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.     

Petrology and geochronology of basalt breccia from the 1996 earthquake swarm of Loihi seamount, Hawaii: magmatic history of its 1996 eruption

 Samples of basalt were collected during the Rapid Response cruise to Loihi seamount from a breccia that was probably created by the July to August 1996 Loihi earthquake swarm, the largest swarm ever recorded from a Hawaiian volcano. ²¹⁰Po–²¹⁰Pb dating of two fresh lava blocks from this breccia indicates that they were erupted during the first half of 1996, making this the first documented historical eruption of Loihi. Sonobuoys deployed during the August 1996 cruise recorded popping noises north of the breccia site, indicating that the eruption may have been continuing during the swarm. All of the breccia lava fragments are tholeiitic, like the vast majority of Loihi's most recent lavas. Reverse zoning at the rim of clinopyroxene phenocrysts, and the presence of two chemically distinct olivine phenocryst populations, indicate that the magma for the lavas was mixed just prior to eruption. The trace element geochemistry of these lavas indicates there has been a reversal in Loihi's temporal geochemical trend. Although the new Loihi lavas are similar isotopically and geochemically to recent Kilauea lavas and the mantle conduits for these two volcanoes appear to converge at depth, distinct trace element ratios for their recent lavas preclude common parental magmas for these two active volcanoes. The mineralogy of Loihi's recent tholeiitic lavas signify that they crystallized at moderate depths (∼8–9 km) within the volcano, which is approximately 1 km below the hypocenters for earthquakes from the 1996 swarm. Taken together, the petrological and seismic evidence indicates that Loihi's current magma chamber is considerably deeper than the shallow magma chamber (∼3–4 km) in the adjoining active shield volcanoes. Received: 21 August 1997 / Accepted: 15 February 1998     

The kinematics of the ionized gas in the Circinus galaxy

The TAURUS-2 Fabry–Perot interferometer, mounted on the 3.9-m Anglo-Australian Telescope, has been used to observe the Circinus galaxy. We have mapped the intensity and velocity distribution of the ionized hydrogen in the galaxy using the Balmer series Hα spectral line.
The semiresolved core (observed with a seeing disc of 30 pc) appears amorphous in shape, which is commonly observed in Seyfert 2 galaxies. Its peak coincides with the core position measured in the radio continuum, suggesting that ionized gas surrounds a non-thermal source.
A circumnuclear ring or spiral of radius 220 pc and a rotational velocity of 350 km s⁻¹ (assuming circular motions) surrounds the core. The inclination angle of this feature, i =40°±10°, is less than that of the previously observed radio continuum disc. The velocity channel maps obtained for the Hα ring show that the kinematics resemble those of a rotating ring and the intensity displays a complex structure indicative of several, unresolved, H II regions. We believe the ring to represent a circumnuclear starburst.
Our Hα data also show the presence of the previously detected [O III ] ionization cone to the north-west of the core, measuring more than 400 pc in length. We suggest that the ionization cone lies in a different plane from that of the starburst ring and is directed away from us. Several kinematic components of the core are derived and we calculate an outflow velocity in excess of 150–200 km s⁻¹ for gas above the core of Circinus. We also present evidence for inflowing ionized gas at the centre of Circinus.
The correlation of the Hα and radio continuum features is discussed, as well as the possible presence of a starburst-driven superwind in the Circinus galaxy.     

Sedimentation in Lake Biel,an eutrophic,hard-water lake in northwestern Switzerland

A 2-year study of sedimentation in Lake Biel reveals that three major factors can account for the spatial and temporal patterns of tripton sedimentation. Allochthonous inputs of particulate matter mostly derived from the Aare river during spring snowmelt and other high-water periods, provide about 50% of the carbonate and 50% of the siliceous matter collected in sediment traps. Phytoplankton activity in this eutrophic, hard-water lake accounts for the rest of the carbonate and siliceous matter, the latter being mostly diatom frustules. Sedimentation rates are thus highest during periods of maximum river flooding, maximum phytoplankton activity and following the breakdown of the thermocline, at which time trapped particles settle out. Resuspension of sediment is important in at least one basin. Resolution of carbonate appears to be minor.     

