Hornblende–garnet–plagioclase thermobarometry: a natural assemblage calibration of the thermodynamics of hornblende

Calibrations are presented for an independent set of four equilibria between end-members of garnet, hornblende, plagioclase and quartz. Thermodynamic data from a large internally-consistent thermodynamic dataset are used to determine the ΔG° of the equilibria. Then, with the known mixing properties of garnet and plagioclase, the non-ideal mixing in amphibole is derived from a set of 74 natural garnet–amphibole–plagioclase–quartz assemblages crystallised in the range 4–13 kbar and 500–800 °C. The advantage of using known thermodynamic data to calculate ΔG° is that correlated variations of composition with temperature and pressure are not manifested in fictive derived entropies and volumes, but are accounted for with non-ideal mixing terms. The amphibole is modelled using a set of ten independent end-members whose mixing parameters are in good agreement with the small amount of data available in the literature. The equilibria used to calibrate the amphibole non-ideal mixing reproduce pressures and temperatures with average absolute deviations of 1.1 kbar and 35 °C using an average pressure–temperature approach, and 0.8 kbar with an average pressure approach. The mixing data provide not only a basis for thermobarometry involving additional phases, but also for calculation of phase diagrams in complex amphibole-bearing systems. Received: 8 November 1999 / Accepted: 7 July 2000     

A Compensated-Redlich-Kwong (CORK) equation for volumes and fugacities of CO2 and H2O in the range 1 bar to 50 kbar and 100–1600°C

We present a simple virial-type extension to the modified Redlich-Kwong (MRK) equation for calculation of the volumes and fugacities of H₂O and CO₂ over the pressure range 0.001–50 kbar and 100 to 1400°C (H₂O) and 100 to 1600°C (CO₂). This extension has been designed to: (a) compensate for the tendency of the MRK equation to overestimate volumes at high pressures, and (b) accommodate the volume behaviour of coexisting gas and liquid phases along the saturation curve. The equation developed for CO₂ may be used to derive volumes and fugacities of CO, H₂, CH₄, N₂, O₂ and other gases which conform to the corresponding states principle. For H₂O the measured volumes of Burnham et al. are significantly higher in the range 4–10 kbar than those presented by other workers. For CO₂ the volume behaviour at high pressures derived from published MRK equations are very different (larger volumes, steeper (P/T)_V, and hence larger fugacities) from the virial-type equations of Saxena and Fei. Our CORK equation for CO₂ yields fugacities which are in closer agreement with the available high pressure experimental decarbonation reactions.     

Sapphirine and spinel phase relationships in the system FeO-MgO-Al2O3-SiO2-TiO2-O2 in the presence of quartz and hypersthene

Sapphirine and spinel can accommodate significant ferric iron and therefore the mineral equilibria involving these phases must be sensitive to a(O₂). In this paper we examine the theoretical phase relationships involving sapphirine and spinel in addition to sillimanite, garnet, cordierite, rutile, hematite-ilmenite solid solution (henceforth ilmenite), and magnetite-ulvospinel solid solution (henceforth magnetite), in the presence of quartz and hypersthene in the system FeO-MgO-Al₂O₃-SiO₂-TiO₂-O₂ (FMASTO), with particular reference to the topological inversion in P-T postulated by Hensen (Hensen 1986). Documented natural associations suggest that the appropriate topology for assemblages involving magnetite and ilmenite is Hensen's higher a(O₂) one, while, in contrast, the topology for assemblages involving ilmenite and rutile is the lower a(O₂) one. The exact configuration of the inversion between these two topologies remains uncertain because of uncertainties in the ferric/ferrous iron partitioning between sapphirine and spinel-cordierite at high temperatures. By comparison with experimental data and natural occurences, the sillimanite-sapphirine-cordierite-garnet-hypersthene-quartz assemblage is in equilibrium at about 1000°–1020° C and 7–8 kbars, while sapphirine-cordierite-spinel-garnet-hypersthene-quartz occurs at temperatures in excess of those attainable during crustal metamorphism, for ilmenite-rutile buffered assemblages. This implies that sapphirine-rutil-ehypersthene-quartz assemblages, as found in the Napier Complex, Antarctica, can only occur at > 1000° C. Also, spinel-rutile-hypersthene-quartz assemblages should not be found in rocks because temperatures in excess of 1100° C are expected to be involved in their formation. The temperatures of formation of spinel-sillimanite-sapphirine-garnethypersthene-quartz, sapphirine-spinel-cordierite-sillimanite-hypersthene-quartz, and sillimanite-spinel-cordieritegarnet-hypersthene-quartz in assemblages buffered by magnetite and ilmenite are less well constrained, but are likely to be in the range 900°–1000° C. These conclusions apply to rocks with compositions close to FMASTO; the perturbing effects of substantial concentrations of additional components, in particular Ca, mainly in garnet, and Zn and Cr, mainly in spinel, may invalidate these conclusions.     

