Sm---Nd age and REE geochemistry of Proterozoic arc-related igneous rocks in the Richtersveld subprovince, Namaqua Mobile Belt, Southern Africa

Igneous rocks of the Richtersveld Subprovince in South Africa and Namibia form a Palaeo-Mesoproterozoic arc complex, dominated by extrusive andesites and their plutonic equivalents (diorites, tonalites), although the whole spectrum of rock types from ultramafic to felsic is present. Sm---Nd isotope data indicate an extrusion age of 2000 Ma, thereby confirming previously published Rb---Sr and U---Th---Pb ages. Initial Nd, Sr and Pb isotope ratios indicate a juvenile crust-producing episode at this time, with rapid recycling of young crust to generate rhyolitic and granitic components within the arc complex. The Richtersveld Subprovince represents the oldest crust in the western Namaqua Province, which was subsequently recycled during post 2.0 Ga tectonothermal events, especially the 1200–1000 Ma Kibaran episode.     

Silicate determination in sea water: Toward a reagentless electrochemical method

Silicate has been determined in sea water by four different electrochemical methods based on the detection of the silicomolybdic complex formed in acidic media by the reaction between silicate and molybdenum salts. The first two methods are based on the addition of molybdate and protons in a seawater sample in an electrochemical cell. Cyclic voltammetry presents two reduction and two oxidation peaks giving four values of the concentration and therefore increasing the precision. Then chronoamperometry is performed on an electrode held at a constant potential. A semi-autonomous method has been developed based on the electrochemical anodic oxidation of molybdenum, the complexation of the oxidation product with silicate and the detection of the complex by cyclic voltammetry. This method is tested and compared with the classical colorimetric one during ANT XXIII/3 cruise across Drake Passage (January–February 2006). The detection limit is 1 μM and the deviation between both methods is less than 3% for concentrations higher than 10 μM. Finally a complete reagentless method with a precision of 2.6% is described based on the simultaneous formation of the molybdenum salt and protons in a divided electrochemical cell. This latter method should be very useful for developing a reagentless sensor suitable for long term in situ deployments on oceanic biogeochemical observatories.     

The structure of a typical double-ring planetary nebula NGC 2392

Monochromatic photographs in H, [Nii] 6584 and [Oiii] 5007 Å show many different details in the morphological structure of the Eskimo Nebula (NGC 2392). H and [Nii] images show, in a first approximation, similar structure (elliptical inner ring and broken outer ring) whereas both rings in [Oiii] are quite circular and regular in brightness. A photometric study using the method described by Louise (1974) gives various geometrical parameters of both rings which are practically the same for the observed lines. In other words, the classical stratification structure in planetary nebulae is not clearly observed in NGC 2392, in good agreement with previous observations (Wilson, 1950). This fact is probably a consequence of the peculiar structure in the geometry of the nebula. A model consisting of an inner toroid surrounded by a spherical shell is proposed to account for both photometric and spectroscopic observations.     

Sur un formalisme explicitant la loi des distances des planetes

The well-known Titius-Bode law (T-B) giving distances of planets from the Sun was improved by Basano and Hughes (1979) who found: $$a_n = 0.285 \times 1.523^n ;$$ a _n being the semi-major axis expressed in astronomical units, of then-th planet. The integern is equal to 1 for Mercury, 2 for Venus etc. The new law (B-H) is more natural than the (T-B) one, because the valuen=?∞ for Mercury is avoided. Furthermore, it accounts for distances of all planets, including Neptune and Pluto. It is striking to note that this law:

1. does not depend on physical parameters of planets (mass, density, temperature, spin, number of satellites and their nature etc.).
2. shows integers suggesting an unknown, obscure wave process in the formation of the solar system.

In this paper, we try to find a formalism accounting for the B-H law. It is based on the turbulence, assumed to be responsible of accretion of matter within the primeval nebula. We consider the function $$\psi ^2 (r,t) = |u^2 (r,t) - u_0^2 |$$ , whereu ²(r, t) stands for the turbulence, i.e., the mean-square deviation velocities of particles at the pointr and the timet; andu ₀ ² is the value of turbulence for which the accretion process of matter is optimum. It is obvious that Ψ²(r _n,t₀) = 0 forr _n=0.285×1.523 ⁿ at the birth timet ₀ of proto-planets. Under these conditions, it is easily found that $$\psi ^2 (r,t_0 ) = \frac{{A^2 }}{r}\sin ^2 [\alpha log r - \Phi (t_0 )]$$ With α=7.47 and Φ(t ₀)=217.24 in the CGS system, the above function accounts for the B-H law. Another approach of the problem is made by considering fluctuations of the potentialU(r, t) and of the density of matter ρ(r, t). For very small fluctuations, it may be written down the Poisson equation $$\Delta \tilde U(r,t_0 ) + 4\pi G\tilde \rho (r,t_0 ) = 0$$ , withU(r, t)=U ₀(r)+?(r, t ₀ ) and \(\tilde \rho (r,t_0 )\) . It suffices to postulate \(\tilde \rho (r,t_0 ) = k[\tilde U(r,t_0 )/r^2 ](k = cte)\) for finding the solution $$\tilde U(r,t_0 ) = \frac{{cte}}{{r^{1/2} }}\cos [a\log r - \zeta (t_0 )]$$ . Fora=14.94 and ζ(t ₀)=434.48 in CGS system, the successive maxima of ?(r,t ₀) account again for the B-H law. In the last approach we try to write Ψ(r, t) under a wave function form $$\Psi ^2 (r,t) = \frac{{A^2 }}{r}\sin ^2 \left[ {\omega \log \left( {\frac{r}{v} - t} \right)} \right].$$ It is emphasized that all calculations are made under mathematical considerations.     

