The dynamics of xenolith assimilation

Xenolith assimilation has been simulated with experiments involving melting wax spheres into hot water and aqueous solutions and characterised by a theoretical analysis. Both the cases of neutrally buoyant stationary spheres and spheres sinking through the hot host fluid are examined. Melt generated on a sphere's surface flows (compositional convection) in two regimes; as a sheet over one hemisphere and then detaching as finger plumes from the other. Positional variations in the melting rate are dominantly controlled by differences in the melt layer thickness which influence the thermal gradient and heat flux across the layer. The theoretical model predicts melt layer thicknesses and the heat flux from the surrounding fluid. Calculated melting rates agree well with experimental measurements. Partial melting of non-eutectic compositions produces a layer of crystal-melt mush at the xenolith's surface. The theoretical analysis is extended to account for variation in rheological properties across the mush layer. When stoped into typical magmas, xenoliths of common continental crust lithologies are predicted to melt at rates in the order of 2 mm/hour. Thicknesses of the mobile mush layer around xenoliths are predicted to be typically a few centimetres. Relatively mafic lithologies can melt quicker than silicic compositions because, although they are typically more refractory, their lower melt viscosities result in thinner mush layers and so higher heat fluxes. Especially quick melting of water-saturated lithologies occurs as a consequence of both the reduction in melting temperatures and melt viscosities. Due to hot ambient conditions in the lower continental crust the assimilation of xenoliths into underplated basaltic magma can be very rapid. For granulites and mafic-granulites the predicted melting rates are up to 17 mm/hour. Fast rates of melting and efficient mixing of melt into the host magma indicate that assimilation of xenoliths will have a significant influence on the compositional and thermal evolution of magmas. Received: 7 November 1996 / Accepted: 5 January 1998     

The problem of rock assimilation by Somma-Vesuvius magma

Mineralogical and chemical compositions of ejected carbonate inclusions of Vesuvian gaseous phase are compared with those of carbonate sediments of the Somma-Vesuvius area. The basement of Vesuvius mainly consists of Mesozoic limestones. Most of these are characterized by extremely low insoluble residues. In this area thick dolomite beds occur in the Triassic system only. A calcareous layer of approximately 100 to 150 meters thickness characterized by high Sr contents (0.19% Sr in the average) is to be found within the Triassic dolostones. Several carbonate ejecta also show high Sr contents (0.1% Sr) but chemical composition of some of these ejecta differs somewhat from that of the Triassic layer high in Sr. Contact with the volcanic volatile phase and melt has produced some alterations in the composition of many ejecta. Magnesian calcites are abundant and periclase, brucite, tremolite, phlogopite and magnesite were found in the ejecta examined. Silicon, manganese, iron, zinc and, to a smaller extent, potassium and copper have been most probably transported from the volcanic gas phase into ejected carbonate inclusions. Owing to metasomatic actions of the volcanic volatile components, rearrangement and alteration of Ca and Mg contents occurred in the carbonate minerals of several ejecta. Under the influence of volcanic pressure and temperature, magnesium content originally in dolomite might be transformed into the calcite structure. \(\frac{{{\text{MgO}}}}{{{\text{CaO + MgO}}}}\) molar ratios of several carbonate ejecta do not correspond with those found in sedimentary limestones and dolostones. It cannot be proved whether the Mg of the mixed calcite-dolomite ejecta has been partially introduced from the volatiles or lost from the carbonate phases.     

The problem of rock assimilation by Somma-Vesuvius magma

New chemical and modal analyses are presented of magmatic rocks and pyroxenes nodules from the Somma-Vesuvius volcano and of trachytes from the surrounding area. Geochemical evidence is employed in checking the generally accepted suggestion that magma composition develops from that of trachyte into phonolitic tephrite and finally into tephritic leucitite (vesuvite) by assimilation of dolomite. At the Somma stage of the volcano, phonolitic tephrites (tephritic phonolites) alone have been produced. Vesuvius lavas (tephritic leucitites) are comparatively high in K₂O, CaO, F, Cl, Mn, Cu, Sr and Ba and low in SiO₂ and Nb. The formation of vesuvites by assimilation of dolomitic sedimentary rocks, combined with gravity-separation of early-formed pyroxenes from a trachytic or tephritic magma, is improbable as shown by chemical balances between the respective igneous and sedimentary rocks.     

