Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.     

Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Long-term seismic noise investigations on Shikotan Island: First results

In 2003–2004, long-term seismic noise observations were launched on Shikotan Island (Lesser Kuril Range) based on the “Shikotan” dormant regional seismic station. The geological and geophysical data on the registration area are reported. Information about the equipment and its technical specifications is given. The precursors to the strongest local earthquakesthat occurred in the Shikotan Island region in January 2005–March 2007 are identified.     

The qualitative zoning record of minerals. A method for determining the duration of metamorphic events?

Summary The efficacy of ion exchange in petrological systems, for example the Fe-Mg exchange between garnet and biotite, is a function of grainsize, temperature, rates of temperature change and diffusion parameters. The combination of these variables determines the final zoning profile of minerals. Therefore, zoning profiles may be used to derive one of these variables if the others are known. For example, a mineral grain that experienced a short thermal event may still preserve a zoning profile characteristic of the heating path. In contrast, if that grain experienced a long thermal event it may develop a zoning profile typical of the cooling path. Conversely, for the same temperature-time cycle, large grains may not completely equilibrate at the metamorphic peak, and in smaller grains any previous record may have been erased. This is commonly observed in natural rocks where different grains within one thin section preserve often qualitatively different zoning profiles. Thus, a critical grainsize,l _crit, may exist that separates grains with qualitatively different zoning profiles so that grains of sizel > l _crit still retain zoning information about the heating path and grains of sizel <l _crit contain only information about the cooling path. If the critical grainsize can be measured and an independent estimate for the peak metamorphic temperature exists, the duration of the thermal event may, in principle, be estimated.The applicability of this method to natural garnets is hampered by a range of uncertainties. However, a parameterisation of the critical grain size may be used to illustrate the relative importance of grain size, temperature and event duration to the equilibration of minerals. In this paper, the critical grainsize is parameterized for various temperature-time cycles and its dependence on diffusion parameters is discussed. It is shown that, for Barrovian conditions,l _crit between 0.1 and 1 mm separates garnets retaining prograde information from garnets retaining cooling path information. For illustration, we compare the results with the critical grainsize of garnets from two metamorphic terranes, the Prydz Bay region (Antarctica) and the Koralm complex (Eastern Alps). Despite the large range of uncertainties attached to the method, it is shown that the critical grainsize of garnets in both terranes is consistent with a very short duration of the last thermal event that affected the two regions.

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Die qualitative Form von Zonierungsprofilen in Mineralen. Information über die Dauer metamorpher Ereignisse?

Zusammenfassung Zonierungsprofile von Paragenesen im Ionenaustausch, zum Beispiel das Fe-Mg Austauschsgleichgewicht zwischen Granat und Biotit, sind eine Funktion von (i) Korngröße, (ii) Temperatur, (iii) Kühl- und Heizgeschwindigkeit sowie (iv) den Diffusionskonstanen. Es sollte daher möglich sein, Zonierungsprofile dazu zu verwenden, einen dieser Parameter zu bestimmen, wenn die anderen bekannt sind. Zonierungsprofile von Kristallen die ein kurzes thermisches Ereignis erfahren haben, mögen daher prograde Information beinhalten, wogegen derselbe Kristall ein retrogrades Profil aufweisen mag, wenn er einem langlebigen thermischen Ereignis unterlag (prograd und retrograd ist hier als: bei ansteigender Temperatur und bei abfallender Temperatur definiert). In Kristallen die dem gleichen Temperatur-Zeitpfad unterworfen waren, könnten kleine Körner nur die Kühlgeschichte dokumentieren, wogegen große noch Zonierungsinformation vom Heizpfad aufweisen. In natürlichen Gesteinen wird das oft dadurch beobachtet, daß verschiedene Körner auseinem Dünnschliff qualitativ verschiedene Zonierungsprofile aufweisen. Es ist daher möglich eine kritische Korngöße,l _crit, zu definieren, die Korngrößen mit qualitativ verschiedenen Zonierungsprofilen voneinander trennt. Körner mit einem Durchmesserl > l _crit haben, zumindest teilweise, noch prograde Profile, wogegen Körner mitl <l _crit nur retrograde Information dokumentieren. Wenn man diese kritische Korngröße messen kann, sollte sie dazu benutzt werden können, etwas über die Dauer des thermischen Ereignisses auszusagen.Die Anwendbarkeit dieser Methode ist durch eine Reihe von Fehlern limitiert. Nichtsdestotrotz, ist eine Parameterisierung der kritischen Korngröße nützlich um die relative Wichtigkeit von Korngröße, Temperatur und Zeit, für die Entwicklung von Zonierungsprofilen, zu illustrieren. Unser Modell kann dazu benutzt werden, um die Größenordnung von Granaten abzuschätzen, die noch prograde Information dokumentieren können. Die Abhängigkeit der kritischen Korngröße von Diffusionsparametern und der Form des Temperatur-Zeit Pfades wird ebenfalls diskutiert. Es wird gezeigt, daß für Metamorphose in der mittleren Grünschiefer und Amphibolit fazies,l _crit zwischen 0.1 and 1 mm prograd zonierte von retrograd zonierten Granaten trennt. Um das Modell zu illustrieren, werden die Ergebnisse auf die Prydz Bay Region (Antarktis) und den Koralm Komplex (Ostalpen) angewendet. Trotz der großen Fehlergrenzen der Methode glauben wir zeigen zu können, daß die kritische Korngröße beider Terrains andeutet, daß das letzte thermische Ereignis in beiden Gebieten kurzlebig war.

