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.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

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.     

Neutron stars in the multidimensional einstein theory of gravitation

The radius, mass, total number of baryons, and other parameters of static, spherically symmetric, superdense stars are calculated. A model with one Ricci-flat inner space of arbitrary dimensionality and the approximation p₁=?0.5ε + ap for additional components of the energy — momentum tensor are used (ε and ρ are the total energy density and the pressure of the stellar matter and a is a fitting parameter). In the case of white dwarfs, the results of the multidimensional theory do not depend on the dimensionality D of space-time for ?10 ? a ? 10 and coincide with the analogous data of the general theory of relativity (GTR). For neutron stars there is a dependence on D and a. For D>4, in particular, the greatest mass M_max of a neutron star as a function of a has a maximum at 3<a(D) ? 4, which exceeds the greatest mass M _max ⁰ =2.14 M_⊙ in the GTR. A comparison of theoretical results with observational data determines the allowable values of a. Data for PSR 1913 + 16 lead to 0.2 ≤ a ≤ 9.2 in the case of D=26, while the results of [P. C. Joss and S. A. Rappaport, Annu. Rev. Astron. Astrophys.,22, 537 (1984)] lead to the stricter limits 1 ≤ a ≤ 7.4.     

Imaging coronal emission lines under high sky-background conditions

We have obtained images in solar coronal emission lines under high sky-background conditions by making precise differential measurements between the coronal emission line and the near-by continuum, which is primarily due to scattered light from the solar disk. Chopping between the two wavelengths was performed at 100 kHz to avoid artifacts from fast-flying dust particles and other aerosols, and also from seeing effects. The differential signal was detected with a novel CCD camera that demodulates signals up to 100 kHz. These preliminary observations show coronal emission at the 0.2% level of the scattered-light background and pave the way to efficient and precise imaging of coronal emission features under less than ideal coronal-sky conditions.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.     

Mixed-layer characteristics as related to the monsoon climate of New Delhi,India

Annual variations of mixed-layer characteristics at New Delhi, India have been studied for a weak monsoon (1987) and a strong monsoon (1988) year. In the weak monsoon year (1987), the maximum mixing depthh _max was found to have a value of around 3000 m during the pre-monsoon, less than 2000 m during the summer monsoon, around 2000 m during the post-monsoon, and less than 1000 m in the winter season. For the strong monsoon year (1988),h _max values were less than 1987 values for comparable periods throughout the year. The seasonal and yearly differences ofh _max were explained by the surface energy balance and potential temperature gradient at a time close to sunrise. According to the spatial patterns of obtained by an objective analysis of the 850 to 700 hPa layers. mixed-layer characteristics obtained at New Delhi are representative of the north and central regions of India.     

The shoshonite porphyry Cu-Au association in the Goonumbla District,N.S.W., Australia

Summary The Goonumbla porphyry copper-gold deposit in N.S.W., Australia, is hosted by late Ordovician (439.2 ± 1.2 Ma)shoshonitic igneous rocks. In terms of their petrography, the rocks vary from andesitic to dacitic lavas and tuffs which are partly intruded by monzonite stocks; they are characterized by high and variable Al₂O₃ (13.4–19.9 wt%), very high K₂O values (up to 6.8 wt%), and high K₂O/Na₂O ratios (0.58–1.48), which are typical for the shoshonite association. The rocks also have enriched LILE concentrations (Ba up to 1200 ppm, Sr up to 1350 ppm), low HFSE (TiO₂ < 0.67 wt%, Zr < 125 ppm, Nb < 10 ppm, Hf < 3.4 ppm), and very low LREE (La < 22.4 ppm, Ce < 31 ppm), which are typical for potassic volcanic rocks formed in alate oceanic-arc setting.Mineral chemistry of selected magmatic mica and apatite phenocrysts from host rocks reveals relatively high SrO and BaO contents (micas: 0.15 wt% and up to 0.28 wt%, respectively; apatites: up to 0.28 wt% and 0.19 wt%, respectively) and very high halogen concentrations. Micas are characterized by up to 3.9 wt% F and 0.14 wt% Cl, whereas apatites have up to 3.6 wt% F and 0.68 wt% Cl. These very high halogen contents compared to those from barren intrusions imply that the shoshonitic magmatism was the source of mineralization.Copper-gold mineralization consists mainly of bornite, chalcopyrite, chalcocite and minor pyrite and tetrahedrite. Native gold occurs mainly as minute grains within silicates of the host rocks, and more rarely as fine inclusions in the sulphides. Mineralization is accompanied by wallrock alteration comprising a spatially restricted potassic type and a regional propylitic alteration type.Thus, the porphyry copper-gold deposit in the Goonumbla district can be viewed as an additional example of a worldwide association between potassic/shoshonitic magmatism and base- and precious-metal mineralization. More specifically, it appears to be the oldest recorded example of a shoshontie-associated porphyry Cu-Au deposit from a late oceanic-arc setting, a possible modern analogue being Ladolam at Lihir Island, Papua New Guinea

