A multifractal analysis of lidar measured water vapour

Accurate and fast-response measurements of space-time observations of specific humidity were made above a drying land surface at the University of California at Davis, using the Los Alamos water Raman-lidar. In an attempt to quantify the space-time intermittency features of turbulent flows in the lower atmosphere, a multifractal analysis of these water vapour measurements was performed. The structure of the specific humidity, (x, t), was analyzed quantifying a scalar gradient measure both in time and space, for all possible one-dimensional cuts, i.e. and . The results confirm the multifractal nature of this scalar gradient measure (a type of scalar dissipation rate) and show that humidity measurements at fixed times (x) are more intermittent (e.g. have less entropy dimension) than those at fixed locations in space (t). Similar multifractal behaviour of the spatial data, with and without a transformation from the observed wind velocities, supports the validity of Taylor's hypothesis for the studied fields.     

Daily rainfall domains in Mallorca

Summary A Pearson Product Moment Correlation matrix for four years of daily rainfall from 96 sites on the island of Mallorca has been used to derive and map correlation fields and construct composite correlation fields for different parts of the island based on previously defined daily rainfall affinity areas. Significant variations in rainfall organisation over the island are revealed. These reflect the dominance of uplift and exposure by upland areas in the generation of rainfall, evidenced in strongly anisotropic correlation fields. Further anisotropy along lowland coasts normal to the relief trend indicate the role of local rainfall generation along sea-breeze fronts. Near isotropic fields for central island locations highlight the importance of local convection and local convergence between opposing sea breeze systems and inland convection. Linear correlation distance-decay trends are determined for the island and for the predetermined rainfall affinity areas, including estimates of distance-decay rates along field axes. A suite of exponential cone functions is derived to model the empirically observed fields, representing their typical bidimensional structure. Use of the fitted cones to model a typical rainfall day, where the rainfall distribution mimics quite closely the longer term average, yields quite good results and suggests that their use may be more appropriate than applying more conventional general interpolation techniques in the mapping of spatial rainfall distributions.With 14 Figures     

Chemical composition of hard- and softrock groundwaters from central Norway with special consideration of fluoride and Norwegian drinking water limits

Groundwaters from crystalline and metamorphic rocks (hardrocks) and from Quaternary deposits, i.e., alluvial and glacial deposits (softrocks) from the counties of Nord-Trøndelag and Sør-Trøndelag were analyzed for major and minor elements and ions including fluoride. The median concentration of F^– in water from the hardrock aquifers is 0.28 mg/l (14.7 eq/l) in contrast to water from softrock aquifers in which it is found to be 0.05 mg/1 (2.6 eq/l). More importantly, ca. 15% of the locations where water was abstracted from hardrock wells contain 1.5 mg/l (78.9 eq/l) F^– or more. Thus, 15% of all hardrock wells returned F^– results that are at or above the maximum recommended value for drinking water. Of the softrock wells, none are above 1 mg/l. Geologists would normally expect higher F^–contents in groundwaters derived from acid rocks, e.g., in granitic or gneissic areas. When comparing the host lithology with the observed F^–contents, however, no clear relationship between F^– content and lithology is visible. The highest observed F^– values actually occur in gneissic host rocks. However, wells drilled in amphibolites/greenstones, mica schists, calcareous rocks, and sedimentary rocks all returned some analytical results above 1.5 mg/l F^–. These results suggest that all hardrock wells drilled should be tested for F^– and the users informed about the results and advised to take any necessary precautions. When applying the recently proposed Norwegian drinking water limits to our data, 51% of all softrock well waters and 56% of all hardrock well waters are unfit for consumption without prior treatment, although we analyzed only for about half of the proposed elements/parameters. This result seriously questions the concept of fixed action levels—many of them with totally unproven health implications—for so many parameters/elements for hardrock groundwaters.     

