Observations on seismic wave equation and reflection coefficient symmetries in stratified media

Summary. The equations describing seismic waves in a stratified earth have a number of symmetry properties, one of which has recently been used by Garmany to derive a simple expression for the inverse of the matrix of eigenvectors appearing in the solution of the equations. We review these symmetries of the wave equation in several notations to demonstrate that the property used by Garmany is distinct from the usual symmetries found in the seismological literature. Like the others, the new symmetry has implications for the reflection and transmission properties of a medium. These implications are briefly reviewed in order to show how the new symmetry is placed relative to the others. A limited discussion of the physical origins of the symmetries is given and, though the overall picture is incomplete, it is noted that the new symmetry yields conservation of energy for reflection/transmission at a single interface in all types of media (anisotropic, lossy, etc.).     

关于中尺度对称运动的稳定性及其演变

本文首先建立了中尺度对称运动的Hamihon函数,并用变分原理导出了对称运动稳定的充分条件,然后再用Lagrange变分导出了缓变介质中对称运动的波作用量方程,这种波作用量方程与用WKB方法所得到的结果是相同的。同时,本文进一步讨论了中尺度对称扰动渡包的演变规律,并获得了对称运动发展的判据。     

Chloride in precipitation and streamwater for the upland catchment of river severn,mid-wales; some consequences for hydrochemical models

Variations in the concentration of Cl in rainfall and stream runoff are presented for two catchments in the Hafren forest of mid-Wales, Great Britain. Despite the large fluctuations in rainfall concentrations, Cl in the streamwater remains relatively constant. Using the two-reservoir Birkenes model, an attempt was made to simulate observed Cl in streamwater. The original model was unable to reproduce the observations and several modifications are suggested to provide better simulations. The resulting model is not the only one capable of reproducing the observations; other hydrochemical models will most probably also achieve this although emphasis will in each case be placed on different aspects. In this paper, it is suggested that the stochastic properties of water movement and chemical processes can account for the streamwater chemistry responses observed. On the catchment scale these processes will lead to an apparently deterministic behaviour that may well be described by simple relationships.     

BOOK REVIEWS

Books reviewed in this article: The Mexican Colonial Copper Industry. Elinore M. Barrett . The Control Revolution: Technological and Economic Origins of the Information Society . James R. Beniger . Land Degradation and Society . Piers M. Blaikie And Harold C. Brookfield , Eds . La carte, mode d'emploi. Roger Brunet . France: les dynamiques du territoire . Roger Brunet AND Jacques Sallois , EDS. At the Crossroads—The Mineral Problems of the United States . Eugene N. Cameron . A Census of One Billion People , Papers for International Seminar on China's 1982 Population Census. Li Chengrui , ED. Les Milieux “Naturels” du Globe . Jean Demangeot . The Geophysiology of Amazonia: Vegetation and Climate Interactions : Robert E. Dickinson , ED. Tenn-Tom Country . James F. Doster And David C. Weaver . Family Farming in Europe and America . Boguslaw Galeski And Eugene Wilkening , EDS. The Geography of Urban Transportation . Susan Hanson , Ed. Combating Desertification in Developing Countries . J. K. Jain , ED. Cartography in France—1660–1848. Science, Engineering and Statecraft . Josef W. Konvitz . Distribution of Distances in Pregeographical Space . Hans Kuiper . Physical Geography Lab Manual: A New Experimental Approach . Neal G. Lineback And John M. Harlin . Physical Geography: A Landscape Appreciation , 2nd ed. Tom L. Mc Knight . The Desert Is No Lady: Southwestern Landscapes in Women's Writing and Art . Vera Norwood And Janice Monk , EDS. France: A Geographical, Social, and Economic Survey . Philippe Pinchemel , translated, by D. Elkins and T. H. Elkins. Gene Banks and the World's Food . Donald L. Plucknett , Nigel J. H. Smith , J. T. Williams , And N. Murthi Anishetty . Latin American Development: Geographical Perspectives . David Preston , Ed. Making Sense of Development: An Introduction to Classical and Contemporary Theories of Development and Their Application to Southeast Asia . P. W. Preston . The History of the Countryside. Oliver Rackham . The Third World in Perspective . H. A. Reitsma AND J. M. G. Kleinpenning . The Industrial Geography of Australia . David C. Rich . The Recruiting Game , 2nd Ed., revised. John F. Rooney , JR. A Cultural Geography of North American Indians . Thomas E. Ross AND Tyrel G. Moore , EDS. Eastern Europe . Dean S. Rugg . Human Territoriality: Its Theory and History . Cambridge Studies in Historical Geography: 7. Robert David Sack . Experimental Fluvial Geomorphology . Stanley A. Schumm , M. Paul Mosley , AND William E. Weaver . The New Urban Landscape . David Schuyler . Atlas of American Women . Barbara Gimla Shortridge . Impacts of Hazardous Technology: The Psycho-Social Effects of Restarting TMI-1 . John Sorensen , Jon Soderstrom , Emily Copenhaver , Sam Carnes AND Robert Bolin . Modern Physical Geography , 3rd Ed., (Third Edition). Arthur N. Strahler AND Alan H. Strahler . India: Economic Resource Base and Contemporary Political Patterns . B. L. Sukhwal .     