不同滤波算法在土壤湿度同化中的应用

为研究不同滤波算法在土壤湿度同化中的有效性,以及土壤湿度模拟结果对模型参数的敏感性,结合简单生物圈模型SiB2,设置敏感性实验,探求土壤饱和水力传导度对土壤湿度模拟结果的影响;并在此基础上,采用集合卡尔曼滤波（EnKF）、无迹卡尔曼滤波（UKF）和无迹粒子滤波（UPF）开展土壤湿度实时同化实验。结果表明：土壤饱和水力传导度能显著影响土壤湿度模拟精度;利用EnKF、UKF、UPF同化站点观测数据,均能改善土壤湿度模拟结果;3种同化方法在不同土壤层的同化效果不同,在土壤表层,EnKF的有效性优于UKF和UPF,在根域层和土壤深层,3种滤波方法有效性在降雨前后相差较大。因此,针对性地选择同化方法,是提高土壤湿度模拟精度的有效手段。     

基于集合卡尔曼平滑算法的土壤水分同化

为研究观测资料稀少情况下土壤质地及有机质对土壤水分同化的影响,发展了集合卡尔曼平滑(Ensemble Kalman Smooth, EnKS)的土壤水分同化方案。利用黑河上游阿柔冻融观测站2008年6月1日至10月29日的观测数据,使用EnKS算法将表层土壤水分观测数据同化到简单生物圈模型(Simple Biosphere Model 2, SiB2)中,分析不同方案对土壤水分估计的影响,并与集合卡尔曼滤波算法(EnKF)的结果进行比较。研究结果表明,土壤质地和有机质对表层土壤水分模拟结果影响最大而对深层的影响相对较小;利用EnKF和EnKS算法同化表层土壤水分观测数据,均能够显著提高表层和根区土壤水分估计的精度,EnKS算法的精度略高于EnKF且所受土壤质地和有机质的影响小于EnKF;当观测数据稀少时,EnKS算法仍然可以得到较高精度的土壤水分估计。     

An inversion approach to assimilation and fractional crystallisation processes

A numerical inversion program has been developed to investigate isotope and trace element variations in suites of related rocks in terms of assimilation and fractional crystallisation processes. Major element compositions constrain the degree of fractionation, and the program may be used to calculate the isotope and trace element composition of either the crustal contaminant, or of the parental magmas once the contaminant is known. The ratio of the rate of assimilation to the rate of fractional crystallisation, and the bulk partition coefficients, can be varied with changes in magma composition. The approach is illustrated with a suite of calc-alkaline rocks from the Cerro Galan centre in NW Argentina, and a suite of continental flood basalts from the southern Paraná in Brazil. Both exhibit striking increases in ⁸⁷Sr/⁸⁶Sr with increasing SiO₂ consistent with progressive contamination during differentiation within the continental crust. In detail, both suites contain a subset of samples which have undergone relatively little contamination, and a subset characterised by relatively high SiO₂ and ⁸⁷Sr/⁸⁶Sr reflecting larger crustal contributions. Individual samples within the more contaminated subset can be modelled in terms of assimilation with fractional crystallisation (AFC) processes, although no clear progressively contaminated liquid lines of descent are preserved. At both Cerro Galan and the southern Paraná, the associated dacites and rhyodacites appear to have similar compositions to the crustal contaminants. Thus the inversion program has been used to investigate the amount of contamination, the relationship between the amount of contamination and the amount of crystals removed by fractional crystallisation, and the isotope and trace element contents of the parental magmas prior to AFC. The latter are estimated to have had ⁸⁷Sr/⁸⁶Sr=0.7055 and ¹⁴³Nd/¹⁴⁴Nd=0.51256 at Cerro Galan, and 0.7090 and 0.51226 respectively in the southern Paraná.     

A stochastic collocation based Kalman filter for data assimilation

In this paper, a stochastic collocation-based Kalman filter (SCKF) is developed to estimate the hydraulic conductivity from direct and indirect measurements. It combines the advantages of the ensemble Kalman filter (EnKF) for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, the random log hydraulic conductivity field is first parameterized by the Karhunen–Loeve (KL) expansion and the hydraulic pressure is expressed by the PCE. The coefficients of PCE are solved with a collocation technique. Realizations are constructed by choosing collocation point sets in the random space. The stochastic collocation method is non-intrusive in that such realizations are solved forward in time via an existing deterministic solver independently as in the Monte Carlo method. The needed entries of the state covariance matrix are approximated with the coefficients of PCE, which can be recovered from the collocation results. The system states are updated by updating the PCE coefficients. A 2D heterogeneous flow example is used to demonstrate the applicability of the SCKF with respect to different factors, such as initial guess, variance, correlation length, and the number of observations. The results are compared with those from the EnKF method. It is shown that the SCKF is computationally more efficient than the EnKF under certain conditions. Each approach has its own advantages and limitations. The performance of the SCKF decreases with larger variance, smaller correlation ratio, and fewer observations. Hence, the choice between the two methods is problem dependent. As a non-intrusive method, the SCKF can be easily extended to multiphase flow problems.     

