66 resultados para Constraints of monotonicity
Resumo:
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.
Resumo:
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.
Resumo:
The volcanic rocks of the Rhön area (Central European Volcanic Province, Germany) belong to a moderately alkali basaltic suite that is associated with minor tephriphonolites, phonotephrites, tephrites, phonolites and trachytes. Based on isotope sytematics (87Sr/86Sr: 0.7033–0.7042; 143Nd/144Nd: 0.51279–0.51287; 206Pb/204Pb: 19.1–19.5), the inferred parental magmas formed by variable degrees of partial melting of a common asthenospheric mantle source (EAR: European Asthenospheric Reservoir of Cebriá and Wilson, 1995). Tephrites, tephriphonolites, phonotephrites, phonolites and trachytes show depletions and enrichments in some trace elements (Sr, Ba, Nb, Zr, Y) indicating that they were generated by broadly similar differentiation processes that were dominated by fractionation of olivine, clinopyroxene, amphibole, apatite and titaniferous magnetite ± plagioclase ± alkalifeldspar. The fractionated samples seem to have evolved by two distinct processes. One is characterized by pure fractional crystallization indicated by increasing Nb (and other incompatible trace element) concentrations at virtually constant 143Nd/144Nd ~ 0.51280 and 87Sr/86Sr ~ 0.7035. The other process involved an assimilation–fractional crystallization (AFC) process where moderate assimilation to crystallization rates produced evolved magmas characterized by higher Nb concentrations at slightly lower 143Nd/144Nd down to 0.51275. Literature data for some of the evolved rocks show more variable 87Sr/86Sr ranging from 0.7037 to 0.7089 at constant 143Nd/144Nd ~ 0.51280. These features may result from assimilation of upper crustal rocks by highly differentiated low-Sr (< 100 ppm Sr) lavas. However, based on the displacement of the differentiated rocks from this study towards lower 143Nd/144Nd ratios and modeled AFC processes in 143Nd/144Nd vs. 87Sr/86Sr and 207Pb/204Pb vs. 143Nd/144Nd space assimilation of lower crustal rocks seems more likely. The view that assimilation of lower crustal rocks played a role is confirmed by high-precision double-spike Pb isotope data that reveal higher 207Pb/204Pb ratios (15.62–15.63) in the differentiated rocks than in the primitive basanites (15.58–15.61). This is compatible with incorporation of radiogenic Pb from lower crustal xenoliths (207Pb/204Pb: 15.63–15.69) into the melt. However, 206Pb/204Pb ratios are similar for the differentiated rocks (19.13–19.35) and the primitive basanites (19.12–19.55) implying that assimilation involved an ancient crustal end member with a higher U/Pb ratio than the mantle source of the basanites. In addition, alteration-corrected δ18O values of the differentiated rocks range from c. 5 to 7‰ which is the same range as observed in the primitive alkaline rocks. This study confirms previous interpretations that highlighted the role of AFC processes in the evolution of alkaline volcanic rocks in the Rhön area of the Central European Volcanic Province.