Understanding Perturbation on the Simplex: A Simple Method to Better Visualize and Interpret Compositional Data in Ternary Diagrams

Perturbation is an operation defined on the simplex and can be used for centering compositional data in a ternary diagram, applying objective criteria. Because a straight line in the original diagram is still astraight line in the perturbed diagram, gridlines or compositional fields defined by straight lines can easily be included in the operation. Simultaneous perturbation of data, gridlines, and/or compositional fields is shown to improve both visualization and graphical interpretation of compositions in ternary diagrams. This is illustrated by some examples using simulated as well as real data.     

Compositional Geometry and Mass Conservation

A geometrical structure is imposed on compositional data by physical and chemical laws, principally mass conservation. Therefore, statistical or mathematical investigation of possible relations between data values and such laws must be consistent with this structure. This demands that geometrical concepts, such as points that specify both mass and composition in linear space, and lines in projective space that specify composition only, be clearly defined and consistent with mass conservation. Mass thus becomes the norm in composition space in place of the Euclidean norm of ordinary space. Coordinate transformations inconsistent with this geometry are accordingly unnatural and misleading. They are also unnecessary because correlation arising from the constant mass presents no unusual difficulty in the analysis of the underlying quadratic form.     

云南墨江金厂金矿床含铬层状硅酸盐矿物成分标型特征

含铬绢云母类矿物在云南墨江金厂金矿床中广泛出现于黄铁铬绢英岩、黄铁硅质岩、黄铁铬云母岩和石英脉中。含铬绿泥石类矿物主要出现在石英脉、硅质岩、黄铁铬绢英岩中。蒙脱石出现于蚀变围岩中，而高岭石出现于富金石英脉中。本文通过对72个上述矿物电子探针数据的分析，确定了与其成因产状对应的含铬绢云母、含铬伊利石、含铬绿泥石、含铬蒙脱石、高岭石矿物的系列成分标型。研究表明，具最高铬含量的上述矿物样品均位于近金厂岩体穿脉的最北端。在铬铝云母SiO2-Cr2O3关系图上可以看出，不同成矿背景的铬铝绢云母，其Cr、Si离子数有分区特点，而本矿床的铬铝云母成分标型反映其富硅富铬的特点，与金厂超基性岩体的变质热液有关。     

Chemistry and Sulfur Isotopes in a Chert-dominant Sequence around the Stratiform Manganese Deposit of the Noda-Tamagawa Mine, Northern Kitakami Terrane, Northeast Japan: Implication for Paleoceanographic Environmental Setting

Abstract. Chemistry and sulfur isotopes are analyzed for a series of rocks in the chert‐dominant sequence around the stratiform manganese ore deposit of the Noda‐Tamagawa mine in the northern Kitakami Terrane, northeast Japan. The sequence is litholog‐ically classified into six units in ascending order: lower bedded chert, lower black shale, massive chert, manganese ore, upper black shale, and upper bedded chert. The rocks around the manganese ore deposit exhibit anomalous enrichment in Ni (max. 337 ppm), Zn (102) and U (30) in the upper part of lower bedded chert, Mo (122), Tl (79) and Pb (33) in the lower black shale, MnO, Cu (786) and Co (62) in the manganese ore, and As (247) and Sb (17) in the upper black shale. The aluminum‐normalized profiles reveal zonal enrichment of redox‐sensitive elements around the manganese bed: Zn‐Ni‐Fe‐Mo‐U(‐Co), Tl‐Pb(‐Mo), Mn‐Fe‐Cu‐V‐Cr‐Co(‐Zn) and As‐Sb in ascending order. The uppermost part of the lower bedded chert and black shale exhibit negative Ce/Ce* values, whereas the massive chert, manganese ore and lower part of the upper bedded chert display positive values. The isotopic δ³⁴S values are 0±6 % in the lower part of the lower bedded chert, ‐19 to ‐42 % in the upper part of the lower bedded chert, ‐36 to ‐42 % in the lower black shale, ‐28 to ‐35 % in the massive chert, manganese ore and upper black shale, and ‐23±5 % in the upper bedded chert. Thus, there is a marked negative shift in δ³⁴S values in the lower bedded chert, and an upward‐increasing trend in δ³⁴S through the manganese ore horizon. The present data provide evidence for a change in the paleoceanographic environmental resulting from inflow of oxic deepwater into the stagnant anoxic ocean floor below the manganese ore horizon. This event is likely to have triggered the precipitation of manganese oxyhydroxides. The redistribution of redox‐sensitive elements through the formation of metalliferous black shale and manganese carbonate ore may have occurred in association with bacterial decomposition of organic matter during early diagenesis of initial manganese oxyhydroxides.     

