Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Grain size distribution in surface sediments samples of the continental shelf and slope of southeast Greenland

During "Meteor" Cruise 6/1966 in the northwest Atlantic a systematic survey of the bottom topography of the southeast Greenland continental margin was undertaken. Eighty-seven profiles transverse to the shelf edge at distances of 3-4 nautical miles and two longitudinal profiles parallel to the coast were carried out with the ELAC Narrow Beam Echo-Sounder giving a reliable record of even steep slopes. On the basis of the echo soundings the topography and morphology of the continental shelf and slope are evaluated. A detailed bathymetric chart and a serial profile chart were designed as working material for the morphological research. These maps along with the original echograms are morphometrically evaluated. The analysis of the sea bottom features is the basis of a subsequent morphogenetical interpretation, verified and extended by means of interpretation of magnetic data and sediment analysis (grain size, roundness, lithology). The results of the research are expressed in a geomorphological map. The primary findings can be summarized as follows: 1) The southeast Greenland shelf by its bottom topography can be clearly designated as a glacially formed area. The glacial features of the shelf can be classified into two zones nearly parallel to the coast: glacial erosion forms on the inner shelf and glacial accumulation forms on the outer shelf. The inner shelf is characterized by the rugged and hummocky topography of ice scoured plains with clear west/east slope asymmetry. On the outer shelf three types of glacial accumulation forms can be recognized: ice margin deposits with clearly expressed terminal moraines, glacial till plains and glaciomarine outwash fans. Both zones of the shelf can be subdivided into two levels of relief. The ice scoured plains, with average depths of 240 meters (m), are dissected to a maximum depth of 1060 m (Gyldenloves Trough) by trough valleys, which are the prolongations of the Greenland fjords. The banks of the outer shelf, with an average depth of 180 m, surround glacial basins with a maximum depth of 670 meters. 2) The sediments of the continental shelf can be classified as glacial due to their grain size distribution and the degree of roundness of the gravel particles. The ice margin deposits on the outer shelf can be recognized by their high percentage of gravels. On the inner shelf a rock surface is suggested, intermittently covered by glacial deposits. In the shelf troughs fine-grained sediments occur mixed with gravels. 3) Topography and sediments show that the southeast Greenland shelf was covered by an ice sheet resting on the sea floor during the Pleistocene ice-age. The large end moraines along the shelf edge probably indicate the maximum extent of the Wurm shelf ice resting on the sea floor. The breakthroughs of the end moraines in front of the glacial basins suggest that the shelf ice has floated further seaward over the increasing depths. 4) Petrographically the shelf sediments consist of gneisses, granites and basalts. While gneisses and granites occire on the nearby coast, basalt is not known to exist here. Either this material has been drifted by icebergs from the basalt province to the north or exists on the southeast Greenland shelf itself. The last interpretation is supported bythe high portion of basalt contained in the sediment samples taken and the strong magnetic anomalies probably caused by basaltic intrusions. 5) A magnetic profile allows the recognition of two magnetically differing areas which approximately coincide with the glacial erosion and accumulation zones. The inner shelf shows a strong and variable magnetic field because the glacially eroded basement forms the sea floor. The outer shelf is characterized by a weak and homogenous magnetic field, as the magnetized basement lies at greater depthy, buried by a thick cover of glacial sediments. The strong magnetic anomalies of the inner shelf are probably caused by dike swarms, similar to those observed further to the north in the Kangerdlugssuaq Fjord region. This interpretation is supported by the high basalt content of the sediment samples and the rough topography of the ice scoured plains which correlates in general with the magnetic fluctuations. The dike structures of the basement have been differentially eroded by the shelf ice. 6) The continental slope, extending from the shelf break at 313 m to a depth of 1270 m with an average slope of 11°, is characterized by delta-shaped projections in front of the shelf basins, by marginal plateaus, ridges and hills, by canyons and slumping features. The projections could be identified as glaciomarine sediment fans. This conclusion is supported by the strong decrease of magnetic field intensity. The deep sea hills and ridges with their greater magnetic intensities have to be regarded as basement outcrops projecting through the glaciomarine sediment cover. The upper continental rise, sloping seaward at about 2°, is composed of wide sediment fans and slump material. A marginal depression on the continental rise running parallel to the shelf edge has been identified. In this depression bottom currents capable of erosion have been recorded. South of Cape Farvel the depression extends to the accumulation zone of the "Eirik" sedimentary ridge. 7) By means of a study of the recent marine processes, postglacial modification of the ice-formed relief can be postulated. The retention effect of the fjord troughs and the high velocity of the East Greenland stream prevents the glacial features from being buried by sediments. Bottom currents capable of active erosion have only been found in the marginal depression on the continental rise. In addition, at the time of the lowest glacio-eustatic sea level, the shelf bottom was not situated in the zone of wave erosion. Only on the continental slope and rise bottom currents, sediment slumps and turbidity currents have led to significant recent modifications. Considering these results, the geomorphological development of the southeast Greenland continental terrace can be suggested as follows: 1. initial formation of a "peneplain", 2. fluvial incision, 3. submergence, and finally 4. glacial modification.

