Spherical Slepian functions and the polar gap in geodesy

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.     

Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth

The   M _w γ 9.0  2004 December 26 Sumatra-Andaman and   M _w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.     

Palaeovariations in the East-Asian Monsoon Regime Geochemically Recorded in Varved Sediments of Lake Sihailongwan (Northeast China, Jilin Province). Part 1: Hydrological Conditions and Dust Flux

The varved sediments of the dimictic Lake Sihailongwan (Long Gang mountain area, Jilin Province, Northeast China) represent a palaeoclimatic archive which documents the local precipitation frequency during the summer monsoon, and variations in the aeolian flux of dust with their remote sources in the arid and semi-arid regions of inner Asia. Based on a detailed discussion of sediment genesis in Lake SHL, dust flux rates and palaeohydrological conditions were reconstructed on a decadal scale over the past 220 years. The aeolian influx by dry and wet deposition was quantified and characterised in its chemical composition. Photosynthetic production in the lake is positively correlated with the inflow of nutrient-rich groundwater. The groundwater discharge largely reflects the strength of the summer monsoon. Net accumulation rates for biogenic silica were determined for annually laminated sediments from the centre of the U-shaped lake basin based on sediment data. In a Si-balance model of the modern lake, the depositional flux of biogenic silica could be independently quantified on the base of hydrochemical monitoring data. Comparison of the both estimates allowed to asses the focussing of the particle flux in the lake. Though water retention in Lake SHL is rather high (ca. 30 years), changes in the hydrological conditions are sensitively recorded in the sediments because (i) nutrient-rich groundwater discharges into the productive zone of the lake, (ii) a substantial proportion of the total dissolved Si-inventory of the mixed lake (ca. 30%) is annually consumed by diatom growth, and (3) sediment accumulation is substantially focussed towards the flat bottom of the lake basin. The bulk siliciclastic sediment fraction (ca. 75 wt.%) largely originates from influx of dust of remote provenance. In sediment thin-sections, the dry-deposited dust fraction is microscopically identifiable as seasonal silt layer. Aeolian input by wet-deposition shows a distinctly higher variability than the influx of dust by dry-deposition. As diatom production, wet-deposition of dust is positively correlated with the rainfall during the summer monsoon. The inferred positive correlation between rainfall and dust flux during the summer monsoon implies that dust deposition is determined by the out-wash efficiency of mineral particles for a permanent high atmospheric dust concentration over Northeast China in the last 220 years.     

Natural and man-induced stress evolution of slopes: the Monte Mario hill in Rome

The paper deals with stress-release effects induced by man-made cuts or excavations into natural stiff clay slopes that experienced erosion in response to valley deepening. The study was focused on the Monte Mario hill in Rome (Italy), which formed part of an area of recent urban expansion. The methodology of the study relied on a reference engineering-geology model, which was developed on the basis of site and laboratory data and stress–strain analyses. The latter analyses were carried out with the finite-difference code FLAC 4.0. Numerical modelling was based on a sequential approach, taking into account the main evolutionary stages of the Tiber river valley in Romeȁ9s urban area and then making cuts at the bottom of the slope located south of the Monte Mario Astronomical Observatory. The simulation revealed the stress-release effects that fluvial erosion and excavation fronts have caused on the investigated slopes and their consequent gravitational instabilities. These processes appear with metre-scale displacements, followed by stress-release cracks (actually observed on the slopes under review). In quantifying stress-release deformations, the simulation took into account the possible role of creep in the observed retardation of stress-release effects.Research activities were carried on with the co-operation of Dȁ9Arcangelo A. (Consorzio TREESSE, andrea.darcangelo@libero.it) and Moretti S. (IMG S.r.l. Servizi Tecnici per lȁ9Ingegneria e lȁ9Ambiente, moretti@img-srl.it)     

Lead, zinc, and antimony contamination of the Rio Chilco-Rio Tupiza drainage system, Southern Bolivia

An intense, but localized rainfall event in February 2003, led to the severe erosion and failure of a tailings disposal impoundment at the Abarόa Antimony Mine in southern Bolivia. The failure released approximately 5,500 m³ of contaminated tailings into the Rio Chilco-Rio Tupiza drainage system. The impacts of the event on sediment quality are examined and compared to contamination resulting from historic mining operations in the headwaters of the basin. Of primary concern are contaminated floodplain soils located along downstream reaches of the Rio Tupiza which were found to contain lead (Pb), zinc (Zn), and antimony (Sb) concentrations that locally exceed Canadian, German, and Dutch guidelines for agricultural use. Spatial patterns in sediment-borne trace metal concentrations, combined with Pb isotopic data, indicate that Pb, Zn, and Sb are derived from three tributary basins draining the Abarόa, Chilcobija, and Tatasi-Portugalete mining districts. Downstream of each tributary, geographical patterns in trace metal concentrations reflect local geomorphic changes throughout the drainage system. Trace metal concentrations within the Rio Chilco decrease rapidly downstream as a result of dilution by uncontaminated sediments and storage of metal enriched particles (e.g., sulfide minerals) in the channel bed as a result of ongoing aggradation. Storage in the floodplains is limited. These processes significantly reduced the dispersal and, thus, the relative environmental affects of tailings eroded from the Abarόa Mine during the 2003 flood. In contrast, storage of Pb, Zn, and Sb in floodplains along the Rio Tupiza is significant, the majority of which is derived from historic mining operations, particularly mining within the Tatasi-Portugalete district.     

Effect of temperature and pressure on the composition of oils from the Bazhenovskaya Formation in the latitudinal segment of the Ob River area

Detailed data obtained on surface oil samples from the Bazhenovskaya Formation in the latitudinal segment of the Ob River area indicate that the composition of the oil is largely controlled by the P-T conditions in the reservoir. It was determined that the generation of hydrocarbon fluids starts at higher temperatures (T _f > 100°C) if the fluid reflux is hindered and the formation pressures are anomalously high. In systems with the free reflux of hydrocarbon fluids, the processes generating oil and gas are different. The composition of oil in the Bazhenovskaya Formation with the free reflux of hydrocarbon fluids is largely controlled by migration processes, which determine, along with the P-T parameters, the physicochemical characteristics of the oils and their concentrations of hydrocarbon groups and individual hydrocarbons. Original Russian Text ? O.F. Stasova, A.I. Larichev, N.I. Larichkina, 2006, published in Geokhimiya, 2006, No. 9, pp. 996–1005.     

Diffusion-limited REE uptake by eclogite garnets and its consequences for Lu–Hf and Sm–Nd geochronology

Garnets from the Zermatt-Saas Fee eclogites contain narrow central peaks for Lu + Yb + Tm ± Er and at least one additional small peak towards the rim. The REE Sm + Eu + Gd + Tb ± Dy are depleted in the cores but show one prominent peak close to the rim. These patterns cannot be modeled using Rayleigh fractionation accompanied by mineral breakdown reactions. Instead, the patterns are well explained using a transient matrix diffusion model where REE uptake is limited by diffusion in the matrix surrounding the porphyroblast. Observed profiles are well matched if a roughly linear radius growth rate is used. The secondary peaks in the garnet profiles are interpreted to reflect thermally activated diffusion due to temperature increase during prograde metamorphism. The model predicts anomalously low ¹⁷⁶Lu/¹⁷⁷Hf and ¹⁴⁷Sm/¹⁴⁴Nd ratios in garnets where growth rates are fast compared to diffusion of the REE, and these results have important implications for Lu–Hf and Sm–Nd geochronology using garnet.