Damage formation associated with bending under a constant moment

Deformation within the Earth's lithosphere is largely controlled by the rheology of the rock. Fracture and faulting are characterized by elastic rheologies with brittle mechanisms, while folding and flow are characterized by plastic and/or viscous rheologies due to ductile mechanisms. However, it has been recognized that deformation that resembles ductile behavior can be produced within the confines of the brittle lithosphere. Specific examples are folds that form in the shallow crust, steep hinges at subduction zones that are accompanied by seismicity, and large-scale deformation at plate boundaries. In these cases, the brittle lithosphere behaves elastically with fracture and faulting yet produces ductile behavior. In this paper, we attempt to simulate such ductile behavior in elastic materials using continuum damage mechanics. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. We utilize a modified form of damage mechanics that represents a reduction in frictional strength of preexisting fractures and faults. We use this empirical approach to simulate the bending of the lithosphere under the application of a constant moment.We use numerical simulations to obtain elastostatic solutions for plate bending and where the longitudinal stress at a particular node exceeds a yield stress, we apply damage to reduce Young's modulus at the node. Damage is calculated at each time step by a power-law relationship of the ratio of the yield stress to the longitudinal stress and the yield strain to the longitudinal strain. This results in the relaxation of the material due to increasing damage. To test our method, we apply our damage rheology to an infinite plate deforming under a constant bending moment. We simulate a wide range of behaviors from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Using this method, stress relaxation produces elastic-perfectly plastic behavior in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage leading to failure, analogous to the acceleration of microcrack formation and acoustic emissions prior to failure. The changes in the rate of damage accumulation in failure cases are similar to the changes in b-values of acoustic emissions observed in triaxial compression tests of fractured rock and b-value changes prior to some large earthquakes. Thus continuum damage mechanics can simulate the phenomenon of ductile behavior due to brittle mechanisms as well as observations of laboratory experiments and seismicity.     

Lead isotopes by LA-MC-ICPMS: Tracking the emergence of mantle signatures in an evolving silicic magma system

At Long Valley (LV) model Sr isotope phenocryst ages and absolute U-Pb zircon ages from precaldera Glass Mountain (GM) and caldera-related Bishop Tuff (BT) rhyolites show that these crystals track >1 Myr of evolution of a voluminous rhyolite magmatic system. In detail, strong disparities between the different age populations complicate ideas for a unified model for rhyolite generation, differentiation, and storage. To better elucidate the age discrepancies a new in situ Pb isotope technique has been developed to measure the compositions of 113 individual LV feldspars (mainly sanidine) and their host glasses by UV laser ablation MC-ICPMS. Given sufficient signal the accuracy and precision of this technique approaches that of double-spike thermal ionization mass spectrometry. The utility of our technique for many geologic materials is, however, limited to determining Pb isotope ratios that include ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb, but exclude ²⁰⁴Pb. New zircon ²³⁸U-²⁰⁶Pb crystallization ages were also obtained for two older Glass Mountain domes.A >1.5‰ difference between the Pb isotope compositions of feldspars from older (1.7-2.2 Ma) precaldera Glass Mountain (GM) rhyolites and younger LV rhyolites, including the BT, is found. The Pb isotope data for feldspars and their host glasses lie along a regional trend line between young basalts and evolved crust compositions, spanning ∼15% of that isotopic difference, and show a secular change towards increasing mantle contribution. Most feldspars have Pb isotope compositions that are similar to their host glasses and, as such, there persists an apparent >100 k.y. difference between Sr model feldspar ages and zircon ages for some GM rhyolites. Collectively, the feldspars define a Sr-Pb isotope mixing curve. Evidence for mixing complicates the interpretation that the Sr isotope data solely reflect radiogenic ingrowth. Where isotopically heterogeneous feldspar populations occur, there is greater uncertainty about the veracity of the Sr model ages. Specifically, we find no Pb isotope evidence that BT feldspars grew from older GM-like magmas.The distinct Pb isotope signatures for individual rhyolites and their feldspars support evidence based on zircon dating that LV volcanism did not erupt from a single long-lived magma chamber but rather tapped a number of different magmas. Moreover, contrary to the conventional model of gradual build-up prior to cataclysmic eruption, secular changes in the U-Pb age constraints on magma residence times and the magmas’ distinct Pb isotopic compositions suggest that, at Long Valley, eruptive volumes increase with shorter magma residence time and correlate with greater mantle input. Evidently, the plumbing and therefore activity at Long Valley was influenced by the evolving interaction between source and crustal magma system.