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     

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.     

Radiometric constraints on hydrothermal circulation in cooling granite plutons

Improved precision of radiometric dating of ore deposits can provide information about the thermal history of hydrothermal circulation in cooling plutons. In Jales a Hercynian porphyritic two-mica granite and pre-Ordovician mica schists are cut and intensely altered by the Campo gold-quartz vein. The unaltered granite must be younger than 320 ± 6 Ma, and gives mica Rb-Sr ages of 308.5 ± 2.4 (1) Ma (muscovite) and 294.5 ± 1.1 Ma (biotite). Alteration muscovites from the granite give a weighted mean Rb-Sr age of 308.1 ± 1.5 Ma, and a mean ³⁹Ar-⁴⁰Ar age of 300.7 ± 2.8 Ma. Alteration muscovites from the mica schists give similar ³⁹Ar-⁴⁰Ar ages, averaging 303.0 ± 2.8 Ma. The results suggest that circulation of the Campo mineralising fluids took place no more than 2–4 Ma after the granite cooled through the muscovite Rb-Sr closure temperature, about 500 °C, and that subsequent cooling to biotite closure at about 300 °C took place at less than 14°C/Ma. The mean cooling rate following emplacement was 15 to 25 °C/Ma. The most detailed comparable published data, for the Cornubian ore field, imply much faster cooling rates.     

A sulfur isotope study of volcanogenic massive sulfide deposits of the Eastern Black Sea province,Turkey

Kuroko-type massive sulfide deposits of the Eastern Black Sea province of Turkey are related to the Upper Cretaceous felsic lavas and pyroclastic rocks, and associated with clay and carbonate alteration zones in the footwall and hangingwall lithologies. A complete upward-vertical section of a typical orebody consists of a stringer-disseminated sulfide zone composed mainly of pyrite and chalcopyrite; a massive pyrite zone; a massive yellow ore consisting mainly of chalcopyrite and pyrite; a black ore made up mainly of galena and sphalerite with minor amounts of chalcopyrite, bornite, pyrite and various sulfosalts; and a barite zone. Most of the deposits in the province are associated with gypsum in the footwall or hangingwall. The paragenetic sequence in the massive ore is pyrite, sphalerite, chalcopyrite, bornite, galena and various sulfosalts, with some overlap between the mineral phases. Massive, stringer and disseminated sulfides from eight kuroko-type VMS deposits of the Eastern Black Sea province have a ³⁴S range of 0–7 per mil, consistent with the ³⁴S range of felsic igneous rocks. Sulfides in the massive ore at Madenköy (4.3–6.1 per mil) differ isotopically from sulfides in the stringer zone (6.3–7.2 per mil) suggesting a slightly increased input of H₂S derived from marine sulfate with time. Barite and coarse-grained gypsum have a ³⁴S range of 17.7–21.5 per mil, a few per mil higher than the ³⁴S value of contemporaneous seawater sulfate. The deposits may, therefore, have formed in restricted basins in which bacterial reduction of sulfate was taking place. Fine-grained, disseminated gypsum at Kutlular and Tunca has ³⁴S values (2.6–6.1 per mil) overlapping those of ore sulfides, indicating sulfide oxidation during waning stages of hydrothermal activity.     

在应用计算机解释印度拉贾斯坦邦西部贾伊萨梅尔地区比尔马尼亚盆地地质特征中地质数据的分析

最近十年来研究的地质数据包括比尔马尼亚盆地岩相的地层、岩性、岩石、粒度和地球化学资料。这些数据已进入专用的“Ｆｏｘｓｅｄｂａ”数据表以建立比尔马尼亚盆地的数据总库。采用Ｈａｒｗａｒｄ制图法在ｘ－ｙ轴（粒度参数和地球化学数据）上作图。该盆地各种岩相的环境解释模式都配备有“图象”软件。最后,上述资料被用来解释所推断的比尔马尼亚盆地各种岩相的沉积环境。该盆地的沉积充填物含硅质碎屑、碳酸盐和磷块岩相的混合组合,指示变幻不定的沉积环境,即有若干具间歇海进事件的沉积海退事件。结果,磷块岩主要形成一种浅水正化学沉积和异化学沉积的复杂组合。     

Episode 49 of the Pu'u 'O'o-Kupaianaha eruption of Kilauea volcano-breakdown of a steady-state eruptive era

The Pu'u 'O'o-Kupaianaha eruption (1983-present) is the longest lived rift eruption of either Kilauea or neighboring Mauna Loa in recorded history. The initial fissure opening in January 1983 was followed by three years of episodic fire fountaining at the Pu'u 'O'o vent on Kilauea's east rift zone 19km from the summit (episodes 4–47). These spectacular events gave way in July 1986 to five and a half years of nearcontinuous, low-level effusion from the Kupaianaha vent, 3km to the cast (episode 48). A 49th episode began in November 1991 with the opening of a new fissure between Pu'u 'O'o and Kupaianaha. this three week long outburst heralded an era of more erratic eruptive behavior characterized by the shut down of Kupaianaha in February 1992 and subsequent intermittent eruption from vents on the west flank of Pu'u 'O'o (episodes 50 and 51). The events occurring over this period are due to progressive shrinkage of the rift-zone reservoir beneath the eruption site, and had limited impact on eruption temperatures and lava composition.     

The age of the Kagenfels granite (northern Vosges) and its bearing on the intrusion scheme of late Variscan granitoids

In the Saxothuringian part of the Vosges (France), a first series of Variscan plutonic rocks (diorites to granites) has been intruded by several younger granites. Rocks of both the older generations have been cross-cut by the late orogenic Kagenfels granite. The averages of the hitherto published mineral ages of the earlier rock generations are 331 and 334 Ma, respectively, whereas Rb-Sr and K-Ar dates around 290 Ma have been reported for the Kagenfels granite. Because of the unlikely large age hiatus, a redetermination of the intrusion age of the Kagenfels granite formation appeared to be irrevocable. The newly obtained mineral ages on the Kagenfels granite (K-Ar and ⁴⁰Ar/³⁹Ar biotite ages as well as single zircon radiogenic ²⁰⁷Pb/²⁰⁶Pb data: 331 ± 5 Ma) are about 40 Ma older than the previous results. They are interpreted as giving the time of emplacement of the Kagenfels granite during the latest Visan. The mineral ages of the earlier plutonic rocks in this part of the Variscan Orogeny in all probability are not significantly different from their ages of intrusion. Therefore the age concordance of all three granitoid generations constrains a rather narrow time interval of orogenic magmatism close to the Lower-Upper Carboniferous boundary.