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With 5 Figures     

LREE distribution in perovskite,apatite and titanite from South West Ugandan xenoliths and kamafugite lavas

Summary In-situ microprobe LREE analyses of perovskite and titanite (La, Ce, Nd), and apatite (La, Ce), from SW Ugandan clinopyroxenite xenoliths and kamafugite lavas indicate that LREE distribution in these minerals is determined by a number of factors related to their different parageneses: In particular LREE content is affected by whether the LREE-bearing minerals have crystallised from metasomatic carbonate or from silicate (i.e. metasomatic or magmatic) melts in the mantle. In this situation LREE partition favours carbonate over silicate melts. Distribution of LREE in perovskite and apatite crystallised from magmatic mantle melts or mantle-derived lavas is chiefly determined by preference of LREE for perovskite > apatite > titanite. LREE zoning in perovskite is influenced by changes in melt structure: increasing melt polymerisation enhancing mineral_LREE/melt_LREE partition into perovskite rims in magmatic xenoliths; decreasing melt polymerisation depleting LREE in lava perovskite rims. This zoning is reinforced by perovskite competition with apatite for LREE: perovskite (cores/rims) co-crystallising with apatite is reduced in LREE. There are 37 instances of perovskitewith Ce below detection while La and Nd levels are normal. These occur in both xenoliths and lavas; in grain zones or whole grains. Likewise Ce alone of the LREE is below detection in six out of ten titanite analyses. These observations are interpreted as evidence for increased f_{O 2}, Ce⁴ + being excluded from these mineral structures. Recognition of these various processes can elucidate the interpretation of bulk rock and bulk mineral LREE signatures in kamafugite volcanism.

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LREE Verteilung in Perovskit, Apatit und Titanit aus Xenolithen und kamafugitischen Laven Südwest-Ugandas

Zusammenfassung In-situ LREE Analysen von Perovskit und Titanit (La, Ce, Nd) und Apatit (La, Ce) aus Klinopyroxenit-Xenolithen und kamafugitischen Laven Südwest-Ugandas zeigen, daß die LREE Verteilung in diesen Mineralen durch eine Vielzahl von Faktoren, die mit Unterschieden in den Paragenesen zusammenhängen, bestimmt wird: Der LREE-Gehalt wird im besonderen davon bestimmt, ob die LREE-führenden Minerale aus metasomatischen Karbonat- oder aus (metasomatischen oder magmatischen) Silikatschmelzen im Mantel auskristallisierten. Dabei erfolgt die LREE Fraktionierung zu Gunsten der Karbonatschmelzen. Die LREE-Verteilung von Perovskit und Apatit, die aus magmatischen Mantelschmelzen oder -laven kristallisierten, wird vorrangig durch den bevorzugten Einbau der LREE in Perovskit > Apatit > Titanit kontrolliert. Der LREE Zonarbau von Perovskit wird durch die Änderungen der Schmelzstruktur beinflußt: Verstärkte Schmelzpolymerisation führt zu verstärkter Mineral_LFEE/Schmelze_LREE Fraktionierung in den Perovskiträndern magmatischer Xenolithe, eine Abnahme der Schmelzpolymerisation hingegen resultiert in einer Abreicherung der LREE in den Perovskiträndern. Diese Art der Zonierung wird durch den Wettbewerb von Perovskit mit Apatit um die LREE verstärkt. Perovskit (Kerne/Ränder), der mit Apatit gemeinsam auskristallisierte, ist ärmer an LREE. 37 Fälle, in denenCe nicht nachweisbar war, La und Nd aber in normaler Konzentration auftreten, wurden sowohl in den Xenolithen als auch in den Laven gefunden; und zwar entweder in Kornbereichen oder in ganzen Körnern. Vergleichsweise liegt Ce nur in sechs von zehn Titanitproben unterhalb der Nachweisgrenze. Diese Beobachtungen werden als Hinweise auf erhöhte SauerstoffFugazitäten, bei denen Ce^4– aus der Mineralstruktur ausgeschlossen wird, angesehen.Ein Verständnis dieser verschiedenen Prozesse kann zur besseren Interpretation von LREE Gesamtgesteins- und Gesamtmineral-Signaturen in Kamafugiten beitragen.

