Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Provenance discrimination of Lower Cretaceous synrift sandstones (eastern Iberian Chain Spain) Constraints from detrital modes heavy minerals and geochemistry

Petrography, geochemical whole-rock composition, and chemical analyses of tourmaline were performed in order to determine the source areas of Lower Cretaceous Mora, El Castellar, and uppermost Camarillas Formation sandstones from the Iberian Chain, Spain. Sandstones were deposited in intraplate subbasins, which are bound by plutonic and volcanic rocks of Permian, Triassic, and Jurassic age, Paleozoic metamorphic rocks, and Triassic sedimentary rocks. Modal analyses together with petrographic and cathodoluminescence observations allowed us to define three quartz-feldspathic petrofacies and recognize diagenetic processes that modified the original framework composition. Results from average restored petrofacies are: Mora petrofacies = P/F >1 and Q(r)70 F(r)22 R(r)9; El Castellar petrofacies = P/F >1 and Q(r)57 F(r)25 R(r)18; and Camarillas petrofacies = P/F ∼ zero and Q(r)64 F(r)28 R(r)7 (P—plagioclase; F—feldspar; Q—quartz; R—rock fragments; r—restored composition). Trace-element and rare earth element abundances of whole-rock analyses discriminate well between the three petrofacies based on: (1) the Rb concentration, which is indicative of the K content and reflects the amount of K-feldspar modal abundance, and (2) the relative modal abundance of heavy minerals (tourmaline, zircon, titanite, and apatite), which is reproduced by the elements hosted in the observed heavy mineral assemblage (i.e., B and Li for tourmaline; Zr, Hf, and Ta for zircon; Ti, Ta, Nb, and their rare earth elements for titanite; and P, Y, and their rare earth elements for apatite). Tourmaline chemical composition for the three petrofacies ranges from Fe-tourmaline of granitic to Mg-tourmaline of metamorphic origin. The three defined petrofacies suggest a mixed provenance from plutonic and metamorphic source rocks. However, a progressively major influence of granitic source rocks was detected from the lowermost Mora petrofacies toward the uppermost Camarillas petrofacies. This provenance trend is consistent with the uplift and erosion of the Iberian Massif, which coincided with the development of the latest Berriasian synrift regional unconformity and affected all of the Iberian intraplate basins. The uplifting stage of Iberian Massif pluton caused a significant dilution of Paleozoic metamorphic source areas, which were dominant during the sedimentation of the lowermost Mora and El Castellar petrofacies. The association of petrographic data with whole-rock geochemical compositions and tourmaline chemical analysis has proved to be useful for determining source area characteristics, their predominance, and the evolution of source rock types during the deposition of quartz-feldspathic sandstones in intraplate basins. This approach ensures that provenance interpretation is consistent with the geological context.

The behaviour of incompatible elements during hydrous melting of metasomatized peridotite at 4–6 GPa and 1000 °C–1200 °C

Trace element behavior during hydrous melting of a metasomatized garnet–peridotite was examined at pressures of 4–6 GPa and temperatures of 1000 °C–1200 °C, conditions appropriate for fluid penetrating the mantle wedge atop the subducting slab. Experiments were performed in a rocking multi-anvil apparatus using a diamond-trap setup. The compositions of the fluid and melt phases were measured using the cryogenic LA-ICP-MS technique. The water-saturated solidus of the K-lherzolite composition is located between 900 °C and 1000 °C at 4 GPa and between 1000 °C and 1100 °C at 5 and 6 GPa. The partition coefficients between fluid or melt and clinopyroxene reveal an asymmetric MREE trough with a minimum at Dy. The clinopyroxene in equilibrium with aqueous fluids is characterized by DUfluid–cpx > DThfluid–cpx while DUmelt–cpx tends to be similar to DThmelt–cpx. The partition coefficients between fluid or melt and garnet reveal very strong light to heavy REE fractionation, DLa/DLu from 95 (hydrous melt) to 1600 (aqueous fluid). The LILE are highly incompatible with partition coefficients > 50. The behavior of HFSE are decoupled, with DZr,Hf close to 1 while DNb,Ta > 10. Garnet is characterized by DUmelt/fluid–garnet < DThmelt/fluid–garnet. A comparison of our experimental partitioning results for trivalent cations as well as the results from the literature and the calculations carried out using the lattice strain model adapted to the presence of water in the bulk system indicates that H2O in the fluid or melt phase has a prominent effect on trace element partitioning. Garnet in mantle rocks in equilibrium with an aqueous fluid is characterized by significantly higher Do(3 +) for REE in the X site of the garnet compared with the partitioning values of the optimal cation in garnet in equilibrium with hydrous melts. Our data show for the first time that the change in the nature of the mobile phase (fluid vs. melt) does affect the affinities of trace elements into the garnet crystal at conditions below the second critical endpoint of the system. The same also applies for clinopyroxene, although this is less clear. Consequently, our new data allow for refinements in predictive modeling of element transfer from the slab to the mantle wedge and of possible compositions of metasomatized mantle that sources OIB magmatism.