Quantification of the environmental structural risk with spoiling ties: is randomization worthwhile?

Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three different strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it is investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given.     

Stability and phase relations of nonstoichiometric clinopyroxenes in the join diopside-Ca-Eskola component at high pressures

The stability of nonstoichiometric clinopyroxenes in the Di-CaEsk join was experimentally studied, and phase diagrams were constructed for this join at pressures of 2.0 and 3.0 GPa. It was found that melting in the diopside part of the join occurs at anomalously low temperatures, and nonstoichiometric clinopyroxene coexists with a phase approaching diopside in composition. Phase relations along the Di-CaEsk join can be described and consistently interpreted only assuming that the diopside phase (α-diopside) is thermodynamically stable. The following phase volumes were observed along the solidus of the join at a pressure of 3.0 GPa: Cpx, αDi+Cpx, αDi+Cpx+Qtz, αDi+Cpx+Grt+Qtz, Cpx+Grt+Qtz, Cpx+Grt+Ky+Qtz, Grt+Ky+Qtz. Melting occurs via the eutectic reaction αDi+Cpx+Grt+Qtz=L at a temperature of about 1200°C in the diopside part of the system and via the eutectic reaction Cpx+Grt+Ky+Qtz=L at a temperature of 1400°C in the calcium-rich part of the system. At a pressure of 2.0 GPa, melting occurs at temperatures of 1200–1300°C via the eutectic reaction αDi+Cpx+ An + Qtz=L. The invariant equilibrium (L, An, Cpx, Grt, αDi, Qtz) lies within the pressure range 2.0–3.0 GPa. Nonstoichiometric clinopyroxenes form complex solid solutions, the compositions of which are not strictly confined to the Di-CaEsk join and depend on temperature, pressure, and phase association. Grossular garnets coexist with nonstoichiometric clinopyroxenes and α-diopside.     

FORWARD MODELING IN THE FREQUENCY-SPACE DOMAIN*

Forward modeling of zero-offset data is performed in the frequency-space domain using a one-way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero-offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.     

Fractional Crystallization and Liquid Immiscibility Processes in the Alkaline-Carbonatite Complex of Juqui (So Paulo, Brazil)

The Juqui circular intrusion, which is Cretaceous in age (130–135Ma), crops out in the Precambrian gneissic basement in Brazilover an area of 14 km2. It consists of olivine clinopyroxen-itecumulates (with minor olivine gabbros) in the northeastern sector(74 vol.%), whereas ijolites-melteigites-urtites (4%) and nephelinesyenites with minor essexites and syenodiorites (21%) outlinesubannular concentric patterns with an Mg-carbonatite core (1%), in the southwestern part of the complex. Petrographical, bulk rock, and mineral compositional trendsindicate that the origin of the complex can be largely accountedfor by shallow-level fractional crystallization of a carbonatedbasanitic parental magma. Such a magma was generated deep inthe subcontinental lithosphere by low-degree partial meltingof a garnet-phlogopite peridotite source. Mass-balance calculations in agreement with field volume estimatespermit definition of several fractionation stages of the magmaticevolution under nearly closed-system conditions, with inwarddevelopment of zonally arranged side-wall cumulates. These stagesinvolved: (1) fractionation from basanite to essexite magma(liquid fraction F = 33–5%) by crystallization of olivineclinopyroxenite plus minor olivine alkali gabbro cumulates;(2) derivation of the least differentiated mafic nepheline syenite(F = 5–5 %) from essexitic magma by subtraction of a syenodioriteassemblage; (3) exsolution of a carbonatite liquid (5%) froma CO₂-enriched mafic nepheline syenite magma, which also underwentcontinuous fractionation giving rise to ijolite-melteigite-urtitecumulates. The proportion of cumulus clinopyroxene and biotiteand intercumulus nepheline and alkali feldspar in these lastrocks, as well as the absence of alkalis in carbonatite, maybe attributed, at least in part, to loss of alkali-rich hydrousfluids released during and after the unmixing formation of thetwo conjugate liquids. The KD values determined for Mg-carbonatite/nepheline syeniteare lower (1–4–2–9) for light rare earth elements(LREE) than for REE from Eu to Yb (4–6–7–8),in contrast to recent experimental results (Hamilton et al.,1989). A possible explanation is that Juquia Mg-carbonatiterepresents an alreadydifferentiated magma, which underwent extensivefractionation of LREE-enriched calcite. In this way, the highvariability of K₀ REE patterns observed in several alkaline-carbonatitecomplexes can also be accounted for. The remarkably constant initial ⁸⁷Sr/⁸⁶Sr ratios (mostly between0–7052 and 0–7057) support the interpretation ofthe intrusion as having been generated by fractrional crystallizationand liquid immiscibility from a common parental magma. Iligherisotopic ratios (0–7060–0–7078), found mainlyin dykes and in the border facies of the intrusion, may be dueto contamination by the gecissic basement.     

