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Mathematical Aspects Of Seismology

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Author : Markus Båth
language : en
Publisher: Elsevier
Release Date : 2013-09-24

Mathematical Aspects Of Seismology written by Markus Båth and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Science categories.

Developments in Solid Earth Geophysics, 4: Mathematical Aspects of Seismology introduces studies of the more advanced parts of theoretical seismology. The manuscript first ponders on contour integration and conformal transformation, methods of stationary phase and steepest descent, and series integration. Discussions focus on Love waves in heterogeneous isotropic media, Laguerre's differential equation, Hermite's differential equation, method of steepest descent, method of stationary phase, contour integration in the complex plane, and conformal transformation. The text then examines series integration, Bessel functions, Legendre functions, and wave equations. Topics include general considerations of the wave equation, expansion of a spherical wave into plane waves, common features of special functions and special differential equations, applications of Legendre functions, Legendre polynomials, Bessel's differential equation, and properties of Bessel coefficients. The book explores the influence of gravity on wave propagation, matrix calculus, wave propagation in liquid media, integral equations, calculus of variations, and integral transforms. The text is a valuable source of data for researchers wanting to study the mathematical aspects of seismology.

Mathematical Aspects Of Seismology

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Author : Markus Båth
language : en
Publisher:
Release Date : 1984

Mathematical Aspects Of Seismology written by Markus Båth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Seismology categories.

Mathematical Aspects Of Seismology

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Author : Markus Bath
language : en
Publisher:
Release Date : 1968

Mathematical Aspects Of Seismology written by Markus Bath and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.

Seismic Waves And Sources

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Author : A. Ben-Menahem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Seismic Waves And Sources written by A. Ben-Menahem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Earthquakes come and go as they please, leaving behind them trails of destruc tion and casualties. Although their occurrence is little affected by what we do or think, it is the task of earth scientists to keep studying them from all possible angles until ways and means are found to divert, forecast, and eventually control them. In ancient times people were awestruck by singular geophysical events, which were attributed to supernatural powers. It was recognized only in 1760 that earthquakes originated within the earth. A hundred years later, first systematic attempts were made to apply physical principles to study them. During the next century scientists accumulated knowledge about the effects of earthquakes, their geographic patterns, the waves emitted by them, and the internal constitution of the earth. During the past 20 years, seismology has made a tremendous progress, mainly because of the advent of modern computers and improvements in data acquisi tion systems, which are now capable of digital and analog recording of ground motion over a frequency range of five orders of magnitude. These technologic developments have enabled seismologists to make measurements with far greater precision and sophistication than was previously possible. Advanced computational analyses have been applied to high-quality data and elaborate theoretical models have been devised to interpret them. As a result, far reaching advances in our knowledge of the earth's structure and the nature of earthquake sources have occurred.

Waves And Rays In Seismology Answers To Unasked Questions Third Edition

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Author : MICHAEL A. SLAWINSKI
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-11-13

Waves And Rays In Seismology Answers To Unasked Questions Third Edition written by MICHAEL A. SLAWINSKI and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with categories.

This is a book on seismology dealing with advanced aspects of wave propagation in complex media. It can also be viewed as a book on mathematical modelling, wherein the accuracy of describing seismic phenomena exemplifies the modelling itself. The book gives an insight into the power of abstractness by applying the same mathematical methods and strategies to solve a variety of different physical problems. This book covers a broad range of topics in an advanced yet accessible manner. Each chapter is accompanied by a number of solved exercises, which render the book convenient for a lecturer and facilitate its use for an independent study. The details of mathematical methods are discussed in the appendices, which form a substantial portion of the book.

Seismic Waves And Rays In Elastic Media

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Author : M.A. Slawinski
language : en
Publisher: Elsevier
Release Date : 2003-08-04

Seismic Waves And Rays In Elastic Media written by M.A. Slawinski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-04 with Science categories.

This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves. The book is divided into three parts: Elastic continua, Waves and rays, and Variational formulation of rays. In Part I, continuum mechanics are used to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such material. In Part II, these equations are used to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, the high-frequency approximation is used and establishes the concept of a ray. In Part III, it is shown that in elastic continua a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary travel time.

Introduction To Seismology

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Author : M. Bath
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Introduction To Seismology written by M. Bath and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.

