Estimating the uncertainty of coral isochron U–Th ages

Recently, alternative models to estimate the age of diagenetically altered fossil reef corals have been presented based on either redistribution of U or its immediate daughters ²³⁴Th and ²³⁰Th. Here, we present three methods to estimate the uncertainty of ages derived using an amended version of our coral isochron method [Scholz et al., 2004. U-series dating of diagenetically altered fossil reef corals. Earth and Planetary Science Letters 218, 163–178], which is based on addition/loss of U. The obtained uncertainties are substantially larger than those previously published and should, in general, be more reliable. The isochron method yields larger uncertainties than alternative models based on Th redistribution due to -recoil processes. However, comparison of model open-system ages based on such redistribution of U-series daughters for different sub-samples from an individual coral specimen shows that the smaller errors derived with these models cannot account for the observed variability. We recognise that none of the available models is applicable to all corals, probably reflecting different diagenetic processes even in different sub-samples from one coral specimen. To better understand the diagenetic processes and precisely constrain the uncertainties of the ages derived from diagenetically altered corals, the application of all available models is recommended.     

Experimental study of bubble coalescence in rhyolitic and phonolitic melts

We have experimentally studied the process of bubble coalescence in rhyolite and phonolite melts of natural composition. The experiments involved decompression of water-saturated melts equilibrated at pressures and temperatures from 100 to 150 MPa and 775 to 840 °C in vertically oriented, rapid-quench capable, cold seal pressure vessels. One type of experiments (rhyolite MCR-100, 120, 150 and phonolite LSP-120 series') approximates a “static” bubble coalescence case, where we held the decompressed samples for ∼5 seconds to 4320 minutes (3 days) before quenching. The second type (rhyolite LPC-100 series) replicates an “expanding” bubble coalescence environment, where we continually decompressed the experiments at a rate of 0.5 MPa/s, examining samples quenched at ending pressures between 10 and 80 MPa. Our “static” case (MCR-100, 120, and 150, and LSP-120) results show significant increases in the modal bubble sizes and in the sizes of the largest bubbles, corresponding to measurable broadening in the size distributions. Their bubble number densities (N_V) decrease as a function of hold time at their final pressures (P_F), and can be fit well by power law functions. Our “expanding” case experiments (LPC-100) show a significant drop in N_V during the duration of the experiments that can be fit by an exponential equation as N_V vs. either time or P_F. Average estimates of bulk coalescence rates indicate a ∼1 order of magnitude drop in N_V for “static” case rhyolites in a 2-3 day period, and ∼2 orders of magnitude for phonolites within a 3 day period. Despite a ∼2 order of magnitude difference in viscosity, coalescene in the phonolite is only slightly faster than the rhyolite. The “expanding” case experiments show a ∼1 order of magnitude drop in N_V over 180 seconds. Thus, N_V's decrease 4 orders of magnitude faster in expanding vs. static bubbly rhyolite melts. Our results imply that significant bubble coalescence can occur in rhyolite magmas at relatively fast (∼20 m/s) ascent rates in the conduit. Thus, bubble interconnectivity, leading to high permeability, is possible during ascent. Bubble coalescence may occur during second boiling in magma bodies that are stalled in the crust. The timescales over which this occurs is much faster than the estimated rise rates for bubbles to reach the top of the magma chamber.     

Heterogeneous bubble nucleation on Fe-Ti oxide crystals in high-silica rhyolitic melts

The nucleation of H₂O bubbles in magmas has been proposed as a trigger for volcanic eruptions. To determine how bubbles nucleate heterogeneously in silicate melts, experiments were carried out in which high-silica rhyolitic melts were hydrated at 740-800°C and 50-175 MPa, decompressed by 20-70 MPa, and held at the lower pressures for ≥10 s before being quenched. The hydration conditions were subliquidus, and all samples contain blocky magnetite + needle-shaped hematite ± plagioclase. Magnetite is abundant at 800°C and high pressures, whereas hematite becomes more abundant at lower temperatures and pressures. Bubbles nucleated in a single event in all samples, with the number density (N_T) of bubbles varying between 2 × 10⁷ and 1 × 10⁹ cm⁻³. At low degrees of supersaturation, one to a few bubbles nucleate on faces of magnetite, but at medium to high degrees of supersaturation, multiple bubbles nucleate on single magnetite grains. On hematite, one to a few bubbles nucleated at the ends of the needle-shaped crystals at medium supersaturations, but formed along their entire lengths at high supersaturations. N_T increases as water diffusivity decreases, indicating that the number of bubbles nucleated is influenced by their growth, which depletes the melt with respect to H₂O and lowers supersaturation. If volcanic eruptions are triggered by bubble formation in magmas stored in shallow-level magma chambers, then the supersaturations needed for heterogeneous nucleation suggest that only small amounts of crystallization are needed, whereas homogeneous nucleation is unlikely to trigger eruptions.     

