Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity - I. Fundamental solutions

This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations.     

Application of particle dynamics to derive a general circulation in low latitudes

Summary In Section 1 are set out the reasons for the use of particle dynamics in this investigation. In Section 2 are solved the equations of motion for particles constrained to move along a horizontal surface under the action of a constant meridional pressure gradient force to obtain (a) velocities in spherical polar co-ordinates with naturally varying Coriolis terms, and (b) velocities and trajectories in plane cartesian co-ordinates in which the Coriolis parameter is assumed constant. Results obtained in each system are compared, showing that the plane co-ordinates as used are not significantly inaccurate, and trajectories of air particles obtained by application significantly inaccurate, and trajectories of air particles obtained by application of this system in steps of 5° of latitude are plotted to show the production of belts of convergence at some distance from the equator under the action of meridional pressure gradient forces.The approximation of these idealised particle trajectories to actual streamlines of the air flow are discussed in Section 3, and the concept of the production of belts of convergence is used to formulate a theory of formation and maintenance of the sub-tropical anticyclones. In Section 4 this theory is applied to observed average temperature data and the calculated results compared with observed average pressure data. A possible synoptic application of the theory is then indicated in Section 5.

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Zusammenfassung Im ersten Abschnitt werden Gründe für die Anwendung der Dynamik von Massenteilchen in der vorliegenden Arbeit dargelegt. Abschnitt 2 enthält die Lösungen der Gleichungen für die Bewegung von Massenteilchen auf horizontalen Flächen unter der Einwirkung eines konstanten meridionalen Druckgradienten. Die Lösungen ergeben a) die Geschwindigkeiten in sphärischen Polarkoordinaten mit variablem Coriolis-Term (entsprechend natürlichen Verhältnissen) und b) Geschwindigkeiten und Trajektorien in ebenen kartesischen Koodinaten in denen der Coriolis-Parameter als konstant angenommen wird. Die Ergebnisse für beide Koordinatensysteme werden verglichen und es zeigt sich, daß bei Verwendung der ebenen Koordinaten keine wesentlichen Ungenauigkeiten auftreten. Zeichnet man schrittweise von 5 zu 5° (Fig. 1) die Trajektorien der Luftteilchen, so ergeben sich als Folge der meridionalen Druckgradienten Konvergenzzonen in einigem Abstand vom Äquator.Die Annäherung dieser idealisierten Trajektorien an tatsächliche Stromlinien der Luft wird in Abschnitt3 diskutiert. An Hand der Vorstellungen von der Entstehung der Konvergenzzonen wird eine Theorie der Entstehung und Erhaltung subtropischer Antizyklonen gegeben. Im vierten Abschnitt wird diese Theorie auf beobachtete Mitteltemperaturen angewendet und die Ergebnisse der Berechnung werden mit beobachteten mittleren Luftdruckwerten verglichen. Auf eine mögliche synoptische Anwendung der vorliegenden Ergebnisse wird in Abschnitt 5 hingewiesen.

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Résumé La première partie contient les motifs de l'emploi de la dynamique de points pesants dans la présente étude. La deuxième partie donne les solutions des équations du mouvement de points pesants sur des surfaces horizontales sous l'effet d'un gradient méridien constant. Ces solutions fournissent les vitesses en coordonnées polaires sphériques avec un terme Coriolis variable, ainsi que les vitesses et les trajectoires en coordonnées cartésiennes planes en admettant un paramètre de Coriolis constant. On compare les résultats pour les deux systèmes de coordonnées et l'on constate que l'emploi des coordonnées planes n'introduit pas d'erreurs appréciables. Si l'on dessine les trajectoires de 5 en 5 degrés on voit apparaître des zones de convergence à quelque distance de l'équateur par suite des gradients méridiens.Dans la troisième partie on discute la similitude plus ou moins grande de ces trajectoires idéalisées avec les lignes de courant réelles. Parant de l'origine possible des zones de convergence, on établit une théorie de l'origine et du maintien des anticyclones subtropicaux. Dans la quatrième partie on applique cette théorie aux températures moyennes observées et l'on compare les résultats avec les valeurs moyennes observées de la pression. Dans la cinquième partie enfin on montre l'application possible des résultats obtenus à la synoptique.

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This paper is published with the permission of the Director of the meteorological Office.     

Lunar behaviour of boron contrasted with the terrestrial boron cycle

Abstract— Fifty-eight lunar rocks have been analysed by prompt gamma neutron activation for B, Gd and Sm. The data were interpreted together with published analyses for Li and other elements. The behaviour of B in lunar rocks is virtually identical to that of Sm, Gd, Li and the other incompatible LIL (Large Ion Lithophile) and HFS (High Field Strength) elements, collectively known as the KREEP component. To a first approximation, the distribution of B concentrations in all lunar rocks can be described as a two-component mixture of KREEP, with ～32 ppm, and B-free mare basalts and anorthositic rocks. The lunar B abundance, estimated from correlations with other KREEP elements, is ～0.14 ppm. Alpha-track images of the analysed lunar rocks were made from thin sections specially prepared to avoid contamination from terrestrial B. They provided surprising evidence that the distributions of B and Li within individual rocks fall into four categories: (1) substitution in mineral structures; (2) in irregular minute particles, disseminated through the rock with no apparent connection with mineralogy; (3) as aggregate properties of rock fragments, acquired prior to assembly in a breccia; and, (4) as aggregate properties of a breccia matrix, distinct from unaffected clasts. Only category (1) is encountered in terrestrial rocks. Categories (2), (3) and (4) become progressively more important as the abundance of KREEP components increases, and it is concluded that the alpha-track images probably show the localisation of not only B and Li but all the KREEP elements. In terrestrial rocks, such textures could be understood in terms of successive episodes of permeation by solutions followed by brecciation, then cementation. It is difficult to adapt such a mechanism to a dry Moon, with brecciation imposed by impact melting. The linear correlation of lunar B and Gd contrasts strongly with the relationship seen in terrestrial rocks, where the presence of water creates a terrestrial B cycle quite different from that of Gd and other lunar incompatible elements.     