Investigation of a eutrophic tidal basin: part 1—factors affecting the distribution and biomass of macroalgae

The distribution and biomass of macroalgae, principally Enteromorpha spp., have been estimated in Langstone Harbour, a 19 km² tidal basin in southenrn England. Comprehensive mapping was carried out annually at the time of maximum biomass and monthly mapping of selected areas allowed seasonal changes to be studied. Aerial false-colour photography and ground-level mapping were used for assessing the area and density of cover of macroalgae, but have identified no continuous trends between 1973 and 1982. In nine years, some 48% of the intertidal mudflat has supported >75% macroalgal cover at some stage, but generally only one-third of this potential has been achieved annually. The average peak biomass was determined by a stratified sampling method and varied about a mean of 38.5 g dry weight per square metre and showed significant annual differences. The processes controlling macroalgal growth and distribution reviewed, but, in general, factors other than nutrient availability are effective in determining areas supporting high macroalgal cover in any particular year.     

Effects of CO2 on benthic biota: An in situ benthic chamber experiment in Storfjorden (Norway)

Carbon capture and storage (CCS) methods, either sub-seabed or in ocean depths, introduces risk of CO₂ leakage and subsequent interaction with the ecosystem. It is therefore important to obtain information on possible effects of CO₂. In situ CO₂ exposure experiments were carried out twice for 10 days during 2005 using a Benthic Chamber system at 400 m depth in Storfjorden, Norway. pCO₂ in the water above the sediment in the chambers was controlled at approximately 500, 5000 and 20,000 μatm, respectively. This article describes the experiment and the results from measured the biological responses within the chamber sediments. The results show effects of elevated CO₂ concentrations on biological processes such as increased nanobenthos density. Methane production and sulphate reduction was enhanced in the approximately 5000 μatm chamber.     

Spatial Breakdown Point of Variogram Estimators

In the context of robust statistics, the breakdown point of an estimator is an important feature of reliability. It measures the highest fraction of contamination in the data that an estimator can support before being destroyed. In geostatistics, variogram estimators are based on measurements taken at various spatial locations. The classical notion of breakdown point needs to be extended to a spatial one, depending on the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdown point in the regular unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in IR² , as well as some simulations on irregular grids. In order to study the global effects of perturbations on variogram estimators, further simulations are carried out on data located on a regular or irregular bidimensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, the number of initial data likely to be contaminated before destruction of the estimator is roughly 30% on average. Theoretical results confirm the previous statement on data in IR^d , d 1.     

REE constraints on fractionation processes of massive-type anorthosites on the Lofoten Islands, Norway

Summary Rare Earth Element (REE) data of 34 samples of magmatic rocks from the Lofoten Islands in Norway lend support to the derivation of anorthosites, ferrodiorites and jotunites by fractionation and cumulus processes from typical basaltic magma. Both REE concentration and Eu anomalies (expressed as Eu/Eu^*) form continuous linear trends from anorthosite towards gabbro, ferrodiorite and jotunite in discrimination diagrams against molar CaO/Al₂O₃ ratios indicating the predominant accumulation of plagioclase. Eu/Eu^* decreases from about 4 in the cumulates (anorthosites) to around 1 in the fine-grained gabbroic dikes and to below 1 in some ferrodiorites and the jotunite. The various types of ferrodiorites and the jotunite are regarded as residual liquids, in some cases with variable amounts of cumulus plagioclase. The whole fractionation series from gabbro towards anorthosites and ferrodiorites can be observed in a single intrusion. With increasing fractionation, the REE patterns generally change from flat, slightly LREE-enriched or LREE-depleted to steep and strongly LREE-enriched. These changes and the REE abundances are mainly controlled by the abundance of apatite. Temporally and spatially related mangerites and charnockites form a trend from low-SiO₂ mangerites with Eu/Eu^* > 1 to intermediate-SiO₂ acidic mangerites with Eu/Eu^* ≈ 1 and charnockites with Eu/Eu^* < 1. Accordingly, the low-SiO₂ mangerites are interpreted as alkali feldspar-rich cumulates and the charnockites as residual liquids derived from the acidic mangerites. The mangerites with Eu/Eu^* around 1 have patterns similar to those of some highly evolved ferrodiorites possibly indicating a genetic link. Received December 12, 1999; revised version accepted November 15, 2000