A poincaré model for the earth's fluid core

Abstract

The superconducting-gravimeter data of Melchior and Ducarme (1986) has been interpreted as internal motion in the Earth's core by Aldridge and Lumb (1987) using a Poincaré model. Several low-order modes with periods of 13–16 hours have been tentatively identified in the core which is taken to be an incompressible, homogeneous fluid within a rigid, rotating container. The identification is based on asymptotic values of the frequencies which change slowly with time while the modes decay with an e-folding time of about 280 days. The slow change in frequency with time implies a small temporal variation in the rotation rate of the core. This mean flow is a nonlinear effect often observed in laboratory experiments designed to excite Poincaré modes. Interaction among modes during free ringdown is also observed in those experiments and apparently in the data of Melchior et al. (1988) as well. Laboratory work thus provides the link to extend the Poincaré model to include viscous and nonlinear effects in order to interpret the gravimetric observations as core modes.     

The analysis of drainage network composition

The Horton method of analyzing drainage network composition is reviewed, with the conclusion that it has not been very effective either in improving understanding or in developing useful methods of characterizing drainage basins. New methods which are based on the link rather than the Horton (or Strahler) stream are described. A number of detailed examples of the application of these new methods to the topologic and geometric properties of networks are provided. The results are compared with the predictions of the random model. Data used in the analysis were obtained from 1:24,000 U.S.G.S. topographic maps of eastern Kentucky. Thirty drainage basins were selected and their channel networks were outlined first by the contour-crenulation (CC) method and then by another, more objective, method (SC) in which stream sources were identified by a quantitative slope criterion. The CC and SC samples comprise about 8,700 and 1,700 links, respectively. The three most important results of the analysis are: (1) the channel networks are slightly but significantly more elongated than predicted by the random model, (2) there are fewer second magnitude links than predicted, and (3) the length distribution for interior links depends upon the kind of link (interior or exterior) joined downstream. These features are found in both CC and SC networks.     

State-of-the-art of geotechnical earthquake engineering practice

Major developments in geotechnical earthquake engineering practice over the last 15 years are reviewed. The objectives of the review are to present a coherent view of the current state of practice at the highest level and to examine trends, which may shape practice in the future. Developments are described in the following areas: specification of design ground motions, dynamic response analysis, evaluation of liquefaction potential, evaluation of residual strength of liquefied soil, post-liquefaction displacement analysis, and seismic risk analysis.     

Relation between the extreme angular and areal distortion in cartographic representation

Summary The paper presents the method of deriving representations, optimal from the point of view of global characteristics, for areal and extreme angular distortion (3), (7), if one is optional and the other characteristic is minimized at the same time. If a special minimization method (Section 5) is used for computer processing, the problem can be solved in the region of representation equations in the form of polynomials of the 3rd or 5th degree, while assuming symmetry relative to the equator and the central meridian. Thus, the method enables both the fundamental global characteristics to be regulated freely. Their dependence is illustrated in graphs (Figs 2 and 6) depending on the selected examples of representations of the whole globe. The latter shows that method is a contribution for cartographic practice as well.     

Acid volcanism on the south Arabian coast

Along the south coast of Arabia, between Aden and the southern entrance to the Red Sea, there are six central vent volcanoes of probable Pliocene age. All are characterised by the interstratification of basic and acidic extrusives, the formation of large central calderas at a late stage in the volcanic cycle and the subsequent infilling of these calderas with horizontal acidic ignimbrites and basic lavas. Lying 60 miles to the west of Aden and of particular interest is Jebel Khariz, the largest and best preserved of the six volcanic centres, covering a roughly circular area of about 100 square miles and rising to a height of 2,766 feet. The volcanic sequence of Jebel Khariz is broadly divisible into two suites: a) alkali-rich rhyolites and trachytes which occur as flows and pyroclastic horizons and form about 80 per cent of the volume of the cone, and b) effusives of basaltic composition that occur in the caldera, locally on the south-east and south-west flanks and in a small parasitic cone on the northern flank. The alkali-rich acidic suite includes lavas, ash-flow and ash-fall rocks as well as vent and flow breccias, Generally, all rocks of this suite have phenocrysts of anorthoclase, and may contain phenocrysts of fayalitic olivine, aegirine-augite, magnetite and/or quartz. The fine grained matrix is composed of the same minerals with skeletal riebeckite and, in some cases, cossyrite. The basaltic suite is characteristically porphyritic, the phenocrysts being of calcic plagioclase, clinopyroxene, olivine and magnetite in a fine-grained mesostasis of plagioclase, olivine, clinopyroxene and ore. The plagioclase, on initial investigation, appears to lie in the labradorite-bytownite range, the olivine is commonly replaced by iddingsite and the clinopyroxene is most commonly a pale mauve titanaugite. Near the centre of the volcanic pile, as exposed in the caldera wall, masses of rhyolitic composition can be seen to form over half of the volcanic sequence. These masses are markedly lenzoid in cross-section normal to the flow direction and display intricate flow folding; they are considered to have been extruded as viscous lava. Further from the volcanic centre, these acidic extrusives become less markedly lenzoid until in the distal areas of individual units, some 5 miles from the caldera, they have spread out to form sheet-like masses covering as much as 10 square miles to a uniform thickness rarely exceeding 25 feet. The presence of agglomeratic bases, hard compact central sections and less compact upper divisions, together with the ubiquitous presence of columnar jointing and occasional shard textures suggest that these distal parts of each extrusive unit have been formed by an ash-flow/ash-fall mechanism. It is postulated that the majority of the Jebel Khariz volcanic pile was formed by emission of acidic material, effusive in the central area, but deposited mainly by an ash-flow mechanism around the flanks of the cone. This could be due to either the synchronous eruption of viscous lava from the central vent with ash flow eruptions on the flanks; or, more probably, to the progression of an individual volcanic episode through an initial ash-flow phase followed by the effusion of viscous lava, all emanating from the central vent.     

