Fitting matrix-valued variogram models by simultaneous diagonalization (Part I: Theory)

Suppose that ¯(x₁),...,¯Z(x_n). are observations of vector-valued random function ¯(x). In the isotropic situation, the sample variogram γ^*(h) for a given lag h is $$\bar \gamma ^ * (h) = \frac{1}{{2N(h)}}\mathop \sum \limits_{s(h)} (\overline Z (x_1 ) - \overline Z (x_1 )) \overline {(Z} (x_1 ) - \overline Z (x_1 ))^T $$ where s(h) is a set of paired points with distance h and N(h) is the number of pairs in s(h).. For a selection of lags h₁, h₂, .... h_k such that N (h₁) > O. we obtain a ktuple of (semi) positive definite matrices $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ . We want to determine an orthonormal matrix B which simultaneously diagonalizes the $\bar \gamma ^ * (h_{ 1} ),. . . ., \bar \gamma ^ * (h_{ k} )$ or nearly diagonalizes them in the sense that the sum of squares of offdiagonal elements is small compared to the sum of squares of diagonal elements. If such a B exists, we linearly transform $\overline Z (x)$ by $\overline Y (x) = B\overline Z (x)$ . Then, the resulting vector function $\overline Y (x)$ has less spatial correlation among its components than $\overline Z (x)$ does. The components of $\overline Y (x)$ with little contribution to the variogram structure may be dropped, and small crossvariograms fitted by straightlines. Variogram models obtained by this scheme preserve the negative definiteness property of variograms (in the matrix-valued function sense). A simplified analysis and computation in cokriging can be carried out. The principles of this scheme arc presented in this paper.     

Inner product matrices, kriging, and nonparametric estimation of variogram

Two important problems in the practical implementation of kriging are: (1) estimation of the variogram, and (2) estimation of the prediction error. In this paper, a nonparametric estimator of the variogram to circumvent the problem of the precise choice of a variogram model is proposed. Using orthogonal decomposition of the kriging predictor and the prediction error, a method for selecting, what may be considered, a statistical neighborhood is suggested. The prediction error estimates based on this scheme, in fact, reflects the true prediction error, thus leading to proper coverage for the corresponding prediction interval. By simulations and a reanalysis of published data, it is shown that the proposals made in this paper are useful in practice.     

Kriging with imprecise (fuzzy) variograms. II: Application

The geostatistical analysis of soil liner permeability is based on 20 measurements and imprecise prior information on nugget effect, sill, and range of the unknown variogram. Using this information, membership functions for variogram parameters are assessed and the fuzzy variogram is constructed. Both kriging estimates and estimation variances are calculated as fuzzy numbers from the fuzzy variogram and data points. Contour maps are presented, indicating values of the kriged permeability and the estimation variance corresponding to selected membership values called levels.     

Neotectonics of the Somogy hills (Part II): Evidence from seismic sections

The Somogy hills are located in the Pannonian Basin, south of Lake Balaton, Hungary, above several important tectonic zones. Analysis of industrial seismic lines shows that the pre-Late Miocene substratum is deformed by several thrust faults and a transpressive flower structure. Basement is composed of slices of various Palaeo-Mesozoic rocks, overlain by sometimes preserved Paleogene, thick Early Miocene deposits. Middle Miocene, partly overlying a post-thrusting unconformity, partly affected by the thrusts, is also present. Late Miocene thick basin-fill forms onlapping strata above a gentle paleo-topography, and it is also folded into broad anticlines and synclines. These folds are thought to be born of blind fault reactivation of older thrusts. Topography follows the reactivated fold pattern, especially in the central-western part of the study area.

The map pattern of basement structures shows an eastern area, where NE–SW striking thrusts, folds and steep normal faults dominate, and a western one, where E–W striking thrusts and folds dominate. Folds in Late Neogene are also parallel to these directions. A NE–SW striking linear normal fault and associated N–S faults cut the highest reflectors. The NE–SW fault is probably a left-lateral master fault acting during–after Late Miocene. Gravity anomaly and Pleistocene surface uplift maps show a very good correlation to the mapped structures. All these observations suggest that the main Early Miocene shortening was renewed during the Middle and Late Miocene, and may still persist.

