Tracer anomaly evolution in the flow field of an isolated eddy

We explore the horizontal stirring of a passive tracer field in the vicinity of an isolated, finite amplitude, quasigeostrophic, β-plane eddy. We consider stirring in the presence of a uniform background gradient of tracer concentration as well as cases in which the tracer anomaly is initially contained within the eddy.This paper reports a survey of phenomenology based upon numerical experiments. We explore the sensitivity of results to physical parameters and to various aspects of the numerical simulation.Under the joint effects of β and of non-linearity, the eddy center migrates. Time dependent effects in a radiated wake provide important stirring mechanisms for the background tracer field. An unexpected, persistent result is a tendency to propel a tendril of tracer westward from near the launch latitude of the eddy. In some cases, the westward penetration of the tendril is even further than the migration of the eddy center.Tracer properties characteristics of the launch site of the eddy tend to be captured and carried with the eddy. However, tracer leaks from the eddy, due to both explicit diffusion-like effects and eddy interaction with background flow features, can result in drawing off of secondary tracer patches.We also calculate trajectories of Lagrangian particles launched in and around the eddy.     

Stratified flow in pyroclastic surges

Stratified flow theory is applied to pyroclatic surges in an effort to gain insight into transport dynamics during explosive eruptions. Particle transport is assumed to be by turbulent suspension, and calculations contained herein show that this is likely for many cases including the 18 May 1980 blast at mount St. Helens. The discussion centers on the Rouse number (Pn), which represents a ratio of particle settling velocity to scale of turbulence; the Brunt-Väisälä frequency (N), which is the maximum possible frequency of internal waves; the Froude number (Fr), representing the ratio of inertial forces to gravitational forces; and the Richardson number (Ri), a ratio of buoyant restoring forces to turbulent mixing forces. The velocity or flow power dependence of bed-form wavelength in surge deposits is related to a velocity dependence of wavelength of internal waves in the turbulent surge. This produces a decrease in dune wavelength with increasing distance from vent. Migration direction of bed forms is related toFr as it is defined for a continuously stratified flow. Proximal to distal facies variations in surge deposits reflect increasingPn andRi as the flows move away from their sources. This produces the progression from sandwave to massive to planar facies with increasing distance from vent. Where the long axis of topography is at low angles to the flow direction, massive facies in topographic lows may from concurrently with sandwave facies on highs, due to the higher particle concentration in the lows. Where long axis of topography is at high angles to flow direction, denser lower parts of the surge may be dammed or blocked. Blocked material tends to form massive flows that may move down slope independent of the overriding surge. A model incorporating turbulent transport, stratified flow, and time evolution of pyroclastic surges is proposed for deposits which have been attributed to both pyroclastic flow and pyroclastic surge transport by various workers. During the initial high energy (waxing) phase of the eruptive event,Pn is sufficiently low that only coarse, but poorly sorted, material is deposited to form relatively coarse bottom layers. As the event wanes, remaining finer material is deposited through a thin bed load to produce overlying bedded and cross-bedded veneer deposits. Throughout most of the event, blocking occurs to produce relatively thick and massive deposits in valley bottoms.     

Reliability analysis of drilled shaft behavior using finite difference method and <Emphasis Type="Italic">Monte Carlo</Emphasis> simulation

Load displacement analysis of drilled shafts can be accomplished by utilizing the “t-z” method, which models soil resistance along the length and tip of the drilled shaft as a series of springs. For non-linear soil springs, the governing differential equation that describes the soil-structure interaction may be discretized into a set of algebraic equations based upon finite difference methods. This system of algebraic equations may be solved to determine the load–displacement behavior of the drilled shaft when subjected to compression or pullout. By combining the finite difference method with Monte Carlo simulation techniques, a probabilistic load–displacement analysis can be conducted. The probabilistic analysis is advantageous compared to standard factor of safety design because uncertainties with the shaft–soil interface and tip properties can be independently quantified. This paper presents a reliability analysis of drilled shaft behavior by combining the finite difference technique for analyzing non-linear load–displacement behavior with Monte Carlo simulation method. As a result we develop probabilistic relationships for drilled shaft design for both total stress (undrained) and effective stress (drained) parameters. The results are presented in the form of factor of safety or resistance factors suitable for serviceability design of drilled shafts.     