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With 3 Figures     

Evidence for Multiple Mechanisms of Crustal Contamination of Magma from Compositionally Zoned Plutons and Associated Ultramafic Intrusions of the Alaska Range

Models of continental crustal magmagenesis commonly invoke theinteraction of mafic mantle-derived magma and continental crustto explain geochemical and petrologic characteristics of crustalvolcanic and plutonic rocks. This interaction and the specificmechanisms of crustal contamination associated with it are poorlyunderstood. An excellent opportunity to study the progressiveeffects of crustal contamination is offered by the compositeplutons of the Alaska Range, a series of nine early Tertiary,multiply intruded, compositionally zoned (Peridotite to granite)plutons. Large initial Sr and Nd isotopic contrasts betweenthe crustal country rock and likely parental magmas allow evaluationof the mechanisms and extents of crustal contamination thataccompanied the crystallization of these ultra-mafic throughgranitic rocks. Three contamination processes are distinguishedin these plutons. The most obvious of these is assimilationof crustal country rock concurrent with magmatic fractionalcrystallization (AFC), as indicated by a general trend towardcrustal-like isotopic signatures with increasing differentiation.Second, many ultramafic and mafic rocks have late-stage phenocrystreaction and orthocumulate textures that suggest interactionwith felsic melt. These rocks also have variable and enrichedisotopic compositions that suggest that this felsic melt wasisotopically enriched and probably derived from crustal countryrock. Partial melt from the flysch country rock may have reactedwith and contaminated these partly crystalline magmas followingthe precipitation and accumulation of the cumulus phenocrystsbut before complete solidification of the magma. This suggeststhat in magmatic mush (especially of ultramafic composition)crystallizing in continental crust, a second distinct processof crustal contamination may be super imposed on AFC or magmamixing involving the main magma body. Finally, nearly all rocks,including mafic and ultramafic rocks, have (⁸⁷Sr/⁸⁶Sr)_i thatare too high, and (T) _Nd that are too low, to represent theexpected isotopic composition of typical depleted mantle. However,gabbro xenoliths with typical depicted-mantle isotopic compositionsare found in the plutons. This situation requires either anadditional enriched mantle component to provide the parentalmagma for these plutons, or some mechanism of crustal contaminationof the parent magma that did not cause significant crystallizationand differentiation of the magma to more felsic compositions.Thermodynamic modeling indicates that assimilation of alkali-andwater-rich partial melt of the metapelite country rock by fractionating,near-liquidus basaltic magma could cause significant contaminationwhile suppressing significant crystallization and differentiation. KEY WORDS: crustal contamination; Alaska Range; isotope geochemistry; zoned plutons; assimilation ^*Corresponding author. e-mail: preiners{at}u.washington.edu; fax: (206) 543-3836.     