Towards an understanding of joint roughness

Summary It is argued that the currently available joint models are incapable of accurate predictions of joint shear behaviour without resorting to substantial levels of empiricism. This is because these models fail to adequately quantify joint roughness, or appreciate the importance of scale. A novel approach, which uses fractal geometry to investigate joint roughness, is described. This approach goes beyond describing the symptoms of roughness and seeks to find the cause. In the application of this approach, the concepts of fractal geometry, fractal dimension and self similarity are described and used as a framework to formulate a statistically based and practical model for the characterisation of rock joint roughness. Important relationships between the fractal dimension and the more useful statistical parameters of standard deviation of both asperity angles and asperity heights are derived. These relationships not only provide a useful, working method for quantifying joint roughness, but are also shown to provide a basis for understanding the Barton empirical JRC-JCS model. In addition, the fractal model is able to provide conceptual models for the effects of normal stress on the shear behaviour of joints and the scale-dependence of joints.     

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.     

Textures in a poikilitic olivine gabbro cumulate: Evidence for supercooling

Summary Supercooling of repeated influxes of high-MgO ( 13.5 wt% MgO) tholeiitic magma emplaced along the floor of the Kap Edvard Holm magma chamber led to the formation of fine grained, intraplutonic quench zones that define the bases of 12 macrorhythmic units. The quench zones grade upwards into poikilitic cumulates containing olivine dendrites, suggesting supercooling by 40°C. Supercooling led to early, precumulus crystallization of metastable, non-equilibrium plagioclase, followed by co-precipitation of cumulus plagioclase and olivine. Later nucleation of clinopyroxene followed by rapid growth led to crystallization of zoned oikocrysts during the cumulus stage, followed by postcumulus overgrowth and crystallization of discrete intercumulus grains. At least four generations of plagioclase crystals appear to be preserved.

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Gefüge in einem poikilitischen Olivingabbro-Kumulat: Hinweis auf Unterkühlung

Zusammenfassung Unterkühlung von mehrmals nachströmendem MgO-reichen (ca. 13,5 Gew.% MgO), tholeiitischen Magma, das sich am Boden der Magmenkammer vom Kap Edvard Holm sammelte, führte zur Bildung von feinkbrnigen Zonen mit Abschreckungsgefüge, die jeweils die Basis von 12 makrorhythmischen Einheiten bilden. Diese Zonen gehen im Hangenden in poikilitische Kumulate über, die Olivin-Dendriten enthalten, was auf eine Unterkühlung um ca. 40°C hindeutet. Die Unterkühlung führte zu einer frühen präkumulativen Kristallisation von metastabilem, nicht im Gleichgewicht befindlichem Plagioklas, gefolgt von gleichzeitiger Präzipitation von Kumulus-Plagioklas und -Olivin. Eine spätere Keimbildung von Klinopyroxen, die von raschem Wachstum abgelöst wurde, führte während der Akkumulation zur Kristallisation von zonierten Oikokrysten. Danach folgte eine postkumulative Überwachsung und die Kristallisation von Einzelkörnern in den Zwischenräumen. Zumindest vier Generationen von Plagioklaskristallen scheinen erhalten zu sein.

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With 5 Figures     

Geochemical and structural evolution of micas in the Rožná and Dobrá Voda pegmatites,Czech Republic

Summary The chemistry, structural parameters, polytypism, optical properties and Rb-Sr isotopes were examined in 11 to 60 samples of biotite, muscovite and lepidolite from the pegmatites at Roná (the type locality of lepidolite; 323 ± 4Ma) and Dobrá Voda (306 ± 9Ma) in western Moravia. At both localities, early endocontact biotite is followed inwards by muscovite and lepidolite, which is concentrated in and around the core. At Roná, a 1M lepidolite follows after 2M₁ muscovite but all later generations of lepidolite are 2M₂, close to Tri₅₀ Ply₅₀ and in part associated with muscovite 2M₁. At Dobrá Voda, all lepidolite types are 1M and free of muscovite, and the late varieties approximate Tri₃₀ Ply₇₀. At both localities, a trend of increasing HF is indicated during the progress of mica crystallization, culminating in precipitation of topaz. Polytypism of lepidolite is not correlatable with any compositional or growth feature, or their combination. Throughout the mica crystallization, Rb/Cs decreases but K/Rb becomes reversed after an initial decrease. Boron is partitioned preferentially into muscovite (up to 1.10 wt.% B₂O₃) but Be, Zn, Mn and Sc are enhanced in lepidolite. A slight increase in Fe, Ba and Cl in the last generation of lepidolite might be possibly due to mixing of residual pegmatite fluids with metamorphic pore solutions.

