Control‐volume mixed finite element methods

A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large‐scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control‐volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular (i.e., distorted logically rectangular) block‐centered quadrilateral grids. The control‐volume formulation of Darcy’s law can be viewed as a discretization into element‐sized “tanks” with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block‐by‐block conservation in the usual mixed discretization of the mass‐conservation equation. Numerical results in two dimensions show second‐order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.     

The Development of Laser Ablation ICP-MS and Calibration Strategies: Examples from the Analysis of Trace Elements in Volcanic Glass Shards and Sulfide Minerals

This contribution presents a review of the recent developments in laser ablation inductively coupled plasma-mass spectrometry. We describe the important developments which have occurred in the laser systems used, leading to a spatial resolution of around 20 (im, and give an overview of the major instrument developments which have affected the geological applications of laser ablation ICP-MS. We describe the calibration of laser ablation for the analysis of trace elements in two different matrices: volcanic glass shards and sulfide minerals. We show how single glass shards can be analysed using the National Institute of Standards and Technology (NIST) glass certified reference materials for calibration and demonstrate the effect of using single spot analyses compared to rastering of the calibration sample. We show the importance of inter-shard variation and demonstrate that averaged single shard analyses produce data which compare well with bulk analyses. The calibration of the laser system for sulfide mineral analysis is discussed and two different strategies are proposed, one using spiked pressed powder pellets of sulfides and the other metal reference materials. We present conclusions and recommendations for the calibration of laser ablation ICP-MS instruments.     

ELNES spectroscopy of mixed Si coordination minerals

 Si K- and L-edge ELNES spectroscopy and multiple-scattering (MS) calculations are used to examine mixed Si coordination compounds varying in Si^VI:Si^IV ratio. As in previous studies, the edges are influenced mainly by silicon coordination (tetrahedral vs. octahedral), as supported by the MS calculations. We demonstrate two methods semi-quantitatively to extract the value of Si^VI/(Si^VI+Si^IV): (1) A linear relationship between the L_2,3-L₁ splitting and Si^VI/(Si^VI+Si^IV) is observed, (2) a fitting method based on the coaddition of reference tetrahedral and octahedral Si spectra is applied to both Si K- and L-edge ELNES spectra. Received: February 10, 1997 / Revised, accepted: May 23, 1997     

Diatoms in sediments of perennially ice-covered Lake Hoare, and implications for interpreting lake history in the McMurdo Dry Valleys of Antarctica

Diatom assemblages in surficial sediments, sediment cores, sediment traps, and inflowing streams of perennially ice-covered Lake Hoare, South Victorialand, Antarctica were examined to determine the distribution of diatom taxa, and to ascertain if diatom species composition has changed over time. Lake Hoare is a closed-basin lake with an area of 1.8 km², maximum depth of 34 m, and mean depth of 14 m, although lake level has been rising at a rate of 0.09 m yr^-1 in recent decades. The lake has an unusual regime of sediment deposition: coarse grained sediments accumulate on the ice surface and are deposited episodically on the lake bottom. Benthic microbial mats are covered in situ by the coarse episodic deposits, and the new surfaces are recolonized. Ice cover prevents wind-induced mixing, creating the unique depositional environment in which sediment cores record the history of a particular site, rather than a lake-wide integration. Shallow-water (<1 m) diatom assemblages (Stauroneis anceps, Navicula molesta, Diadesmis contenta var. parallela, Navicula peraustralis) were distinct from mid-depth (4–16 m) assemblages (Diadesmis contenta, Luticola muticopsis fo. reducta, Stauroneis anceps, Diadesmis contenta var. parallela, Luticola murrayi) and deep-water (26–31 m) assemblages (Luticola murrayi, Luticola muticopsis fo. reducta, Navicula molesta). Analysis of a sediment core (30 cm long, from 11 m water depth) from Lake Hoare revealed two abrupt changes in diatom assemblages. The upper section of the sediment core contained the greatest biomass of benthic microbial mat, as well as the greatest total abundance and diversity of diatoms. Relative abundances of diatoms in this section are similar to the surficial samples from mid-depths. An intermediate zone contained less organic material and lower densities of diatoms. The bottom section of core contained the least amount of microbial mat and organic material, and the lowest density of diatoms. The dominant process influencing species composition and abundance of diatom assemblages in the benthic microbial mats is episodic deposition of coarse sediment from the ice surface.     

The diets of common and Brünnich's guillemots Uria aalge and U. lomvia in the Barents Sea region

Guillemots Uria spp. account for ca. 70% of the total harvest of prey taken by seabirds breeding in the Barents Sea region. This paper presents guillemot chick diet data collected recently at four localities (Finnmark, Murman, Bjørnøya and Spitsbergen) and collates all the data found by the authors in the literature and in the archives of Tromsø Museum, the Norwegian Polar Institute and Kandalaksha State Nature Reserve. Guillemots consume a wide variety of prey and, in comparison to the harvest by predatory fish and marine mammals, their impact on the Barents Sea ecosystem is considered to be minimal. We point out the need for more systematic collection of data from different regions and at different times of the year before a final impact assessment can be made.     

Numerical models of mantle convection with secular cooling

A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0°C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finite-amplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For upper-mantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the core-mantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity.     

Comment on: 'Can horizontal P waves be trapped and resonate in a shallow sedimentary basin?' by F. J. Sácnhez-Sesma and F. LuzÓ

We show that most of the arguments in the above paper are either incorrect or irrelevant to the point the authors are trying to make. We show that their results have no bearing on the model proposed by our group, as they claim. They discuss the seismic response of a valley with a 2-D trapezoidal cross-section in a vertical plane, whereas we dealt with a closed basin with a 2-D cross-section but of arbitrary geometry and in the horizontal plane. Even more significantly, the width of the valley they use is much smaller than the wavelength of the horizontal P waves that can resonate, thereby precluding any possibility of them being trapped. Therefore, their arguments do not clarify the issue posed in the title of their article.