Heterogeneous magnesium isotopic composition of the upper continental crust

High-precision Mg isotopic data are reported for ∼100 well-characterized samples (granites, loess, shales and upper crustal composites) that were previously used to estimate the upper continental crust composition. Magnesium isotopic compositions display limited variation in eight I-type granites from southeastern Australia (δ²⁶Mg = −0.25 to −0.15) and in 15 granitoid composites from eastern China (δ²⁶Mg = −0.35 to −0.16) and do not correlate with SiO₂ contents, indicating the absence of significant Mg isotope fractionation during differentiation of granitic magma. Similarly, the two S-type granites, which represent the two end-members of the S-type granite spectrum from southeastern Australia, have Mg isotopic composition (δ²⁶Mg = −0.23 and −0.14) within the range of their potential source rocks (δ²⁶Mg = −0.20 and +0.15) and I-type granites, suggesting that Mg isotope fractionation during crustal anatexis is also insignificant. By contrast, δ²⁶Mg varies significantly in 19 A-type granites from northeastern China (−0.28 to +0.34) and may reflect source heterogeneity.Compared to I-type and S-type granites, sedimentary rocks have highly heterogeneous and, in most cases, heavier Mg isotopic compositions, with δ²⁶Mg ranging from −0.32 to +0.05 in nine loess from New Zealand and the USA, from −0.27 to +0.49 in 20 post-Archean Australian shales (PAAS), and from −0.52 to +0.92 in 20 sedimentary composites from eastern China. With increasing chemical weathering, as measured by the chemical index of alternation (CIA), δ²⁶Mg values show a larger dispersion in shales than loess. Furthermore, δ²⁶Mg correlates negatively with δ⁷Li in loess. These characteristics suggest that chemical weathering significantly fractionates Mg isotopes and plays an important role in producing the highly variable Mg isotopic composition of sedimentary rocks.Based on the estimated proportions of major rock units within the upper continental crust and their average MgO contents, a weighted average δ²⁶Mg value of −0.22 is derived for the average upper continental crust. Our studies indicate that Mg isotopic composition of the upper crust is, on average, mantle-like but highly heterogeneous, with δ²⁶Mg ranging from −0.52 to +0.92. Such large isotopic variation mainly results from chemical weathering, during which light Mg isotopes are lost to the hydrosphere, leaving weathered products (e.g., sedimentary rocks) with heavy Mg isotopes.     

Lithium isotopic composition and concentration of the upper continental crust

The Li isotopic composition of the upper continental crust is estimated from the analyses of well-characterized shales, loess, granites and upper crustal composites (51 samples in total) from North America, China, Europe, Australia and New Zealand. Correlations between Li, δ⁷Li, and chemical weathering (as measured by the Chemical Index of Alteration (CIA)), and δ⁷Li and the clay content of shales (as measured by Al₂O₃/SiO₂), reflect uptake of heavy Li from the hydrosphere by clays. S-type granites from the Lachlan fold belt (-1.1 to -1.4‰) have δ⁷Li indistinguishable from their associated sedimentary rocks (-0.7 to 1.2‰), and show no variation in δ⁷Li throughout the differentiation sequence, suggesting that isotopic fractionation during crustal anatexis and subsequent differentiation is less than analytical uncertainty (±1‰, 2σ). The isotopically light compositions for both I- and S-type granites from the Lachlan fold belt (-2.5 to + 2.7 ‰) and loess from around the world (-3.1 to + 4.5‰) reflect the influence of weathering in their source regions. Collectively, these lithologies possess a limited range of Li isotopic compositions (δ⁷Li of −5‰ to + 5‰), with an average (δ⁷Li of 0 ± 2‰ at 1σ) that is representative of the average upper continental crust. Thus, the Li isotopic composition of the upper continental crust is lighter than the average upper mantle (δ⁷Li of + 4 ± 2‰), reflecting the influence of weathering on the upper crustal composition. The concentration of Li in the upper continental crust is estimated to be 35 ± 11 ppm (2σ), based on the average loess composition and correlations between insoluble elements (Ti, Nb, Ta, Ga and Al₂O₃, Th and HREE) and Li in shales. This value is somewhat higher than previous estimates (∼20 ppm), but is probably indistinguishable when uncertainties in the latter are accounted for.     

