The qualitative zoning record of minerals. A method for determining the duration of metamorphic events?

Summary The efficacy of ion exchange in petrological systems, for example the Fe-Mg exchange between garnet and biotite, is a function of grainsize, temperature, rates of temperature change and diffusion parameters. The combination of these variables determines the final zoning profile of minerals. Therefore, zoning profiles may be used to derive one of these variables if the others are known. For example, a mineral grain that experienced a short thermal event may still preserve a zoning profile characteristic of the heating path. In contrast, if that grain experienced a long thermal event it may develop a zoning profile typical of the cooling path. Conversely, for the same temperature-time cycle, large grains may not completely equilibrate at the metamorphic peak, and in smaller grains any previous record may have been erased. This is commonly observed in natural rocks where different grains within one thin section preserve often qualitatively different zoning profiles. Thus, a critical grainsize,l _crit, may exist that separates grains with qualitatively different zoning profiles so that grains of sizel > l _crit still retain zoning information about the heating path and grains of sizel <l _crit contain only information about the cooling path. If the critical grainsize can be measured and an independent estimate for the peak metamorphic temperature exists, the duration of the thermal event may, in principle, be estimated.The applicability of this method to natural garnets is hampered by a range of uncertainties. However, a parameterisation of the critical grain size may be used to illustrate the relative importance of grain size, temperature and event duration to the equilibration of minerals. In this paper, the critical grainsize is parameterized for various temperature-time cycles and its dependence on diffusion parameters is discussed. It is shown that, for Barrovian conditions,l _crit between 0.1 and 1 mm separates garnets retaining prograde information from garnets retaining cooling path information. For illustration, we compare the results with the critical grainsize of garnets from two metamorphic terranes, the Prydz Bay region (Antarctica) and the Koralm complex (Eastern Alps). Despite the large range of uncertainties attached to the method, it is shown that the critical grainsize of garnets in both terranes is consistent with a very short duration of the last thermal event that affected the two regions.

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Die qualitative Form von Zonierungsprofilen in Mineralen. Information über die Dauer metamorpher Ereignisse?

Zusammenfassung Zonierungsprofile von Paragenesen im Ionenaustausch, zum Beispiel das Fe-Mg Austauschsgleichgewicht zwischen Granat und Biotit, sind eine Funktion von (i) Korngröße, (ii) Temperatur, (iii) Kühl- und Heizgeschwindigkeit sowie (iv) den Diffusionskonstanen. Es sollte daher möglich sein, Zonierungsprofile dazu zu verwenden, einen dieser Parameter zu bestimmen, wenn die anderen bekannt sind. Zonierungsprofile von Kristallen die ein kurzes thermisches Ereignis erfahren haben, mögen daher prograde Information beinhalten, wogegen derselbe Kristall ein retrogrades Profil aufweisen mag, wenn er einem langlebigen thermischen Ereignis unterlag (prograd und retrograd ist hier als: bei ansteigender Temperatur und bei abfallender Temperatur definiert). In Kristallen die dem gleichen Temperatur-Zeitpfad unterworfen waren, könnten kleine Körner nur die Kühlgeschichte dokumentieren, wogegen große noch Zonierungsinformation vom Heizpfad aufweisen. In natürlichen Gesteinen wird das oft dadurch beobachtet, daß verschiedene Körner auseinem Dünnschliff qualitativ verschiedene Zonierungsprofile aufweisen. Es ist daher möglich eine kritische Korngöße,l _crit, zu definieren, die Korngrößen mit qualitativ verschiedenen Zonierungsprofilen voneinander trennt. Körner mit einem Durchmesserl > l _crit haben, zumindest teilweise, noch prograde Profile, wogegen Körner mitl <l _crit nur retrograde Information dokumentieren. Wenn man diese kritische Korngröße messen kann, sollte sie dazu benutzt werden können, etwas über die Dauer des thermischen Ereignisses auszusagen.Die Anwendbarkeit dieser Methode ist durch eine Reihe von Fehlern limitiert. Nichtsdestotrotz, ist eine Parameterisierung der kritischen Korngröße nützlich um die relative Wichtigkeit von Korngröße, Temperatur und Zeit, für die Entwicklung von Zonierungsprofilen, zu illustrieren. Unser Modell kann dazu benutzt werden, um die Größenordnung von Granaten abzuschätzen, die noch prograde Information dokumentieren können. Die Abhängigkeit der kritischen Korngröße von Diffusionsparametern und der Form des Temperatur-Zeit Pfades wird ebenfalls diskutiert. Es wird gezeigt, daß für Metamorphose in der mittleren Grünschiefer und Amphibolit fazies,l _crit zwischen 0.1 and 1 mm prograd zonierte von retrograd zonierten Granaten trennt. Um das Modell zu illustrieren, werden die Ergebnisse auf die Prydz Bay Region (Antarktis) und den Koralm Komplex (Ostalpen) angewendet. Trotz der großen Fehlergrenzen der Methode glauben wir zeigen zu können, daß die kritische Korngröße beider Terrains andeutet, daß das letzte thermische Ereignis in beiden Gebieten kurzlebig war.