Chemical Profiles across a Jurassic Stratiform Manganese Deposit at Katsuyama in the Mino Terrane of Central Japan: Implications for Depositional Environment, Diagenetic Metal Redistribution and Paleoceanography

Abstract. Inorganic chemical compositions are determined for a series of rocks crossing an Early Jurassic stratiform manganese ore deposit in a chert‐dominant sequence at Katsuyama, in the Mino Terrane of central Japan. The lithology in the vicinity of the manganese ore bed is classified into lower bedded chert, black shale, massive chert, manganese ore and upper bedded chert, in ascending order. The rocks surrounding the manganese deposit are anomalously high in certain elements: Pb (max. 29 ppm), Ni (1140) and Co (336) in the lower bedded chert, Mo (438), As (149), Tl (29) and U (12) in the black shales, V (210) and Cr (87) in the massive chert, and MnO and W (24) in the manganese ore. The aluminum‐normalized profiles reveal a distinct zonation of redox‐sensitive elements: Pb‐Zn, Ni‐Co‐Cu(‐Zn) and U‐Cr in the lower bedded chert, Mo‐As‐Tl in the black shale, V(‐Cr) in the massive chert, and Mn‐Fe‐Ba‐W in the manganese ore, in ascending order. The lower and upper bedded cherts and manganese ore generally exhibit flat rare earth element patterns with positive Ce anomalies, whereas the uppermost part of the lower bedded chert, the black shale and massive chert have flat patterns with weak or nonexistent negative Ce anomalies and weak positive Eu anomalies. The strong enrichment in Ni, Co, W, Tl and As detected in the Katsuyama section is not recognized in other sediments, including those of anoxic deposition origin, but is identified in modern ferromanganese nodules, suggesting that metal enrichment in the Katsuyama section is essentially due to the formation of ferromanganese nodules rather than to deposition in an anoxic environment. The observed elemental zonation is well explained by equilibrium calculations, reflecting early diagenetic formation and associated gradual reduction with depth. The concentration profiles in combination with litho‐ and biostratigraphical features suggest that formation of these bedded manganese deposits was triggered by an influx of warm, saline and oxic water into a stagnant deep ocean floor basin in Panthalassa at the end of the middle Early Jurassic. Paleoceanographic environmental controls thus appear to be important factors in the formation and preservation of this type of stratiform manganese deposit.     

Late Quaternary chironomid community structure shaped by rate and magnitude of climate change

Much is known about how climate change impacts ecosystem richness and turnover, but we have less understanding of its influence on ecosystem structures. Here, we use ecological metrics (beta diversity, compositional disorder and network skewness) to quantify the community structural responses of temperature-sensitive chironomids (Diptera: Chironomidae) during the Late Glacial (14 700–11 700 cal a bp ) and Holocene (11 700 cal a bp to present). Analyses demonstrate high turnover (beta diversity) of chironomid composition across both epochs; however, structural metrics stayed relatively intact. Compositional disorder and skewness show greatest structural change in the Younger Dryas, following the rapid, high-magnitude climate change at the Bølling–Allerød to Younger Dryas transition. There were fewer climate-related structural changes across the early to mid–late Holocene, where climate change was more gradual and lower in magnitude. The reduced impact on structural metrics could be due to greater functional resilience provided by the wider chironomid community, or to the replacement of same functional-type taxa in the network structure. These results provide insight into how future rapid climate change may alter chironomid communities and could suggest that while turnover may remain high under a rapidly warming climate, community structural dynamics retain some resilience.     