Chemical composition and fractionation of the continental crust

A new estimate of the bulk continental crust is reported consisting of 57 percent lower crust (60% felsic and 40% mafic granulites) and 43 percent upper crust. The proportions of crustal units are based on petrological observations (Bohlen &Mezger, 1989). The estimate of a bulk composition is intermediate between andesite and tonalite and is higher in Si, K, Rb, Sr, Zr, Nb, Ba, LREE, Pb, Th concentrations and lower in Mg, Ca, Sc, Mn, Fe than the crustal abundances reported byTaylor &McLennan (1985). Equal chemical composition between the upper crust and the felsic part of the lower crust is attained in balance computations if one restores a fraction of 12.5 percent S-type granite from the upper into the lower crust. An example of water-undersaturated partial melting and separation of a fraction of about 35 percent granitic magma at the conversion from amphibolite-into granulite-facies metasediments has been balanced bySchnetger (1988) in the Ivrea area (N. Italy). The worldwide observed discrepancy between a larger negative Eu anomaly in the upper crust compared with the half as large positive anomaly of the lower crust increasing from the early Precambrian to present has been explained by recycling of Ca-rich restite into the upper mantle. The composition of the Archean crust (example: Greenland) does not differ systematically from the post-Archean crust.

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Zusammenfassung Die chemische Zusammensetzung der gesamten kontinentalen Kruste, die zu 57% aus der Unterkruste (60% felsische und 40% mafische Granulite) und zu 43% aus Oberkruste besteht, wurde neu ermittelt. Die Proportionen der Krusteneinheiten beruhen auf petrologischen Beobachtungen (Bohlen &Mezger, 1989). Die geschätzte Zusammensetzung der Gesamtkruste liegt zwischen Andesit und Tonalit. Sie ist höher in den Gehalten an Si, K, Rb, Sr, Zr, Nb, Ba, LREE, Pb, Th und niedriger im Mg, Ca, Sc, Mn, Fe als die vonTaylor &McLennan (1985) mitgeteilten mittleren Krustenwerte. Die chemischen Unterschiede zwischen Ober- und Unterkruste werden ausgeglichen, wenn man die Substanz von 12,5% S-Typ-Granit von der Oberkruste abzieht und zur Unterkruste hinzufügt. Als typisches Beispiel der Abtrennung granitischer Partialschmelzen im wasseruntersättigten System wird das der variskischen Metamorphose von Metasedimenten in der Ivreazone (Nord-Italien) angesehen.Schnetger (1988) konnte hier mit einer chemischen Bilanz zeigen, daß die Umwandlung von amphibolitfaziellen zu granulitfaziellen Gesteinen mit dem Verlust von etwa 35% granitischer Schmelze verbunden war. Die negative Eu-Anomalie der Oberkruste ist weltweit doppelt so groß wie die positive Anomalie der Unterkruste. Diese in der Zeit vom Archaikum bis heute vergrößerte Diskrepanz läßt sich nur mit dem Verlust von Ca-reichen Restiten aus der Kruste an den Mantel erklären. Die chemische Zusammensetzung der kontinentalen Kruste hat sich sonst seit dem Archaikum nicht systematisch geändert, wie am Beispiel Grönlands gezeigt wird.

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Résumé Cette note propose une nouvelle estimation de la composition chimique d'ensemble de la croûte continentale, constituée pour 57% de croûte inférieure (60% de granulites felsiques et 40% de granulites mafiques) et pour 43% de croûte supérieure. Les proportions de ces unités crustales sont basées sur les observations pétrologiques (Bohlen etMezger 1989). La composition d'ensemble proposée est intermédiaire entre celles d'une andésite et d'une tonalite; par rapport aux abondances crustales données parTaylor etMcLennan (1985), les teneurs sont plus élevées en Si, K, Rb, Sr, Zr, Nb, Ba, LEE, Pb, Th et moins élevées en Mg, Ca, Sc, Mn, Fe. Si on tranfère de la croûte supérieure à la croûte inférieure la matière correspondant à 12,5% de granite de type S, la différence de composition entre ces deux croûtes disparaît. Un exemple typique de fusion partielle granitique en système sous-saturé en eau est fourni par le métamorphisme varisque de métasédiments dans la zone d'Ivrée (Italie du Nord). D'après ce bilan chimique établi parSchnetger (1988), le passage des roches du faciès des amphibolites à celui des granulites s'accompagne de la production d'environ 35% de magma granitique. L'anomalie négative en Eu de la croûte supérieure est partout le double de l'anomalie positive de la coûte inférieure. Cette différence, qui s'est accrue depuis l'Archéen jusqu'aujourd'hui, s'explique par le passage de restites riches en Ca dans le manteau supérieur. La composition d'ensemble de la croûte continentale ne s'est toutefois pas modifiée depuis l'Archéen, comme le montre l'exemple du Groenland.