Essai sur la structure des domaines émergés autour de la Méditerranée occidentale

Résumé De travaux menés dans les zones littorales de l'Afrique du Nord et dans tout le S de l'Espagne, l'auteur tire une nouvelle définition des grands ensembles structuraux péri-méditerranéens. Ces ensembles sont, dans les Cordillères bétiques, du N au S: zones externes (Prébétique, Subbétiques, Pénibétiques), zones internes (Flyschs gaditans, Malaguides, Alpujarrides, Nevadides 1). Dans le Rif marocain, symétriquement, on rencontre du S au N: zones externes (Autochtone de l'Atlas, nappes prérifaines et intrarifaines), zones internes (Flyschs nord-rifains, Tétouanides 2), Ghomarides 3), Sebtides 4); la plupart de ces zones se poursuivent vers l'E, jusqu'en Tunisie et en Sicile.Le fait majeur, à souligner au départ, est la parfaite symétrie de la chaîne alpine de la Méditerranée occidentale: les nappes rifaines ne le cèdent pas en importance aux nappes bétiques. Les diverses unités des deux systèmes se raccordent de manière évidente par la courbure de Gibraltar. L'âge du paroxysme tectonique paraît entièrement compris entre Oligocène supérieur et Miocène supérieur, aucune preuve objective n'existant de nappes plus anciennes.La remise en place des divers ensembles structuraux dépend de l'hypothèse générale définie au départ. Il est d'abord fait allusion à l'interprétation classique, par charriages modérés, ne faisant pas appel à des modifications importantes dans l'emplacement des bassins sédimentaires, actuellement visibles en plan. Les objections à ce premier schéma paraissent déterminantes.Une deuxième interprétation, que l'auteur a déjà partiellement esquissée auparavant, sera envisagée: les unités externes (s'empilant sur elles-mêmes) et leurs socles s'enfonceraient sous les zones internes qui, par réaction, seraient poussées vers l'extérieur de la chaîne: chacune des nappes dépasserait la nappe plus basse, au cours de ce mouvement. Dans le cas de l'Espagne, avant les charriages, les domaines sédimentaires des zones internes se placeraient à l'inverse de la disposition actuelle, soit du N au S: Nevadides, Alpujarrides, Malaguides, Pénibétique et Flyschs gaditans (ultras). Du côté marocain, nous aurions de même du S au N: Sebtides, Ghomarides, Tétouanides, Flyschs nord-rifains (ultras). Cela obligerait, au total, à faire rapprocher l'un de l'autre, en profondeur, les bâtis de la Meseta ibérique et de l'Atlas marocain, d'environ 300 à 500 km, l'actuelle largeur de la mer d'Alboran (150 km) ne permettant pas de reloger les domaines de toutes les nappes. Un axe d'enfouissement serait à rechercher sous l'actuelle Méditerranée.Une troisième interprétation, proposée aujourd'hui par l'auteur, considère que la chaîne péri-méditerranéenne montre une cicatrice structurale fondamentale, qui séparerait domaines internes bétiques et rifains, d'une part, domaines bétiques et rifains plus externes, de l'autre. Cette cicatrice se couderait au niveau de Gibraltar. Les nappes internes seraient comme aspirées vers la cicatrice ainsi que, en sens inverse, les nappes externes. La reconstitution paléogéographique finale est fort satisfaisante et l'ampleur des rétrécissements sensiblement diminuée.La position du domaine des Flyschs kabyles, nord-rifains et gaditans, fait enfin l'objet d'un examen nouveau: sans rejeter l'origine ultra, déjà proposée, l'auteur envisage d'autres solutions, qui auraient l'avantage de mieux s'intégrer dans l'image proposée aujourd'hui.     

Interprét ation des graphiques de relation entre deux éléments chimiques en solution dans l'eau souterraine

The relationship line between two chemical constituents dissolved in groundwater does not always begin at the graph origin, but at a fixed coordinates point. This allows the separation between rain water, infiltrating water and groundwater. Besides, this relationship line is not always linear. Equations are given for the curvilinear case.     

Earthquake analysis of axisymmetric towers partially submerged in water

A method for analysis of response of axisymmetric towers partly submerged in water to earthquake ground motion is presented. The tower is idealized as a finite element system. The hydrodynamic terms are determined by solving the Laplace equation, governing the dynamics of incompressible fluids, subject to appropriate boundary conditions. For cylindrical towers, these solutions are obtained as explicit mathematical solutions of the boundary value problems; whereas they are obtained by the finite element method in case of towers with non-cylindrical outside surface. The response to earthquake ground motion is determined by step-by-step integration of the equations of motion. Analyses of two actual intake towers are presented to illustrate results obtained by this method. The small computation times required for these analyses demonstrate that the method is very efficient. The effectiveness of this formulation lies in avoiding the analysis of a large system by using a substructure approach and in exploiting the important feature that structural response to earthquake ground motion is essentially contained in the first few modes of vibration of the tower with no surrounding water.