structural state of the lower continental crust. Most rockforming minerals, among them ortho- and clinopyroxene and cordierite, show recrystallization structures. Quarz basal subgrain boundaries are developed in lower levels of the lower crust and disappear toward higher levels. In addition to dimensional orientations of the rockforming minerals, the preferred crystallographic orientations of plagioclases, cordierite, amphibole, pyroxenes and, rarely, quartz reflect the strain orientation of the prograde high-T deformation. During this deformation, the stretching direction was constant NNE-SSW throughout the exposed lower crustal section. Shear indicators are rare. This points to the fact that deformation has been homogeneous and coaxial flattening. There is only a small variation in orientation and strength of textures throughout the exposed lower crust. Therefore, neighbouring layers of different composition rather than different deformation might serve as seismic reflectors in the former lower crust.

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Zusammenfassung In der nördlichen Serre (Süditalien) ist ein zusammenhängender Bereich einer ehemaligen kontinentalen Unterkruste aufgeschlossen (Schenk 1984, 1985). Diese granulitfaziellen Gesteine sind bei ihrem Aufstieg in höhere Krustenbereiche nicht durchgreifend überprägt worden. Deshalb läßt sich an ihnen noch der strukturelle Zustand der ehemaligen Unterkruste studieren. Außer in Feldspäten, Quarz und Amphibol tritt auch in Ortho- und Klinopyroxen und in Cordierit Rekristallisation auf. In tieferen Krustenniveaus sind im Quarz basisparallele Subkorngrenzen entwickelt, die in höheren Krustenbereichen nicht auftreten. Sowohl die Gestaltregelungen der gesteinsbildenden Minerale als auch die kristallographischen Plagioklas-, Cordierit-, Amphibol-, Pyroxen- und (seltener) Quarzregelungen spiegeln die Strain-orientierung der prograden hochtemperierten Deformation wider. Während dieser Deformation blieb die Streckung im gesamten Unterkrustenbereich konstant NNE-SSW orientiert. Scherindikatoren sind selten. Beides deutet darauf hin, daß die Deformation homogen und als koachsiale Plättung abgelaufen ist. Im gesamten aufgeschlossenen Unterkrustenbereich variieren weder Intensität noch Orientierung der kristallographischen und gestaltlichen Regelungen der gesteinsbildenden Minerale wesentlich. Deshalb sollten in der ehemaligen Unterkruste Lagen unterschiedlicher Deformation weniger als seismische Reflektoren in Frage kommen als Lagen unterschiedlicher Zusammensetzung.

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Résumé Le Massif de la Serre Septentrionale en Calabre (Sud de l'Italie) représente un tronçon d'une ancienne croûte continentale profonde (Schenk 1984, 1985). Les roches du faciès granulite qui le constituent n'ont pas subi de déformation penetrative lors de leur ascension dans les niveaux plus superficiels de la croûte. Leur étude permet donc de reconstruire les caractéristiques structurales de l'ancienne croûte profonde. Non seulement les feldspaths, le quartz et l'amphibole, mais encore l'orthopyroxène, le clinopyroxène et la cordiérite ont recristallisé. Dans les niveaux les plus profonds de la croûte on observe dans les cristaux de quartz des bordures de sous-grains parallèles à la base. Celles-ci n'apparaissent plus dans les niveaux plus superficiels. L'orientation des cristaux des minéraux constitutifs des roches, de même que l'orientation des réseaux cristallins du plagioclase, de la cordiérite, de l'amphibole, du pyroxène et (mais plus rarement) du quartz réflètent la direction de contrainte de la phase de déformation prograde de haute température. Pendant cette phase de déformation, la direction d'extension est demeurée NNE-SSW. Les témoins de cisaillement sont rares, ce qui montre que la déformation s'est effectuée de façon homogène, en relation avec un aplatissement coaxial. Les textures varient très peu en orientation comme en intensité dans toute la coupe de croûte profonde exposée. En conséquence, l'existence de réflecteurs sismiques devrait refléter des différences dans les compositions minéralogiques des roches plutôt que dans leurs caractéristiques structurales.

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Serre (Schenk, 1984, 1985). . . , , . , , . , , , , () . NNE-SSW. . , . , , . , , .

     

Coulomb-trapped particles in the electromagnetic fields of an oblique magnetic rotator

An oblique, rotating magnetized sphere emits electromagnetic waves which, for large magnetization, can quickly accelerate charged particles to very high energies. A central, attractive Coulomb force can trap particles in the region beyond the light cylinder by balancing the accelerating influence of the radiation on the particles. We sample some of the particle orbits possible under these dynamical conditions. A general feature of these orbits is that non-interacting particles started with random initial conditions in the domain of attraction of these orbits will arrange themselves on a curve corotating with the axis of magnetization. Such particle configurations can be a source of pulsed radiation. In the idealized case of no interparticle interactions the spectral index for the radiation emitted by one frequently occurring configuration is found to be –2/3, for emission from radio to -ray frequencies. The dynamical conditions in this simple model closely match those prevalent in outer pulsar magnetospheres, making it possible that part of the radiation from pulsars is emitted by trapped plasma in the region beyond the light cylinder.     

On the systematic errors of the determinations of the absolute orientation of the meridian marks

The classical method of determination of the absolute azimuth (or Bessel's parameter n) can secure sufficiently precision for RA from observations of stars at high geographical latitudes during polar night only.