ALBERT

Description: High-resolution sampling in monogenetic fields has the potential to reveal fine-scale heterogeneity of the mantle, a feature that may be overwhelmed by larger fluxes of magma, or missed by under-sampling. The Quaternary Auckland Volcanic Field (AVF) in northern New Zealand is a basaltic field of 51 small-volume volcanic centres, and is one of the best-sampled examples of a monogenetic volcanic field. We present data for 12 centres in the volcanic field. These show the large compositional variations between volcanoes as well as through single eruptive sequences. Whole-rock compositions range from subalkaline basalt in the larger centres, through alkali basalt to nephelinite in the smallest centres. Fractional crystallization has had a limited effect in many of the centres, but high-pressure clinopyroxene crystallization may have occurred in others. Three end-members are observed in Pb isotope space, indicating that distinct mantle source components are involved in the petrogenesis of the magmas. Whole-rock multi-element patterns show that the larger centres have prominent positive Sr anomalies and lack K anomalies, whereas the smaller centres have prominent negative K anomalies and lack Sr anomalies. The melting parameters and compositions of the sources involved are modelled using trace element ratios and multi-element patterns, and three components are characterized: (1) fertile peridotite with a Pb-isotope composition similar to Pacific mid-ocean ridge basalt; (2) eclogite domains with a HIMU-like isotope composition dispersed within the fertile peridotite; (3) slightly depleted subduction-metasomatized peridotitic lithospheric mantle (containing c . 3% subduction fluids). Modelling shows that melting in the AVF begins in garnet-bearing fertile asthenosphere (with preferential melting of eclogite domains) and that melts are variably diluted by melts of the lithospheric source. The U–Th isotope compositions of the end-members in the AVF show 230 Th excess [( 230 Th/ 232 Th) ratios of 1·11–1·38], with the samples of lower ( 230 Th/ 232 Th) exhibiting higher ( 238 U/ 232 Th), which we attribute to the dilution effect of the melts from the lithospheric mantle source. Modelling reveals a correlation between melting in the asthenosphere, the degree of melting and incorporation of the metasomatized lithospheric mantle source, and the resultant size of the volcanic centre. This suggests that the scale of the eruption may essentially be controlled by asthenospheric mantle dynamics.

Description: We develop fully noncommutative Feynman–Kac formulae by employing quantum stochastic processes. To this end, we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterized under alternative assumptions of separability or Markov regularity. Our results generalize those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.

Description: Arc magmas are commonly assumed to form by melting of sub-arc mantle that has been variably enriched by a component from the subducted slab. Although most magmas that reach the surface are not primitive, the impact of assimilation of the arc crust is often ignored with the consequence that trace element and isotopic compositions are commonly attributed only to varying contributions from different components present in the mantle. This jeopardises the integrity of mass balance recycling calculations. Here we use Sr and O isotope data in minerals from a suite of volcanic rocks from St Lucia, Lesser Antilles arc, to show that assimilation of oceanic arc basement can be significant. Analysis of 87Sr/86Sr in single plagioclase phenocrysts from four Soufrière Volcanic Complex (SVC; St Lucia) hand samples with similar composition (87Sr/86Sr = 0.7089–0.7091) reveals crystal isotopic heterogeneity among hand samples ranging from 0.7083 to 0.7094 with up to 0.0008 difference within a single hand sample. measurements in the SVC crystals show extreme variation beyond the mantle range with +7.5 to ‰ for plagioclase (), +10.6 to ‰ for quartz (), +9.4 to ‰ for amphibole () and +9 to ‰ for pyroxene () while older lavas (Pre-Soufriere Volcanic Complex), with less radiogenic whole rock Sr composition (87Sr/86Sr = 0.7041–0.7062) display values closer to mantle range: +6.4 to ‰ for plagioclase () and +6 to ‰ for pyroxene (). We argue that the 87Sr/86Sr isotope disequilibrium and extreme values provide compelling evidence for assimilation of material located within the arc crust. Positive correlations between mineral and whole rock 87Sr/86Sr, 143Nd/144Nd and 206,207,208Pb/204Pb shows that assimilation seems to be responsible not only for the isotopic heterogeneity observed in St Lucia but also in the whole Lesser Antilles since St Lucia encompasses almost the whole-arc range of isotopic compositions. This highlights the need for detailed mineral-scale investigation of oceanic arc suites to quantify assimilation that could otherwise lead to misinterpretation of source composition and subduction processes.