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     

A rooftop tuned mass damper frame

This article documents the analytical study and feasibility of placing a tuned mass damper in the form of a limber rooftop moment frame atop relatively stiff structures to reduce seismic acceleration response. Six existing structures were analytically studied using a suite of time history and response spectra records. The analyses indicate that adding mass in conjunction with a limber frame results in an increase in the fundamental period of each structure. The fundamental period increase generally results in a decrease in seismic acceleration response for the same time history and response spectra records. Owing to the limber nature of the rooftop frames, non‐linear analysis methods were required to evaluate the stability of the rooftop tuned mass damper frame. The results indicate the addition of a rooftop tuned mass damper frame reduces the seismic acceleration response for most cases although acceleration response can increase if the rooftop frame is not tuned to accommodate the specific structure's dynamic behaviour and localized soil conditions. Appropriate design of the rooftop tuned mass damper frame can result in decreased seismic acceleration response. This translates to safer structures if used as a retrofit measure or a more economical design if used for new construction. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of Hilbert‐like transforms for enhanced processing of full tensor magnetic gradient data

Commonly, geomagnetic prospection is performed via scalar magnetometers that measure values of the total magnetic intensity. Recent developments of superconducting quantum interference devices have led to their integration in full tensor magnetic gradiometry systems consisting of planar‐type first‐order gradiometers and magnetometers fabricated in thin‐film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than those produced via conventional magnetometers. In order to preserve the high data quality in this work, we develop a workflow containing all the necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise, and artefactless two‐dimensional maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth‐centred Earth‐fixed coordinate frame. As the magnetometers have sensitivity lower than that of gradiometers and the total magnetic intensity is not directly recorded, we employ Hilbert‐like transforms, e.g., integration of the gradient tensor components or the conversion of the total magnetic intensity derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar total magnetic intensity measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing full tensor magnetic gradiometry data.     

A pockmark field in the Patras Gulf (Greece) and its activation during the 14/7/93 seismic event

During a recent oceanographical-geophysical survey carried out in the southeastern part of the Gulf of Patras in Western Greece for the construction of an outfall, an active pockmark field was found. The pockmark field was formed in soft layered Holocene silts. The pockmarks are associated with acoustic anomalies attributed to gas-charged sediments. The pockmarks vary in size and shape from 25 to 250 m in diameter and from 0.5 to 15 m in depth and are among the largest and deepest observed in the world.

On July 14th, 1993, during the survey, a major earthquake of magnitude 5.4 on the Richter scale occurred in the area. During the 24 hour period prior to the earthquake the bottom water temperature anomalously increased on three occasions, whilst for a few days after the earthquake it was noted that the majority of the pockmarks were venting gas bublles.

It is considered that the three abrupt sea-water temperature increases were probably the result of upward migrating high-temperature gas bubbles in the water column. It is further suggested that the earthquake was the triggering mechanism and that the gas expulsion was caused by the reduction in the pore volume in the sediments resulting from changes in the stress regime prior to the earthquake. Therefore, it can be suggested that in seismic areas adjacent to pockmark fields, earthquake prediction may be achieved by monitoring the water temperature and/or the rate of gas venting in the pockmark field.

Our analysis indicates that the pockmark field in the Patras Gulf has formed slowly during the Holocene by continuous gas venting, which is periodically being interrupted by short-duration events of enhanced gas seepage triggered by earthquakes.     

Comparison of the LEW88516 and ALHA77005 martian meteorites: Similar but distinct

Abstract By mineral and bulk compositions, the Lewis Cliff (LEW) 88516 meteorite is quite similar to the ALHA77005 martian meteorite. These two meteorites are not paired because their mineral compositions are distinct, they were found 500 km apart in ice fields with different sources for meteorites, and their terrestrial residence ages are different. Minerals in LEW88516 include: olivine, pyroxenes (low- and high-Ca), and maskelynite (after plagioclase); and the minor minerals chromite, whitlockite, ilmenite, and pyrrhotite. Mineral grains in LEW88516 range up to a few mm. Texturally, the meteorite is complex, with regions of olivine and chromite poikilitically enclosed in pyroxene, regions of interstitial basaltic texture, and glass-rich (shock) veinlets. Olivine compositions range from Fo₆₄ to Fo₇₀, (avg. Fo₆₇), more ferroan and with more variation than in ALHA77005 (Fo₆₉ to Fo₇₃). Pyroxene compositions fall between En₇₇Wo₄ and En₆₅Wo₁₅ and in clusters near En₆₃Wo₉ and En₅₃Wo₃₃, on average more magnesian and with more variation than in ALHA77005. Shock features in LEW88516 range from weak deformation through complete melting. Bulk chemical analyses by modal recombination of electron microprobe analyses, instrumental neutron activation, and radiochemical neutron activation confirm that LEW88516 is more closely related to ALHA77005 than to other known martian meteorites. Key element abundance ratios are typical of martian meteorites, as is its non-chondritic rare earth pattern. Differences between the chemical compositions of LEW88516 and ALHA77005 are consistent with slight differences in the proportions of their constituent minerals and not from fundamental petrogenetic differences. Noble gas abundances in LEW88516, like those in ALHA77005, show modest excesses of ⁴⁰Ar and ¹²⁹Xe from trapped (shock-implanted) gas. As with other ALHA77005 and the shergottite martian meteorites (except EETA79001), noble gas isotope abundances in LEW88516 are consistent with exposure to cosmic rays for 2.5–3 Ma. The absence of substantial effects of shielding from cosmic rays suggest LEW88516 spent this time as an object no larger than a few cm in diameter.     

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.