Descriptive statistics for N -dimensional closed arrays: A spherical coordinate approach

Recent publications have demonstrated that the composition of a system can be described by the angles which define the vector resulting from the projection of the composition onto the unit hypersphere. Although published trigonometric relationships allow determination of the angles in any number of dimensions, no general hyperdimensional recursive formulae exist for the calculation of these quantities and their variances and covariances. A general methodology for calculating the angles which describe the compositions of systems in any number of dimensions is presented. These angles can be used to calculate statistics (central moments and resultant vectors) describing the central tendency and dispersion among rock compositions, as well as to quantify the angular differences between compositions. Equations that relate the variances and covariances of these angular variables to the variances and covariances of the actual component proportion variables are presented, allowing projection of these measurements from one reference frame to another (cartesian to spherical and vice versa).     

Transmission fluctuations across an array and heterogeneities in the crust and upper mantle

Adopting the spectral approach, we derive the formulation of angular coherence and transverse coherence of transmission fluctuations. Our derivation and results provide new insight on transmission fluctuation analysis. A review of research work on fluctuation analysis using observations at large seismic arrays such as LASA and NORSAR-follows. We point out that the model of a single-layer Gaussian medium cannot explain the angular coherence of NORSAR data and a more general model of a non-Gaussian, multi-scale, vertically inhomogeneous random media is needed. The model of a two-layer power-law medium proposed by Flatté and Wu is among the simplest of such models.     

Monitoring active volcanoes and mitigating volcanic hazards: the case for including simple approaches

Simple approaches to problems brought about eruptions and their ensuing hazardous effects should be advocated and used by volcanologists while awaiting more sophisticated remedies. The expedients we advocate have all or many of the following attributes: only locally available materials are required; no extensive training of operators or installation is necessary; they are affordable and do not require foreign aid or exports; they are often labor intensive and are sustainable without outside assistance. Where appropriate, the involvement of local residents is advocated. Examples of simple expedients which can be used in forecasting or mitigating the effects of crises emphasize the relative ease and the less elaborate requirements with which simple approaches can be activated. Emphasis is on visual observations often by untrained observers, simple meteorogical measurements, observations of water level in lakes, temperature and chemistry of springs and fumaroles, new springs and collapse areas and observations of volcanic plumes. Simple methods are suggested which can be applied to mitigating damage from mudflows, nuées ardentes, tephra falls and gas discharge. A review in hindsight at Ruiz includes the use of both chemical indicators and simple mudflow alarms. Simple expedients are sufficiently effective that any expert volcanologist called to aid in a crisis must include them in the package of advice offered. Simple approaches are a critical and logical complement to highly technical solutions to hazardous situations.     

Raindrop impact and water flow on the vegetative surfaces of trees and the effects on stemflow and throughfall generation

The physical processes of raindrop impact and water flow on the leaves and branches of selected tropical tree species were examined under laboratory conditions using simulated rainfall. Inclined branches were found to be particularly efficient in detaining impacting water droplets. This efficiency in raindrop detention increases linearly as a function of branch inclination on branches that are initially dry. On branches that have been thoroughly wetted, this increase in raindrop detention with branch inclination is best expressed as a logarithmic function. At branch inclinations of 60° above the horizontal, the quantity of branchflow was found to be > 80 per cent of the total quantity of impacting rainfall, indicating that < 20 per cent was lost to rainsplash. The strong positive relationship between branchflow and branch inclination explains why trees with large projected areas of steeply inclined upthrust branches have significant quantities of intercepted water draining from their branches and trunks under heavy rainfall conditions. This drainage from the woody frame of trees influences surficial processes by generating both stemflow and large throughfall droplets.     