Coarse-scale data assimilation as a generic alternative to localization

Coarse-scale data assimilation (DA) with large ensemble size is proposed as a robust alternative to standard DA with localization for reservoir history matching problems. With coarse-scale DA, the unknown property function associated with each ensemble member is upscaled to a grid significantly coarser than the original reservoir simulator grid. The grid coarsening is automatic, ensemble-specific and non-uniform. The selection of regions where the grid can be coarsened without introducing too large modelling errors is performed using a second-generation wavelet transform allowing for seamless handling of non-dyadic grids and inactive grid cells. An inexpensive local-local upscaling is performed on each ensemble member. A DA algorithm that restarts from initial time is utilized, which avoids the need for downscaling. Since the DA computational cost roughly equals the number of ensemble members times the cost of a single forward simulation, coarse-scale DA allows for a significant increase in the number of ensemble members at the same computational cost as standard DA with localization. Fixing the computational cost for both approaches, the quality of coarse-scale DA is compared to that of standard DA with localization (using state-of-the-art localization techniques) on examples spanning a large degree of variability. It is found that coarse-scale DA is more robust with respect to variation in example type than each of the localization techniques considered with standard DA. Although the paper is concerned with two spatial dimensions, coarse-scale DA is easily extendible to three spatial dimensions, where it is expected that its advantage with respect to standard DA with localization will increase.     

Uncertainty analysis of groundwater model based on data assimilation北大核心CSCD

黑河流域中下游地下水系统受上游冰冻圈融水和降雨的补给,由气候变暖导致的冰冻圈萎缩致使中下游地下水系统的稳定性面临更多的风险。地下水模型是地下水系统稳定性评估的有效手段,但是地下水模型参数往往存在较大的不确定性。为此,本文提出了基于数据同化算法的不确定性分析方法,通过包含观测资料信息减小模型不确定性。采用所提方法分析了(基于MODFLOW构建)黑河流域中游地下水模型中13个参数的不确定性,讨论了算法超参数的影响及其最优取值,分析了地下水模型参数的不确定性。实验结果证明数据同化算法可有效减小地下水模型参数的不确定性,观测资料的种类与数量对参数不确定性的减小起到重要作用;不同地下水模型参数的不确定性不同,地表水与地下水相互作用频繁的区域参数不确定性较大;含水层渗透系数、含水层给水度以及灌溉回流系数对模型输出的地下水位输出影响显著,河床水力传导系数对模型输出的河流流量影响较大。本研究将为地下水研究提供更加可靠的模型方法,为西北内流区地下水哺育的绿洲生态系统稳定可持续研究提供重要支撑。     

Geochemical effects of decoupled fractional crystallization and crustal assimilation

Most models of crustal assimilation assume that the amount of assimilant added to the magma is proportional to each infinitesimally small amount of solid removed during crystallization (AFC). In some magmatic systems, however, assimilation and crystallization are not strictly related and the mass assimilated is decoupled from, and therefore varies independently of, the mass crystallized (FCA). The geochemical consequences of FCA are examined and compared to those of AFC. The behavior of incompatible elements is identical during AFC and FCA, and ratios of these elements do not allow discrimination between the two processes. Major-oxide least-squares mass-balance models do not discriminate between AFC and FCA at F ≥ 0.7 (F = fraction of melt remaining). However, FCA yields magmas richer in compatible elements and with higher Sr-isotopic ratios than AFC at a given value of F. Repeated cycles of FCA and AFC combined with magma mixing (FAM) may result in unusual geochemical trends, such as the evolution of a calc-alkaline basaltic parent to a tholeiitic daughter magma, or the evolution of low- and medium-K calc-alkaline basalts to high-K andesites, dacites, trachyandesites or trachydacites. Lavas erupted by the volcano Micro Profitis Ilias on Santorini, Hellenic arc, Greece, provide an example of magmas which evolved by combined fractionation, assimilation by FCA and mixing.     