Maximum-likelihood ambiguity resolution based on Bayesian principle

 Based on the Bayesian principle and the fact that GPS carrier-phase ambiguities are integers, the posterior distribution of the ambiguities and the position parameters is derived. This is then used to derive the maximum posterior likelihood solution of the ambiguities. The accuracy of the integer ambiguity solution and the position parameters is also studied according to the posterior distribution. It is found that the accuracy of the integer solution depends not only on the variance of the corresponding float ambiguity solution but also on its values. Received: 27 July 1999 / Accepted: 22 November 2000     

Seasonal variation in the biogeochemical cycling of seston in Grand Traverse Bay, Lake Michigan

This study describes the biogeochemical cycling of seston in Grand Traverse Bay, Lake Michigan. Seston was characterized by carbon and nitrogen elemental and isotopic abundances. Fluorescence, temperature, light transmittance, and concentrations of dissolved inorganic nitrogen were also determined. PCBs were analyzed from surface (10 m) seston and ΣPCB was calculated by summing all of the congeners quantified in each sample. The vertical and seasonal trends in the δ¹³C values of seston exhibited a broad range from −30.7 to −23.9‰. Low δ¹³C values that occur concurrently with a peak in fluorescence below the thermocline reflect uptake of ¹³C depleted respiratory CO₂ and/or the accumulation of ¹³C depleted lipids by phytoplankton. High δ¹³C values late in the season likely result from a reduction in photosynthetic fractionation associated with a decrease in the CO₂ pool. Seasonal δ¹⁵N values of seston were high in the spring and declined through August. The δ¹⁵N values of seston reflect a balance between fractionation during assimilation of NH₄⁺ or NO₃⁻ and degradative processes. The seston ΣPCB and fluorescence were both high in the spring and subsequently declined, suggesting that the concentrations of PCBs in seston were associated with labile material derived from primary productivity. The strong seasonal trends in the organic geochemical characteristics of seston and concentrations of PCBs emphasize the complex nature of particle cycling in aquatic environments.     

Holocene reef growth in Torres Strait

The platform and fringing reefs of Torres Strait are morphologically similar to reefs of the northern Great Barrier Reef to the south, except that several are elongated in the direction of the strong tidal currents between the Coral Sea and the Gulf of Carpentaria. Surface and subsurface investigations and radiocarbon dating on Yam, Warraber and Hammond Islands reveal that the initiation and mode of Holocene reef growth reflect antecedent topography and sea-level history. On the granitic Yam Island, fringing reefs have established in some places over a Pleistocene limestone at about 6 m depth around 7000 years BP. Emergent Holocene microatolls of Porites sp. indicate that the reefs have prograded seawards while sea level has fallen gradually from at least 0.8 m above present about 5800 years BP. On the Warraber Island reef platform drilling near the centre indicated a Pleistocene limestone foundation at a depth of about 6 m over which reefs established around 6700 years BP. Reef growth lagged behind that on Yam Island. Microatolls on the mature reef flat indicate that the reef reached sea level around 5300 years BP when the sea was around 0.8–1.0 m above present. On the reef flat on the western side of Hammond Island bedrock was encountered at 7–8 m depth, overlain by terrigenous mud. A progradational reef sequence of only 1–2 m thickness has built seaward over these muds, as sea level has fallen over the past 5800 years. Reef-flat progradation on these reefs is interpreted to have occurred by a series of stepwise buildouts marked by lines of microatolls parallel to the reef crest, marking individual coalescing coral heads. Detrital infill has occurred between these. This pattern of reef progradation is consistent with the radiocarbon dating results from these reefs, and with seismic investigations on the Torres Reefs.