A thermodynamic model for Ca–Na clinoamphiboles in Na2O–CaO–FeO–MgO–Al2O3–SiO2–H2O–O for petrological calculations

A calibration is presented for an activity–composition model for amphiboles in the system Na₂O–CaO–FeO–MgO–Al₂O₃–SiO₂–H₂O–O (NCFMASHO), formulated in terms of an independent set of six end‐members: tremolite, tschermakite, pargasite, glaucophane, ferroactinolite and ferritschermakite. The model uses mixing‐on‐sites for the ideal‐mixing activities, and for the activity coefficients, a macroscopic multicomponent van Laar model. This formulation involves 15 pairwise interaction energies and six asymmetry parameters. Calibration of the model is based on the geometrical constraints imposed by the size and shape of amphibole solvi inherent in a data set of 71 coexisting amphibole pairs from rocks, formed over 400–600 °C and 2–18 kbar. The model parameters are calibrated by combining these geometric constraints with qualitative consideration of parameter relationships, given that the data are insufficient to allow all the model parameters to be determined from a regression of the data. Use of coexisting amphiboles means that amphibole activity–composition relationships are calibrated independently of the thermodynamic properties of the end‐members. For practical applications, in geothermobarometry and the calculation of phase diagrams, the amphibole activity–composition relationships are placed in the context of the stability of other minerals by evaluating the properties of the end‐members in the independent set that are in internally consistent data sets. This has been performed using an extended natural data set for hornblende–garnet–plagioclase–quartz, giving the small adjustments necessary to the enthalpies of formation of tschermakite, pargasite and glaucophane for working with the Holland and Powell data set.     

THE PERFORMANCE OF OPTIMUM STACKING FILTERS IN SUPPRESSING UNCORRELATED NOISE*

Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.     

POST‐LITTLE ICE AGE PATTERNED GROUND DEVELOPMENT ON TWO PYRENEAN PROGLACIAL AREAS: FROM DEGLACIATION TO PERIGLACIATION

This study aims to observe post‐Little Ice Age glacier retreat and the constitutive patterned ground development at two French Pyrenean glacier forelands (Taillon Glacier and Pays Baché Glacier). Periglacial feature observations are associated with periods of deglaciation using aerial photos and archive files. Four conclusions are drawn. (1) The two glaciers have lost respectively 68% and 92% of their surface since 1850, which corroborates observations on other Pyrenean glaciers. (2) Patterned ground can develop very rapidly, sometimes only 10 years after deglaciation. (3) Patterned ground size does not systematically increase as a function of the time elapsed since deglaciation. (4) All the forms, even those developing near the Little Ice Age moraines, are active. We propose that the location, activity and size of patterned ground are more probably linked to drift characteristics and local wetness conditions than to the time elapsed since deglaciation.     

Positional accuracy and measurement error in digital databases of land use: an empirical study

This paper discusses the issues of positional accuracy and measurement error in the context of a large empirical study of landscape change in England and Wales. The epsilon band model of digitizing accuracy is used to make estimates of the levels of positional uncertainty and measurement error that is due to digitizing polygon outlines. The degree of error expected had the same polygons been captured in raster format is then determined. These results prompt a general discussion of the nature of error in spatial databases.     

Book Reviews

Regular grid sampling structures in the plane are a common spatial framework for many studies. Constructing grids with desirable properties such as equality of area and shape is more difficult on a sphere. We studied the distortion characteristics of recursive partitions of the surface of the globe starting with the octahedron and icosahedron polyhedral models. We used five different methods for mapping from the polyhedral model to the surface of the sphere: the Gnomonic projection, Fuller's Dymaxion projection, Snyder's equal area polyhedral projection, direct spherical subdivision, and a recursive polyhedral projection. We increased partition density using both a 4-fold and a 9-fold ratio at each level of recursive subdivision by subdividing to the 8th level with the 4-fold density ratio (65 536 cells per polyhedral face) and to the fifth level with the 9-fold density ratio (59 049 cells per polyhedral face). We measured the area and perimeter of each cell at each level of recursion for each method on each model using each density ratio. From these basic measurements we calculated the range and standard deviation of the area measurement, and the mean, range, and standard deviation of a compactness measurement defined as the ratio of (the ratio of the perimeter to the area of the cell) to (the ratio of the perimeter to the area of a spherical circle with the same area). We looked at these basic measurements and their statistics using graphs of variation with recursion level, sums of squares analyses of variation, histograms of the distributions, maps of the spatial variation, and correlograms. The Snyder projection performed best in area distortion and the Gnomonic projection performed best in compactness distortion. The Fuller projection and the Sphere method had moderate distortion in both area and compactness relative to the worst methods. There was little difference in distortion performance between partitions using the 4-fold density ratio and those using the 9-fold density ratio. Partitions based on the icosahedron performed better for all statistics than those based on the octahedron.     