Two types of deformational pattern may explain the structural and topographic features. A NW–SE shortening creates right-lateral slip along E–W faults, and overthrusts on NE–SW striking ones. Another, NNE–SSW shortening creates thrusting and uplift along E–W striking faults and transtensive left-lateral slip along NE–SW striking ones. Traces of both deformation patterns can be found in Quaternary exposures and they seem to be consistent with the present day stress orientations of the Pannonian Basin, too. The alternation of stress fields and multiple reactivation of the older fault sets is thought to be caused by the northwards translation and counter-clockwise rotation of Adria and the continental extrusion generated by this convergence.     

土工膜应变计的研制及其应用(II):应用

将研制的土工膜应变计应用于三峡工程二期上游围堰现场,以监测防渗土工膜在工程中产生的实际应变,并获得了满意的大应变监测成果。埋设于上游围堰不同高程的18支土工膜应变计,在较长时段内,不仅全部观测到防渗土工膜在施工阶段围堰填土碾压产生的应变规律,如0 500断面的10支土工膜应变计均测得11%～19%的大应变值,而且大部份应变计一直工作到极限量程才损坏。其中除了0 500断面因施工加载速率过快而导致防渗土工膜较早产生较大的变形,使得10支应变计在埋设后的施工填土3个多月内即陆续超量程损坏之外,其余的土工膜应变计工作寿命长达3年多。埋设于0 500子堰和0 930断面的土工膜应变计,在2000年和2001年夏季汛期中及汛期后,有些监测点的应变陡增到16%～20%之间,据此可以推测,此时该测点处的堰体产生了较大的变形。防渗土工膜的应变监测结果不仅与围堰构筑时的加载速率相关,并与围堰拆除时所发现的变形情况相吻合。     

Indirect determination of weighted joint density (wJd) by empirical and fuzzy models: Supren (Eskisehir, Turkey) marbles

Correct block size assessment is the most important stage for rock quarry management. Although volumetric joint count (J_v) and weighted joint density (wJd) were proposed for this purpose, simple prediction method for these indices is not encountered in literature. Due to the fact that some rock masses such as marbles contain less discontinuity, collection of representative amount of data from in situ line surveys for statistical assessments is highly difficult. For this reason, the main targets of the present paper are to apply photoanalysis approach for collecting additional discontinuity data and to obtain some simple statistical and fuzzy models for predicting weighted joint density to evaluate block size in engineering practice for marbles around Supren (Eskisehir, Turkey). In addition, a new and simple approach to predict volumetric decrease caused by chemical weathering is introduced. For these purposes, extensive field and photoanalysis studies were performed and the data obtained from both field and photoanalysis studies were assessed by regression and fuzzy approaches. The results revealed that the prediction performance of the fuzzy inference system is higher than that of the regression equation.     

Microanalysis of primary fluid inclusions in halite: constraints for an evaporitic sedimentation modeling. Application to the Mulhouse Basin (France)

The chemistry of the waters from which the evaporitic minerals crystallized in the lower part of the Salt IV unit of the Mulhouse Basin (France) has been investigated. The lithological and fluid inclusion data have been compared to the output data of the mass transfer program NEWEQUI which simulates the change in brine composition during its evaporation advancement. The results show that the evolution of the composition of the brine is compatible with the calculated sequence of evaporation of a parent water corresponding to a seawater modified by CaCl₂-rich hydrothermal water. In the studied sequence fluid inclusion data provide useful constraints for reconstructing the paleoenvironment controlling the evaporitic sedimentation. They also provide data on the water stratification in the basin and on its connectivity with the open sea, and important parameters controlling the productivity (possible sources for the nutrients) and the preservation of organic matter in the sediment.     

