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.     

Geochemical Evidence for Subduction Fluxes, Mantle Melting and Fractional Crystallization Beneath the South Sandwich Island Arc

The volcanoes of the South Sandwich island arc follow threedistinct series: low-K tholeiitic (followed by Zavodovski, Candlemas,Vindication, Montagu and Bristol), tholeiitic (followed by Visokoi,Saunders and Bellinghausen) and calcalkaline (followed by Leskov,Freehand and part of Cook and Thule). Flux calculations indicatethat the percentage contribution of the subduction componentto the mantle source of all three series varies from undetectable(e.g. Zr) through small (e.g. Nd=20%) and moderate (e.g. La,Ce, Sr=50–80%) to dominant (e.g. Pb, K, Ba, Rb, Cs >90%)with little change along the arc. Isotope systematics (Pb, Nd,Sr) show that this subduction component obtains a greater contributionfrom altered oceanic crust than from pelagic sediment. Elementsfor which the subduction contribution is small show that themantle is already depleted relative to N-MORB mantle (equivalentto loss of an 2•5% melt fraction) before melting beneaththe arc. After addition of the subduction component, dynamicmelting of this depleted mantle then causes the variations inK that distinguish the three series. The estimated degree ofpartial melting (20%) is slightly greater than that beneathocean ridges, though geothermometry suggests that the primarymagma temperature (1225C) is similar to that of primary MORB.About half of the melting may be attributed to volatile addition,and half to decompression. Dynamic melting involving three-dimensional,two-phase flow may be needed to explain fully the inter-islandvariations. KEY WORDS: geochemistry; petrology; fluxes; melting; subduction ^*Corresponding author     

The Lilloise Intrusion, East Greenland: Fractionation of a Hydrous Alkali Picritic Magma

The Lilloise is an 8 km4 km layered mafic intrusion which cutsthe plateau basalts of the East Greenland Tertiary province.Lilloise was intruded at 50 Ma, 4–5 Ma after cessationof the voluminous tholeiitic magmatism which accompanied riftingof the East Greenland continental margin. Lilloise is unusualamong layered intrusions in the province because it had a hydrousalkali picrite parent magma and generated a late-stage effluxof magmatic water from the intrusion into the aureole rocks.The three major subdivisions of the layered rocks are: olivine-clinopyroxene,olivine-clinopyroxene-plagioclase and plagioclase-amphibolecumulates. Massive subsidence of the intrusion before completesolidification resulted in deformation of the internal layeringand downturn of the bedding in the surrounding basalts. A strikingfeature of the intrusion is the injection of the layered rocksby a plexus of magmatic sheets which formed at the time of subsidence.The composition of these sheets is representative of the fractionationtrend of the intrusion and ranges from hawaiite to mildly saturatedquartz trachyte. The fractionation trend is successfully explainedby extraction of cumulus minerals of the layered rocks froma parent magma represented by alkali picrite dykes of a contemporaneousregional dyke swarm. Saturated to mildly over-saturated syenitesare a major component of the East Greenland province and theLilloise intrusion is illustrative of an important magmatictrend towards such compositions at this stage in the openingof the North Atlantic. KEY WORDS: Lilloise intrusion; East Greenland; alkali picrite magma; layered intrusion; magmatic differentiation ^*Corraponding author     

Interstellar water in meteorites?

D/H ratios of two meteorites (Renazzo CR and Semarkona LL3), which are known to exhibit the largest departures from the terrestrial hydrogen isotopic ratios, have been determined with the CRPG Nancy ion microprobe. Correlations between the D/H ratios and the chemical compositions (H2O, K, Si, C/H) of plausible hydrogen carriers were observed. From these correlations, it is possible to show that, contrary to previous interpretations, phyllosilicates are the carriers of the deuterium-rich hydrogen in Semarkona and Renazzo: 870 x 10(-6) > or = D/H > or = 670 x 10(-6) (+4600 > or = deltaD > or = 3300%) and > or = 320 x 10(-6) (deltaD > or = 1050%), respectively. Hydrogen is also present in the chondrules of these two deuterium-rich meteorites. The large differences in D/H ratios between matrix (up to 700 x 10(-6), deltaD up to +3500%) and chondrules (from 120 x 10(-6) (deltaD = -230%) to 230 x 10(-6) (deltaD = +475%)) show that hydrogen in chondrules cannot originate from the matrix by simple contamination or diffusion processes. The high D/H ratios measured in water-bearing minerals could not have been produced thermally within a dense solar nebula. Chemical reactions (i.e., involving ions or radicals), taking place in interstellar space or in the outer regions of the nebula at 110-140K are presently the only conceivable mechanisms capable of yielding such isotopic enrichments. Water in these meteorites should no longer be considered as a simple product of nebular condensation under equilibrium thermodynamic conditions at T > or = 160K.     

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.     

