An introduction to Maslov's asymptotic method

Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.     

Longitudinal dispersion compensation for the Very Large Telescope Interferometer

The Very Large Telescope Interferometer [1,13] will be operated in air which will introduce small optical path fluctuations due to internal turbulence [4,6] and dispersion effects. Both may contribute to fringe contrast decrease. Longitudinal dispersion effects can be corrected by inserting an appropriate glass of variable thickness in one arm of the interferometer [3,5,11,12]. This paper presents a new method applied to VLTI in order to select the optimum glass, according to both the observing wavelength and the spectral bandpath, and to calculate its thickness. Results are presented in terms of improvement on the fringe contrast.     

Determinants and characteristics of female migration: a case study of Salem City in Tamil Nadu,India

A random sample of 521 male and 481 female migrants surveyed in Salem city in Tamil Nadu, India, during 1980-1981 was analyzed on the basis of a classification related to reasons (association, marriage, distress, and voluntary) for migration. Women were found to outnumber males in associational migration, both in rural to urban and urban to urban streams. They also formed almost all the marriage migrants. They were more numerous in distress migration as well. There were, however, comparatively few women among voluntary migrants. The incidence of illiteracy among migrant women was generally high, except for voluntary migrants who had completed high school. The share of working women was not negligible, but in most cases present work status was achieved after migrating.     

Assessment of sandstone deterioration at Ta Keo temple (Angkor): first results and future prospects

A first application of geomorphological methods to the assessment of sandstone deterioration at Angkor is presented. Damage diagnosis was carried out on the first eastern tier of the central pyramid of the 1,000 year-old Ta Keo temple. Methods combine field observations and measurements at 230 sampling points, high-resolution lasergrammetry and stereophotogrammetry on a 2-m² test zone, and SEM observations. The first results indicate that decay operates through a synergistic combination of weathering phenomena dominated by scaling and solution, and exhibits a high spatial variability. Percentages of deteriorated surfaces vary from 17.6 to 93.8%, and average stone recession values from 0.00 to 2.71 cm (minimum) and 0.34 to 5.49 cm (maximum). On the test-zone, stereophotogrammetry and 3D-mapping of the present and reconstructed initial states using lasergrammetry indicate that erosion scars up to 6 cm deep have formed since 1963. On the whole, the amount of deteriorated surfaces more than tripled between 1963 and 2008. The degree of implication of salts in stone decay remains unclear for most efflorescences are composed of calcite (CaCO3), with secondary importance of barite (BaSO4) and gypsum (CaSO₄·2H₂O). Future prospects aim to evaluate the impact on stone decay of the clearing out of the temple from the forest in the 1920s.     

Flexural isostatic response of the Alps to increased Quaternary erosion recorded by foreland basin remnants,SE France

We test the hypothesis that flexural isostatic compensation of the mass removed by enhanced Quaternary erosion is responsible for uplift of the Western European Alps and their forelands. We use two well‐preserved and well‐dated (1.8 Ma) abandonment surfaces of foreland basin remnants in SE France (the Chambaran and Valensole plateaux) as passive benchmarks for tilting of the foreland. Estimating their initial slope from morphometric scaling relationships, we determine bulk post‐depositional tilting of 0.5–0.8% for these surfaces. The calculated isostatic response of the Alpine lithosphere to erosional unloading, using the method recently proposed by Champagnac et al. [Geology 35 (2007) 195–198] , yields a predicted tilting of 0.3–0.4% in the considered areas, explaining approximately half of the determined post‐depositional tilting. Such long‐term deformation being insensitive to cyclic loading/unloading because of glaciations, we suspect the other half to be related to as yet undetermined long‐wavelength and long‐lived tectonic process(es).     

Ionization above theF2-peak,as affected by the interplanetary gas

Summary The atmospheres of the earth, the sun and other bodies are surrounded by gas that is nearly uniform in number densityn and kinetic temperatureT, over spaces much greater than those occupied by the atmospheres. This gas may be called theambium of the atmosphere. In total it is much more massive than the atmosphere it encloses. The conditions in the ambium must powerfully affect the state of the outer atmosphere. In particular, there must be a continuous transition of the values ofn andT between the ambium and the atmosphere. In the case of the earth, the sun and other hot stars, both the ambium and the outermost part of the atmosphere will consist of atomic hydrogen. The temperature of the ambium will determine whether this hydrogen and that of the outermost atmosphere are mainly ionized or neutral.The nature of the terrestrial ambium depends on the extension of the sun's atmosphere. This atmosphere is hot and highly ionized in its inner parts. At some radius not yet known, the solar atmospheric gas must become cool and neutral. The state of the earth's outermost atmosphere depends greatly on whether the earth lies in the ionized or the neutral part of the sun's atmosphere, or in the solar ambium.Evidence will be presented favoring the view that the earth's ambium consists of ionized solar atmospheric hydrogen. If this be so, the outermost part of the earth's atmosphere is likewise hot and ionized. It must enclose an extensive layer of mainly neutral atomic hydrogen.The part of this work done at High Altitude Observatory was supported by the National Bureau of Standards and the Air Force Cambridge Research Center.