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.     

On the use of gravity and magnetic anomalies for locating probable areas of metallic mineralization in South Sinai, Egypt

The present study deals with processing and interpreting the potential gravity and magnetic data in order to locate promising sites for metallic mineral occurrences in the basement rocks of South Sinai. Two promising sites were anticipated by combining the geophysical results and the available geological information. Each site was profiled and interpreted to the nearly approximated subsurface feature model, and the geometrical parameters of the expected subsurface structures may form mineralized bodies such as depth, thickness, width, dipping, density contrast, and magnetic susceptibility contrast could be delineated. Detailed ground Very Low Frequency (VLF) and Vertical Magnetic Gradient (VMG) methods were carried out in the site A2, eight VLF and VMG anomalies were determined, and their depths were calculated.     

Transition from eclogite to amphibolite-facies metamorphism in the Austroalpine Ulten Zone

Summary The Ulten Zone of the Austroalpine crystalline basement south-west of Meran (Italy) contains metapelitic schists and granoblastic paragneisses, leucocratic orthogneisses, migmatites (in both gneiss-lithologies), metabasites and ultramafic lenses. Metamorphic textures of the metapelitic schists and granoblastic paragneisses indicate two different metamorphic events, characterized by two mineral assemblages, which differ in mineral chemistry: (1) an eclogite facies mineral assemblage (M1) comprising Grt-Ky I-Bt. Ms-Kfs-PI-Qtz-Rt, and (2) an amphibolite facies mineral assemblage (M2) comprising Grt-KyII-Bt-Ms-PI-Qtz-Ilm±St. For the M1 event, pressures of at least 15kbar and temperatures of about 700°±50°C can be estimated. The later amphibolite facies overprint occurred at pressures of 6 to 8kbar and about 600°±50°C. The M1 and M2 assemblages belong to a continuous clockwise metamorphic evolution during the Variscan orogeny. Evidence for Alpine metamorphism can only be detected by sericite rims around kyanite and reset biotite ages. The migmatites, which contribute about 15–30vol.% of all rocks in the investigated area, were formed on the prograde path during the M1 event. Dissolution of H₂O in the melted part of the migmatites resulted in a CO₂dominated fluid, which was trapped in primary kyanite (M1) fluid inclusions. Secondary H₂O-rich fluid inclusions are found in quartz grains and may represent the fluid which enabled a pervasive equilibration during M2.

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Übergang von eklogit-zu amphibolitfazieller Matamorphose in der austroalpinen Ultenzone

Zusammenfassung Die Ulten Zone, ein Teil des ostalpinen kristallinen basements, südwestlich von Meran, wird aus Metapeliten and granoblastischen Paragneisen, leukokraten Orthogneisen, Migmatiten (in beiden Lithologien), Metabasiten and ultramafischen Linsen aufgebaut. Metamorphe Texturen der Metapelite und granoblastischen Paragneise lassen auf zwei verschiedene metamorphe Ereignisse schließen, die durch unterschiedliche Mineral-chemismen und Paragenesen charakterisiert sind: (1) eine eklogitfazielle Paragenese (M1), bestehend aus Grt-KyI-Bt-Ms-Kfs-P1-Qtz-Rt und (2) eine amphibolitfazielle Paragenese (M2), bestehend aus Grt-KyII-Bt-Ms-P1-Qtz-Ilm±St. Für M1 konnten Minimaldrucke von 15kbar und Temperaturen von 700°±50°C abgeleitet werden. Die spätere amphibolitfazielle Überprägung fand bei 6 bis 8kbar und 600°±50°C statt. M1 und M2 gehören einer kontinuierlichen Metamorphoseentwicklung während der variszischen Orogenese an.Die Migmatite, ungefähr 15–30vol.% der Gesteine im untersuchten Gebiet, wurden am prograden Pfad während des M1 Ereignisses gebildet. Aufgrund der höheren Löslichkeit von H₂0 in der Schmelze, blieb ein CO₂, reiches Fluid zurück, das im primären Kyanit (M1) eingeschlossen wurde. Wässrige Flüssigkeitseinschlüsse können in Quarzkörnern gefunden werden. Dieses Fluid ist wahrscheinlich für die Reequilibrierung zu amphibolitfaziellen Bedingungen verantwortlich.

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With 5 Figures     

Spatial orientation of the spin vectors of the disk galaxies in the Virgo cluster I. A catalogue of the disk galaxies in the Virgo cluster

Based on four UK Schmidt Telescope (UKST) IIIa-j direct plates which had been digitized by the Automated Plate Measuring System (APM), a detailed identification of the disk galaxies in the Virgo cluster has been carried out. The certain and possible member galaxies are mainly selected from the updated Catalogue of 2096 Galaxies in the Virgo Cluster Area (VCC). The area of this identification covers a 85 square degree region centered on this cluster. As a result, we compiled a new catalogue of 340 certain and possible member disk galaxies, including 85 lenticulars (SO), 136 spirals (S) and 119 irregulars (Irr), where the APM-measured values of the position angle (P.A.) and diameters of 299 disk galaxies are provided. For at least 149 galaxies, the values of the P.A. and diameters are published for the first time.Comparison between the APM-measured P.A. and diameters of galaxies and those given by the Uppsala General Catalog of Galaxies (UGC) demonstrates the reliability of our data. The statistical properties and completeness of this database are also discussed. Compared with the UGC-given P.A. and diameters which were determined by eyes, our data has no selection effect owing to the instrument measurements. Within our searching region, this might be the largest and relatively complete photometric database published so far for investigating the spatial orientation of the spin vectors of galaxies in the Virgo cluster.     

Detection of a new interstellar molecular ion, H2COH+ (protonated formaldehyde)

A new interstellar molecular ion, H2COH+ (protonated formaldehyde), has been detected toward Sgr B2, Orion KL, W51, and possibly in NGC 7538 and DR21(OH). Six transitions were detected in Sgr B2(M). The 1(1,0)-1(0,1) transition was detected in all sources listed above. Searches were also made toward the cold, dark clouds TMC-1 and L134N, Orion (3N, 1E), and a red giant, IRC + 10216, without success. The excitation temperatures of H2COH+ are calculated to be 60-110 K, and the column densities are on the order of 10(12)-10(14) cm-2 in Sgr B2, Orion KL, and W51. The fractional abundance of H2COH+ is on the order of 10(-11) to 10-(9), and the ratio of H2COH+ to H2CO is in the range 0.001-0.5 in these objects. The values in Orion KL seem to be consistent with the "early time" values of recent model calculations by Lee, Bettens, & Herbst, but they appear to be higher than the model values in Sgr B2 and W51 even if we take the large uncertainties of column densities of H2CO into account. We suggest production routes starting from CH3OH may play an important role in the formation of H2COH+.