北美西部内陆海盆Niobrara组的钙质超微化石及其环境意义——Ⅱ：古环境研究

沉积于北美西部白垩纪内陆海盆的Niobrara组，是一套以白垩，白垩质灰岩，以及钙质页岩为主的海相沉积，其中自垩的主要组分为颗石藻及其它钙质超微化石。通过对Kansas州西部和South Dakota州东部四条剖面中Niobrara组的岩性，沉积物厚度，及钙质超微化石的研究，证明北美西部内陆海盆的沉积环境及水体温度在Niobrara组沉积时期因地而异。在Niobrara组沉积初期，海盆内的水体温度为北冷南暖，其后，至少在位于Kansas西部海域的海水温度呈与时逐渐降低趋势。钙质超微化石有关属种在盆地内的分布差异，进一步说明海水变冷的直接原因源自北极海域水体的缓慢南浸。     

Magmatic-to-hydrothermal crystallization in the W–Sn mineralized Mole Granite (NSW, Australia): Part II: Evolving zircon and thorite trace element chemistry

The Sn–W mineralized Mole Granite in Eastern Australia hosts zircon populations that crystallized at several stages during a protracted magmatic to hydrothermal evolution. Thirty-four elements have been quantified by laser-ablation inductively-coupled-plasma mass-spectrometric microanalysis with the aim of relating the chemistry of zircon to its growth environment. Trace element contents are highly variable for all textural occurrences. Zircon inclusions in earliest quartz phenocryst suggest that zircon was a liquidus phase that crystallized probably deep in the crust. Trace element contents are conspicuously high, showing only a slight positive Ce anomaly but a pronounced negative Eu-anomaly. Successive crystallization stages of magmatic zircon are characterized by progressive depletion in trace element contents, notably the rare earth elements, with an increasingly important positive Ce-anomaly. This evolution reflects saturation of REE accepting minerals such as monazite, thorite, xenotime and possibly apatite and is affected little by the exsolution of a magmatic–hydrothermal fluid. Zircon that is interpreted to have precipitated from aqueous fluids in Sn–W-bearing quartz veins shows REE patterns indistinguishable from those of late magmatic zircon. When combined with experimental evidence on the fluid–melt partitioning of REE, it indicates that the REE distribution coefficients for zircon/melt and zircon/fluid are largely comparable.

The second example of hydrothermal zircon crystallized some 2 My after the host granite. These crystals reveal an intragranular zonation of increasing trace element concentrations from core to rim. Therefore, REE abundances and patterns alone are not conclusive indicators of the geological environment in which zircon crystallized. Nevertheless, variations in trace element contents of zircon that relate to the chemistry of the melt or fluid from which zircon crystallized, as measured in cogenetic melt and fluid inclusions, are promising for future petrogenetic modeling.

Lead and Cs are strongly incompatible in hydrothermal zircon, with estimated zircon–fluid distribution coefficients D ≤ 0.001, while Sn and Li are moderately incompatible, D_Sn  0.6 and D_Li  0.1, and Ce is compatible, D_Ce  14. Moreover, hydrothermal zircon has a more pronounced negative Eu-anomaly and higher Ta/Nb and U/Th ratios than the magmatic zircons of the Mole Granite.     

Two‐layer scree/snow‐avalanche triggered by rockfall (Eastern Alps): Significance for sedimentology of scree slopes

Rockfalls that trigger scree‐laden snow avalanches are common in mountain ranges, but the resulting avalanche development and its role in understanding the sedimentology of scree slopes are rarely described in detail. On Riepenwand (2774 m above sea‐level, Kalkkögel range, Alps), on 6 May 2011 a 5800 m³ rockfall of dolostone detached from the flank of a gorge in the upper part of the mountain. After first collapsing into the gorge, the fragmented rock mass fell down freely for 150 m onto a talus covered by coarse‐granular snow. Rockfall impact triggered a medium‐scale avalanche that developed: (i) a lower layer A of entrained, pure snow; and (ii) an upper layer B of clay‐sized to boulder‐sized fragments mixed with snow. This ‘two‐layer scree/snow avalanche’ halted in the distal slope segment of the talus. Boulders within layer B mainly came to rest in the distal part of the avalanche deposit. Fragments smaller than cobble‐size grade did not show obvious downslope segregation. With snowmelt, the rockfall fragments dispersed in layer B were concentrated to a clast‐supported veneer that was draped over the older talus surface upon slower melting of avalanche layer A. In the grain‐size fraction ≤16 mm, a mean of 5 wt% matrix (silt‐sized to clay‐sized grains) of the rockfall‐derived scree of layer B is similar to a mean matrix content of 7 wt% within stratified talus slopes of the Kalkkögel range. This similarity suggests that a major share of matrix – widespread in stratified talus – stems from rockfalls. The characteristics of the scree veneer as melt‐lag of a scree‐laden snow avalanche will be blurred with time. Fossil talus successions may contain a substantial proportion of scree carried down by snow avalanches. The formation of a distinct sedimentary facies of snow avalanche‐deposited scree is impeded by processes of redeposition and deposit modification on talus.     

