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.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Mafic magma batches at Vesuvius: a glass inclusion approach to the modalities of feeding stratovolcanoes

Glass inclusions in olivine and diopside phenocrysts from pyroclasts of various eruptions of Vesuvius are representative of the magmas that supplied the volcano in the last 4–5000 years. During this interval the volcano alternated between open conduit activity (e.g. 1944 and 1906 eruptions) with long pauses interupted by Plinian and sub-Plinian eruptions (e.g. 3360 B.P. Avellino, A.D. 79 Pompei, A.D. 472 Pollena). The eruptive behaviour was conditioned in all cases by the presence of shallow reservoirs: two cases are distinguished: (1) small and very shallow, 1906-type; (2) large and deeper Plinian-sub-Plinian magma chamber. Lapilli of 1906 lava fountains contain olivine (Fo_89.5–90.4) including Cr-spinel [Cr/(Cr+Al)] (Cr#>75) and volatile-K-rich tephritic glasses, which represent the first recognized Vesuvius primary magmas. Mg-poorer olivine (Fo_83–89) also occurs in 1906 and 1944 products; it formed within the shallow reservoir, together with pyroxene and leucite, between 1200 and 1130°C, from K-tephritic melts (MgO=6–8 wt%). The Plinian and sub-Plinian pumices contain diopside, phlogopite and minor olivine (Fo_85–87) representing adcumulates wrenched from the chamber walls. Glass inclusions in diopside (and some olivine) range from K-basalt to K-tephrite (MgO=6–8 wt%), with homogenization temperature of 1130–1170°C. They have been regarded as representative of the magmas supplying the Plinian-sub-Plinian chamber(s). The Avellino glass inclusions have K-basaltic compositions, contrasting with the mostly K-tephritic Pompei and Pollena inclusions. They display lower C1 and P contents with respect to the younger tephritic melts, and these variations should reflect primary features of the mantle-derived magmas. The primary and the near-primary Vesuvius magmas, as illustrated by melt inclusions, emphasize high K, P and volatile (H₂O, Cl, F, S) contents, with high K₂O/H₂O (2–2.5), Cl/F (2.5) and Cl/S (2–3) ratios, consistent with a metasomatized mantle source, and distinguishing the Vesuvius potassic primary magmas from those of the northern part of the Roman Province.     

The Late Cretaceous Impact of the Trindade Mantle Plume: Evidence from Large-volume, Mafic, Potassic Magmatism in SE Brazil

When the subcontinental lithospheric mantle undergoes heatingand/or extension, some of the earliest mafic melts to be generatedare those rich in volatUes and potassium. In some cases, e.g.when a plume impinges on thick cratonic lithosphere or whenthe amount of extension is very small, K-rich mafic igneousrocks may be the only surface expression of mantle melting.The Alto Paranaiba Igneous Province, in SE Brazil, is one ofthe world's most voluminous mafic potassic provinces (>15000km³),which until recently was relatively unknown. The magmas wereemplaced into a narrow Proterozoic mobile belt close to thesurface margin of the Sao Francisco craton, and it is one ofseveral Cretaceous alkaline igneous provinces that are locatedaround the margin of the Parana sedimentary basin in Braziland Paraguay.Detailed geochemical analyses of samples from throughoutthe Alto Paranaiba Igneous Province show that it is composedof a relatively diverse suite of ultrapotassic-potassic, ultramaficmqfic,silica-undersaturated lavas and hypabyssal intrusions, i.e.kimberlites, madupitic olivine lamproites and kamafugitic rocks.These all have very high concentrations of incompatible traceelements and are all strongly enriched in light rare earth relativeto heavy rare earth elements (e.g. La/Yb=50-230). Wide variationsin major element ratios, which are unrelated to the effectsof crystal fractionation in these magmas (e.g. CaO/Al₂O₃), suggestthat the mafic potassic rocks were derived from a heterogeneousmantle source. They show relatively restricted ranges of initial⁸⁷Sr/⁸⁶Sr (070436-070588) and Nd₂₅ values of -4 to -8, intermediatebetween Group I and II South African kimberlites. T_DM Nd isotopemodel ages of 900 Ma suggest that the magmas were derived bythe remobilization of subcontinental lithospheric mantle thathad been enriched by small-volume K-rich melt fractions sincethe Late Proterozoic.New K/Ar ages for mica separates show thatthe kimberlites, madupitic olivine lamproites and kamafugiticrocks were emplaced together with large carbonatite-bearingplutonic complexes at 85 Ma. Reconstructions of plate motionsshow that, at this time, the location of the Alto ParanaibaIgneous Province coincided with the postulated position of thepresent-day Trindade(or Martin Vaz) plume. We propose that thewidespread Late Cretaceous alkaline magmatism in SE Brazil mayhave been caused by impingement of this plume on the base ofthe subcontinental lithosphere. Heat penetrating the lithosphere,both by conduction and advection by asthenospheric-source decompressionmelts, may have caused melting of the readily fusible partsof the lithospheric mantle and the genesis of mafic potassicand (after fractionation) carbonatite magmas. The Proterozoicmobile belt (the Brasilia Belt) appears to have acted as a Hhinspofrelative to the adjacent Sao Francisco craton, allowing greaterupwelling and melting of the asthenosphere. Subsequently, asthe craton passed over the plume, volcanism was switched off'until the Early Tertiary when the plume reemerged from beneaththe westward drifting South America continent and was the magmasource for oceanic-islands and seamounts of the Trindade-Vitriachain. Corresponding author     

