Waves And Rays In Elastic Continua
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Waves And Rays In Elastic Continua
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Author : Michael A. Slawinski
language : en
Publisher: World Scientific
Release Date : 2010
Waves And Rays In Elastic Continua 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 2010 with Science categories.
This is the second edition of the textbook that was first published by Elsevier Science. Professor Slawinski has the copyright to the textbook and the second edition is significantly extended. The present book emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves. The book is divided into three main sections: elastic continua, waves and rays and variational formulation of rays. There is also a fourth part, which consists of appendices. In Part 1, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Part 2, we use these equations 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, we use the high-frequency approximation and, hence, establish the concept of a ray. In Part 3, we show 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 traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In Part 4, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.
Waves And Rays In Elastic Continua 3rd Edition
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Author : Michael A Slawinski
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-12-15
Waves And Rays In Elastic Continua 3rd 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 2014-12-15 with Science categories.
The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations 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, we invoke the concept of a ray. In Variational Formulation of Rays, we show 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 traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.
Waves And Rays In Elastic Continua Fourth Edition
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Author : Michael A Slawinski
language : en
Publisher: World Scientific
Release Date : 2020-09-24
Waves And Rays In Elastic Continua Fourth 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 2020-09-24 with Science categories.
Seismology, as a branch of mathematical physics, is an active subject of both research and development. Its reliance on computational and technological advances continuously motivates the developments of its underlying theory. The fourth edition of Waves and Rays in Elastic Continua responds to these needs.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for the senior undergraduate and graduate courses, as well as for an independent study. Used in its entirety, the book could serve as a sole textbook for a year-long course in quantitative seismology. Its parts, however, are designed to be used independently for shorter courses with different emphases. The book is not limited to quantitive seismology; it can serve as a textbook for courses in mathematical physics or applied mathematics.
Seismic Waves And Rays In Elastic Media
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Author : Michael A. Slawinski
language : en
Publisher: Elsevier
Release Date : 2003
Seismic Waves And Rays In Elastic Media written by Michael 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 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.
Waves And Rays In Seismology Answers To Unasked Questions Second Edition
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Author : Michael A Slawinski
language : en
Publisher: World Scientific
Release Date : 2018-05-04
Waves And Rays In Seismology Answers To Unasked Questions Second 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 2018-05-04 with Science categories.
'In summary, Professor Slawinski has written an engaging volume covering an unfamiliar topic in a highly accessible fashion. Non-specialists will gain a significant appreciation of the unique complexities associated with seismology.'Contemporary PhysicsThe 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.
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.
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.
Mathematical Methods For Wave Propagation In Science And Engineering
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Author : Mario Durán
language : en
Publisher: Ediciones UC
Release Date : 2017
Mathematical Methods For Wave Propagation In Science And Engineering written by Mario Durán and has been published by Ediciones UC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This series of books deals with the mathematical modeling and computational simulation of complex wave propagation phenomena in science and engineering. This first volume of the series introduces the basic mathematical and physical fundamentals, and it is mainly intended as a reference guide and a general survey for scientists and engineers. It presents a broad and practical overview of the involved foundations, being useful as much in industrial research, development, and innovation activities, as in academic labors.
Fundamentals Of Ultrasonic Nondestructive Evaluation
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Author : Lester W. Schmerr Jr.
language : en
Publisher: Springer
Release Date : 2016-04-30
Fundamentals Of Ultrasonic Nondestructive Evaluation written by Lester W. Schmerr Jr. and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-30 with Technology & Engineering categories.
This extensively revised and updated second edition of a widely read classic presents the use of ultrasound in nondestructive evaluation (NDE) inspections. Retaining the first edition's use of wave propagation /scattering theory and linear system theory, this volume also adds significant new material including: the introduction of MATLAB® functions and scripts that evaluate key results involving beam propagation and scattering, flaw sizing, and the modeling of ultrasonic systems. elements of Gaussian beam theory and a multi-Gaussian ultrasonic beam model for bulk wave transducers. a new chapter on the connection between ultrasonic modeling and probability of detection (POD) and reliability models. new and improved derivations of ultrasonic measurement models. updated coverage of ultrasonic simulators that have been developed around the world. Students, engineers, and researchers working in the ultrasonic NDE field will find a wealth of information on the modeling of ultrasonic inspections and the fundamental ultrasonic experiments that support those models in this new edition.
Seismic Wave Theory
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Author : Edward S. Krebes
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Seismic Wave Theory written by Edward S. Krebes and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-28 with Mathematics categories.
Concise textbook on seismic wave theory, with detailed derivations of formulas, clear explanations of topics, exercises, and selected answers.