The double solid reactant method: II. An application to the shallow groundwaters of the Porto Plain,Vulcano Island (Italy)

This paper presents an example of application of the double solid reactant method (DSRM) of Accornero and Marini (Environmental Geology, 2007a), an effective way for modeling the fate of several dissolved trace elements during water–rock interaction. The EQ3/6 software package was used for simulating the irreversible water–rock mass transfer accompanying the generation of the groundwaters of the Porto Plain shallow aquifer, starting from a degassed diluted crateric steam condensate. Reaction path modeling was performed in reaction progress mode and under closed-system conditions. The simulations assumed: (1) bulk dissolution (i.e., without any constraint on the kinetics of dissolution/precipitation reactions) of a single solid phase, a leucite-latitic glass, and (2) precipitation of amorphous silica, barite, alunite, jarosite, anhydrite, kaolinite, a solid mixture of smectites, fluorite, a solid mixture of hydroxides, illite-K, a solid mixture of saponites, a solid mixture of trigonal carbonates and a solid mixture of orthorhombic carbonates. Analytical concentrations of major chemical elements and several trace elements (Cr, Mn, Fe, Ni, Cu, Zn, As, Sr and Ba) in groundwaters were satisfactorily reproduced. In addition to these simulations, similar runs for a rhyolite, a latite and a trachyte permitted to calculate major oxide contents for the authigenic paragenesis which are comparable, to a first approximation, with the corresponding data measured for local altered rocks belonging to the silicic, advanced argillic and intermediate argillic alteration facies. The important role played by both the solid mixture of trigonal carbonates as sequestrator of Mn, Zn, Cu and Ni and the solid mixture of orthorhombic carbonates as scavenger of Sr and Ba is emphasized.

Evaluation and validation of landslide-susceptibility maps obtained by a GIS matrix method: examples from the Betic Cordillera (southern Spain)

This work presents the results of applying the matrix method in a Geographic Information System (GIS) to the drawing of maps of susceptibility to slope movements in different sectors of the Betic Cordillera (southern Spain). In addition, the susceptibility models built by the matrix method were compared with a multivariate statistical method, and the first method gave the best results. The susceptibility maps drawn by the GIS matrix method were validated by calculating the coefficients of association with the degree of fit between recent slope movements registered in 1997 and the different levels of susceptibility of previously drawn maps (1995–1996) in different representative zones of the Betic Cordillera (southern Spain). The first sector studied showed excellent degrees of fit, with an error of less than 10% for all the slope failures and 3% when considering only failures of natural origin. In the second sector, the relative errors were less than 5%. In the third sector, the error hardly exceeded 6%. The results are discussed in the different zones and for each type of slope movement. In any case, these results evidence the predictive capacity of susceptibility maps drawn in GIS by the matrix method, for a great number of slope movements.     