AIDS NORTH AND SOUTH: DIFFUSION PATTERNS OF A GLOBAL EPIDEMIC AND A RESEARCH AGENDA FOR GEOGRAPHERS *

Apart from the tragic certainty of death which accompanies AIDS everywhere, the means of its transmission, the spatial patterns of its diffusion, and the groups at highest risk of infection vary considerably among world regions. This paper reviews the disease and its transmission, then proposes three models of AIDS diffusion to assess the implications of the epidemic on various regions. AIDS North, of North America and western Europe, is urban based and primarily confined to homosexuals and IV drug abusers. AIDS South, in central Africa and the Caribbean, is spreading from cities into rural regions and affects primarily heterosexuals. The third, an AIDS North/South hybrid, is postulated as a model of diffusion of the disease in other Third World regions. The final section addresses the potential contribution of geographic research to policy-makers in attempting to cope with the diffusion of AIDS and in curbing the epidemic's advance.     

The identification of conceptual hydrological models for surface water acidification

Ambiguity in parameter identification represents a potentially serious limitation to the application of models of surface water acidification. Previous work has concentrated on manipulation of two of the three factors affecting model identifiability, namely model structure and estimator properties. A new technique is proposed which uses different modes of response within the data to improve parameter identification. Preliminary results, obtained using the Birkenes model of surface water acidification, appear to show promise. The technique is robust in recovering model parameters from synthetic data, with and without error, and in assimilating problems of structural error.     

Are Io's Alfvén wings filamented? Galileo observations

The interaction of Io with the Jovian magnetosphere generates auroral and radio emissions. The underlying electron acceleration process is not understood and few observations exist to constrain the theoretical models. The source of energy for the electron acceleration is in all likelihood supplied from the Alfvén wings that stretch out from both poles of Io into the two Jovian hemispheres. The form of the current system associated with the Alfvén wings has been disputed, some suggesting that the greatly slowed flow near Io implies that a steady current loop links Io to Jupiter's ionosphere, others arguing that the return waves appear only downstream of Io and others suggesting that both forms develop. Given the finite inclination of the Alfvén wings implied by the finite value of the Alfvén Mach number and the strong reflection that occurs at the boundary of the Io torus, we argue that no steady current loop can be invoked between Io and Jupiter's ionosphere. However, the energetics of the auroral and radio emissions imply that most of the energy in the Alfvén wings is transformed into electron acceleration at high-latitudes, that is, outside the Io torus. The dilemma then is to understand how a large fraction of the power penetrates the reflecting boundary. We present data from Galileo's multiple flybys of Io that suggest that the coupling with the Jovian ionosphere is mediated by filamentary Alfvén wings associated with electromagnetic waves propagating out of the torus. In particular, we report on the systematic observation, within the cross-section of Io's Alfvén wings and in their immediate vicinity, of intense electromagnetic waves at frequencies up to several times the proton gyrofrequency. We interpret these “high-frequency/small-scale” waves as the signature of a strong filamentation/fragmentation of the Alfvén wings before they reflect off of the sharp boundary gradient of the Io torus. As a consequence, we suggest that most of the primary energy is converted into “high-frequency/small-scale” electromagnetic waves that can propagate out from the torus toward Jupiter's ionosphere. Reaching high-latitudes, these waves are able to accelerate electrons to almost relativistic speeds.     

The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense–Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12,270 km of the existing LAGEOS and inclination i = 70°) by inserting the new spacecraft in a relatively low, and cheaper, orbit (a = 7500–8000 km, i  70°) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first two even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J₂, J₄ along with their temporal variations , . The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to 1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K₁ tidal perturbation, would amount to 10² days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.     

Asperity models and characteristic earthquakes

Summary. An asperity model is presented, including the effects of coupled elementary faults. This coupling is introduced by way of percolation theory. We postulate that the elementary faults have a typical size, whose dimensions are of order 0.3–0.4 km, and two kinds of characteristic earthquakes are obtained, one in the low magnitude range involving the rupture of a single elementary fault, and one in the high magnitude range involving a percolated cluster of faultlets, whose dimensions are proportional to the total fault. The magnitude–frequency relation of this model is constructed and the Gutenberg–Richter relation is obtained with a b value of 1 in the range of intermediate earthquakes. A relative enhancement in the probability of occurrence of large earthquakes is also observed. This effect is associated with 'characteristic earthquakes', whose magnitudes are related to the size of the active fault. Possible premonitors are discussed.     

Pollen percentages,tree abundances and the Fagerlind effect

Pollen diagrams traditionally are read as if pollen percentages were linearly related to relative tree abundances, although the slopes and intercepts of these relationships are accepted to differ among taxa. Corresponding map patterns of modern pollen and tree percentages support this assumption of linearity, which also underlies the use of linear regression on percentage data for pollen-tree calibration. Fagerlind, however, showed that the theoretical relationship need not be linear and may be confounded by interdependencies among taxa. Regressions and scatter plots of modern pollen and tree percentages are here compared with results of extended R-value (ERV) models, which correct for the ‘Fagerlind effect’. Three data sets from Wisconsin and Michigan, USA illustrate that regression coefficients provide a first approximation to their ERV equivalents, but scatter plots derived from the ERV analyses show reduced scatter about linearised relationships.