Simultaneous curve simplification

In this paper we present a method for simultaneous simplification of a collection of piecewise linear curves in the plane. The method is based on triangulations, and the main purpose is to remove line segments from the piecewise linear curves without changing the topological relations between the curves. The method can also be used to construct a multi-level representation of a collection of piecewise linear curves. We illustrate the method by simplifying cartographic contours and a set of piecewise linear curves representing a road network.      

Petrology and metamorphic evolution of ultramafic rocks and dolerite dykes of the Betic Ophiolitic Association (Mulhacén Complex, SE Spain): evidence of eo-Alpine subduction following an ocean-floor metasomatic process

The Betic Ophiolitic Association, cropping out within the Mulhacén Complex (Betic Cordilleras), is made up of numerous metre- to kilometre-sized lenses of mafic and/or ultramafic and meta-sedimentary rocks. Pre-Alpine oceanic metasomatism and metamorphism caused the first stage of serpentinization in the ultramafic sequence of this association, which is characterized by local clinopyroxene (Cpx) breakdown and Ca-depletion, and complementary rodingitization of the basic dykes intruded in them. Subsequent eo-Alpine orogenic metamorphism developed eclogite facies assemblages in ultramafic and basic lithotypes, which were partly retrograded in Ab-Ep-amphibolite facies conditions during a meso-Alpine event. The heterogeneous development of the oceanic metasomatism in the ultramafic rock-types led to the patchy development of highly serpentinized Ca-depleted domains, without gradual transition to the host, and less serpentinized, Cpx-bearing ultramafites, mainly lherzolitic in composition. The high-pressure eo-Alpine recrystallization of these ultramafites in subduction conditions originated secondary harzburgites in the Ca-depleted domains, consisting of a spinifex-like textured olivine+orthopyroxene paragenesis, and a diopside+Ti-clinohumite paragenesis in the enclosing lherzolitic rocks. During the meso-Alpine event, secondary harzburgites were partly transformed into talc+antigorite serpentinites, whereas the diopside and clinohumite-bearing residual meta-lherzolites were mainly transformed into Cpx-bearing serpentinites. Relics of mantle-derived colourless olivine may be present in the more or less serpentinized secondary harzburgites. These relics are overgrown by the eo-Alpine brown pseudo-spinifex olivine, which contains submicroscopic inclusions of chromite, ilmenite and occasional halite and sylvite, inherited from its parental oceanic serpentine. The same type of mantle-derived olivine relics is also preserved within the Cpx-bearing serpentinites, although it has been partly replaced by the eo-Alpine Ti-clinohumite. The dolerite dykes included in the ultramafites were partly rodingitized in an oceanic environment. They were then transformed during the eo-Alpine event into meta-rodingites in their border zones and into eclogites towards the innermost, less-rodingitized portions. Estimated P–T conditions for the high-pressure assemblages in ultramafic and basic lithotypes range from 650 to 750°C and 16–25 kb.     

Upper Cretaceous bottom current deposits,north-east Greenland

Reported ancient bottom current deposits in deep marine settings are scarce and most of them remain contentious. This study describes sedimentological, ichnological and petrographical characteristics of a drill core that covers ca 10 Myr of Upper Cretaceous stratigraphy at Hold with Hope, north-east Greenland. The core is divided into four facies associations, which are interpreted to reflect deposition from bottom currents, turbidity flows and hemipelagic settling in slope and/or near slope environments. The evidence for bottom current influence is three-fold. Firstly, pervasive indications of winnowing such as marine bioclast-rich lags and outsized clasts on ‘mud on mud’ contacts are suggestive of low-sediment concentration flows capable of transporting up to pebble-sized clasts. Common Mn–Fe–Mg rich carbonate matrix cements and various types of hiatal chemogenic lag deposits showing glauconite, apatite and carbonate clasts also point to condensation, prolonged exposure at the sediment–water interface and recurrent phases of sea-floor erosion. Secondly, such deposits can show indicators for tidal processes such as double mud-drapes, tangential bottom sets in dune-scale cross-bedding and cyclic rhythmites. Thirdly, inverse to normal grading at various scales is common in fully marine, commonly seafloor-derived sediments. Ichnological data indicate considerable taxonomic variability in the bottom current deposits, but recurrent fabrics are characteristically dominated by morphologically simple burrows such as Thalassinoides and Planolites, with secondary Phycosiphon, Nereites, Zoophycos and/or Chondrites. In general, opportunistic taxa are common whereas mature composite ichnofabrics are rare. The omission surfaces are locally burrowed with stiffground to firmground trace fossil suites. The results contribute to establishing sedimentological, ichnological and mineralogical criteria for recognition of bottom current deposits as well as to the understanding of the Late Cretaceous palaeoenvironmental evolution of the Arctic region.     