Mössbauer spectroscopic and x-ray powder diffraction studies of synthetic micas on the join annite KFe3AlSi3O10(OH)2-phlogopite KMg3AlSi3O10(OH)2

Micas of the composition K(Fe_3–x Mg _x )AlSi₃ O₁₀(OH)₂ (x=0.6, 1.2, 1.8, 2.4 and 3.0, corresponding to ann₈₀phl₂₀, ann₆₀phl₄₀, ann₄₀phl₆₀, ann₂₀phl₈₀ and ann₀phl₁₀₀) were synthesized hydrothermally under controlled oxygen fugacity conditions. Lattice parameters a ₀ and b ₀ show a distinct linear decrease with increasing Mg content. With increasing ferric iron content a deviation from this linear trend is observed especially within iron rich samples. The tetrahedral rotation angle increases smoothly from 0° in annite to 9.1° in phlogopite. Mössbauer spectra show Fe²⁺ and Fe³⁺ on the octahedral M1 and M2 sites and partially also Fe³⁺ on the tetrahedral site. There is a smooth increase of the quadrupole splitting on both the M1 and the M2 site going from annite to phlogopite, probably due to changes in the lattice contribution to the electric field gradient, assuming a positive correlation between quadrupole splitting and distortion. Fe³⁺ contents, as determined by Mössbauer spectroscopy, versus oxygen fugacity shows that, depending on the composition of the micas, minimum amounts of Fe³⁺ are present. For ann₈₀phl₂₀ this minimum amount of Fe³⁺ is about 8% decreasing to about 1–2% Fe³⁺ for ann₂₀phl₈₀.The molar volume of each solid solution member has been estimated from the determined relations of the molar volume versus % Fe³⁺ contents, extrapolated back to 0% Fe³⁺. Plotting these volumes as a function of X_phl shows that negative excess volume occur in the annitephlogopite join, with the maximum deviation from ideality around X _phl=0.3. Margules volume parameters have been constrained as: Wv, AnnPhl=0.018±0.016 J/(bar.mol) and Wv, PhlAnn=-0.391±0.025 J(bar.mol) (three site basis).     

The Panafrican Stratoid Granites of Madagascar: Alkaline Magmatism in a Post-Collisional Extensional Setting

A major alkali province of late Panafrican age occupies centralMadagascar and takes the form of a thick sequence of ‘stratoid’(sheet-like)granites emplaced in a mid-crustal gneissic basement This alkalinemagmatism has been interpreted as a consequence of extensionaltectonics accompanying the collapse of the Mozambique belt.The rocks belong to three petrographic types: subsolvus granites,hypersolvus alkaline granites and syenites. Major and traceelement analyses have typical A-type characteristics. Two distinctmagmatic suites are recognized: a mildly alkaline suite includingall the subsolvus granites and a strongly alkaline suite includingthe hypersolvus alkaline granites and the syenites. We proposethat the mildly alkaline suite was derived from a granodioriticcrustal protolith. Some of the strongly alkaline granites andthe quartz syenites display low ¹⁸O isotopic signatures of around+6.The parental magmas for this suite are most probably of mantlederivation. The more evolved compositions are consistent withcrystal fractionation processes. Contemporaneous alkaline silicicplutonismoccurs in many parts of the Panafrican belt of Eastern Africa;however, sheet-like intrusions have rarely been described. Asa large-scale province, the nearest analogues of the stratoidgranites of Madagascar are the rapakivi granites of earlierProterozoic age in Scandinavia and Greenland. KEY WORDS: alkaline granite; Madagascar; Panafrican; pastcollisional magmatism ^*Corresponding author     

Direct shear tests on Mexico City clay with reference to friction pile behaviour

Summary This paper presents results of static and cyclic direct shear tests performed on undisturbed and remoulded samples of Mexico City clays, including results of soil-on-interface tests. Experiments show that the static adhesion coefficient depends on the soils' liquidity index and that it diminishes due to the effect of repeated dynamic loads. Dynamic overstrength effects were not apparent, as has been observed when testing this clay in other apparatus. Interface strength in remoulded clays is initially less than half the strength of interfaces with undisturbed materials but it increases with time. At least in the materials tested in this research, it did not equal the strength of interfaces with undisturbed materials. Correction factors derived from experimental data can be used to modify the adhesion coefficient to account for dynamic and remoulding effects.     

Search for low energyν e,μ,τ andv e,μ,τ in coincidence with BATSE gamma ray bursts

A search for low energy neutrinos of all flavours in correlation with 553 ray bursts detected by BATSE aboard the Compton Observatory has been performed by the LSD (Liquid Scintillator Detector) neutrino telescope. No excess ofe,, orv _e,, candidate has been detected by LSD during the time interval in which BATSE detected the 90% of the photon flux for any of the GRBs analyzed. Upper limits on the neutrino fluxes are given in the paper.     

Electromagnetic bursting of a rapidly rotating magnetized neutron star in a close binary system

We examine a possible manifestation of the electromagnetic activity of a magnetized, rotating neutron star in a binary system. Accreting matter from the companion is initially accumulated at the magnetosphere. When the accumulated mass is such that the inflow can start, together with the accretion flare there will be a burst due to the closure of electric currents. The luminosity associated to the latter effect may be as large as 10⁴² erg/s, if a neutron star possesses the following characteristics: massM =M , period of rotationP = 5 ms, magnetic fieldB ₀ = 10¹² G, and radiusr ₀ = 10⁶ cm. The electromagnetic activity might be relevant for understanding soft gamma ray repeaters.