A Chemical Equilibrium Model for Natural Waters

This paper reviews the present status of the Pitzer chemical equilibrium model, which can be used to characterize the one-atmosphere activity coefficients of ionic and non-ionic solutes in natural waters as a function of temperature and ionic strength. The model considers the ionic interactions of the major seasalt ions (H, Na, K, Mg, Ca, Sr, Cl, Br, OH, HCO₃, B(OH)₄, HSO₄, SO₄, CO₃, CO₂, B(OH)₃, H₂O) and is based on the 25 °C model of Weare and co-workers. The model has been extended by a number of workers so that reasonable estimates can be made of the activity coefficients of most of the major seasalt ions from 0 to 250 °C. Recently coefficients for a number of solutes that are needed to determine the dissociation constants of the acids from 0 to 50 °C (H₃CO₃, B(OH)₃, H₂O, HF, HSO ₄ ^- , H₃PO₄, H₂S, NH ₄ ⁺ etc.) have been added to the model. These results have been used to examine the carbonate system in natural waters and determine the activity of inorganic anions that can complex trace metals. The activity and osmotic coefficients determined from the model are shown to be in good agreement with measured values in seawater. This model can serve as the foundation for future expansions that can examine the activity coefficient and speciation of trace metals in natural waters. At present this is only possible from 0 to 50 °C over a limited range of ionic strengths (<1.0) due to the limited stability constants for the formation of the metal complexes. The future work needed to extend the Pitzer model to trace metals is discussed.     

Geochemistry and origin of massif-type anorthosites

Samples of Proterozoic anorthosite complexes from the Adirondack Mountains of New York, Burwash Area of Ontario, and the Nain Complex of Labrador, ranging in composition from anorthosite to anorthositic gabbro, have been analyzed for major elements, Rb, Sr, Ba and nine rare-earth elements (REE), in order to set limits on the compositions and origins of their parent magmas. Similar rock types from the different areas have similar major and trace element compositions. The anorthosites have high Sr/Ba ratios, low REE abundances (Ce about 10, Yb about 0.5–1.5 times chondrites) and large positive Eu anomalies. The associated anorthositic gabbros have lower Sr/Ba ratios, REE abundances nearly an order of magnitude higher than the anorthosites, and small to negligible positive Eu anomalies.Model calculations using the adcumulate rocks with the lowest REE abundances and published distribution coefficients yield parent liquids having REE abundances and patterns similar to those of the associated anorthositic gabbros with the highest REE abundances. Rocks with intermediate REE abundances are the result of incorporation of a liquid component by a plagioclase-rich cumulate similar to the adcumulate samples. The analytical data and model calculations both suggest parent liquids having compositions of 50–54% SiO₂, greater than 20% Al₂O₃, about 1% K₂O, atomic Mg/(Mg+Fe²⁺) ratios (Mg No.'s) of less than 0.4, 15–30 ppm Rb, 400–600 ppm Sr and 400–600 ppm Ba, 40–50 times chondrites for Ce and 8–10 times chondrites for Yb.The low atomic Mg/(Mg+Fe²⁺) values for these rocks combined with geophysical evidence suggesting there are not large quantities of ferromagnesian material at depth, indicate that the anorthositic masses are not products of fractional crystallization of mafic melt derived from melting of the mantle. Rather, it is suggested that they are a result of partial melting of tholeiitic compositions at depths shallower than the basalt-eclogite transformation, leaving a pyroxene-dominated residue.     

Sur lesStaurastrum du lac Léman

Among the Desmids which have been observed in the plankton of the lake of Geneva, organisms having 4 processes have been discovered. Their frequency in the water samples and the results of in vitro studies on their progeny when cultivated in several environmental conditions, allow us to consider these organisms as a form ofStaurastrum sebaldi. The triradiate organisms have been incorrectly named and one must now consider three different species.      

The application of trace elements to the petrogenesis of igneous rocks of granitic composition

Although trace element modeling has been used to great advantage for petrogenetic interpretations of basaltic systems, similar studies on igneous rocks of granitic composition have been fewer. In general the mineral/melt distribution coefficients for rare earth elements (REE) in granitic melts are equal to or greater than those for similar minerals in the basaltic system. Thus the effects of these minerals on the REE patterns of granitic melts during partial melting or differentiation are exaggerated as compared to basaltic systems, making detection of residual phases easier. For the K/Rb ratio, if neither a K-feldspar component nor biotitephlogopite is present in the residue, it is difficult to reduce the K/Rb ratio of the melt relative to the parent by a factor of two by either differentiation or partial melting.The petrogenesis of four distinctly different rocks are received: (1) an Archean tonalite presumably derived by partial melting of an Archean tholeiite at mantle depths, leaving a garnet plus clinopyroxene residue; (2) an Archean quartz monzonite presumably derived by partial melting of a short-lived graywacke-argillite sequence at crustal depths; (3) a dacite from Saipan presumably derived by differentiation from a basaltic parent; and (4) a trachyte from Ross Island, Antarctica, presumably derived by differentiation from a basanitoid parent and contaminated by continental crustal components.     

Propagator matrices in elastic wave and vibration problems

The boundary value problems most frequently encountered in studies of elastic wave propagation in stratified media can be formulated in terms of a finite number of linear, first order and ordinary differential equations with variable coefficients. Volterra (1887) has shown that solutions to such a system of equations are conveniently represented by the product integral, or propagator, of the matrix of coefficients. In this paper we summarize some of the better known properties of propagators plus numerica methods for their computation. When the dispersion relation is somem ^th order minor of the integral matrix it is possible to deal withm ^th minor propagators so that the dispersion relation is a single element of them ^th minor integral matrix. In this way one of the major sources of loss of numerical accuracy in computing the dispersion relation is avoided. Propagator equations forSH and forP-SV waves are given for both isotropic and transversely isotropic media. In addition, the second minor propagator equations forP-SV waves are given. Matrix polynomial approximations to the propagators, obtained from the method of mean coefficients by the Cayley-Hamilton theorem and the Lagrange-Sylvester, interpolation formula, are derived.