Thermal evolution of an extensional detachment as constrained by organic metamorphic data and thermal modeling: Graz Paleozoic Nappe Complex (Eastern Alps)

Following Early Cretaceous nappe stacking, the Eastern Alps were affected by late-orogenic extension during the Late Cretaceous. In the eastern segment of this range, a Late Cretaceous detachment separates a very low- to low-grade metamorphic cover (Graz Paleozoic Nappe Complex, GPNC) above a low- to high-grade metamorphic basement. Synchronously, the Kainach Gosau Basin (KGB) collapsed and subsided on top of the section.Metamorphism of organic material within this section has been investigated using vitrinite reflectance data and Raman spectra of extracted carbonaceous material. In the southern part of the GPNC, vitrinite reflectance indicates a decrease in organic maturity towards the stratigraphic youngest unit. The remaining part of the GPNC is characterized by an aureole of elevated vitrinite reflectance values and Raman R2 ratios that parallels the margins of the GPNC. Vitrinite reflectance in the KGB shows a steep coalification gradient and increases significantly towards the western basin margin. The observed stratigraphic trend in the southern GPNC is a result of deep Paleozoic to Early Cretaceous burial. This maturity pattern was overprinted along the margins by advective heat and convective fluids during Late Cretaceous to Paleogene exhumation of basement rocks.During shearing, the fault zone was heated up to ca. 500 °C. This overprint is explained by a two-dimensional thermal model with a ramp-flat fault geometry and a slip rate of 1 to 1.5 cm/year during 5 Ma fault movement. The collapse basin above the detachment subsided in a thermal regime which was characterized by relaxing isotherms.     

Cementation of kerogen-rich marls by alkaline fluids released during weathering of thermally metamorphosed marly sediments. Part II: Organic matter evolution,magnetic susceptibility and metals (Ti,Cr, Fe) at the Khushaym Matruk natural analogue (Central Jordan)

Spontaneous combustion, less than 1 Ma ago, affected a 60-m thick sediment pile of biomicrite at the Khushaym Matruck site (Jordan). The present study shows that three retrograde alteration stages occurred: weathering, thermal stress and oxidative alkaline perturbation. μ-FT-i.r. spectra of isolated kerogens and oxygen index of whole rocks indicate that oxidation of organic matter occurred down to ∼10 m beneath the metamorphosed zone at Khushaym Matruck. The occurrence of the oxidative weathering bacterially mediated, as suggested by the mass chromatograms of saturated hydrocarbons, can explain high Rock-Eval T_max values and low petroliferous potential measured along the sedimentary pile. On the other hand, the thermal extent of combustion events was limited to the first 2 m from the contact. The mean reflectance of 0.20–0.24% and porosity of ca. 50% of the grey clayey biomicrites indicate that organic matter was very immature and sediments were unconsolidated at the time of the combustion event. Using mineralogy, microscopic analyses of vegetable debris and magnetic susceptibility, a suite of characteristic points corresponding to the thermal imprint can be assessed: (i) x = 0m, T ∼ 1000 °C, (ii) x = 1 m, T ∼ 350 °C, (iii) x = 2 m, T ∼ 150 °C and (iv) x > ∼ 8 m, T ∼ 30 °C. Paleocirculation of meteoric groundwater in the ‘cement-marbles’ generated high-pH fluids that have circulated via fractures and through the matrix porosity of the underlying biomicrites but have also induced alkaline hydrolysis and oxidative attack of the organic matter. The polysaccharide/lignin ratio derived from μ-FT-i.r. analyses shows that the delignification of vegetable debris and degradation of polysaccharides progressively decline in the indurated zone, which indicates a decrease in the pH of migrating solutions. The latter also severely oxidized organic matter at 2.10 and 3.05 m as revealed by the oxygen index and induced the generation of bitumen. The spatial correlation between the oxidation levels of organic matter and the metal contents (Fe, Ti and Cr) suggests that redox reactions were responsible for the immobilization of metals in the indurated biomicrites. The intensity of these reactions is attributed to changes in the fluid flow regime within the sedimentary column.     