Phase equilibria modelling of kyanite‐bearing anatectic paragneisses from the central Grenville Province

Kyanite‐bearing paragneisses from the Manicouagan Imbricate Zone and its footwall (high‐P belt of the central Grenville Province) preserve evidence of partial melting with development of metamorphic textures involving biotite–garnet ± kyanite ± plagioclase ± K‐feldspar–quartz. Garnet in these rocks displays a variety of zoning patterns with respect to Ca. Pseudosection modelling in the Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–O (NCKFMASHTO) system using measured bulk rock compositions accounts for the textural evolution of two aluminous and two sub‐aluminous samples from the presumed thermal peak to conditions at which retained melt solidified. The prograde features are best explained by pseudosections calculated with compositions to account for melt loss. The intersection of isopleths of grossular content and Fe/(Fe + Mg) relating to large porphyroblasts of garnet provide constraints on the P–T conditions of the metamorphic peak. These P–T estimates are considered to be minima because of the potential for diffusional modification of the composition of garnet at high‐T and during the early stages of cooling. However, they are consistent with textural observations and pseudosection topology, with peak assemblages best preserved in rocks for which the calculated pseudosections predict only small changes in mineral proportions in the P–T interval, in which retrograde reactions are inferred to have occurred between the thermal peak and the solidus. Maximum P–T conditions (14.5–15.5 kbar and 840–890 °C) and steep retrograde P–T paths inferred for rocks from the Manicouagan Imbricate Zone are comparable with those determined for mafic rocks from the same area. In contrast, maximum P–T conditions of 12.5–13 kbar and 815–830 °C and flatter P–T paths are inferred for the rocks of the footwall to the Manicouagan Imbricate Zone. The general consistency between textures, mineral compositions and the topologies of the calculated pseudosections suggests that the pseudosection approach is an appropriate tool for inferring the P–T evolution of high‐P anatectic quartzo‐feldspathic rocks.     

The Geochemistry of Scapolite Part II. Trace Elements, Petrology, and General Geochemistry

Fifty scapolites have been analysed spectrographically for numerouselements. Average concentrations (p.p.m.) were as follows: B25, Be 9-3, Ga 33, Ti 82, Li 56, Cu 4-4, Zr 59, Mn 57, Sr 1,800,Pb 45, Ba 120, Rb 20. The following were seldom or never detected:Cr, Ni, Co, Mo, Sn, V, Sc, Ag, Y, La. The major elements Ca,Na, K were also determined. The distribution of the trace elementscan be explained by isomorphous substitution, but no detailedcorrelation of trace elements with each other or with majorelements was found. Refractive indices were determined and the relation betweenaverage index and per cent Me was examined: correlation waspoor, which may in part be attributed to analytical error. Examination of scapolite parageneses shows that scapolite characteristicallyoccurs in the upper amphibolite facies or the pyroxene hornfelsfacies: it is not restricted to these and may occur in any faciesfrom zeolitic to granulitic and in any hornfels facies. Theelements generally concentrated in scapolite include Ca, Na,C, Cl, S, H, B, Be, Li, Sr, Pb. The presence of C, Cl, S, Htestify to genesis in the presence of high partial pressureof CO₂, Cl₂, SO₃, H₂O (or related compounds), that is in pneumatolytic,pegmatitic, or hydrothermal environments. The concentrationof B, Be, Li can also be attributed to these conditions. The source of the elements concentrated in scapolite must inpart be common rocks. In a limited contact zone, the nearbymagma supplied some elements, but where regional scapolitizationhas taken place the presence of magma is less clear. Many commonrocks or rock series contain all the necessary constituents,but some particular conjunction of conditions is necessary forscapolite to form, or it would be more common.     

Aegirine-Riebeckite Schists from South Westland, New Zealand

Schists with the mineral assemblage quartz-albite-dolomite-greenbiotite-aegirine-rie-beckite, occur as thin bands ? to I metrewide, within albite-epidote greenschists and garnet-plagioclasequartzo-feldspathic schists of the oligoclase zone of SouthWestland, New Zealand. Optical and chemical date show that the aegirine contains anegligible amount of the jadeite molecule whilst the opticsof the riebeckite indicate that it is a member of the arfvedsonite-riebeckiteseries. A typical schist has a high soda content, a molecularratio Na₂O+K₂O? Al₂O₃>1, a high oxidation ratio, and a lowlime content. These data, together with the fact that the calculatedmineral assemblage of the molecular mesonorm is identical withthat of the rocks, are taken as evidence that the schists resultfrom recrystallization of a rock with unusual chemical compositionunder P-T conditions on the boundary between those giving riseto the greenschist facies and the almandine-amphibolite facies.     

False metamorphic events inferred from misinterpretation of microstructural evidence and P–T data

Geometrical relationships involving inclusions and partial inclusions in metamorphic microstructures can be inadequate for inferring an order of crystallization and hence a metamorphic reaction. Unique spatial and/or chemical relationships need to be defined for mineral inclusions, in the context of a reference paragenesis, commonly the matrix assemblage. Corona microstructures are reliable indicators of metamorphic reactions, but require considerable care when used to infer reactions or changes in P–T conditions, owing to kinetic problems, as well as to changes in the effective reaction volume during changes across relatively broad P–T stability fields of assemblages. Mineral equilibria models, most commonly implemented through P–T pseudosections, may allow the order in which different minerals become stable along a given P–T path to be inferred. However, the order in which two minerals become stable may be different from the order in which two grains of these minerals nucleate. Furthermore, such diagrams cannot make predictions about which minerals will form porphyroblasts and which minerals will form inclusions in porphyroblasts. An evaluation of three examples from the Australian Proterozoic shows that modelling, in combination with inclusion‐host relationships, is a powerful tool for understanding the metamorphic evolution of a rock, but involves considerable uncertainty.