The aerodynamic behaviour of volcanic aggregates

A large proportion of solid material transported within the atmosphere during volcanic eruptions consists of particles less than 500 m in diameter. The majority of these particles become incorporated into a wide range of aggregate types, the aerodynamic behaviour of which has not been determined by either direct observation or in the laboratory. In the absence of such data, theoretical models of fallout from volcanic plumes make necessarily crude assumptions about aggregate densities and fall velocities. Larger volcanic ejecta often consists of pumice of lower than bulk density. Experimental data are presented for the fall velocities of porous aggregates and single particles, determined in systems analogous to that of ejecta falling from a volcanic plume. It is demonstrated that the fall of aggregates may be modelled in identical fashion to single particles by using a reduced aggregate density dependent on the porosity, and a size corresponding to an enclosing sphere. Particles incorporated into aggregates attain a substantially higher fall velocity than single particles. This is due to the larger physical dimensions of the aggregate, which overcomes the effect of lower aggregate density. Additionally, the internal porosity of the aggregate allows some flow of fluid through the aggregate and this results in a small increase in fall velocity. The increase in fall velocity of particles incorporated into aggregates, rather than falling individually, results in the enhanced removal of fine material from volcanic plumes.     

Sedimentation of tephra by volcanic plumes: I. Theory and its comparison with a study of the Fogo A plinian deposit,Sao Miguel (Azores)

Sedimentation of ejecta from volcanic plumes has been studied as a function of distance from the source in the Fogo A plinian deposit, Sao Miguel, Azores. The Fogo A trachytic pumice deposit is reversely graded and can be divided into two parts on the basis of pumice colour, abundance of syenite accessory lithic clasts and distribution. The lower syenite-poor part was dispersed to the south and was clearly influenced by wind. The upper syenite-rich part is coarsegrained and has a nearly symmetrical distribution around the vent. Elongation of isopachs to the east indicate a weak wind influence. The grain-size variations of lithic and crystal components in the upper coarse part were studied. Total accumulation and accumulation per unit area (expressed in kg/m²) show good fits to a gaussian function at distances greater than 7 km for grain diameters less than 2 cm. These results agree with a theoretical model for a radially spreading turbulent current moving over a quiescent fluid. The gaussian coefficient is shown to be a function of grain size and the flow rate of material into the umbrella region of the eruption column. The coefficient is therefore also a function of column height. The column height deduced from these data is 21 km, which is in broad agrrement with the column height of 27 km deduced from maximum clast dispersal using the method of Carey and Sparks (1986). The accumulation of clasts larger than 2 cm agrees with a theory for the fallout of clasts from the margins of the ascending eruption column, which treats the plume as a succession of large eddies that decrease their mass of particles as an exponential function of time. Calculations are also presented for the influence of the radial inflow of surrounding air into the column on the deposition of clasts. These calculations constrain the wind speed during the later part of the Fogo A eruption to be at most a few metres per second. The study has allowed four different dynamic categories of clast behaviour to be recognised in eruption columns.     

Geochemistry and origin of massif-type anorthosites

Samples of Proterozoic anorthosite complexes from the Adirondack Mountains of New York, Burwash Area of Ontario, and the Nain Complex of Labrador, ranging in composition from anorthosite to anorthositic gabbro, have been analyzed for major elements, Rb, Sr, Ba and nine rare-earth elements (REE), in order to set limits on the compositions and origins of their parent magmas. Similar rock types from the different areas have similar major and trace element compositions. The anorthosites have high Sr/Ba ratios, low REE abundances (Ce about 10, Yb about 0.5–1.5 times chondrites) and large positive Eu anomalies. The associated anorthositic gabbros have lower Sr/Ba ratios, REE abundances nearly an order of magnitude higher than the anorthosites, and small to negligible positive Eu anomalies.Model calculations using the adcumulate rocks with the lowest REE abundances and published distribution coefficients yield parent liquids having REE abundances and patterns similar to those of the associated anorthositic gabbros with the highest REE abundances. Rocks with intermediate REE abundances are the result of incorporation of a liquid component by a plagioclase-rich cumulate similar to the adcumulate samples. The analytical data and model calculations both suggest parent liquids having compositions of 50–54% SiO₂, greater than 20% Al₂O₃, about 1% K₂O, atomic Mg/(Mg+Fe²⁺) ratios (Mg No.'s) of less than 0.4, 15–30 ppm Rb, 400–600 ppm Sr and 400–600 ppm Ba, 40–50 times chondrites for Ce and 8–10 times chondrites for Yb.The low atomic Mg/(Mg+Fe²⁺) values for these rocks combined with geophysical evidence suggesting there are not large quantities of ferromagnesian material at depth, indicate that the anorthositic masses are not products of fractional crystallization of mafic melt derived from melting of the mantle. Rather, it is suggested that they are a result of partial melting of tholeiitic compositions at depths shallower than the basalt-eclogite transformation, leaving a pyroxene-dominated residue.     