Large Magellanic Cloud Planetary Nebula Morphology: Probing Stellar Populations and Evolution

Planetary nebulae (PNe) in the Large Magellanic Cloud (LMC) offer the unique opportunity to study both the population and evolution of low- and intermediate-mass stars, by means of the morphological type of the nebula. Using observations from our LMC PN morphological survey, and including images available in the Hubble Space Telescope Data Archive and published chemical abundances, we find that asymmetry in PNe is strongly correlated with a younger stellar population, as indicated by the abundance of elements that are unaltered by stellar evolution (Ne, Ar, and S). While similar results have been obtained for Galactic PNe, this is the first demonstration of the relationship for extragalactic PNe. We also examine the relation between morphology and abundance of the products of stellar evolution. We found that asymmetric PNe have higher nitrogen and lower carbon abundances than symmetric PNe. Our two main results are broadly consistent with the predictions of stellar evolution if the progenitors of asymmetric PNe have on average larger masses than the progenitors of symmetric PNe. The results bear on the question of formation mechanisms for asymmetric PNe-specifically, that the genesis of PNe structure should relate strongly to the population type, and by inference the mass, of the progenitor star and less strongly on whether the central star is a member of a close binary system.     

Magnetostratigraphy and palaeoclimatic significance of Late Tertiary aeolian sequences in the Chinese Loess Plateau

The aeolian Red Clay sequence in the central part of the Chinese Loess Plateau was investigated in an attempt to obtain magnetostratigraphic and palaeoclimatic records. From the results, we deduce that aeolian dust accumulation and the related East Asia palaeomonsoon system began at least 7.6  Myr ago, and that the Tibetan Plateau had reached a significant elevation by that time. The Late Tertiary palaeoclimatic history of the Red Clay as reflected by magnetic susceptibility is reconstructed for the time period 7.6–2.5  Ma. Increases in aeolian dust accumulation for the last 7.6  Myr appear to have a close relation with the uplift processes of the Tibetan Plateau. The remarkable increase of aeolian dust accumulation beginning at 3.2  Ma appears to reflect the influence of an increasing global ice volume on the East Asian monsoon and aeolian dust accumulation.     

Mechanisms of orthopyroxene dissolution in silica-undersaturated melts at 1 atmosphere and implications for the origin of silica-rich glass in mantle xenoliths

Experiments dissolving orthopyroxene (En₉₃) in a variety of Si-undersaturated alkaline melts at 1 atmosphere and variable f _O2 demonstrate that orthopyroxene dissolves to form olivine, Si-rich melt and clinopyroxene. These phases form a texturally and chemically distinct boundary layer around the partly dissolved orthopyroxene crystals. The occurrence of clinopyroxene in the boundary layer is due to inward diffusion of Ca from the solvent melt to the boundary layer causing clinopyroxene saturation. Compositional profiles through the solvent and the boundary layer for a number of experiments demonstrate rapid diffusion of cations across the boundary layer – solvent interface. SiO₂ diffuses outward from the boundary layer whereas CaO and Al₂O₃ diffuse toward the Si-enriched boundary layer melt. The rate of Al diffusion is slower under reducing conditions compared to the rates in experiments performed in air. Concentrations of FeO and MgO in the boundary layer and solvent are approximately equal indicating rapid diffusion and attainment of equilibrium despite ongoing crystallisation of clinopyroxene within the boundary layer. The behaviour of Na₂O and K₂O is strongly affected by f _O2. Under reducing conditions Na₂O and K₂O concentrations are approximately equal in the boundary layer and solvent indicating normal diffusion down the concentration gradient and attainment of equilibrium. Under oxidising conditions, K₂O and to a lesser extent Na₂O, have compositional profiles indicative of uphill diffusion likely due to their preference for more polymerised Si- and Al-rich melts. Under reduced conditions Al-enrichment in the boundary layer melt is not as extreme and uphill diffusion did not occur. The composition of the solvent melt after the experiments indicates that it was contaminated by the boundary layer by convective mixing due to the onset of hydrodynamic instabilities brought on by density and viscosity contrasts between the two melts. Despite using a wide variety of solvent melt compositions we find that the boundary layer melts converge toward a common composition at high SiO₂ contents. The composition of glass generated by orthopyroxene dissolution at 1 atmosphere is similar in many respects to Si-rich glass found in many orthopyroxene-rich mantle xenoliths that have been attributed to high pressure in situ processes including mantle metasomatism. The results of this study suggest that at least some Si-rich melts are likely to have formed by dissolution of xenolith orthopyroxene at low pressure possibly by their Si-undersaturated host magmas. Received: 30 August 1996 / Accepted: 15 April 1998     

Effects of core formation

Two sets of earth models have been generated which simulate the process of core formation in the earth. The results allow the evaluation of the distribution of energy release by core formation and thus an estimate of the early temperature profile following core formation. The process itself is likely to have taken 20 Ma or less, although a longer induction period during which some metal phase exists as a melt is probable. Much of the energy (half or more) ends up in a hot core with the mantle relatively cold. These results suggest the occurrence of mantle wide convection, leading to homogenization and the possible stripping of some elements from the mantle.