RegCM3模式在西北地区的应用研究Ⅱ:区域选择及参数化方案的敏感性

通过数值模拟方法,研究了降水对区域尺度、积云对流参数化等的敏感性.结果表明:由于较小区域尺度的模式内部场和大尺度分析场激发的外强迫之间有更强的束缚,这种束缚使得内外强迫更容易达到一致.小区域尺度模拟的降水型比大的区域尺度的模拟更好,但同时,大的区域尺度消弱了由于模式侧边界效应产生的虚假动力效应,模拟的降水在量值上更加接近于观测值.因此,进行区域气候模拟时,须根据需要对模式区域进行仔细的选择.结果同时表明,由于Grell方案倾向于模拟更多的对流降水,因此Kuo-Anthes方案对西北地区降水型和量值的模拟比Grell方案更接近于实际.由于地形对于降水的重要意义,在复杂地形下进行区域气候模拟时有必要在模式中仔细描述地形.     

二氧化碳注入下岩层变形和流体运移分析:(Ⅱ)实例分析

第I部分[1]提出了一个两相流-岩层流固耦合模型,为了应用该模型对超临界二氧化碳注入过程中岩层力学响应和流体运移进行评估,采用Comsol商业程序,提出了相应的数值分析方法。给出了模型参数的确定方法,并采用室内试验数据对模型进行了验证;通过现场的温度和压力条件以及岩层的Van Genuchten参数,确定了二氧化碳的密度和黏度。基于三轴压缩试验、有效应力系数试验和渗透性试验,对力学模型及耦合关系中的参数进行了验证。最后给出一个应用实例,该岩层位于地下680⁷00 m深度,宽度为100 m,分析了不同二氧化碳注入速率下注入压力的演化规律,得到了岩层中孔隙压力、竖向应变和损伤变量的分布,并对二氧化碳的运移规律也进行了分析。研究结果为超临界二氧化碳注入过程中岩层力学响应和流体运移的评估提供了理论基础。     

The Urumieh Plutonic Complex (NW Iran): Record of the geodynamic evolution of the Sanandaj–Sirjan zone during Cretaceous times – Part II: Magnetic fabrics and plate tectonic reconstruction

The Urumieh complex, to the north of the Sanandaj–Sirjan zone (NW Iran), belongs to a plutonic arc that took place above the northeastward dipping subduction of Arabia under Iran during Late Cretaceous times. Seven granitoid bodies occupying an area of 300 km² can be sorted into three suites. According to the isotope chronology study of Ghalamghash et al. [Ghalamghash, J., Nédélec, A., Bellon, H., Vousoughi-Abedini, M., Bouchez, J.L., in press. The Urumieh Plutonic Complex: a magmatic record of the geodynamic evolution of the Sanandaj–Sirjan zone (NW Iran) during Cretaceous times – Part II: petrogenesis and 40K/40Ar dating. Journal of Asian Earth Sciences], the two first suites were emplaced during the same event at 100 Ma, and the third one was emplaced 20 Ma later: (1) the diorites form the largest bodies and comprise the Ghamishlu and Dourbeh stocks; (2) the biotite-granites are composed by the Sehkani, Nari and Doustak bodies, and (3) the younger bodies are represented by the Bardkish syenite and the Dourbeh granite. These bodies were subjected to systematic microstructural observations, and magnetic fabric measurements that yield information about their emplacement kinematics. The magnetic lineations of the diorites and biotite-granites (the early suites) call for a dominant NW-trending stretching during their intrusion, attributed to the transpressive deformation of the overriding Sanandaj–Sirjan microplate during the north-to northeastward motion of the subducting western branch of the Neo-Tethys. Oblique plate motion with 20% of strain partitioning along a NNW-trending plate boundary accounts for the observed magmatic structures. Intrusion of the younger bodies took place after consumption of this western oceanic domain at about 80 Ma. The NW-trending lineations of the syenite suggest that the transpressive regime was continuing, while the steep lineations and the peculiar microstructures of the Dourbeh granite call for a forceful intrusion. Our study suggests that the motion of Arabia with respect to Central Iran was more northerly directed than estimated before, for the 100–80 Ma time interval during which plate tectonic markers are not available.     

