Trend-surface analysis

This paper is largely an exposition of the work of the French geostatistian G. Matheron and his school in English and at a simpler mathematical level. The probability theory on which it is based is essentially all contained in the references cited, most of which will be unfamiliar to mathematical geologists. The important method of universal kriging is explained intuitively. The genuine statistical problems, which have yet to be overcome, are pointed out.Research supported by the Office of Naval Research under contract NONR 4010(09) awarded to the Department of Statistics, The Johns Hopkins University. This paper in whole or in part may be reproduced for any purpose of the United States Government.     

Generalized Born scattering of elastic waves in 3-D media

It is well known that when a seismic wave propagates through an elastic medium with gradients in the parameters which describe it (e.g. slowness and density), energy is scattered from the incident wave generating low-frequency partial reflections. Many approximate solutions to the wave equation, e.g. geometrical ray theory (GRT), Maslov theory and Gaussian beams, do not model these signals. The problem of describing partial reflections in 1-D media has been extensively studied in the seismic literature and considerable progress has been made using iterative techniques based on WKBJ, Airy or Langer type ansätze. In this paper we derive a first-order scattering formalism to describe partial reflections in 3-D media. The correction term describing the scattered energy is developed as a volume integral over terms dependent upon the first spatial derivatives (gradients) of the parameters describing the medium and the solution. The relationship we derive could, in principle, be used as the basis for an iterative scheme but the computational expense, particularly for elastic media, will usually prohibit this approach. The result we obtain is closely related to the usual Born approximation, but differs in that the scattering term is not derived from a perturbation to a background model, but rather from the error in an approximate Green's function. We examine analytically the relationship between the results produced by the new formalism and the usual Born approximation for a medium which has no long-wavelength heterogeneities. We show that in such a case the two methods agree approximately as expected, but that in a media with heterogeneities of all wavelengths the new gradient scattering formalism is superior. We establish analytically the connection between the formalism developed here and the iterative approach based on the WKBJ solution which has been used previously in 1-D media. Numerical examples are shown to illustrate the examples discussed.     

Exhumation during oblique transpression: The Feiran–Solaf region, Egypt

The Feiran–Solaf metamorphic complex of Sinai, Egypt, is one of the highest grade metamorphic complexes of a series of basement domes that crop out throughout the Arabian-Nubian Shield. In the Eastern Desert of Egypt these basement domes have been interpreted as metamorphic core complexes exhumed in extensional settings. For the Feiran–Solaf complex an interpretation of the exhumation mechanism is difficult to obtain with structural arguments as all of its margins are obliterated by post-tectonic granites. Here, metamorphic methods are used to investigate its tectonic history and show that the complex was characterized by a single metamorphic cycle experiencing peak metamorphism at ∼700–750 °C and 7–8 kbar and subsequent isothermal decompression to ∼4–5 kbar, followed by near isobaric cooling to 450 °C. Correlation of this metamorphic evolution with the deformation history shows that peak metamorphism occurred prior to the compressive deformation phase D ₂, while the compressive D ₂ and D ₃ deformation occurred during the near isothermal decompression phase of the P–T loop. We interpret the concurrence of decompression of the P–T path and compression by structural shortening as evidence for the Najd fault system exhuming the complex in an oblique transpressive regime. However, final exhumation from ∼15 km depth must have occurred due to an unrelated mechanism.     

Model for large strain consolidation with compressible pore fluid

A numerical model, called CCPF1 (C onsolidation with C ompressible P ore F luid 1 ), is presented for one‐dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

A hybrid Bayesian back‐propagation neural network approach to multivariate modelling

There is growing interest in the use of back‐propagation neural networks to model non‐linear multivariate problems in geotehnical engineering. To overcome the shortcomings of the conventional back‐propagation neural network, such as overfitting, where the neural network learns the spurious details and noise in the training examples, a hybrid back‐propagation algorithm has been developed. The method utilizes the genetic algorithms search technique and the Bayesian neural network methodology. The genetic algorithms enhance the stochastic search to locate the global minima for the neural network model. The Bayesian inference procedures essentially provide better generalization and a statistical approach to deal with data uncertainty in comparison with the conventional back‐propagation. The uncertainty of data can be indicated using error bars. Two examples are presented to demonstrate the convergence and generalization capabilities of this hybrid algorithm. Copyright © 2003 John Wiley & Sons, Ltd.     

Microplane constitutive model for porous isotropic rocks

The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane‐type constitutive model for hardening and softening non‐linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shear‐enhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress–strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete—an artificial rock. The model is intended for large explicit finite‐element programs. Copyright © 2002 John Wiley & Sons, Ltd.     

BOOK REVIEWS

Book Reviewed in this article: Marine Resources of Kuwait: Their Role in the Development of Non-oil Resources . Fatimah H. Y. al -Abdul -Razzak Recollections of a Revolution: Geography as Spatial Science . Mark Billinge , Derek Gregory and Ron Martin Entre l'Eden et l'Utopie . Luc Bureau Developments in Political Geography . M. A. Busteed The Elements of Graphing Data . William S. Cleveland Rural Resource Management . Paul J. Cloke and Chris C. Park Third World Atlas . Ben Crow and Alan Thomas Exploitation, Conservation, Preservation: A Geographic Perspective on Natural Resource Use . Susan L. Cutter , Hilary Lambert Renwick, and William H. Renwick . Wine Regions of the Southern Hemisphere . Harm Jan de Blij Regional Development: Problems and Policies in Eastern and Western Europe . George Demko The Geographer at Work . Peter R. Gould Change in the Amazon Basin . John Hemming Geography Since the Second World War . R. J. Johnston and P. Claval Urbanization in China: Town and Countryside in a Developing Economy 1949–2000 A.D. , R. J. R. Kirkby Transport and Communications for Pacific Microstates: Issues in Organisation and Management . Christopher C. Kissling Fluvial Forms and Processes . David Knighton The Urban Millennium . Josef W. Konvitz Technological Transition in Cartography . Mark Stephen Monmonier Field Guide to Soils and the Environment: Applications of Soil Surveys . Gerald W. Olson Northern Australia: The Arenas of Life and Ecosystems on Half a Continent . Don Parkes A Killing Rain: The Global Threat of Acid Rain . Thomas Pawlick From the Family Farm to Agribusiness: The Irrigation Crusade in California and the West, 1850–1931 . Donald J. Pisani Hybrid Maize Diffusion in Kenya . Franz -Michael Rundquist Warning and Response to the Mount St. Helens Eruption . Thomas F. Saarinen and James L. Sell Coastal Geomorphology in Australia . B. G. Thom Tropical Rain Forests of the Far East , 2nd ed . T. C. Whitmore The Dark Side of the Earth . Robert Muir Wood Categorical Data Analysis for Geographers and Environmental Scientists , Neil Wrigley     

Surface sediment analysis of a rock glacier

Three trend surface techniques are used to evaluate the nature and distribution of the surface sediments of a rock glacier. Trend surface analysis, vector trend analysis, and most predictable surface (MPS)mapping suggest that long-term rock glacier creep causes the highly variable debris cover to display crude sorting and orientation patterns. Poorly sorted and randomly oriented surface materials may be the result of insufficient time for slowly evolving rock glacier sediment distributions to be established and/or the site of glacial erosion or deposition.