Nickel-copper mineralization at Talnotry,Newton Stewart,Scotland

Summary Nickel-copper mineralization occurs near the base of a diorite intrusion close to its contact with hornfelsed Ordovician and Silurian shales and greywackes. The principal ore minerals are nickeline, gersdorffite, pyrrhotine, pentlandite and chalcopyrite with minor amounts of molybdenite, tellurobismutite, gold, sphalerite and argentopentlandite. Pyrite, marcasite, violarite and goethite also occur but are interpreted as later alteration products. Much of the pyrrhotine-rich mineralization at the base of the intrusion is in the form of blebs and interstitial aggregates with amphiboles, plagioclase feldspar, biotite, chlorite and quartz. Chalcopyrite-rich and nickeline-gersdorffite-rich mineralization occurs above this and immediately below unmineralized diorite in the form of patches, lenticular masses and stringers along joints and fractures.Whole rock and ore analyses and electron microprobe data on the silicates, sulphides and sulpharsenides are presented.The unmineralized diorite has low SiO₂ and high MgO contents compared to typical diorites and relatively high Cr, Ni and Ti trace element values. In the mineralized diorite, platinum-group elements occur in very low concentrations in the pyrrhotineand chalcopyrite-rich assemblages but Pt, Pd and Au show significant enrichment in the nickeline-gersdorffite-rich mineralization.A magmatic origin for the mineralization is proposed rather than formation by hydrothermal solutions or metasomatism.

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Die nickel-kupfer vererzung von Talnotry, Newton Stewart, Schottland

Zusammenfassung Die Nickel-Kupfer Vererzung befindet sich im Kontaktbereich einer Dioritintrusion mit hornfelsdurchdrungenen silurischen und ordovizischen Grauwacken. Die am häufigsten auftretenden Erzmineralien sind Nickelin, Gersdorffit, Pyrrhotin, Pentlandit, und Chalcopyrit mit kleineren Mengen von Molybdenit, Tellurwismuth, Gold, Sphalerit und Argentopentlandit. Weiters treten als spätere Umwandlungsprodukte Pyrit, Markasit, Violarit und Goethit auf. Ein großer Teil der Pyrrhotin-reichen Vererzung am Fuße des eingedrungenen Diorits bildet fleckige, lückenfüllende Aggregate zwischen den Silikatphasen (Amphibol, Plagioklas, Biotit, Chlorit, Quarz). Die Chalcopyrit- und Nickelin-Gersdorffit-reiche Vererzung tritt zwischen dem unvererzten Diorit im Hangenden und der Pyrrhotin-reichen Vererzung im Liegenden als linsige, lappenartige Konzentration und entlang von Fugen und Brücken auf.Vollgesteins-Analysen sowie ausgewählte Erzanalysen und Mikrosondenergebnisse der Silikate, Sulfide und Sulfarsenide liegen vor.Im Unterschied zu den typischen Dioriten zeigt der unvererzte Diorit einen niedrigen SiO₂ und hohen MgO Gehalt und relativ hohe Cr, Ni und Ti Spurenelementwerte. Die Platingruppenelemente sind in den Pyrrhotin- und Chalcopyrit-reichen Vererzungen nur schwach vertreten, jedoch sind Pt, Pd und An in der Gersdorffit-reichen Vererzung stark angereichert.Ein magmatischer Ursprung dieser Vererzung, im Gegensatz zu einer metasomatischen Entstehung oder Bildung aus hydrothermalen Lösungen wird vermutet.

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With 3 Figures     

A statistical method to evaluate homogeneity of structural populations

For any specific rock unit in a discontinuous rock mass, the determination of structural domain boundaries is important because geologic and hydrologic properties vary from one domain to another. A domain can be considered as a structural population characterized by a distinct pattern of structure orientations (i.e., fracture, bedding, or foliation orientations).Boundaries are usually determined by comparing samples of structural data, each of which consists of a Schmidt plot that commonly displays at least 150 poles to fractures. When fracture orientations appear dispersed and random on the plots, visual comparisons are not sufficient to determine whether the samples were obtained from the same structural domain. An appropriate x ² test has been adapted to this situation and is capable of evaluating the homogeneity of structural populations. The method uses a contingency table analysis based on the frequencies of fracture poles that occur in corresponding patches on the Schmidt plots being compared.