Oxygen and carbon isotopic study on the genesis of the Steirischer Erzberg siderite deposit (Austria)

The carbon and oxygen isotopic composition of Fe-carbonate ore and its calcitic to dolomitic Devonian host rocks at the Steirischer Erzberg siderite deposit (Greywacke zone, Upper Austroalpine Unit) were determined in order to constrain the source and nature of the Fe-rich mineralizing fluid. The ¹⁸O-values obtained for various Fe-carbonate generations and the carbonate host lie within a similar range between + 14.6 and + 21.6 (V-SMOW). No good correlation exists between the relative ages of the carbonate phases and their O isotopic composition. The variation in ¹⁸O-values is due to metamorphic recrystallization with locally variable fluid/rock ratios. The average ¹³C-value of the carbonate host is +0.5 ± 1.2 (PDB) which corresponds well to worldwide Phanerozoic marine carbonate values. The first Fecarbonate generation has slightly lower ¹³C-values, on average -1.4 ± 0.8 (PDB). Recrystallization of both the carbonate host minerals and the ankerite/siderite led to significantly lower ¹³C-values of -4.2 ± 0.6 and-4.7 ± 0.7, respectively. Within the basal breccia of the post-Hercynian transgression series matrix calcite/ dolomite shows an average ¹³C-value of -2.9 ± 0.7, and matrix siderite/ankerite an average value of-4.1 ± 0.4. These data, together with Sr isotope data published previously, strongly support a late-diagenetic or epigenetic first Fe-mineralization from convecting formation waters. They ascended along extension faults and were driven by an increased heat flow caused by crustal thinning during a Devonian rifting phase that initiated the separation of the Noric terrane from Africa. A potential source of the Fe could have been the underlying Ordovician acid volcanics. Regional metamorphism related to collision tectonics in the Late Carboniferous (Hercynian) and later during the Alpine orogeny, caused intensive recrystallization and partial mobilization of the various carbonate phases.     

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.     