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Geochemische und strukturelle Entwicklung der Glimmer in den Pegmatiten von Roná und Dobrá Voda, Tschechische Republik

Zusammenfassung In 11 bis 60 Proben von Biotit, Muskovit und Lepidolith aus den Pegmatiten von Roná (Typlokalität des Lepidoliths; 323 ± 9 Ma) in Westmähren wurden Chemie, Struktur-parameter, Polytypie, optische Eigenschaften und Rb-Sr-Isotopie untersucht. An beiden Lokalitäten wird früher Biotit an Endokontakten nach Innen von Muskovit und Lepidolith gefolgt, letzterer ist in und um den Kern konzentriert. In Roná folgt 1M-Lepidolith auf 2M₁-Muskovit, aber alle späteren Lepidolithgenerationen sind 2M₂, nahe Tri₅₀Ply₅₀ und zum Teil mit 2M₁-Muskovit vergesellschaftet. In Dobrá Voda sind alle Lepidolithe vom Typ 1M und frei von Muskovit, die späten Varietäten kommen Tri₅₀Ply₅₀ nahe. An beiden Lokalitäten ist während des Fortschreitens der Glimmerkristallisation eine Tendenz von steigendem HF angezeigt, die in der Ausfällung von Topas ihren Höhepunkt findet. Die Polytypie des Lepidoliths kann nicht mit irgendeiner Eigenheit der Zusammensetzung oder des Wachstums korreliert worden, auch nicht mit einer Kombination von diesen. Während der ganzen Glimmerkristallisation nimmt Rb/Cs ab, aber die Tendenz von K/Rb ändert sich nach anfänglichem Abfall. Das Bor verteilt sich bevorzugt auf den Muskovit (bis zu 1.10 Gew. -% B₂O₃), aber die Be-, Zn-, Mn- und Sc-Gehalte sind im Lepidolith erhöht. Ein leichter Ansteig von Fe, Ba und Cl in der letzten Lepidolithgeneration könnte vielleicht durch eine Mischung von pegmatitischen Restlösungen mit metamorphen Porenlösungen verursacht sein.

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With 9 Figures     

Sector collapse,sedimentation and clast population evolution at an active island-arc volcano: Stromboli,Italy

Sciara del Fuoco is the subaerial part of a partially filled sector-collapse scar that extends to 700 m below sea level on Stromboli volcano. The collapse occurred <5000 years ago, involved 1.81 km³ of rock and is the latest of a series of major collapses on the north-west flank of Stromboli. A north-east trending arc-axial fault system channels magmas into the volcano and has caused tilting and/or downthrow to the north-west. The slope of the partial cone constructed between the lateral walls of the collapse scar acts as a channelway to the sea for most eruptive products. From 700 m below sea level and extending to >2200 m and >10 km from the shore to the NNW, a fan-shaped mounded feature comprises debris avalanche deposits (>4 km³) from two or more sector collapses. Volcaniclastic density currents originating from Sciara del Fuoco follow the topographic margin of the debris avalanche deposits, although overbank currents and other unconfined currents widely cover the mounded feature with turbidites. Historical (recorded) eruptive activity in Sciara del Fuoco is considerably less than that which occurred earlier, and much of the partial fill may have formed from eruptions soon after the sector collapse. It is possible that a mass of eruptive products similar to that in the collapse scar is dispersed as volcanogenic sediment in deep water of the Tyrhennian basin. Evidence that the early post-collapse eruptive discharge was greater than the apparent recent flux (2kg/s) counters suggestions that a substantial part of Stromboli's growth has been endogenous. The partial fill of Sciaria del Fuoco is dominated by lava and spatter layers, rather than by the scoria and ash layers classically regarded as main constituents of Strombolian (cinder) cones. Much of the volcanic slope beneath the vents is steeper than the angle of repose of loose tephra, which is therefore rapidly transported to the sea. Delicate pyroclasts that record the magmatic explosivity are selectively destroyed and diluted during sedimentary transport, mainly in avalanches and by shoreline wave reworking, and thus the submarine deposits do not record well the extent and diversity of explosive activity and associated clast-forming processes. Considerable amounts of dense (non-vesicular) fine sand and silt grains are produced by breakage and rounding of fragments of lava and agglutinate. The submarine extension of the collapse scar, and the continuing topographic depression to >2200 m below sea level, are zones of considerable by-passing of fine sand and silt, which are transported in turbidity currents. Evidently, volcanogenic sediments dispersed around island volcanoes by density currents are unlikely to record well the true spectrum and relative importance of clast-forming processes that occurred during an eruption. Marine sedimentary evidence of magmatic explosivity is particularly susceptible to partial or complete obliteration, unless there is a high rate of discharge of pyroclastic material into the sea.     