Stochastic representation for anisotropic permeability tensor random fields

In this paper, we introduce a novel stochastic model for the permeability tensor associated with stationary random porous media. In the light of recent works on mesoscale modeling of permeability, we first discuss the physical interpretation of the permeability tensor randomness. Subsequently, we propose a nonparametric prior probabilistic model for non‐Gaussian permeability tensor random fields, making use of the information theory and a maximum entropy procedure, and provide a physical interpretation of the model parameters. Finally, we demonstrate the capability of the considered class of random fields to generate higher levels of statistical fluctuations for selected stochastic principal permeabilities. This unique flexibility offered by the parameterization of the model opens up many new possibilities for both forward simulations (e.g. for uncertainty propagation in predictive simulations) and stochastic inverse problem solving. Copyright © 2011 John Wiley & Sons, Ltd.     

A travel time-based variable grid approach for an activity-based cellular automata model

Urban growth and population growth are used in numerous models to determine their potential impacts on both the natural and the socio-economic systems. Cellular automata (CA) land-use models became popular for urban growth modelling since they predict spatial interactions between different land uses in an explicit and straightforward manner. A common deficiency of land-use models is that they only deal with abstract categories, while in reality, several activities are often hosted at one location (e.g. population, employment, agricultural yield, nature…). Recently, a multiple activity-based variable grid CA model was proposed to represent several urban activities (population and economic activities) within single model cells. The distance-decay influence rules of the model included both short- and long-distance interactions, but all distances between cells were simply Euclidean distances. The geometry of the real transportation system, as well as its interrelations with the evolving activities, were therefore not taken into account. To improve this particular model, we make the influence rules functions of time travelled on the transportation system. Specifically, the new algorithm computes and stores all travel times needed for the variable grid CA. This approach provides fast run times, and it has a higher resolution and more easily modified parameters than the alternative approach of coupling the activity-based CA model to an external transportation model. This paper presents results from one Euclidean scenario and four different transport network scenarios to show the effects on land-use and activity change in an application to Belgium. The approach can add value to urban scenario analysis and the development of transport- and activity-related spatial indicators, and constitutes a general improvement of the activity-based CA model.     

Holocene evolution of the crater lake at Malha,Northwest Sudan

A reconstruction of the hydrological and environmental evolution of the crater lake at Malha (Northern Darfur, Sudan) resulted from the mineralogical and biological study of a 9.21 m section of lake sediments, representing an uninterrupted sequence of lacustrine deposition since 8 290 ¹⁴C years BP.Important changes in water supply and conditions of sedimentation are reflected in the nature of the sediments and the morphology and stratigraphical distribution of various salt minerals. Additional information on lake circulation patterns and salinity conditions are obtained from associated benthic paleocommunities, represented by ostracods and dipterid larvae. Combining both lines of evidence, the studied sequence can be divided in six distinct sections, which correspond to six successive periods in the lake's Holocene history. The first three periods, generally characterized by high lake levels, represent three generations of a meromictic lake, two of which have ended with a complete desiccation of the lake basin. Meromixis was stable during Period I, due to wind shelter and pronounced density stratification. In the course of Periods II and III stratification was repeatedly interrupted. During Period II, the disruptions were accompanied by important water budget fluctuations; a superimposed gradual decrease in net water supply eventually resulted in holomictic conditions terminating this period. Evidence of turbulence periodically affecting profundal waters is recorded in the sediments of Period III, suggesting that disruptions of stratification were now initiated by very strong winds. Between Period I and Period III, the littoral mixolimnion gradually evolved from near fresh to mesosaline. In Periods IV to VI, lake level was intermediate to low. The lake was holomictic for most of the time and meso- to hypersaline; during Period V, it repeatedly shrunk to a shallow brine pool.The Holocene evolution of Malha Crater Lake illustrates the progressive increase in aridity over most of North Africa following a well-established, early- to mid-Holocene major humid episode. The uninterrupted sedimentary sequence lends itself for detailed reconstruction of Holocene climatic evolution in arid Northeast Africa, a region where records of continuous lacustrine deposition are extremely scarce. As the chronology of critical events in the lake's history remains as yet unsupported by radiocarbon dates, correlation with other Holocene sequences in the eastern Sahara is highly tentative at this point.     