Grain size investigations of sediments off the coast of Istria

Composition, grain-size distribution, and areal extent of Recent sediments from the Northern Adriatic Sea along the Istrian coast have been studied. Thirty one stations in four sections vertical to the coast were investigated; for comparison 58 samples from five small bays were also analyzed. Biogenic carbonate sediments are deposited on the shallow North Adriatic shelf off the Istrian coast. Only at a greater distance from the coast are these carbonate sediments being mixed with siliceous material brought in by the Alpine rivers Po, Adige, and Brenta. Graphical analysis of grain-size distribution curves shows a sediment composition of normally three, and only in the most seaward area, of four major constituents. Constituent 1 represents the washed-in terrestrial material of clay size (Terra Rossa) from the Istrian coastal area. Constituent 2 consists of fine to medium sand. Constituent 3 contains the heterogeneous biogenic material. Crushing by organisms and by sediment eaters reduces the coarse biogenic material into small pieces generating constituent 2. Between these two constituents there is a dynamic equilibrium. Depending upon where the equilibrium is, between the extremes of production and crushing, the resulting constituent 2 is finer or coarser. Constituent 4 is composed of the fine sandy material from the Alpine rivers. In the most seaward area constituents 2 and 4 are mixed. The total carbonate content of the samples depends on the distance from the coast. In the near coastal area in high energy environments, the carbonate content is about 80 %. At a distance of 2 to 3 km from the coast there is a carbonate minimum because of the higher rate of sedimentation of clay-sized terrestrial, noncarbonate material at extremely low energy environments. In an area between 5 and 20 km off the coast, the carbonate content is about 75 %. More than 20 km from the shore, the carbonate content diminishes rapidly to values of about 30 % through mixing with siliceous material from the Alpine rivers. The carbonate content of the individual fractions increases with increasing grain-size to a maximum of about 90 % within the coarse sand fractions. Beyond 20 km from the coast the samples show a carbonate minimum of about 13 % within the sand-size classes from 1.5 to 0.7 zeta¬? through mixing with siliceous material from the alpine rivers. By means of grain-size distribution and carbonate content, four sediment zones parallel to the coast were separated. Genetically they are closely connected with the zonation of the benthic fauna. Two cores show a characteristic vertical distribution of the sediment. The surface zone is inversely graded, that means the coarse fractions are at the top and the fine fractions are at the bottom. This is the effect of crushing of the biogenic material produced at the surface by predatory organisms and by sediment eaters. lt is proposed that at a depth of about 30 cm a chemical solution process begins which leads to diminution of the original sediment from a fine to medium sand to a silt. The carbonate content decreases from about 75 % at the surface to 65 % at a depth of 100 cm. The increase of the noncarbonate components by 10 % corresponds to a decrease in the initial amount of sediment (CaC03=75 %) by roughly 30 % through solution. With increasing depth the carbonate content of the individual fractions becomes more and more uniform. At the surface the variation is from 30 % to 90 %, at the bottom it varies only between 50 % and 75 %. Comparable investigations of small-bay sediments showed a c1ear dependence of sediment/faunal zonation from the energy of the environment. The investigations show that the composition and three-dimensional distribution of the Istrian coastal sediments can not be predicted only from one or a few measurable factors. Sedimentation and syngenetic changes must be considered as a complex interaction between external factors and the actions of producing and destroying organisms that are in dynamic equilibrium. The results obtained from investigations of these recent sediments may be of value for interpreting fossil sediments only with strong limitations.