A study of bernalite,Fe(OH)3, using Mössbauer spectroscopy,optical spectroscopy and transmission electron microscopy

To study the crystal chemistry of bernalite, Fe(OH)₃, and the nature of the octahedral Fe³⁺ environment, Mössbauer spectra were recorded from 80 to 350 K, optical spectra were recorded at room temperature and a sample was studied using transmission electron microscopy. The Mössbauer spectrum of bernalite consists of a single six-line magnetic spectrum at 80 K. A broadened six-line magnetic spectrum with significantly less intensity is observed at higher temperatures, and is attributed to a small fraction of bernalite occurring as small particles. The variation of hyperfine magnetic field data for bulk bernalite with temperature is well described by the Weiss molecular field model with parameters of H ₀ = 55.7±0.3 T and T _N = 427±5K. The centre shift data were fitted to the Debye model with parameters ₀=0.482±0.005 mm/s (relative to -Fe) and _M=492±30 K. The quadrupole shift is near zero at 300 K, and does not vary significantly with temperature. Absorption spectra in the visible and near infrared range show three crystal field bands of Fe³⁺ at 11 300, 16000 and 23 200 cm^-1, giving a crystal field splitting of 14 570 cm^-1 and Racah parameters of B=629 cm^-1 and C=3381 cm^-1. Infrared reflection spectra show two distinct OH-stretching frequencies, which could correspond to two structurally different types of OH groups. A band was also observed at 2250 cm^-1, suggesting the presence of molecular CO₂ in the large cation site. Analytical transmission electron microscopy indicates that Si occurs within the bernalite structure as well as along domain boundaries. Electron diffraction and imaging show that bernalite is polysynthetically twinned along {100} planes with twin domains ranging from 3 to 20 nm in thickness. Results are discussed with respect to the nature of the octahedral Fe³⁺ site, and compared with values for other iron oxides and hydroxides.     

The solubility of [4H]Si defects in α-quartz and their role in the formation of molecular water and related weakening on heating

The nature of the solubility of water as [4H]_Si defects in quartz, and their role in providing a source of molecular water on heating, is investigated. Existing ab inito energy calculations on the incorporation of water in quartz are used to show that energetically 4H for Si substitution is likely to constitute the most prevalent mode of water uptake on the atomic scale in quartz under equilibrium conditions, and that the planar defects previously observed by a number of different authors by electron microscopy in wet quartz are likely to be planar rafts of aggregated [4H]_Si defects which are formed on supersaturation. These new conclusions call into question the previous identification of the planar defects as high pressure water clusters and require that their role in the production of molecular water in the context of recent theories of hydrolytic weakening be re-assessed. Accordingly the existing ab initio results have been used to establish the characteristics of the phase diagram for the system quartz-water in the temperature and pressure range of interest in hydrolytic weakening. Additional electron-optical experiments on wet quartz show that, on annealing at temperature in the electron microscope, similar planar defects develop in wet quartz by a diffusion process. In the context of existing theories of hydrolytic weakening it is now proposed that the conversion of [4H]_Si defects to molecular water, where this is dictated by the equilibrium phase diagram, leads to a relatively large increase in volume and to the appearance of the bubbles of free water and the nucleation of associated prismatic dislocation loops of Burgers vector b=1/3 a $\langle 11\bar 20\rangle $ as previously observed. Ultimately the development of these loops leads to dislocation-induced plasticity.