Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth

Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.     

The large peculiar velocity of the cD galaxy in Abell 3653

We present a catalogue of galaxies in Abell 3653 from observations made with the 2-degree field (2dF) spectrograph at the Anglo-Australian Telescope. Of the 391 objects observed, we find 111 are bona fide members of Abell 3653. We show that the cluster has a velocity of   cz = 32 214 ± 83  km s⁻¹ ( z = 0.10 738 ± 0.00 027)  , with a velocity dispersion typical of rich, massive clusters of  σ _cz = 880⁺⁶⁶₋₅₄  . We find that the cD galaxy has a peculiar velocity of  683 ± 96  km s⁻¹  in the cluster rest frame – some 7σ away from the mean cluster velocity, making it one of the largest and most significant peculiar velocities found for a cD galaxy to date. We investigate the cluster for signs of substructure, but do not find any significant groupings on any length scale. We consider the implications of our findings on cD formation theories.     

On the fluid and viscoelastic deformations of the planets

The shape of the Earth and of planets depends on the exciting forces and on the rheology of the medium. From the equilibrium equation, we present the main modelisations of the viscous and inviscid fluids and we essentially describe the characteristics of linear viscoelastic deformations, for the Maxwell viscoelastic model of rheology. We use the elastic, viscoelastic and fluid Love numbers in order to investigate the associated relaxation modes. For these various kinds of rheology of the planets interior, we compute the geoid and the topography induced by an internal mass distribution. Finally, we show the importance of this viscoelastic deformation calculations in the study of the celestial body rotations.     

A general model for Mt. Ruapehu lahars

A mathematical model of the motion of lahars is presented. Lahar flows and travel speeds are calculated using a kinematic wave model which equates gravitational accelerations to frictional losses. A chezyor Manning-type law of friction is assumed, in which lahar flow rate is a simple power function of lahar depth, multiplied by another simple power of the chanel slope. Use of the model requires knowledge of essentially only one parameter which appears to be relatively insensitive for flows down a given channel. Variable channel slope effects are removed by a longitudinal scaling which applies to all flows down a given channel. For lahars generated by a single explosive event it is unnecessary to perform numerical calculations to predict lahar flow and travel time, but for lahnars produced by multiple sources in which different lahar flows are interacting, numerical calculations appear necessary. The model is applied to all recorded lahar flows from Mt. Ruapehu, and satisfactorily described all lahar flows generated by a single explosive mechanism. Such flows depend essentially only on total lahar volume. The 1968 Mt. Ruapehu lahar, generated by a series of smaller eruptive mechanisms, was modelled as the interaction of seven point sources of fluid originating from positions mathematically extrapolated up the mountain. Good agreement was obtained between the predicted times of formation of these 1968 lahars, and the times of greatest seismic amplitude.     

Mapping and measuring the ecological embeddedness of food supply chains

The status of nature in food systems is the subject of this paper, which looks into the ecological embeddedness of the Austrian food system both on the national level and in a regional case study. By a first attempt to measure and map ecological embeddedness, the author intends to contribute to the operationalisation of the embeddedness concept, which is characterised as ambivalent, fuzzy and dynamic (see e.g., [Goodman, D., 2003. The quality ‘turn’ and alternative food practices: reflections and agenda. Editorial. Journal of Rural Studies 19 (1), 1-7; Markusen, A., 1999. Fuzzy concepts, scanty evidence, policy distance: the case for rigour and policy relevance in critical regional studies. Regional Studies 33, 869-884; Hess, M., 2004. ‘Spatial’ relationships? Towards a reconceptualization of embeddedness. Progress in Human Geography 28 (2), 165-186]). The paper starts with a critical outline of the academic discourse on embeddedness in food chain studies. In the second section, general developments in the Austrian food system and their ecological implications are illustrated for the national level. Thereafter in a case study, the author tries to map and measure the ecological embeddedness of two conventional bread chains. The focus on conventional food chains provides a contrast with the growing body of embeddedness studies concentrating on alternative food chains. The author concludes that for both conventional as well as alternative food chains, the mode of ecological embeddedness or the degree of a food chain’s commitment to particular landscapes could become important factors for the maintenance, enhancement and capture of ecological value.     