An illustrated flora of the northern United States, Canada and the British possessions, from Newfoundland to the parallel of the southern boundary of Virginia, and from the Atlantic Ocean westward to the 102d meridian, by Nathaniel Lord Britton ... and Hon. Addison Brown ...

v. 1

Grain size and description on gravity core samples from ANT-IV/2 expedition to the Bransfield Strait

From the above and the grafical results it can be concluded that cores in the research area are locally dominated by turbiditic sequences, which can be observed by a strong increase in coarser sediment (>35 µm). These coarser intercalations are lacking in the vicinity of basaltic seamounts, probably due to a shadowing effect of the seamounts. The infill of the King George Basin might be dominated by a north eastern current. Sedimentary structures as observed in the cores are often lacking or vague due to hydrothermal effects (Suess, L, 1986).

Grain size composition of sediment cores from the Weddell Sea, Antarctica

Sedimentary processes in the southeastern Weddell Sea are influenced by glacial-interglacial ice-shelf dynamics and the cyclonic circulation of the Weddell Gyre, which affects all water masses down to the sea floor. Significantly increased sedimentation rates occur during glacial stages, when ice sheets advance to the shelf edge and trigger gravitational sediment transport to the deep sea. Downslope transport on the Crary Fan and off Dronning Maud and Coats Land is channelized into three huge channel systems, which originate on the eastern-, the central and the western Crary Fan. They gradually turn from a northerly direction eastward until they follow a course parallel to the continental slope. All channels show strongly asymmetric cross sections with well-developed levees on their northwestern sides, forming wedge-shaped sediment bodies. They level off very gently. Levees on the southeastern sides are small, if present at all. This characteristic morphology likely results from the process of combined turbidite-contourite deposition. Strong thermohaline currents of the Weddell Gyre entrain particles from turbidity-current suspensions, which flow down the channels, and carry them westward out of the channel where they settle on a surface gently dipping away from the channel. These sediments are intercalated with overbank deposits of high-energy and high-volume turbidity currents, which preferentially flood the left of the channels (looking downchannel) as a result of Coriolis force. In the distal setting of the easternmost channel-levee complex, where thermohaline currents are directed northeastward as a result of a recirculation of water masses from the Enderby Basin, the setting and the internal structures of a wedge-shaped sediment body indicate a contourite drift rather than a channel levee. Dating of the sediments reveals that the levees in their present form started to develop with a late Miocene cooling event, which caused an expansion of the East Antarctic Ice Sheet and an invigoration of thermohaline current activity.

The Holy Bible, containing the authorized and revised versions of the Old and New Testaments, arranged in parallel columns. The text conformable to that of the Universities of Oxford and Cambridge. With a complete concordance and the Psalms of David in metre. Copious marginal references, chronological tables, and many important and useful aids to the study of the Holy scriptures ...

Mode of access: Internet.

Cost of marketing grain; a history of certain carloads of grain from the farmer to the terminal buyer,

Mode of access: Internet.

The ancient liturgy of the Church of England, according to the uses of Sarum, York, Hereford, and Bangor, and the Roman liturgy arranged in parallel columns with preface and notes,

Appendix (p. [279]-333):--Liturgia S. Clementis.--The Order of the Communion, 1548.--The Supper of the Lorde, 1549.

Rudimental lessons in etymology and syntax : in which these two parts of grammar are exhibited in parallel columns : carelfuly [sic] adapted to the capacity of young learners. : Chiefly selected from Murray's grammar. /

Table of contents on last p.