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.     

Approach to Mountain Hazards in Tibet, China

Tibet is located at the southwest boundary of China. It is the main body of the Qinghai-Tibet Plateau, the highest and the youngest plateau in the world. Owing to complicated geology, Neo-tectonic movements, geomorphology, climate and plateau environment, various mountain hazards, such as debris flow, flash flood, landslide, collapse, snow avalanche and snow drifts, are widely distributed along the Jinsha River (the upper reaches of the Yangtze River), the Nu River and the Lancang River in the east, and the Yarlungzangbo River, the Pumqu River and the Poiqu River in the south and southeast of Tibet. The distribution area of mountain hazards in Tibet is about 589,000 km^2, 49.3% of its total territory. In comparison to other mountain regions in China, mountain hazards in Tibet break out unexpectedly with tremendously large scale and endanger the traffic lines, cities and towns, farmland, grassland, mountain environment, and make more dangers to the neighboring countries, such as Nepal, India, Myanmar and Bhutan. To mitigate mountain hazards, some suggestions are proposed in this paper, such as strengthening scientific research, enhancing joint studies, hazards mitigation planning, hazards warning and forecasting, controlling the most disastrous hazards and forbidding unreasonable human exploring activities in mountain areas.     

GEOGRAPHY ON THE PLANETS: GIFT OF REMOTE SENSING*

Extraterrestrial geography has become a reality, as we move from Earth's moon to the planets. A broad-scale regional physiography is being established on twenty planets and satellites through remote sensing techniques. Spacecraft images yield most of the information on Solar System landscapes. Topographic measurements are extracted by monoscopic image-processing, stereophotogrammetry, and radar analysis. Invisible parts of the spectrum furnish non-topographic data.     

A POORLY GRAPHITISED CARBON CONTAMINANT IN STUDIES OF EXTRATERRESTRIAL MATERIALS

Poorly-graphitised carbon particles are formed during manufacture of sample substrates (holey carbon films) for Analytical Electron Microscopy studies of small particles. The particles form during heat treatment of cellulose acetobutyrate at about 975 °C and 1050 °C. In AEM studies of fine-grained carbonaceous extraterrestrial materials, these particles are easily recognised.     

Multiple longshore sand bars in the upper Chesapeake Bay

In the upper Chesapeake Bay (Maryland, U.S.A.) field surveys were conducted at 18 multiple longshore sand bar sites. The multiple bar systems were found in water depths less than approximately 2 m (mean sea level), and exhibited mild bottom slopes of 0·0052 or less. The number of bars composing each system ranged from four to 17 and the spacing between the crests typically increased in the offshore direction, ranging from 12 to 70 m. Bar height also typically increased with distance offshore and ranged from 0·03 to 0·61 m. A grain size analysis of crest and trough sediment did not reveal any significant differences and the sediment was categorized as ‘fine sand’. A review of the literature data indicated that the Chesapeake Bay multiple bars possessed similar characteristics to those found in Gelding Bay (Baltic Sea); similarities in fetch, wave height and tidal range between the two bays may account for this finding. The surf-scaling parameter indicated that the multiple bar systems were extremely dissipative with regard to wave energy, and wave height appeared to be an important factor in controlling bar spacing and bar height. A multiple wave break point hypothesis was discussed as a possible mechanism for the formation of Chesapeake Bay multiple longshore bars, and limited observational evidence appeared to support such a mechanism.     

Chandrasekhar's perturbation method-oriented theories up to third order for uniformly and differentially-rotating polytropic stars: Error-removing techniques

In this paper we analyse error-removing techniques used without sufficient theoretical support in a previous paper, where Chandrasekhar's higher-order perturbation theories were developed for either uniformly or differentially-rotating polytropic stars.     

Ultraviolet reflectance properties of asteroids

An analysis of the UV spectra of 28 asteroids obtained with the Internal Ultraviolet Explorer (IUE) satellite is presented. The spectra lie within the range 2100–3200 Å. Our results are examined in terms of both asteroid classification and of current ideas concerning the surface mineralogy of asteroids. For all the asteroids examined, UV reflectivity declines approximately linearly toward shorter wavelengths. In general, the same taxonomic groups are seen in the UV as in the visible and IR, although there is some evidence for asteroids with anomalous UV properties and for UV subclasses within the S class. No mineral absorption features are reported of strength similar to the strongest features in the visible and IR regions, but a number of shallow absorptions do occur and may provide valuable information on the surface composition of many asteroids.     

Electron microscopy study of the iron meteorite Santa Catharina

Abstract— Characterization of the microstructural features of the metal of the Santa Catharina meteorite was performed using a variety of electron optical techniques. Sample USNM#6293 is chemically homogeneous on the micron scale and has a Ni content of 28.2 wt.%. Its microstructure is similar to that of the Twin City ataxite and contains clear taenite II, i.e., fcc taenite with domains of tetrataenite, < 10 nm in size. Sample USNM#3043 is a more typical Santa Catharina specimen with dark and light regions as observed with the light optical microscope. The dark regions are inhomogeneous and contain 45–50 wt.% Ni and 7–12 wt.% O. The light regions are homogeneous and contain 35 wt.% Ni and no detectable oxygen. The microstructure is that of cloudy zone, i.e., islands of tetrataenite, ～20 nm in size, in a honeycomb matrix. The honeycomb phase contains Ni rich oxide in the dark regions and contains metal, fcc taenite, in the light regions. The original metal structure of USNM#3043 is cloudy zone which formed during cooling into the low temperature miscibility gap of the Fe-Ni phase diagram. The dark regions were developed from the metal by selective corrosion of the honeycomb structure, transforming it into Ni containing oxides, possibly non-stoichiometric Fe₂NiO₄ while retaining the tetrataenite islands. Using the results of this study, many of the existing discrepancies concerning the microstructure of Santa Catharina can be explained.     

Static fields in generalized theory of gravitation

Solutions of field equations of the generalized theory of gravitation for neutral and charged point masses are found. The problem is formulated so that the solution may be expressed in harmonic, isotropic, Schwarzschild and, if necessary, any other coordinates. A method for the solution of the static axisymmetric problem (an analogue of a well-known Weyl's solution) is also proposed.