Pyrite tracks assimilation of crustal sulfur in Pyrenean peridotites

Cobalt-bearing pyrite (0.5?C2.0?wt.% Co) is abnormally abundant (up to 35?vol.% of the total volume of the sulfide phase) in some eastern Pyrenean peridotite massifs, compared to pieces of subcontinental mantle studied so far for sulfides. Pyrite occurs as vermicular intergrowths inside pentlandite and/or chalcopyrite or as coarser, blocky grains in the intergranular pores of host peridotites. Those different pyrites are characterized by different platinum-group element systematics (measured by laser ablation microprobe and ICP-MS). Vermicular pyrite intergrown with pentlandite displays Os-, Ir-, Ru- and Rh-enriched chondrite normalized PGE patterns of Monosulfide solid solution (Mss). In contrast, coarse-grained intergranular (??blocky??) pyrites, are PGE-poor. Chalcophile trace elements (i.e. Zn, Pb, Ag, Au) that are not usually concentrated in mantle-derived sulfides were commonly detected. By contrast, selenium contents are generally low, yielding thus pyrite with high S/Se ratio (>10⁵), consistent with a sedimentary sulfur source. Pyrite microtextures and chalcophile trace element contents support a process of assimilation of crustal sulfur from the metamorphosed sedimentary country rocks. These latter generated highly reactive CO₂-S fluids, which were injected into structural discontinuities of the lherzolitic bodies. Sulfur has reacted at T?=?300?C550°C with pre-existing, mantle-derived, metal-rich sulfide assemblages (pentlandite-chalcopyrite). Addition of crustal sulfur did produce Mss which, on cooling, exsolved the Os-rich pyrite in addition to pentlandite. The coarse-grained pyrite types have crystallized directly from S-rich fluids.     

Impact of 3D Var GSI-ENKF hybrid data assimilation system

The hybrid two-way coupled 3DEnsVar assimilation system was tested with the NCMRWF global data assimilation forecasting system. At present, this system consists of T574L64 deterministic model and the grid-point statistical interpolation analysis scheme. In this experiment, the analysis system is modified with a two-way coupling with an 80 member Ensemble Kalman Filter of T254L64 resolution and runs are carried out in parallel to the operational system for the Indian summer monsoon season (June–September) for the year 2015 to study its impact. Both the assimilation systems are based on NCEP GFS system. It is found that hybrid assimilation marginally improved the quality of the forecasts of all variables over the deterministic 3D Var system, in terms of statistical skill scores and also in terms of circulation features. The impact of the hybrid system in prediction of extreme rainfall and cyclone track is discussed.     

Effects of inhibitors on ferricyanide uptake and assimilation by plants

Effects of inhibitors on uptake and assimilation of ferricyanide by different plants were investigated. Detached roots of plants were kept in a closed-dark hydroponic system with ferricyanide solution amended with various inhibitors. Dissociation of ferricyanide to free cyanide and iron in solution was negligible. The application of inhibitors affected both botanical assimilation and uptake of ferricyanide. Of the inhibitors tested, silver nitrate showed a significantly inhibitory effect on ferricyanide uptake by rice, soybean and maize (P < 0.01), while a negligible effect was found in willows spiked with the same inhibitor (P > 0.05). However, lanthanum chloride showed the most severe effect on botanical assimilation of ferricyanide by maize and rice (P < 0.01), whereas silver nitrate and tetraethylammonium chloride were the most sensitive inhibitors to soybean and willows, respectively (P < 0.01). Botanical assimilation of ferricyanide was observed positively in responses to temperatures, in which maize was more susceptible than other selected plants. In conclusion, application of inhibitors has a substantial influence on the uptake and assimilation of ferricyanide by plants, and the inhibitory efficiency is highly dependent on the species of inhibitors applied.     

Evaluation of Gaussian approximations for data assimilation in reservoir models

The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil–water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification.     

4D-Var data assimilation system for a coupled physical-biological model

A 3-compartment model of phytoplankton growth dynamics has been coupled with a primitive-equation circulation model to better understand and quantify physical and biological processes in the Adriatic Sea. This paper presents the development and application of a data assimilation procedure based on optimal control theory. The aim of the procedure is to identify a set of model coefficient values that ensures the best fit between data and model results by minimizing a function that measures model and data discrepancies. In this sense, twin experiments have been successfully implemented in order to have a better estimation of biological model parameters and biological initial conditions.     

Role of assimilation of mantle material in petrogenesis of basalts

Upon consideration of published data and on the assumption that an alkalic-doleritic magma of the given composition may assimilate, for example, 10% of the ultrabasic substance of the mantle in one case and the same percentage of acidic substance of the crust in another, the calculated product should be either a basalt of the continental olivine-basaltic formation or a traprock of a young platform. -- V.P. Sokoloff     

Fractionation and assimilation in the Borgtinderne syenite,East Greenland

The Borgtinderne nepheline-sodalite syenite is one of the major intrusions in the Tertiary igneous province of East Greenland. The syenite magma, which was evolving towards an undersaturated peralkaline residuum, underwent extensive modification by incorporation of country rock basalt, resulting in the production of a variety of hybrid syenites. Major element variation in the hybrids is essentially linear. Break-up and mechanical incorporation of the basic material was aided by amphibolitisation and metasomatism of the basalt xenoliths.