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With 5 Figures     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

The contact binary system YY Eri

Relatively new and unanalysed photometric data-sets of the contact binary system YY Eri are presented. The light curves have been analysed using information limit optimization techniques, and the Binary Maker program of Bradstreet (1992).Comparison of the results allows insight into determinacy questions affecting the W UMa type of light curve, which relates to our general understanding of contact binaries. A limiting contact configuration cannot be ruled out on the basis of empirical data-analysis alone.Very careful analysis of the photospheric flux distribution over the surface of the Sun may help establish appropriate values of the gravity brightening parameter for cool dwarf stars. At present, however, empirical photometric information on contact binaries is non-discriminatory: i.e. alternative cosmogonies can find alternative support from available evidence. The implication is then for more and better observational data to allow better real independent parameter determination.     

Propagation of MHD body and surface waves in magnetically structured regions of the solar atmosphere

The fact that magnetically structured regions exist in the solar atmosphere has been known for a number of years. It has been suggested that different kinds of magnetohydrodynamic (MHD) waves can be efficiently damped in these regions and that the dissipated wave energy may be responsible for the observed enhancement in radiative losses. From a theoretical point of view, an important task would be to investigate the propagation and dissipation of MHD waves in these highly structured regions of the solar atmosphere. In this paper, we study the behavior of MHD body and surface waves in a medium with either a single or double (slab) magnetic interface by use of a nonlinear, two-dimensional, time-dependent, ideal MHD numerical model constructed on the basis of a Lagrangean grid and semi-implicit scheme. The processes of wave confinement and wave energy leakage are discussed in detail. It is shown that the obtained results depend strongly on the type of perturbations imposed on the interface or slab and on the plasma parameter, . The relevance of the obtained results to the heating problem of the upper parts of the solar atmosphere is also discussed.     

Evolution of cool skin and direct air-sea gas transfer coefficient during daytime

Absorption of solar radiation within the thermal molecular sublayer of the ocean can modify the temperature difference across the cool skin as well as the air-sea gas transfer. Our model of renewal type is based on the assumption that the thermal and diffusive molecular sublayers below the ocean surface undergo cyclic growth and destruction, the heat and gas transfer between the successive burst events are performed by molecular diffusion. The model has been upgraded to include heating due to solar radiation. The renewal time is parameterized as a function of the surface Richardson number and the Keulegan number. A Rayleigh number criterion characterizes the convective instability of the cool skin under solar heating. Under low wind speed conditions, the solar heating can damp the convective instability, strongly increasing the renewal time and correspondingly decreasing the interfacial gas exchange. In the ocean, an additional convective instability caused by salinity flux due to evaporation becomes of importance in such cases. The new parameterization is compared with the cool skin data obtained in the western equatorial Pacific during the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment in February 1993. In combination with a model of the diurnal thermocline it describes main features of the field data both in nighttime and daytime. Under low wind speed conditions (< 5 m s^-1) diurnal variations of the sea surface temperature due to the formation of a diurnal thermocline were substantially larger than those across the cool skin. Under wind speeds > 5 m s^-1, diurnal variations of the surface temperature due to the variations of the thermal molecular sublayer become more important.     

On AGV's navigation in 3-dimensional space

This paper deals with position estimation and path control for Autonomous Guided Vehicles (AGV). To enable a vehicle or a mobile robot in following a continuous virtual path without human control, these techniques play an important role. The relationship between the vehicle's motion in 3-dimensional space and the shape of a curved surface is described. In particular, the introduction of a digital terrain model in dead reckoning is considered. Moreover, a possible nonlinear control is developed based on curvilinear path coordinates, and the proof for global stability is given. To achieve general validity, these topics are treated here independently of the cart's special mechanization (the configuration of steered wheels and driven wheels). Simulation studies are presented to illustrate the investigations.     