Geochronology of zircon megacrysts from nepheline-bearing gneisses as constraints on tectonic setting: implications for resetting of the U-Pb and Lu-Hf isotopic systems

Nepheline-bearing gneisses from the 75 km² Tambani body in the Mozambique Belt of southern Malawi, are miaskitic biotite-nepheline monzodiorites, reflecting an absence of K-feldspar, alkali amphiboles or pyroxenes, and contain euhedral zircon megacrysts up to 5 cm across. The zircons contain U = 1–1,860 ppm, Th = 0–2,170 ppm and Y = 400–1,100 ppm, and very low concentrations of all other measured trace elements except Hf (HfO₂ = 0.53–0.92 wt. %). Cathodoluminescence images reveal oscillatory sector growth zoning and no evidence for xenocrystic cores, indicating that the zircons represent primary magmatic crystallization products that have survived amphibolite grade metamorphism. U-Pb isotopic analyses (by TIMS) yield an upper intercept age of 730 ± 4 Ma (MSWD = 1.7), which we interpret as the time of magmatic crystallization of the zircons. This is coincident with 11 SHRIMP spot analyses, which yield a mean age of 729 ± 7 Ma (MSWD = 0.37). Metamorphism, at 522 ± 17 Ma as suggested by monazite, caused partial Pb-loss during local recrystallization of zircon. Lu-Hf isotopic data for three whole-rock samples of nepheline-bearing gneiss are collinear with those for zircon megacrysts, and correspond to an age of 584 ± 17 Ma (MSWD = 0.37. We interpret the Lu-Hf array to represent a mixing line defined by the Hf isotopic signature of primary zircon and that of the rock-forming minerals reset during metamorphic (re-)crystallization; hence the 584 Ma age is likely geologically meaningless. Given the well-defined association of nepheline syenites (and phonolitic volcanic equivalents) with continental rifting, we suggest that the Tambani body represents a magmatic product formed at 730 Ma during the break-up of the Rodinia supercontinent. The 522 Ma age is akin to other Pan-African metamorphic ages that record collisional suturing events during the final assembly of Gondwana. Zircon-bearing nepheline gneisses thus preserve a record of intra-continental rifting and of continental collision in southern Malawi.     

Changing poverty distribution in Bolivia: the role of rural–urban migration and urban services

Bolivia is a country with high levels of poverty and inequality among its peoples and regions. For the nation and its urban and rural areas, trends in the social and spatial distribution of poverty (and extreme poverty) are identified from 1976 to 2003 using UBN data with minor support where appropriate from poverty lines. The main survey between 1992 and 2001 uses composite and selected UBN to track detailed poverty change for the country’s nine departments, its ten largest cities and a selection of other smaller urban and rural municipalities. Because of rising background increases in population in the various surveyed administrative units, many instances of relative reductions in poverty are accompanied by rising absolute increases. Marked spatial variations in poverty and development in the country over the last several decades are identified as the main driver for the country’s quickening pace of rural–urban migration. As a result, the paper concludes by assessing two different but closely related views. One investigation tests the notion that because more poor people have been living in Bolivia’s cities than in its rural areas since the mid to late 1990s, rapid rural–urban migration has simply shifted the locus of poverty from the countryside to the cities in a process called, the ‘urbanisation of poverty.’ A second, more challenging, investigation assesses the view that the flow of poor rural people to the better serviced urban areas of Bolivia has actually acted to alleviate national poverty levels.     

Upper-mantle structure of the Baltic Shield below the Swedish National Seismological Network (SNSN) resolved by teleseismic tomography

Upper-mantle structure under the Baltic Shield is studied using non-linear high resolution teleseismic P -phase tomography. Observed relative arrival-time residuals from 52 teleseismic earthquakes recorded by the Swedish National Seismological Network (SNSN) are inverted to delineate the structure of the upper mantle. The network consists of 47 (currently working) three-component broad-band stations located in an area about 450 km wide and 1450 km long. In order to reduce complications due to possible significant three-dimensionality of Earth structure, events chosen for this study lay close to in-line with the long-axis of the array  (±30°)  . Results indicate P -wave velocity perturbations of ±3 per cent down to at least 470 km below the network. The size of the array allows inversion for structures even at greater depths, and lateral variations of velocity at depths of up to 680 km appear to be resolved. Below the central part of the array (60°–64° N), where ray coverage is best, the data reveals a large region of relatively low velocity at depths of over about 300 km. At depths less than about 250–300 km, the models include a number of features, including an apparent slab-like structure dipping gently towards the north.     

Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.     

Feasibility of AFC models for the petrogenesis of calc-alkaline magma series

 One of the most popular petrogenetic concepts is that of simultaneous assimilation and fractional crystallisation (AFC). The equations governing these processes are well known and widely applied. The power and attraction of the model are that, with the minimum of constraints, petrogenetic schemes can be erected for essentially any group of rocks. These models are usually based on the observed variations in a small number of trace elements and/or isotopic systems. In this paper we have generated well-constrained AFC models for the Variscan, calc-alkaline Quérigut complex in the French Pyrénées. Our models are based on geological constraints on the identities of the parent magma and candidate assimilants, and the Sm-Nd and Rb-Sr isotope systematics of the rocks. The modelling is successful in mimicking the isotope array for the actual rocks. However, the results are massively inconsistent with those produced using the major- and trace-element concentrations. Our major conclusion is that AFC modelling should be undertaken only with robust initial constraints on the compositions of the parent magma and the proposed assimilant, with due respect for crystal-liquid partition coefficients, in so far as they are known. The results should then be accepted only if the isotope-based model parameters are consistent with those derived from major- and trace-element variations. Received: 19 August 1994/Accepted: 23 March 1995