To Seismology Second, Revised Edition 1979 Springer Basel AG First published under Markus Bath, Introduktion till Seism%gin by Natur och Kultur Stockholm © 1970, Markus Bath and Bokforlaget Natur och Kultur, Stockholm CIP-Kurztitelaufnahme der Deutschen Bibliothek Bath, Markus: Introduction to seismology / Markus Bath. - 2., rev. ed. (Wissenschaft und Kultur; Bd. 27) Einheitssacht. : Introduktion till seismologin (dt.) ISBN 978-3-0348-5285-2 ISBN 978-3-0348-5283-8 (eBook) DOI 10. 1007/978-3-0348-5283-8 All rights reserved No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the publisher English translation © 1973, 1979 Springer Basel AG Urspriinglich erschienen bei Birkhlluser Verlag Basel 1979 Softcover reprint of tbe hardcover 2nd edition 1979 ISBN 978-3-0348-5285-2 The data must be greatly amplified Preface and strengthened. to the First Edition BE NO GUTENBERG (1959) The purpose of this book is to give a popular review of modern seismology, its research methods, problems of current interest and results and also to some extent to elucidate the historical background. Especially in recent years, seismology has attracted much interest from the general public as well as from news agencies. The reasons for this are partly con nected with recordings of large explosions (nuclear tests), partly related to earthquake catastrophes. This interest and the questions which people have asked us for the past years have to a certain extent served as a sti mulus in the preparation of this book.

Waves And Rays In Seismology Answers To Unasked Questions Third Edition

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Author : Michael A Slawinski
language : en
Publisher: World Scientific
Release Date : 2020-11-20

Waves And Rays In Seismology Answers To Unasked Questions Third Edition written by Michael A Slawinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-20 with Science categories.

Waves And Rays In Seismology Answers To Unasked Questions Second Edition

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Author : Slawinski Michael A
language : en
Publisher: World Scientific
Release Date : 2018-05-04

Waves And Rays In Seismology Answers To Unasked Questions Second Edition written by Slawinski Michael A and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.

The author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology -- and in a larger sense, the theory of wave propagation in solids -- is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation. In the second edition, new sections, figures, examples, exercises and remarks are added. Most importantly, however, four new appendices of about one-hundred pages are included, which can serve as a self-contained continuum-mechanics course on finite elasticity. Also, they broaden the scope of elasticity theory commonly considered in seismology. Contents: Science of Seismology Seismology and Continuum Mechanics Hookean Solid: Material Symmetry Hookean Solid: Effective Symmetry and Equivalent Medium Body Waves Surface, Guided and Interface Waves Variational Principles in Seismology Gravitational and Thermal Effects in Seismology Seismology as Science Appendices: On Strains On Stresses On Thermoelasticity On Hyperelasticity On Covariant and Contravariant Transformations On Covariant Derivatives List of Symbols Readership: Students, professionals, researchers, and laypersons interested in seismology. Keywords: Elasticity Theory;Inverse Problems;Seismology;Continuum Mechanics;Mathematical PhysicsReview: "This one-of-a-kind book is refreshing in its presentation of an amazing blend of fundamental scientific and philosophical questions with their practical implications to concrete examples in Seismology. It is refined in its style, in the sophistication of its quotes, in the breadth of its sources and in the many details that reveal a labour of love. As an additional bonus, the book is also extremely useful. It presents the underlying theory of the relevant aspects of Continuum Mechanics in a clear and sufficiently rigorous way, while challenging the reader's intellect at every step of the way ... This inspiring book is highly recommended." Professor Marcelo Epstein University of Calgary, Canada "This book provides an extensive and self-contained treatment of the mathematical theory of wave propagation in elastic continua, with special attention to topics, some of them well advanced, which are most important for their applications in geophysics ... The author's wide culture, clear style and rigorous approach make this book a first foundation stone of a field which should be called Rational Seismology." Professor Maurizio Vianello Politecnico di Milano, Italy 0

Mathematical Problems In Seismology

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Author : William J. Byatt
language : en
Publisher:
Release Date : 1961

Mathematical Problems In Seismology written by William J. Byatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Seismology categories.

This report deals with mathematical problems in seismology. Homogeneous and layered half-spaces are discussed. Expressions are found for the displacement caused by a point source in such models. Numerical results are presented for the displacement caused by the sudden injection of a volume into a homogeneous half-space after the model of E. Pinney. Pinney's results are extended. Numerical ray-tracing calculations are presented. Most of the original work in the report is chiefly concerned with the development of an iteration-variation method for solving wave equations in media of variable index of refraction. This method is promising and is being actively investigated.

Mathematical Aspects Of Seismology

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