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, 57% (60% 40% ), -43%. , (Bohlen & Mezger, 1989). . Taylor & McLennan (1985) Si, K, Rb, Sr, Zr, Nb, Ba, LREE, Pb, Th Mg, Ca, Sc, Mn, Fe. , 12,5% S, , . — , , . Schnetger (1988) , 35%. , . , , , , , . , .

     

Rheology of Indian continental crust and upper mantle

A rheological model of the Indian shield has been constructed using the thermal structure derived from available surface heat flow and heat generation data and the flow properties of characteristic minerals and rocks like quartz, diabase and olivine which respectively represent the upper crust, lower crust and upper mantle. Lateral variations in the thicknesses of the brittle and ductile crust and of the brittle upper mantle have thus been obtained for different tectonic environments. Implications of these results to interpretation of the seismic structure of the Indian shield have been pointed out.     

Element Abundances of China‘s Continental Crust and Its Sedimentary Layer and Upper Continental Crust

China’s continental crust (CCC) has an average thickness of 47km, with the upper continental crust (CUCC) being 31 km and the sedimentary layer(CSL) 5 km in thickness. The CCC, CUCC and CSL measure 12.437 × 10⁻¹⁷, 8.005 × 10⁻¹⁷ and 1.146 × 10¹⁷ metric tons in mass, respectively. The mass ratio of the upper continental crust to the lower one is 1.8:1. The element abundances were calculated for the CCC, CUCC and CSL respectively in terms of the chemical compositions of 2246 samples of various types and some complementary trace element data. The total abundance of 13 major elements accounts for 99.6% of the CCC mass while the other minor elements only account for 0.4%. REE characteristics, the abundance ratios of element pairs and the amounts of ore-forming elements are also discussed in the present paper.     

Sm／Nd Evolution of Upper Mantle and Continental Crust：Constraints on Gowth Rates of the Continental Crust

A new approach to the investigation of the Sm/Nd evolution of the upper mantle directly from the data on lherzolite xenoliths is described in this paper.It is demonstrated that the model age TCHUR of an unmetasomatic iherzolite zenolith ca represent the mean depletion age of its mantle source, thus presenting a correlation trend between f^Sm/Nd and the mean depletion age of the upper mantle from the data on xenoliths.This correlation trend can also be derived from the data on river suspended loads as well as from granitoids.Based on the correlation trend mentioned above and mean depletion ages of the upper mantle at various geological times, an evolution curve for the mean f^Sm/Nd value of the upper mantle through geological time has been established.It is suggested that the upwilling of lower mantle material into the upper mantle and the recycling of continental crust material during the Archean were more active ,thus maintaining fairly constantf^Sm/Nd and εNd values during this time period. Similarly ,an evolution curve for the mean f^Sm/Nd value of the continental crust through geological time has also been established from the data of continental crust material.In the light of both evolution curves for the upper mantle and continental crust ,a growth curve for the continental crust has been worked out ,suggesting that :(1)about 30%(in volume )of the present crust was present as the continental crust at 3.8 Ga ago ;(2)the growth rate was much lower during the Archean ;and (3)the Proterozoic is another major period of time during which the continental crust wsa built up .     