Volcanic hazards to airports

Volcanic activity has caused significant hazards to numerous airports worldwide, with local to far-ranging effects on travelers and commerce. Analysis of a new compilation of incidents of airports impacted by volcanic activity from 1944 through 2006 reveals that, at a minimum, 101 airports in 28 countries were affected on 171 occasions by eruptions at 46 volcanoes. Since 1980, five airports per year on average have been affected by volcanic activity, which indicates that volcanic hazards to airports are not rare on a worldwide basis. The main hazard to airports is ashfall, with accumulations of only a few millimeters sufficient to force temporary closures of some airports. A substantial portion of incidents has been caused by ash in airspace in the vicinity of airports, without accumulation of ash on the ground. On a few occasions, airports have been impacted by hazards other than ash (pyroclastic flow, lava flow, gas emission, and phreatic explosion). Several airports have been affected repeatedly by volcanic hazards. Four airports have been affected the most often and likely will continue to be among the most vulnerable owing to continued nearby volcanic activity: Fontanarossa International Airport in Catania, Italy; Ted Stevens Anchorage International Airport in Alaska, USA; Mariscal Sucre International Airport in Quito, Ecuador; and Tokua Airport in Kokopo, Papua New Guinea. The USA has the most airports affected by volcanic activity (17) on the most occasions (33) and hosts the second highest number of volcanoes that have caused the disruptions (5, after Indonesia with 7). One-fifth of the affected airports are within 30 km of the source volcanoes, approximately half are located within 150 km of the source volcanoes, and about three-quarters are within 300 km; nearly one-fifth are located more than 500 km away from the source volcanoes. The volcanoes that have caused the most impacts are Soufriere Hills on the island of Montserrat in the British West Indies, Tungurahua in Ecuador, Mt. Etna in Italy, Rabaul caldera in Papua New Guinea, Mt. Spurr and Mt. St. Helens in the USA, Ruapehu in New Zealand, Mt. Pinatubo in the Philippines, and Anatahan in the Commonwealth of the Northern Mariana Islands (part of the USA). Ten countries—USA, Indonesia, Ecuador, Papua New Guinea, Italy, New Zealand, Philippines, Mexico, Japan, and United Kingdom—have the highest volcanic hazard and/or vulnerability measures for airports. The adverse impacts of volcanic eruptions on airports can be mitigated by preparedness and forewarning. Methods that have been used to forewarn airports of volcanic activity include real-time detection of explosive volcanic activity, forecasts of ash dispersion and deposition, and detection of approaching ash clouds using ground-based Doppler radar. Given the demonstrated vulnerability of airports to disruption from volcanic activity, at-risk airports should develop operational plans for ashfall events, and volcano-monitoring agencies should provide timely forewarning of imminent volcanic-ash hazards directly to airport operators.     

Hydrochemistry and environmental isotopes of spring water and their relation to structure and lithology identified with remote sensing methods in Wadi Araba,Egypt

Springs located at the historical sites of Wadi Araba (Eastern Desert of Egypt) and emerging from the escarpments of the Northern and Southern Galala Plateaus were investigated. A combination of methods, including hydrochemistry, stable and radioisotope composition, and structural analyses based on satellite data, provided information about the structure of the subsurface and the derived groundwater flow paths. Satellite images reveal karst features within the northern plateau, e.g. conical landforms. Karstic caves were documented along both escarpments. Chemical analysis of floodwater from Wadi Araba indicates higher concentrations of terrestrial salts compared to floodwaters from central and southern parts of the desert. δ¹⁸O and δ²H signatures in spring waters resemble those of floodwater and fall on the global meteoric water line, confirming their fast infiltration with minor influence of evaporation. The aquifer feeding the springs of the Northern Galala Plateau has low retention and the springs dry out quickly, even after heavy rainfall. Contrastingly, ³H activities in springs emerging from the Southern Galala Plateau refer to much slower subsurface passage. With respect to ³H content (3.8 TU) in recent flood waters, the spring water at Southern Galala Plateau contains about 40% recently recharged groundwater. However, its largest spring—the St. Antony spring—discharges water with a radiocarbon age of about 15,000 years. In combination with this spring’s constant and high discharge over a period of several months, that age estimate suggests a large reservoir with moderate to high retention.