The GPS Toolbox

The GPS Toolbox is dedicated to highlighting algorithms utilized by GPS engineers and scientists. If you have an interesting algorithm you would like to share with our readers or if you have a topic you would like to see covered in a future column, contact us at gps-toolbox@ngs.noaa.gov. To comment on the algorithms presented here, or to leave a request for an algorithm you may be looking for, visit our Web site (http://www.ngs.noaa.gov/gps-toolbox). ? 2000 John Wiley & Sons, Inc.     

Off disk-center potential field calculations using vector magnetograms

We investigate a potential field calculation for off disk-center vector magnetograms that uses all the three components of the measured field. There is neither any need for interpolation of grid points between the image plane and the heliographic plane nor for an extension or a truncation to a heliographic rectangle. Hence, the method provides the maximum information content from the photospheric field as well as the most consistent potential field independent of the viewing angle. The introduction of polarimetric noise produces a less tolerant extrapolation procedure than using the line-of-sight extrapolation, but the resultant standard deviation is still small enough for the practical utility of this method.National Research Council Resident Research Associate on leave from Indian Institute of Astrophysics, Bangalore 560034, India.     

Measurement of stress effects (scope for growth) and contaminant levels in mussels (Mytilus edulis) collected from the Irish Sea

The objective of this research was to quantify the impact of pollution along the coastlines of the Irish Sea. Pollution assessment was based on the combined measurement of scope for growth (SFG), and chemical contaminants in the tissues of mussels (Mytilus edulis) collected from 38 coastal sites around the Irish Sea during June-July in 1996 and 1997. On the UK mainland coast, the SFG showed a general trend with a significant decline in water quality in the Liverpool and Morecambe Bay region. High water quality was recorded along the west coast of Wales, as well as southwest England and northwest Scotland (clean reference sites outside the Irish Sea). Along the coast of Ireland there was a similar trend with reduced SFG within the Irish Sea region. SFG was generally low north of Duncannon and then improved north of Belfast. The poor water quality on both sides of the Irish Sea is consistent with the prevailing hydrodynamics and the spatial distribution of contaminants associated with urban/ industrial development. The decline in SFG of mussels on both sides of the Irish Sea was associated with a general increase in contaminant levels in the mussels. Certain contaminants, including PAHs, TBT, sigmaDDT, Dieldrin, gamma-HCH, PCBs, and a few of the metals (Cd, Se, Ag, Pb), showed elevated concentrations. Many of these contaminants were particularly elevated in the coastal margins of Liverpool Bay, Morecambe Bay and Dublin Bay. A quantitative toxicological interpretation (QTI) of the combined tissue residue chemistry and SFG measurements indicated that at the majority of coastal sites, c. 50 to > 80% of the observed decline in SFG was due to PAHs as a result of fossil fuel combustion and oil spills. TBT levels were highest at major ports and harbours, but these concentrations only made a minor contribution to the overall reduction in SFG. At no sites were individual metals accumulated to concentrations that could cause a significant effect on SFG. The study identified many sites where the observed reduction in SFG was far greater than predicted from the limited number of chemical contaminants analysed, thus indicating the presence of additional 'unknown toxicants'. Sewage (containing domestic, agricultural and industrial components) appears to be an important contributor to reduced SFG and linear alkylbenzenes (LABs) and As may provide suitable 'sewage markers'. There was a highly significant positive correlation between SFG and As (P < 0.001). This relationship may be due to reduced As uptake by algal food material and mussels at sites with elevated P04 concentrations (e.g. at sites with sewage inputs). Phosphate is a known competitive inhibitor of As accumulation, at least in algae. The results highlight that further research is required on 'sewage markers' in mussels. The SFG approach therefore provides a rapid, cost-effective and quantitative measure of pollution impact, as well as a means of identifying the causes through a QTI of tissue contaminants levels. It also serves to identify the presence of unidentified toxicants and areas that require further study.     

The Zn abundance and isotopic composition of diatom frustules,a proxy for Zn availability in ocean surface seawater

We have developed cleaning methods for extracting diatomopal from bulk marine sediment samples, for measurement of both zinc (Zn) abundance and isotope composition. This cleaning technique was then applied to a set of Holocene core-top samples from the Southern Ocean. The measured δ⁶⁶Zn (reported relative to the JMC_Lyon standard) and Zn/Si ratios from the Southern Ocean diatom_opal samples range from 0.7 to 1.5‰, and from 14 to 0.9 μmol/mol, respectively. The Zn abundance and isotope composition data show a clear correlation with opal burial rates and other oceanographic parameters. In common with previous work, we interpret the systematic changes in the Zn/Si ratio to be linked to the variability in the concentrations of bioavailable Zn in the ambient surface seawater where the diatom opal is formed. This variability is likely to be primarily controlled by the degree to which Zn is taken up into phytoplankton biomass. The observed systematic pattern in the δ⁶⁶Zn compositions of the diatom_opal core-top samples is, similarly, likely to reflect changes in the δ⁶⁶Zn composition of the ambient Zn in the surface waters above the core-top sites, which is progressively driven towards isotopically heavier values by preferential incorporation of the lighter isotopes into phytoplankton organic material. Thus, the systematic relationship between Zn isotopes and abundance observed in the core-top diatom_opal samples suggests a potential tool for investigating the biogeochemical cycling of Zn in the past surface ocean for down-core diatom_opal material. In this respect, it may be possible to test hypotheses that attribute variations in atmospheric CO₂ on glacial–interglacial timescales to the degree to which trace metals limited primary productivity in HNLC zones.     