Megacrysts and mafic–ultramafic xenolith-bearing ignimbrites from Sirwa Volcano, Morocco: phase petrology and thermobarometry

Summary A suite of clinopyroxene and amphibole megacrysts and mafic–ultramafic xenoliths are present in ignimbritic rocks of trachybasaltic–andesitic composition from the Sirwa volcanic district, Morocco. The stumpy prismatic and sometimes euhedral clinopyroxene megacrysts are Ti–Al-rich diopsides with mg values in the range 0.82–0.87 and Ca/(Ca + Mg) ratios in the range 0.53–0.54. The prismatic, elongated amphibole megacrysts are calcic kaersutites–kaersutites with a narrow mg range (0.66–0.68). The xenoliths are represented by gabbroic and pyroxenitic types. In the gabbroic xenoliths two distinct textural types can be distinguished: medium-sized granular and banded. The granular type is characterized by the mineral assemblage Pl + Amph + Spl + Ilm + Ap. The banded type is distinct for the absence of Ilm and the presence of Cpx and Opx and shows alternating bands enriched in Pl and Amph, respectively. The megacrysts and, probably, the xenoliths are considered not cognate with the present host rocks since the calculated liquids in equilibrium with clinopyroxene and amphibole megacrysts over a wide range of physical conditions have different trace and rare earth element contents. The observed phase relations and thermobarometric calculations indicate that the megacrysts and xenoliths crystallized from their parent melts at P ≥ 10 kbar and T ≤ 1160 °C, i.e., in the upper mantle or near the crust-mantle boundary. A deep ( ≥ 30 km) magmatic chamber, where the megacrysts and xenoliths originated, and a shallow volcanic chamber, energetically activated up to explosive conditions by injection of deep-originated melts, is suggested to explain the occurrence of high-pressure megacrysts and xenoliths in the Sirwa volcanic explosive products. Received October 8, 2000; revised version accepted September 9, 2001     

Is there evidence for magmatic underplating beneath the Oslo Rift?

We challenge some of the long-standing beliefs related to the Permian Oslo Rift structure, often referred to as a case example/type locality for continental rifting. The crustal structure of the Oslo Rift was long presumed to be thinned Proterozoic crust overlying a Permian high-density layer, interpreted as magmatic underplating. New data support an alternative view of the crustal structure in the Oslo Rift region. The Bouguer gravity high in the region shows a strong asymmetry: a steep, westward-facing gradient to the west of the rift, and a much gentler eastern gradient. We present a 3D density model based on petrophysical and seismic information, which accounts for the Bouguer gravity high using an eastward extension of old Precambrian structures, without invoking a prominent magmatic underplated structure. Reactivation of old pre-rift structures appears to be an important feature, affecting the evolution and location of the Permo-Carboniferous Oslo Rift.     

Petrogenesis of Cogenetic Silica-Oversaturated and -Undersaturated Syenites by Periodic Recharge in a Crustally Contaminated Magma Chamber: the Kangerlussuaq Intrusion, East Greenland

The Palaeogene Kangerlussuaq Intrusion (50 Ma) of East Greenlanddisplays concentric zonation from quartz-rich nordmarkite (quartzsyenite) at the margin, through pulaskite, to foyaite (nephelinesyenite) in the centre; modal layering and igneous laminationare locally developed but there are no internal intrusive contacts.This is an apparent violation of the phase relations in Petrogeny'sResidua System. We propose that this intrusion is layered, gradingfrom quartz syenite at the bottom to nepheline syenite at thetop. Mineral and whole-rock major and trace element data andSr–Nd–Hf–Pb isotope data are presented thatprovide constraints on the petrogenesis of the intrusion. Radiogenicisotope data indicate a continuously decreasing crustal componentfrom the quartz nordmarkites (⁸⁷Sr/⁸⁶Sr = 0·7061; _Ndi= 2·3; _Hfi = 5·2; ²⁰⁶Pb/²⁰⁴Pb_meas = 16·98)to the foyaites (⁸⁷Sr/⁸⁶Sr = 0·7043–0·7044;_Ndi = 3·8–4·9; _Hfi = 10·7–11·1;²⁰⁶Pb/²⁰⁴Pb_meas = 17·78–17·88); the foyaitesare dominated by a mantle isotopic signature. The average Mg-numberof amphibole cores becomes increasingly primitive, varying from26·4 in the nordmarkites to 57·4 in the pulaskites.Modal layering, feldspar lamination and the presence of hugebasaltic xenoliths derived from the chamber roof, now restingon the transient chamber floor, demonstrate bottom-upwards crystallization.The intrusion cannot, therefore, have formed in a system closedto magmatic recharge. The lack of gneissic xenoliths in thenordmarkites suggests that most contamination took place deeperin the crust. In the proposed model, the nordmarkitic magmaformed during crustal assimilation in the roof zone of a large,silica-undersaturated alkali basaltic/basanitic, stratifiedmagma chamber, prior to emplacement in the uppermost crust.The more primitive syenites, terminating with foyaite at thetop of the intrusion, formed as a consequence of repeated rechargeof the Kangerlussuaq Intrusion magma chamber by tapping lesscontaminated, more primitive phonolitic melt from deeper partsof the underlying chamber during progressive armouring of theplumbing system. KEY WORDS: Kangerlussuaq; East Greenland; syenite; crustal contamination; magma mixing     