Molecular indicators for palaeoenvironmental change in a Messinian evaporitic sequence (Vena del Gesso, Italy). II: High-resolution variations in abundances and 13C contents of free and sulphur-bound carbon skeletons in a single marl bed

The extractable organic matter of 10 immature samples from a marl bed of one evaporitic cycle of the Vena del Gesso sediments (Gessoso-solfifera Fm., Messinian, Italy) was analyzed quantitatively for free hydrocarbons and organic sulphur compounds. Nickel boride was used as a desulphurizing agent to recover sulphur-bound lipids from the polar and asphaltene fractions. Carbon isotopic compositions (delta vs PDB) of free hydrocarbons and of S-bound hydrocarbons were also measured. Relationships between these carbon skeletons, precursor biolipids, and the organisms producing them could then be examined. Concentrations of S-bound lipids and free hydrocarbons and their delta values were plotted vs depth in the marl bed and the profiles were interpreted in terms of variations in source organisms, 13 C contents of the carbon source, and environmentally induced changes in isotopic fractionation. The overall range of delta values measured was 24.7%, from -11.6% for a component derived from green sulphur bacteria (Chlorobiaceae) to -36.3% for a lipid derived from purple sulphur bacteria (Chromatiaceae). Deconvolution of mixtures of components deriving from multiple sources (green and purple sulphur bacteria, coccolithophorids, microalgae and higher plants) was sometimes possible because both quantitative and isotopic data were available and because either the free or S-bound pool sometimes appeared to contain material from a single source. Several free n-alkanes and S-bound lipids appeared to be specific products of upper-water-column primary producers (i.e. algae and cyanobacteria). Others derived from anaerobic photoautotrophs and from heterotrophic protozoa (ciliates), which apparently fed partly on Chlorobiaceae. Four groups of n-alkanes produced by algae or cyanobacteria were also recognized based on systematic variations of abundance and isotopic composition with depth. For hydrocarbons probably derived from microalgae, isotopic variations are well correlated with those of total organic carbon. A resistant aliphatic biomacromolecule produced by microalgae is, therefore, probably an important component of the kerogen. These variations reflect changes in the depositional environment and early diagenetic transformations. Changes in the concentrations of S-bound lipids induced by variations in conditions favourable for sulphurization were discriminated from those related to variations in primary producer assemblages. The water column of the lagoonal basin was stratified and photic zone anoxia occurred during the early and middle stages of marl deposition. During the last stage of the marl deposition the stratification collapsed due to a significant shallowing of the water column. Contributions from anaerobic photoautotrophs were apparently associated with variations in depth of the chemocline.     

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.     

Measurements in N2-CH4(C2H2) discharges of reaction rates and thermochemical constants for Titan atmosphere study

The kinetic reactions in N2-xCH4(C2H2) gas discharges with x less than 1% have been studied by emission spectroscopy in the afterglow of D.C. discharges and by mass spectroscopy from radiolysis ionization using alpha particles. The pressure range is from several Torr to 100 Torr. At the end of N2 D.C. discharges at room temperature, for a residence time of about 10(-2) s, the dominant active species are the N atoms with density of 10(14)-10(15) cm-3 for N2 density of about 10(17) cm-3 (3 Torr), the N2(X,V) vibrational molecules with for example [N2(X,V = 10)] approximately 10(14) cm-3 and the electronic metastable molecules N2(A 3 sigma u +) with a density of 10(12) cm-3. In such conditions, the following kinetic reactions have been studied: N2(A) + N2(A) --> N2(C,B,V') + N2(X), N2(A) + N2(X,V>5) --> N2(X) + N2(B,V') in pure N2 post-discharges and N2(A) + CH4 --> products, C + N + M2 --> CN(B,V') + M2, N2(X,V>4) + CN --> N2(X) + CN(B,A,V'), in N2-1% CH4 post-discharges. The clustering reactions of N2-(1-5%)CH4(C2H2) gas mixtures after radiolysis ionization have been studied for the H2CN+ nN2 ions and the equilibrium constants have been determined in the temperature range T = 140-300 K.     

The Mauritius Radiotelescope

The Mauritius Radiotelescope (MRT) is a T-shaped array of helical antennas with a 2048 m EW arm and a 890 m South arm. The primary objective of the telescope is to produce a sky survey in the declination zone -15° to -65° with a point source sensitivity of 200 mJy and an angular resolution of 4'×4.6'cosec(z) at 151.6 MHz, z being the zenith angle . This paper describes the telescope and the present status