The application of trace elements to the petrogenesis of igneous rocks of granitic composition

Although trace element modeling has been used to great advantage for petrogenetic interpretations of basaltic systems, similar studies on igneous rocks of granitic composition have been fewer. In general the mineral/melt distribution coefficients for rare earth elements (REE) in granitic melts are equal to or greater than those for similar minerals in the basaltic system. Thus the effects of these minerals on the REE patterns of granitic melts during partial melting or differentiation are exaggerated as compared to basaltic systems, making detection of residual phases easier. For the K/Rb ratio, if neither a K-feldspar component nor biotitephlogopite is present in the residue, it is difficult to reduce the K/Rb ratio of the melt relative to the parent by a factor of two by either differentiation or partial melting.The petrogenesis of four distinctly different rocks are received: (1) an Archean tonalite presumably derived by partial melting of an Archean tholeiite at mantle depths, leaving a garnet plus clinopyroxene residue; (2) an Archean quartz monzonite presumably derived by partial melting of a short-lived graywacke-argillite sequence at crustal depths; (3) a dacite from Saipan presumably derived by differentiation from a basaltic parent; and (4) a trachyte from Ross Island, Antarctica, presumably derived by differentiation from a basanitoid parent and contaminated by continental crustal components.     

Propagator matrices in elastic wave and vibration problems

The boundary value problems most frequently encountered in studies of elastic wave propagation in stratified media can be formulated in terms of a finite number of linear, first order and ordinary differential equations with variable coefficients. Volterra (1887) has shown that solutions to such a system of equations are conveniently represented by the product integral, or propagator, of the matrix of coefficients. In this paper we summarize some of the better known properties of propagators plus numerica methods for their computation. When the dispersion relation is somem ^th order minor of the integral matrix it is possible to deal withm ^th minor propagators so that the dispersion relation is a single element of them ^th minor integral matrix. In this way one of the major sources of loss of numerical accuracy in computing the dispersion relation is avoided. Propagator equations forSH and forP-SV waves are given for both isotropic and transversely isotropic media. In addition, the second minor propagator equations forP-SV waves are given. Matrix polynomial approximations to the propagators, obtained from the method of mean coefficients by the Cayley-Hamilton theorem and the Lagrange-Sylvester, interpolation formula, are derived.     

40Ar/39Ar spectrum ages for biotite,hornblende and muscovite in a contact metamorphic zone

Biotite, hornblende and muscovite from 2700 m.y. old rocks in northeastern Minnesota near the contact of the 1150 m.y. Duluth Complex have been analyzed by ⁴⁰Ar/³⁹Ar technique to determine whether spectrum ages can be used to distinguish partial loss of radiogenic argon due to a reheating event. Biotite and hornblende give plateau ages comparable to the ordinary K-Ar ages for all samples including those with intermediate ages. Muscovite gives plateau ages for the samples with less than 11% argon loss. An intermediate muscovite with a conventional K-Ar age of 1850 m.y. gives progressively older ⁴⁰Ar/³⁹Ar ages for higher temperature fractions.Microprobe analysis reveals no systematic correlation between biotite chemistry and loss of argon in the contact zone. This suggests that the rate-controlling process for the loss of argon from biotite in the contact zone may be volume diffusion or recrystallization without a measurable change in major element composition. Biotites with intermediate ages give plateaus because the rate-controlling processes in the vacuum furnace are related to dehydroxylation and delamination and are unrelated to the process causing loss of argon in the contact zone.The data for the muscovites are not easily interpreted, in part because of the limited number of samples. The hornblende data show a correlation between argon loss and change in major element composition suggesting that recrystallization may be a rate-controlling process for the loss of argon from hornblende in the contact zone. The small number of samples precludes a definitive statement.     

Buying environmental insurance: Prospects for trading of global climate-protection services

In order to alleviate the threat of global climate change, coordinated international action is needed. This cooperation should include multilateral agreements and new economic initiatives to help implement measures that will slow the accumulation of carbon dioxide in the Earth's atmosphere due to tropical deforestation and fossil-fuel use. An international market in environmental services can help to safeguard the Earth's climate and foster economic development through a North-South transfer of financial resources.We suggest international carbon-emission offsets (ICEOs) as a means by which international markets, under a policy umbrella such as a multilateral climate-protection treaty, could trade carbon-saving services. Such a market would provide a currency for rewarding actions that reduce global carbon emissions, allowing carbon emitters to seek the least expensive ways to reduce emissions. This currency would transfer cash and/or debt relief from industrialized nations to developing nations, allowing the developing nations to profit from the use of clean energy technologies and the protection, rather than depletion, of tropical forests.