The Gibraltar Arc seismogenic zone (part 1): Constraints on a shallow east dipping fault plane source for the 1755 Lisbon earthquake provided by seismic data, gravity and thermal modeling

The Great Lisbon earthquake of 1755 with an estimated magnitude of 8.5–9.0 is the most destructive earthquake in European history, yet the source region remains enigmatic. Recent geophysical data provide compelling evidence for an active east dipping subduction zone beneath the nearby Gibraltar Arc. Marine seismic data in the Gulf of Cadiz image active thrust faults in an accretionary wedge, above an east dipping decollement and an eastward dipping basement. Tomographic and other data support subduction and rollback of a narrow slab of oceanic lithosphere beneath the westward advancing Gibraltar block.Although, no instrumentally recorded seismicity has been documented for the subduction interface, we propose the hypothesis that this shallow east dipping fault plane is locked and capable of generating great earthquakes (like the Nankai or Cascadia seismogenic zones). We further propose this east dipping fault plane to be a candidate source for the Great Lisbon earthquake of 1755. In this paper we use all available geophysical data on the deep structure of the Gulf of Cadiz–Gibraltar region for the purpose of constraining the 3-D geometry of this potentially seismogenic fault plane. To this end, we use new depth processed seismic data, have interpreted all available published and unpublished time sections, examine the distribution of hypocenters and perform 2-D gravity modeling. Finally, a finite-element model of the forearc thermal structure is constructed to determine the temperature distribution along the fault interface and thus the thermally predicted updip and downdip limits of the seismogenic zone.     

SIMS Bias on Isotope Ratios in Ca‐Mg‐Fe Carbonates (Part III): δ18O and δ13C Matrix Effects Along the Magnesite–Siderite Solid‐Solution Series

This study explores the effects of cation composition on mass bias (i.e., the matrix effect), which is a major component of instrumental mass fractionation (IMF) in the microanalyses of δ¹³C and δ¹⁸O by SIMS in carbonates of the magnesite–siderite solid‐solution series (MgCO₃–FeCO₃). A suite of twelve calibration reference materials (RMs) was developed and documented (calibrated range: Fe# = 0.002–0.997, where Fe# = molar Fe/[Mg + Fe]), along with empirical expressions for regressing calibration data (affording residuals < 0.5‰ relative to certified reference material NIST‐19). The calibration curves of both isotope systems are non‐linear and have, over a 2‐year period, fallen into one of two distinct but largely self‐consistent shape categories (data from ten measurement sessions), despite adherence to well‐established analytical protocols for carbonate δ¹³C and δ¹⁸O analyses at WiscSIMS (CAMECA IMS 1280). Mass bias was consistently most sensitive to changes in composition near the magnesite end‐member (Fe# 0–0.2), deviating by up to 4.5‰ (δ¹³C) and 14‰ (δ¹⁸O) with increasing Fe content. The cause of variability in calibration curve shapes is not well understood at present and demonstrates the importance of having available a sufficient number of well‐characterised RMs so that potential complexities of curvature can be adequately delineated and accounted for on a session‐by‐session basis.     

Poles apart: A discussion of “Geochemistry of cumulates from the Bjerkreim–Sokndal Intrusion (S. Norway). Part I: Constraints from major elements on the mechanism of cumulate formation and on the jotunite liquid line of descent” by J.C. Duchesne and B. Charlier (Lithos 83, 2005, 229–254)

We dispute Duchesne and Charlier's (Duchesne, J.C., Charlier, B., 2005. Geochemistry of cumulates from the Bjerkreim–Sokndal Intrusion (S. Norway). Part I: Constraints from major elements on the mechanism of cumulate formation and on the jotunite liquid line of descent. Lithos 83, 229–254.) postulate that the major-element compositions of cumulates in the Bjerkreim–Sokndal Intrusion vary linearly between plagioclase and mafic “poles” and their inference that this supports an origin by in situ crystallisation. We use a larger set of major-element data for plagioclase–orthopyroxene–ilmenite cumulates to show that some linear trends in Harker diagrams simply reflect varying amounts of hemo-ilmenite relative to plagioclase and orthopyroxene, while others are probably spurious and induced by variations in modal plagioclase, the most abundant cumulus mineral. Ratios of oxides that enter almost exclusively into orthopyroxene and hemo-ilmenite are shown to be highly dispersed, reflecting differential sorting of the mafic minerals.