A window to the operation of microplate tectonics in the Tethys Ocean: the geochemistry of the Samothrace granite,Aegean Sea

Summary The island of Samothrace, northeastern Aegean Sea, consists of five main geological units: (i) A basement unit consisting of low grade metamorphic rocks (metapelites, marbles, metavolcanic rocks, and a metaconglomerate); (ii) an ophiolitic complex with K-Ar hornblende date of 154 ± 7 and 155 ± 7 Ma; (iii) A granite intrusion with biotite K-Ar dates of 14.5 ± 0.3 and 14.5 ± 0.5 Ma, and a contact metamorphic event dated at 40.9 + 2.2 Ma; (iv) a unit of Cenozoic volcanic rocks: orogenic volcanism apparently occurred in two cycles with Upper Eocene tholeiitic to calc-alkaline volcanic rocks and post-Eocene high-K andesites to trachytes. (v) Quaternary clastic sedimentary rocks which occur around the peripheral parts of the island. The granitic intrusion is predominantly a hornblende-biotite granite, granodiorite or quartz monzonite, with porphyritic variants and mafic enclaves. The pluton is cut by granophyre, aplite and rare granodioritic veins. All lithological units of the Samothrace intrusion show smooth and continuous major element trends and similar chondrite- and Ocean Ridge Granite-normalized incompatible element profiles. ORG-normalized incompatible element contents of Hf, Zr, Sm are explained with fractionation close to the normalizing values Y and Yb contents combined with high K/Yb ratios; Rb and Th are significantly enriched relative to Nb and Ta. In Y-Nb and Rb-SiO₂ space most samples of the Samothrace granite, plot in the volcanic arc and the syn-collisional granite fields. In Y + Nb-Rb space they are equally distributed within and transgress these two domains. The geochemical and regional data suggest a subduction or collision environment but biotite mineral data do not support a collisional setting for magma genesis. The Samothrace granite was probaby associated with a post-collisional domain after the closure of the Axios section of the Tethys Ocean.

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Ein Einblick in das Wirken von Mikroplattentektonik in der Tethys—Die Geochemie des Samothrake Granites, Agäisches Meer

Zusammenfassung Die Insel Samothrake in der nordöstlichen Ägäis besteht aus fünf geologischen Haupteinheiten: (i) einem schwach metamorphen Basement (Metapelite, Marmore, Metavulkanite und Metakonglomerate); (ii) einem ophiolithischem Komplex, der mit K-Ar Datierungen an Hornblende ein Alter von 154 ± 7 und 155 ± 7 Ma ergab; (iii) ein granitischer Intrusionskörper mit K-Ar Altern an Biotit von 14.0 ± 0.3 und 14.5 ± 0.5 Ma und einem kontaktmetamorphen Ereignis, das mit 40.9 ± 2.2 Ma datiert ist; (iv) eine Abfolge känozoischer Vulkanite, wobei der orogene Vulkanismus offensichtlich in zwei Zyklen ablief mit tholeiitischen bis kalkalkalischen Vulkaniten im oberen Eozän und high-K Andesiten bis Trachyten im post-Eozän; (v) quartären klastischen Sedimentgesteinen, die im Randbereich der Insel auftreten. Die Granitintrusion setzt sich hauptsächlich aus Hornblende-Biotitgraniten, Granodioriten oder Quarzmonzoniten mit teilweise porphyrischen und mafischen Enklaven enthaltenden Varietäten zusammen. Der Pluton wird von Granophyren, Apliten und seltener von granodioritischen Gängen durchschlagen. Alle lithologischen Einheiten der Samothrake Intrusion zeigen kontinuierliche Hauptelementtrends und ähnliche Chondrit und ORG-normalisierte inkompatible Elementprofile. Die Gehalte an den inkompatiblen Elementen Hf, Zr, Sm sind sehr ähnlich denen von ozeanischen Graniten (ORG). Die niedrigen Y und Yb-Gehalte und die hohen K/Yb Verhältnisse werden durch Fraktionierung erklärt. Rb und Th sind signifikant angereichert im Vergleich zu Nb und Ta. In Y-Nb und Rb-SiO₂ Diagrammen plotten die meisten Proben des Samothrake Granites im Feld der vulkanischen Inselbogen- und Synkollisionsgranite. Im Y + Nb-Rb Diagramm zeigt sich eine gleichmäßige und überlappende Verteilung. Die geochemischen und regionalen Daten weisen auf einen Subduktions- oder Kollisionsbereich hin, obwohl die Biotitzusammensetzungen nicht für eine Bildung der Magmen in einem Kollisionsbereich sprechen. Die Bildung des Samothrake Granites steht möglicherweise mit post-Kollisionstektonik nach dem Schließen der Axioszone in der Tethys in Zusammenhang.

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With 7 Figures