The geochemical composition of the terrestrial surface (without soils) and comparison with the upper continental crust

The terrestrial surface, the “skin of the earth”, is an important interface for global (geochemical) material fluxes between major reservoirs of the Earth system: continental and oceanic crust, ocean and atmosphere. Because of a lack in knowledge of the geochemical composition of the terrestrial surface, it is not well understood how the geochemical evolution of the Earth’s crust is impacted by its properties. Therefore, here a first estimate of the geochemical composition of the terrestrial surface is provided, which can be used for further analysis. The geochemical average compositions of distinct lithological classes are calculated based on a literature review and applied to a global lithological map. Comparison with the bulk composition of the upper continental crust shows that the geochemical composition of the terrestrial surface (below the soil horizons) is significantly different from the assumed average of the upper continental crust. Specifically, the elements Ca, S, C, Cl and Mg are enriched at the terrestrial surface, while Na is depleted (and probably K). Analysis of these results provide further evidence that chemical weathering, chemical alteration of minerals in marine settings, biogeochemical processes (e.g. sulphate reduction in sediments and biomineralization) and evaporite deposition are important for the geochemical composition of the terrestrial surface on geological time scales. The movement of significant amounts of carbonate to the terrestrial surface is identified as the major process for observed Ca-differences. Because abrupt and significant changes of the carbonate abundance on the terrestrial surface are likely influencing CO₂-consumption rates by chemical weathering on geological time scales and thus the carbon cycle, refined, spatially resolved analysis is suggested. This should include the recognition of the geochemical composition of the shelf areas, now being below sea level.     

Some observations on the stable carbon isotope composition of dissolved and particulate organic carbon in the marine environment

δ¹³C_PDB compositions for 39 samples of dissolved organic carbon (DOC) from the Gulf of Mexico-Caribbean Sea-Atlantic Ocean system, the South Pacific and Ross Sea are reported. Deep water values are similar with a mean of ?21.8%. attesting to the homogeneity of the oceanic DOC pool. In Antarctic waters, a 5%. difference between DOC and particulate organic carbon (POC), with POC having values similar to modern plankton (δ¹³C_PDB approx ?27%.) supports the idea of the transient nature of POC as compared to DOC.Total, lipid, acid hydrolyzed, amino acid and residue fractions of POC are about 5, 3, 7, 5 and 3%. respectively, more negative in 2000 m water as compared to surface water samples from the Gulf of Mexico.     

A damage model for the continuum rheology of the upper continental crust

In orogenic zones it is often considered appropriate to use a continuum rheology to model the deformation of the upper continental crust. In this paper we derive an applicable rheology utilizing fiber-bundle and continuum-damage models. We show that the results are identical and yield a power relation between stress σ and strain rate of the form σ= ^ρ−1. We constrain the applicable values of ρ utilizing Omori's law for the decay of aftershocks and conclude that ρ−1 is in the range of 5–15. With this strong nonlinear viscous rheology the behavior of the deforming upper crust approaches that of a perfect-plastic material.     

中国大陆地壳铅同位素演化的动力学模型

根据中国大陆中、新生代花岗岩长铅同位素数据库,沿用“铅构造模型”的基本思想并作部分改进,建立了中国大陆地壳铅同位素的动力学演化模型。与全球平均的铅同位素演化曲线相比,中国大陆地壳的原始物质相对较贫铀富钍,并且中国大陆的上地壳和下地壳在演化过程中分异得更加彻底。将本模型应用于大别地区中生代花岗岩长石铅同位素数据,结果发现它们具有壳幔铅混合的特征,并且以上下地壳物质混合产生的类地幔铅为主,花岗岩源岩中含有较高的富Th下地壳组分。     

The dissolved Beryllium isotope composition of the Arctic Ocean

We present the first comprehensive set of dissolved ¹⁰Be and ⁹Be concentrations in surface waters and vertical profiles of all major sub-basins of the Arctic Ocean, which are complemented by data from the major Arctic rivers Mackenzie, Lena, Yenisey and Ob. The results show that ¹⁰Be and ⁹Be concentrations in waters below 150 m depth are low and only vary within a factor of 2 throughout the Arctic Basin (350-750 atoms/g and 9-15 pmol/kg, respectively). In marked contrast, Be isotope compositions in the upper 150 m are highly variable and show systematic variations. Cosmogenic ¹⁰Be concentrations range from 150 to 1000 atoms/g and concentrations of terrigenous ⁹Be range from 7 to 65 pmol/kg, resulting in ¹⁰Be/⁹Be ratios (atom/atom) between 0.5 and 14 × 10⁻⁸. Inflowing Atlantic water masses in the Eurasian Basin are characterized by a ¹⁰Be/⁹Be signature of 7 × 10⁻⁸. The inflow of Pacific water masses across the Bering Strait is characterized by lower ratios of 2-3 × 10⁻⁸, which can be traced into the central Arctic Ocean, possibly as far as the Fram Strait. A comparison of the high dissolved surface ¹⁰Be and ⁹Be concentrations (corresponding to low ¹⁰Be/⁹Be signatures of ∼2 × 10⁻⁸) in the Eurasian Basin with hydrographic parameters and river data documents efficient and rapid transport of Be with Siberian river waters across the Siberian Arctic shelves into the central Arctic Basin, although significant loss and exchange of Be on the shelves occurs. In contrast, fresh surface waters from the Canada Basin also show high cosmogenic ¹⁰Be contents, but are not enriched in terrigenous ⁹Be (resulting in high ¹⁰Be/⁹Be signatures of up to 14 × 10⁻⁸). This is explained by a combination of efficient scavenging of Be in the Mackenzie River estuary and the shelves and additional supply of cosmogenic ¹⁰Be via atmospheric fallout and melting of old sea ice. The residence time of Be in the deep Arctic Ocean estimated from our data is 800 years and thus similar to the average Be residence time in the global ocean.     