Tectonic interpretation of metamorphic tectonites: integrating compositional mapping,microstructural analysis and in situ monazite dating

Interpreting tectonic histories from metamorphic tectonites requires an understanding of the linkages and feedbacks between deformation and metamorphism. Relationships between deformation and metamorphism can be divided into two broad groups: active and passive. Active relationships involve direct interactions whereby deformation directly influences metamorphic reactions or metamorphism directly affects the rate or style of deformation. One of the most important ‘active’ relationships is the role that deformation plays in helping to remove unstable reactant phases and to promote the growth of stable product phases. Passive relationships are correlations or linkages that allow the deformation history to be integrated with the metamorphic history. Compositional mapping of major and accessory phases and especially maps of larger thin section domains are particularly valuable for evaluating strain partitioning, scales of equilibrium, relationships between metamorphic textures and deformational fabrics, and in particular, for interpreting geochronological data. Petrological pseudosections are an increasingly utilized tool for interpreting microtextures and for linking deformation, metamorphism, and large‐scale tectonics. In situ geochronology and petrological analysis of chronometer phases (i.e. monazite, xenotime, titanite, allanite, etc.) are a critical part of tectonic analysis of metamorphic rocks. The electron microprobe plays an essential role in characterizing chronometer phases and placing them into the context of silicate fabrics and textures.     

A garnet population in Yellowknife schist, Canada

Abstract Data are presented on a garnet population in a specimen of garnet-biotite-plagioclase-quartz schist from the cordierite zone of an Archaean thermal dome in the Southern Slave Province of the Canadian Shield. Garnet crystals are bounded by planar dodecahedral faces and by trapezohedral faces which on the 10-μm scale are corrugated. Crystal distribution, as revealed by dissection of a small cubic volume of rock, is random. The size distribution is normal, with a mean diameter of 0.81 mm and a standard deviation of 0.32 mm. In the largest crystal of the population (mean radius 0.83 mm), [Mn] = 100 Mn/(Fe + Mg + Mn + Ca) decreases from 14.5 at the centre to 7.5 and then increases in the outer margin to 8.5; [Fe] increases continuously from 67 at the centre to 77 at the surface; [Mg] increases from 12.5 to 13.5 and then falls sharply to 11; [Ca] remains unchanged at 4.0 and then drops to 3.3. Progressively smaller crystals have progressively lower [Mn] and higher [Fe] concentrations at their centres, while all crystals have the same margin composition. Growth vectors extending from given concentration contours to crystal surfaces are of equal length regardless of the size of the crystal in which the vector is located. A garnet-forming model is presented in which reaction was initiated by a rise in temperature. Nucleation sites were randomly selected. The nucleation rate increased with time and then declined. Crystal faces advanced at a constant linear rate, which implies an increase in volume proportional to surface area. Initially, the composition of garnet deposited on crystal surfaces was determined by van Laar equations of equilibrium, which demanded the withdrawal of Mn and Fe from within chlorite crystals. This transfer reaction was then accompanied by an ion exchange reaction which moved Mn and Fe to garnet surfaces from biotite, in exchange for Mg. The exchange reaction provides an explanation for the high overall concentration of Mn and Fe in garnet and for the observed Mn and Mg reversals in the margins of crystals. The increase of garnet volume in the garnet population is found to be parabolic, i.e. Vαα⁵.     

华北地台南缘燕山期板内花岗斑岩类地球化学特征及成分空间变化规律

华北地台南缘燕山期花岗斑岩类小岩体形成于大陆板内环境,它具有类似岛弧—活动大陆边缘钙碱系列岩石地球化学特征,其成分在空间上呈现极性特征。本文探讨了这种成分极性与中、新生代俯冲带花岗岩类的可比性,并根据锶、钕同位素资料揭示成岩物质的可能来源及造成成分空间变化的可能原因。