Noble gas record and cosmic‐ray exposure history of the new CO3 chondrite Moss––Comparison with Lancé and other CO chondrite falls

Abstract– The Moss meteorite is the first CO chondrite fall after a time period of 70 yr and the least terrestrially contaminated member of its group. Its cosmic‐ray exposure (CRE) age (T₃ ～ 13.5 Ma; T₂₁ ～ 14.6 Ma) is distinct among CO chondrites and, within witnessed falls is the shortest after Lancé, which we have reanalyzed. Gas retention ages are approximately 3.95 × 10⁹ yr (U/Th‐He) and approximately 4.43 × 10⁹ yr (K/Ar), respectively. Trapped Ar, Kr, and Xe are present in Moss in abundances typical for CO chondrites, with “planetary” elemental and isotopic compositions. Presence of HL‐xenon from presolar diamonds is observed in the stepwise release analysis of Lancé. It may also be present in Moss, but it is difficult to ascertain in single‐step bulk analyses. It follows from our new data combined with a survey of the literature that the abundance of trapped gases in CO chondrites is not a good indicator of their petrological subtype.     

Weathering rates from top to bottom in a carbonate environment

This study investigates U-series, Sr isotopes, major and trace elements in a chalk aquifer system located in Eastern France. Soil and rock samples were collected along depth profiles down to 45 m in four localities as an attempt to investigate the weathering processes in the soil, the unsaturated zone and the saturated zone of the aquifer. Interstitial water was extracted from soils and rocks by a centrifugation technique. U-series offer a powerful tool to calculate weathering rates because the relative mobility of the U- and Th-isotopes can be precisely measured and it does not require the determination of a reference state as in other approaches. As expected, the data show very large mobile element depletion in the soil with large ²³⁰Th excess relative to ²³⁸U, while the rocks show more limited but not insignificant mobile element depletion. The U-series data have been used to constrain weathering rates based on a 1-D reactive transport model. Weathering rates in the near surface are about 10–100 times faster than at depth. However, when integrated over the depth of the cores, including the unsaturated and the saturated zones, this underground weathering represents more than 30% of the total weathering flux, assuming congruent dissolution of carbonates. The (²³⁴U/²³⁸U) ratios in interstitial water are consistent with solid samples showing ²³⁴U depletion near the surface and an excess ²³⁴U at depth. A leaching experiment performed on chalk shows that the excess ²³⁴U in natural waters percolating through carbonate rocks results both from preferential ²³⁴U leaching and direct recoil in the interstitial water. A new approach was used to derive the recoil ejection factor based on BET measurements and the fractal dimension of chalk surface. Consideration of preferential leaching and recoil allows a more accurate modeling of weathering rates.     

Experimental evidence for U-U fractionation during granite weathering with implications for U/U in natural waters

The daughter to parent (²³⁴U/²³⁸U) activity ratio in natural waters is often out of secular radioactive equilibrium. The major reason for this disequilibrium is related to the energetic α-decay of ²³⁸U and differential release of ²³⁴U relative to ²³⁸U. This disequilibrium originates from (1) preferential release of more loosely bound ²³⁴U from damaged mineral lattice sites or; (2) direct recoil of ²³⁴Th into surrounding media from near mineral surface boundaries, however, it is unclear which of the two mechanisms is most important in nature. To better quantify the effects of preferential release of ²³⁴U, two continuous laboratory granite leaching experiments conducted over 1100 h were performed. The leachates were characterized by declining U concentrations with time and (²³⁴U/²³⁸U) initially greater than unity (up to 1.15), which changed to below unity during leaching (∼0.95). The early elevated (²³⁴U/²³⁸U) suggests that additional ²³⁴U is released into solution by preferential release of ²³⁴U from mineral phases. However, the excess ²³⁴U constitutes a finite pool of easy leachable ²³⁴U and the (²³⁴U/²³⁸U) values become lower than unity when this pool is used up. A model based on first-order kinetics, dissolution rates and preferential release of ²³⁴U from damaged lattice sites was developed and is able to quantitatively predict the observed pattern of (²³⁴U/²³⁸U) values and U concentrations for the two granite leaching experiments. Extending the modeling to longer time scales more comparable to natural systems shows that the production of waters with high (²³⁴U/²³⁸U) ratios can be achieved in two distinct regimes (1) slow weathering where the rate of directly recoiled ²³⁴U near mineral surfaces into waters is high; (2) fast weathering where the role of incipient chemical weathering and preferential release of loosely bound ²³⁴U are important. The model is able to explain apparent opposite correlations between physical erosion rates and (²³⁴U/²³⁸U) in waters and it provides a new framework that will be useful for examining weathering regimes, their timescales and their coupling with physical erosion.