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Author: L. Eskola Publisher: Springer Science & Business Media ISBN: 9401123705 Category : Mathematics Languages : en Pages : 203
Book Description
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a background in the fundamental field theories that form the basis for various geophysical methods, such as potential theory, electromagnetic theory, and elastic strain theory. A fairly extensive knowledge of mathematics, especially in vector and tensor calculus, is also assumed.
Author: L. Eskola Publisher: Springer Science & Business Media ISBN: 9401123705 Category : Mathematics Languages : en Pages : 203
Book Description
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a background in the fundamental field theories that form the basis for various geophysical methods, such as potential theory, electromagnetic theory, and elastic strain theory. A fairly extensive knowledge of mathematics, especially in vector and tensor calculus, is also assumed.
Author: Balgaisha Mukanova Publisher: Springer ISBN: 331972908X Category : Science Languages : en Pages : 162
Book Description
This volume is devoted to the application of the integral equations method (IEM) and boundary elements method (BEM) to problems involving the sounding of geological media using direct current (DC). Adaptive mesh generation algorithms and numerical methods for solving a system of integral equations are discussed. Integral equations for the media, which contains piecewise linear contact boundaries, immersed local inclusions, and subsurface relief, are derived and solved numerically. Both 2.5D and 3D models with ground surface relief are considered. For 2D conductivity distributions, the influence of the relief on the interpretation of results is shown. Search solutions of the direct problem with ground surface relief are compared using the appropriate interpretation of results based on different inversion programs.
Author: Michael S. Zhdanov Publisher: Springer Science & Business Media ISBN: 3642726283 Category : Science Languages : en Pages : 382
Book Description
Integral Transforms of Geophysical Fields serve as one of the major tools for processing and interpreting geophysical data. In this book the authors present a unified treatment of this theory, ranging from the techniques of the transfor- mation of 2-D and 3-D potential fields to the theory of se- paration and migration of electromagnetic and seismic fields. Of interest primarily to scientists and post-gradu- ate students engaged in gravimetrics, but also useful to geophysicists and researchers in mathematical physics.
Author: P. S. Martyshko Publisher: Walter de Gruyter GmbH & Co KG ISBN: 311094328X Category : Mathematics Languages : en Pages : 128
Book Description
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Author: R. Cassinis Publisher: Springer Science & Business Media ISBN: 1468439626 Category : Science Languages : en Pages : 371
Book Description
As is apparent from the table of contents, the lectures at the Third Course of the International School of Applied Geophysics, Erice, March 27-April 4, 1980 (the first part of this volume) dealt with several applications of inversion to different geophy sical methods. For every field, the more general lectures come first, followed by those aimed at more specialized objectives. Not all topics are covered and the coverage is not uniform. The seismological section (especially the seismic reflection methods) is the most developed, and this is only partly due to the actual state of the art. Unfortunately, only abstracts are available for two of the lectures. The second part of the volume contains some short notes and contributions presented either by the lecturers themselves or by other participants. They do not necessarily deal with the process of inversion itself but with the preparation and meaning of the data to be inverted or with some original treatments of problems that were discussed in the afternoon sessions. The discussion sessions and the round table that followed the lectures were essential to the success of the Course and to an understanding ot the difterent perspectives of the various specialists. I hope that the group of very brilliant and willing geophysi cists that made the meeting so interesting will stay ~n touch, grow closer, and meet again. Close scientific cooperation among them could contribute much to the "unification" of geophysical science.
Author: Rudolf Gorenflo Publisher: Springer ISBN: 3540469494 Category : Mathematics Languages : en Pages : 225
Book Description
In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Author: L. Eskola
Author: L. Eskola
Author: Balgaisha Mukanova
Author: Michael S. Zhdanov
Author: P. S. Martyshko
Author: R. Cassinis
Author: Andreas Vogel
Author: Rudolf Gorenflo
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Author: 
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