Carbon isotopic fractionation in lipids from methanotrophic bacteria: relevance for interpretation of the geochemical record of biomarkers

Experiments with cultured aerobic methane oxidising bacteria confirm that their biomarker lipids will be significantly depleted in 13C compared to the substrate. The methanotrophic bacteria Methylococcus capsulatus and Methylomonas methanica, grown on methane and using the RuMP cycle for carbon assimilation, show maximum 13C fractionation of approximately 30% in the resultant biomass. In M. capsulatus, the maximum fractionation is observed in the earliest part of the exponential growth stage and decreases to approximately 16% as cells approach stationary phase. This change may be associated with a shift from the particulate form to the soluble form of the methane monooxygenase enzyme. Less than maximum fractionation is observed when cells are grown with reduced methane availability. Biomass of M. capsulatus grown on methanol was depleted by 9% compared to the substrate. Additional strong 13C fractionation takes place during polyisoprenoid biosynthesis in methanotrophs. The delta 13C values of individual hopanoid and steroid biomarkers produced by these organisms were as much as l0% more negative than total biomass. In individual cultures, squalene was 13C-enriched by as much as 14% compared to the triterpane skeleton of bacteriohopaneaminopentol. Much of the isotopic dispersion in lipid metabolites could be attributed to shifts in their relative abundances, combined with an overall reduction in fractionation during the growth cycle. In cells grown on methanol, where there was no apparent effect of growth stage on overall fractionation there were still significant isotopic differences between closely related lipids including a 5.3% difference between the hopane and 3 beta-methylhopane skeletons. Hopane and sterane polyisoprenoids were also 13C-depleted compared to fatty acids. These observations have significant implications for the interpretation of specific compound isotopic signatures now being measured for hydrocarbons and other lipids present in sediments and petroleum. In particular, biomarker lipids produced by a single organism do not necessarily have the same carbon isotopic composition.     

Partitioning of silver,beryllium and molybdenum among chemical fractions in the sediments from the Labe (Elbe) river in Central Bohemia,Czech Rep.

Sequential extraction of the fine fraction (63 µm) of the bottom sediments of the Labe river in Central Bohemia indicates that the readily reducible sediment fraction is a major reservoir of silver for release into the aqueous phase. Molybdenum is preferentially mobilized by ion-exchange, while beryllium is accumulated in all the chemical fractions of the sediments, especially in the moderately reducible and the organic/sulphidic phases.Contamination of the aquatic system from anthropogenic sources is characterized by the formation of relatively unstable chemical forms and only a small portion of these elements remain in the stable residual fraction.     

Propagation and absorption of cyclotron maser radiation in solar microwave spike bursts

It has been argued that the loss-cone-driven electron cyclotron maser instability can account for the properties of millisecond microwave spike bursts observed during some solar flares. However, as it propagates outward from the corona, maser radiation undergoes gyroresonance absorption when its frequency is a harmonic of the local electron-cyclotron frequency. Existing analytical models using slab geometries predict that this absorption should be sufficiently strong to prevent the radiation from being seen at the observed levels, except under highly restrictive conditions or for unrealistic plasma parameters. A more comprehensive analysis is presented here to determine if and when maser radiation can escape to produce microwave spike bursts. This analysis employs numerical raytracing and incorporates propagation and absorption of fundamental maser emission in a realistic model of a coronal flux loop. It is found that ranges of physical conditions do exist under which maser radiation can escape to an observer and that these conditions are much more limiting for fundamental emission in the extraordinary ()-mode than in the ordinary (o)-mode. Detailed investigation implies that escaping radiation in the -mode is highly directional and chiefly observable toward the center of the solar disk, while escapingo-mode radiation is found to emerge from the corona over a much wider range of directions, with some cases corresponding to radiation observable near the solar limb.     

The effect of an optically thin region on stability of an accretion disk around a supermassive black hole

We analyse conditions of the innermost portion of an accretion disk and establish a set of equations for this region. A stable innermost region may exist, which can probably explain the observed UV and X-ray spectra, avoiding the unstable emission. We then discuss the detailed radial structure of a disk around a black hole for typical AGN parameters and obtain different kinds of- relationships for different regions of a disk. On the basis of this, we discuss the stability. A new type of cycle is present, which we call a double S shaped cycle. In this cycle, the extent of accretion rate variability is much larger than that in dwarf nova cycles. This probably solves the problem of violent variability of AGN. In the meantime, the very high accretion rate at the hottest state in limit cycles in the unstable region may provide continuous injection of matter to the jet and power the relativistic motion of the jet.