Elemental composition of concentrated brines in subduction zones and the deep continental crust

It has been well established that fluids played an important part in determining chemical characteristics in many crustal terranes. Studies of fluid inclusions in eclogites have established that brines coexisted with the primary mineral assemblages during their metamorphic crystallization. These brines are currently multiply saturated in halide salts, carbonates, oxides, and sulfides. As a first step in quantitatively bounding the composition of the brines during metamorphism, the equilibrium compositions of the brines at room temperature were computed using the aqueous speciation codes EQ3/6. The results demonstrate that the brines are high density solutions (ca. 1.4 g/cm³) that have ionic strengths of approximately 8 mol, and are approximately 40% dissolved solids, by weight. These are predominately Na- and K-rich brines, with subordinate Ca and Mg. The approximate Na:K:Ca:Mg molar ratios are 4:2:0.5:0.2, but are sensitive to the assumed HCO₃⁻ concentrations. Charge balance is primarily maintained by the very high Cl concentrations. These brines bear resemblance to brines analyzed from fluid inclusions in metamorphic rocks reported by Roedder (Roedder, E., 1972. Composition of fluid inclusions. US Geol. Surv. Prof. Paper 440JJ, p. 164). Although these fluids have the potential of acting as significant metasomatic agents in subduction zones and deep crustal environments, their impact will be mineralogically discernible only if the fluid release and movement is channelized.     

Enrichments of the mantle sources beneath the Southern Volcanic Zone (Andes) by fluids and melts derived from abraded upper continental crust

Mafic basaltic-andesitic volcanic rocks from the Andean Southern Volcanic Zone (SVZ) exhibit a northward increase in crustal components in primitive arc magmas from the Central through the Transitional and Northern SVZ segments. New elemental and Sr–Nd-high-precision Pb isotope data from the Quaternary arc volcanic centres of Maipo (NSVZ) and Infernillo and Laguna del Maule (TSVZ) are argued to reflect mainly their mantle source and its melting. For the C-T-NSVZ, we identify two types of source enrichment: one, represented by Antuco in CSVZ, but also present northward along the arc, was dominated by fluids which enriched a pre-metasomatic South Atlantic depleted MORB mantle type asthenosphere. The second enrichment was by melts having the characteristics of upper continental crust (UCC), distinctly different from Chile trench sediments. We suggest that granitic rocks entered the source mantle by means of subduction erosion in response to the northward increasingly strong coupling of the converging plates. Both types of enrichment had the same Pb isotope composition in the TSVZ with no significant component derived from the subducting oceanic crust. Pb–Sr–Nd isotopes indicate a major crustal compositional change at the southern end of the NSVZ. Modelling suggests addition of around 2 % UCC for Infernillo and 5 % for Maipo.     

Computer simulation of Pb and Sr isotope evolution of the Earth's crust and upper mantle

Isotope evolution in a differentiated (crust and upper mantle) and chemically heterogeneous Earth has been computed for a model with isotopic exchange between crust and mantle at an exponentially decreasing rate. To simulate the effects of subduction, cells of crust and mantle are selected at random, their contents mixed and then redistributed into the cells from which they came—to give new chemically heterogeneous but momentarily isotopically homogeneous systems. Daughter isotopes in each cell grow according to equations appropriate for closed chemical systems. Rock age distributions and isotopic data created by the computer calculation mimic nature. Pb isotope data changes through geologic time are illustrated to demonstrate that two-stage interpretations applied to Pb data for rocks with complex histories may be misleading. The intercept of the Pb ore growth curve and regressions fit to Pb data gives minimum values only for the duration of heterogeneous $\text{U}\text{Pb}$ systems, not the time when heterogeneous distribution first occurred. An intercept derived time of about 3 b.y., in the Pb system is shown to be quantitatively compatible with an average $\text{Rb}\text{Sr}$ age of crustal rocks of 1.5 b.y. and with a constant degree of chemical heterogeneity for all of Earth history.     