∼3,850 Ma tonalites in the Nuuk region,Greenland: geochemistry and their reworking within an Eoarchaean gneiss complex

The Eoarchaean (>3,600 Ma) Itsaq Gneiss Complex of southern West Greenland is dominated by polyphase orthogneisses with a complex Archaean tectonothermal history. Some of the orthogneisses have c. 3,850 Ma zircons, and they vary from rare single phase metatonalites to more common complexly banded migmatites. This is due to heterogeneous strain, in situ anatexis and granitic veining superimposed during younger tectonothermal events. In the single-phase tonalites with c. 3,850 Ma zircon, oscillatory-zoned prismatic zircon is all 3,850 Ma old, but shows patchy ancient loss of radiogenic Pb. SHRIMP spot analyses and laser ablation ICP-MS depth profiling show that thin (usually < 10 μm) younger (3,660–3,590 Ma and Neoarchaean) shells of lower Th/U metamorphic zircon are present on these 3,850 Ma zircons. Several samples with this simple zircon population occur on islands near Akilia. In contrast, migmatites usually contain more complex zircon populations, with often more than one generation of igneous zircon present. Additional zircon dating of banded gneisses across the Complex shows that samples with c. 3,850 Ma igneous zircon are not just a phenomenon restricted to Akilia and adjacent islands. For example, migmatites from Itilleq (c. 65 km from Akilia) contain variable amounts of oscillatory-zoned 3,850 Ma and 3,650 Ma zircon, interpreted, respectively, as the rock age and the time of crustal melting under Eoarchaean metamorphism. With only 110–140 ppm Zr in the tonalites and likely magmatic temperatures of >850°C, zircon solubility–melt composition relationships show that they were only one-third saturated in zircon. Any zircon entrained in the precursor magmas would thus have been highly soluble. Combined with the cathodoluminesence imaging, this demonstrates that the c. 3,850 Ma oscillatory zoned zircon crystallised out of the melt and hence gives a magmatic age. Thus the rare well-preserved tonalites and palaeosome in migmatites testify that c. 3,850 Ma quartzo–feldspathic rocks are a widespread (but probably minor) component in the Itsaq Gneiss Complex. C. 3,850 Ma zircon with negative Eu anomalies (showing growth in felsic systems) also occurs as detrital grains in rare c. 3,800 Ma metaquartzites and as inherited grains in some 3,660 Ma granites (sensu stricto). These demonstrate that still more c. 3,850 Ma rocks were present, but were recycled into Eoarchaean sediments and crustally derived granites. The major and trace element characteristics (e.g. LREE enrichment, HREE depletion, low MgO) of the best-preserved c. 3,850 Ma rocks are typical of Archaean TTG suites, and thus argue for crust formation processes involving important contributions from melting of hydrated mafic crust to the earliest Archaean. Five c. 3,850 Ma tonalites were selected as the best preserved on the basis of field criteria and zircon petrology. Four of these samples have overlapping initial ɛ_Nd (3,850 Ma) values from +2.9 to +3.6± 0.5, with the fourth having a slightly lower value of +0.6. These data provide additional evidence for a markedly LREE-depleted early terrestrial mantle reservoir. The role of c. 3,850 Ma crust should be considered in interpreting isotope signatures of the younger (3,800–3,600 Ma) rocks of the Itsaq Gneiss Complex. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Marine geology in the environs of Bouvet Island and the South Atlantic triple juction

It is suggested that Bouvet Island is the surface manifestation of a mantle plume which has resulted in the creation of a chain of seamounts in the South Atlantic and a general shoaling of the region.The strike of two newly defined large fracture zones borth and south of the Bouvet Island pedestal have been utilized to determine a pole of rotation at 12.5°S, 12.5°W for the Africa-Antarctica motion. A pole at 75°S, 13°E has been calculated for the South America-Antarctica motion. At the triple junction the South America-Africa relative motion is 3.3 cm yr^-1 (whole rate) at 075°. The Africa-Antarctica motion is 1.7 cm yr^-1 at 065° and the South America-Antarctica motion is 1.6 cm yr^-1 at 085.     

CHROMOSPHERIC AND CORONAL STRUCTURE OF POLAR PLUMES – I. Magnetic Structure and Radiative Energy Balance

The Multi-Spectral Solar Telescope Array (MSSTA), a rocket-borne solar observatory, was successfully launched from White Sands Missile Range, New Mexico, on May 13, 1991 at 19:05 UT. The telescope systems onboard the MSSTA obtained several full disk solar images in narrow bandpasses centered around strong soft X-ray, EUV, and FUV emission lines. Each telescope was designed to be sensitive to the coronal plasmas at a particular temperature, for seven temperatures ranging from 20000 K to 4000000 K. We report here on the images obtained during the initial flight of the MSSTA, and on the chromospheric and coronal structure of polar plumes observed over both poles of the Sun. We have also co-aligned the MSSTA images with Kitt Peak magnetograms taken on the same day. We are able to positively identify the magnetic structures underlying the polar plumes we analyze as unipolar. We discuss the plume observations and present a radiative energy balance model derived from them.     

On mass transport in deep water waves

Summary Various formulations of the mass-transport problem are compared for progressive waves in deep water. In order to calculate the mass-transport velocity as a function of depth in the main body of the fluid, it is necessary to include the effect of viscous wave attenuation. It is shown that the usual assumptions of periodicity in distance and attenuation with time or periodicity in time and attenuation with distance, are both physically unsatisfactory. The first does not specify a unique solution, and the second is incompatible with the assumption of zero surface stress. A certain critical constant tangential wind stress will maintain strictly time-periodic deep water waves. The corresponding attenuation with distance is then calculated to order ³. A constant tangential stress greater or less than the critical causes waves, necessarily decaying with distance, to grow or decay with time.