中国城市群区域城际轨道交通布局模式

我国城市密集区与城市群的迅速发展,对交通网络化、现代化的需求日益迫切,而城际轨道交通是城市群发展的重要条件和前提。国外发达国家发展的经验表明,城际轨道交通是城市群客流运输最佳的交通方式选择,两者相互影响、互为促进,城市群区域和城际轨道交通之间的空间结构存在着必然的空间映射关系。基于此,本文根据我国城市群发展现状及其区域空间结构发展的5种模式,相应提出放射型、钟摆型、串珠型和网络型等4种城际轨道交通布局形式,并阐述各自特点。在未来一定时期,国内城际轨道交通将蓬勃发展,必须根据城市群区域空间结构发展模式,进行科学规划和布局形式的选择,以有效满足日益庞大的客流需求和推动城市群发展战略的实现。     

Assessing housing growth when census boundaries change

The US Census provides the primary source of spatially explicit social data, but changing block boundaries complicate analyses of housing growth over time. We compared procedures for reconciling housing density data between 1990 and 2000 census block boundaries in order to assess the sensitivity of analytical methods to estimates of housing growth in Oregon. Estimates of housing growth varied substantially and were sensitive to the method of interpolation. With no processing and areal‐weighted interpolation, more than 35% of the landscape changed; 75–80% of this change was due to decline in housing density. This decline was implausible, however, because housing structures generally persist over time. Based on aggregated boundaries, 11% of the landscape changed, but only 4% experienced a decline in housing density. Nevertheless, the housing density change map was almost twice as coarse spatially as the 2000 housing density data. We also applied a dasymetric approach to redistribute 1990 housing data into 2000 census boundaries under the assumption that the distribution of housing in 2000 reflected the same distribution as in 1990. The dasymetric approach resulted in conservative change estimates at a fine resolution. All methods involved some type of trade‐off (e.g. analytical difficulty, data resolution, magnitude or bias in direction of change). However, our dasymetric procedure is a novel approach for assessing housing growth over changing census boundaries that may be particularly useful because it accounts for the uniquely persistent nature of housing over time.     

Spatial variability, mechanisms and propagation of change in an active meandering river

This paper addresses questions of the spatial pattern of instability and the mechanisms of change in an active meandering river, particularly whether and how change is propagated. More than 20 years of monitoring of a sequence of nearly 100 bends on one dynamic meandering river, combined with historical data and previous analyses of processes of change, provide a unique insight into the link between annual changes produced by erosion and deposition and the longer-term changes in planform. The study reach of the River Dane in NW England exhibits stable and unstable sections adjacent to one another. Rates of movement range up to 3 m a^− 1, with maxima occurring in high curvature, free bends. Stable reaches are due to factors of gradient, curvature and bank resistance. Analysis of the large amount of data on occurrence of erosion and deposition in each bend each year reveals no definite association of changes in one bend with another. The detailed evidence of the morphological features in the bends shows that changes do not take place by bars moving progressively through reaches. Case studies of bends upstream of constrained, stable reaches indicate an oscillation of widening and narrowing of the channel, over a period of a few years, producing a net rotation of the bend. These areas are zones of stalling of sediment and change takes place by absorption and lateral movement. Overall, changes tend to be localised and fit the bend theory of meanders, but with low sensitivity reaches pinning the planform for longer periods in certain locations.