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Die Shoshonit Porphyry Cu-Au Assoziation im Goonumbla Distrikt, N.S.W., Australien

Zusammenfassung Die Porphyry Cu-Au Vererzung im Goonumbla Distrikt in New South Wales, Australien, sitzt in oberordovizischen (ca. 439.2 ± 1.2 Ma) Shoshoniten auf. Das petrographische Spektrum dieser Gesteine reicht von andesitischen bis dazitischen Laven und Tuffen, die lokal von Monzonit-Stöcken intrudiert werden; die Gesteine besitzen hohe, aber variable Al₂O₃ Gehalte (13.4–19.9 Gew%), sehr hohe K₂O Gehalte (bis zu 6.8 Gew%) und hohe K₂O/Na₂O Verhältnisse (0.58–1.48), die typisch sind für Shoshonite. Außerdem weisen sie hohe Konzentrationen an LILE Elementen (Ba bis 1200 ppm, Sr bis 1350 ppm) auf und geringe Konzentrationen an HFSE (TiO₂ < 0.67 Gew%, Zr < 125 ppm, Nb < 10 ppm, Hf < 3.4 ppm) sowie an LREE (La < 22.4 ppm, Ce < 31 ppm), die als typisch gelten für potassische Vulkanite von ozeanischen Plattengrenzen.Die Mineralchemie von repräsentativen Glimmer- und Apatit-Phänokristallen ist charakterisiert durch hohe SrO und BaO Gehalte (Glimmer: 0.15 Gew%, bzw. bis 0.28 Gew%; Apatite: bis 0.28 Gew%, bzw. 0.19 Gew%). Sie enthalten ferner sehr hohe Halogen-Konzentrationen. Die Glimmer enthalten beispielsweise bis zu 3.9 Gew% F und 0.14 Gew% Cl, während Apatite bis zu 3.6 Gew% F und 0.68 Gew% Ci aufweisen. Dies erscheint nicht ungewöhnlich, weil Glimmer und Apatite von vererzten Mag matiten zumeist deutlich höhere Halogengehalte besitzen, als solche von unvererzten Magmatiten. Die hohen Halogen-Gehalte in Phänokristallen aus den Shoshoniten legen nahe, die Vulkanite als den Ursprung der Vererzung zu interpretieren.Die Cu-Au Vererzung besteht überwiegend aus den Sulfiden Bornit, Kupferkies, Kupferglanz und vereinzelt auftretendem Pyrit und Tetrahedrit. Gediegen Gold wird in der Regel nur als kleine Partikel innerhalb von Silikaten der shoshonitischen Wirtsgesteine und seltener als feine Einschlüsse in Sulfiden gefunden.Die Vererzung wird von hydrothermaler Alteration der Wirtsgesteine begleitet und zwei Alterationsarten lassen sich unterscheiden: eine potassische sowie eine regional zu beobachtende propylitische Alteration.Die Porphyry Cu-Au Lagerstätte im Goonumbla Gebiet ist ein Beispiel für die weltweit beobachtete Assoziation von Bunt- und Edelmetallvererzungen und potassisch/shoshonitischem Magmatismus. Der Goonumbla Distrikt stellt die älteste bisher bekannte Porphyry Cu-Au Lagerstätte aus einerspätgenetischen ozeanischen Plattengrenze dar. Einmodernes Beispiel für eine Cu-Au Lagerstätte vergleichbaren Typs ist Ladolam auf Lihir Island, Papua New Guinea.