The continental shelf benthic iron flux and its isotope composition

Benthic iron fluxes from sites along the Oregon-California continental shelf determined using in situ benthic chambers, range from less than 10 μmol m⁻² d⁻¹ to values in excess of ∼300 μmol m⁻² d⁻¹. These fluxes are generally greater than previously published iron fluxes for continental shelves contiguous with the open ocean (as opposed to marginal seas, bays, or estuaries) with the highest fluxes measured in the regions around the high-sediment discharge Eel River and the Umpqua River. These benthic iron fluxes do not covary with organic carbon oxidation rates in any systematic fashion, but rather seem to respond to variations in bottom water oxygen and benthic oxygen demand. We hypothesize that the highest rates of benthic iron efflux are driven, in part, by the greater availability of reactive iron deposited along these river systems as compared to other more typical continental margin settings. Bioirrigation likely plays an important role in the benthic Fe flux in these systems as well. However, the influence of bottom water oxygen concentrations on the iron flux is significant, and there appears to be a threshold in dissolved oxygen (∼60-80 μM), below which sediment-ocean iron exchange is enhanced. The isotope composition of this shelf-derived benthic iron is enriched in the lighter isotopes, and appears to change by ∼3‰ (δ⁵⁶Fe) during the course of a benthic chamber experiment with a mean isotope composition of −2.7 ± 1.1‰ (2 SD, n = 9) by the end of the experiment. This average value is slightly heavier than those from two high benthic Fe flux restricted basins from the California Borderland region where δ⁵⁶Fe is −3.4 ± 0.4‰ (2 SD, n = 3). These light iron isotope compositions support previous ideas, based on sediment porewater analyses, suggesting that sedimentary iron reduction fractionates iron isotopes and produces an isotopically light iron pool that is transferred to the ocean water column. In sum, our data suggest that continental shelves may export a higher efflux of iron than previously hypothesized, with the likelihood that along river-dominated margins, the benthic iron flux could well be orders of magnitude larger than non-river dominated shelves. The close proximity of the continental shelf benthos to the productive surface ocean means that this flux is likely to be essential for maintaining ecosystem micronutrient supply.     

Sr isotope systematics during melt generation by intrusion of basalt into continental crust

We have studied the Sr isotopic composition of partial melts of biotite granite generated experimentally and by intrusion of basalt into the Sierra Nevada Batholith. The experiments employed large, 3-cm cubes of granite to duplicate natural grain-boundary textures and were performed in air over the temperature interval 1000–1250 °C, to simulate basalt-induced wall rock and xenolith melting in the shallow crust. In both the experimental and natural analogs, fusion of plagioclase + alkali-feldspar ± quartz and biotite + plagioclase ± quartz results in the formation of colorless and brown melt (quenched to glass) respectively. Accordant with this melting behavior, brown glasses are enriched in radiogenic Sr and MgO, FeO, CaO, and TiO₂ relative to colorless glasses. These results support recent studies indicating that the isotopic compositions of crustal melts can reflect the relative contributions of mineral phases entering the melt, rather than the isotopic composition of the bulk source rock. In addition, we show that at shallow-crustal conditions preferential breakdown of biotite leads to initial high-⁸⁷Sr/⁸⁶Sr, low-Sr concentration melts. However, as the degree of melting increases, melts become less radiogenic yet are more enriched in elemental Sr due to loss of biotite from the restite and increased consumption of feldspars. Our results therefore suggest, if partial melts of granitic crust segregate rapidly during episodic magmatic underplating, successive melt batches can evolve from high-⁸⁷Sr/⁸⁶Sr to low-⁸⁷Sr/⁸⁶Sr liquids as melting progresses. Received: 25 August 1998 / Accepted: 10 March 1999