Wavefronts And Rays As Characteristics And Asymptotics 2nd Edition
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Wavefronts And Rays As Characteristics And Asymptotics Third Edition
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Author : Andrej Bona
language : en
Publisher: World Scientific
Release Date : 2020-09-24
Wavefronts And Rays As Characteristics And Asymptotics Third Edition written by Andrej Bona 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.
Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.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 senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
Wavefronts And Rays As Characteristics And Asymptotics
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Author : Andrej B¢na
language : en
Publisher: World Scientific
Release Date : 2011
Wavefronts And Rays As Characteristics And Asymptotics written by Andrej B¢na and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
This textbook ? incorporated with many illuminating examples and exercises ? is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation ? by a pure mathematician's standards ? is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.
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.
Wavefronts And Rays
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Author : Andrej Bóna
language : en
Publisher:
Release Date : 2014
Wavefronts And Rays written by Andrej Bóna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Electronic books categories.
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.
An Introduction To Geometrical Physics
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Author : Aldrovandi Ruben
language : en
Publisher: World Scientific
Release Date : 2016-10-07
An Introduction To Geometrical Physics written by Aldrovandi Ruben and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-07 with Science categories.
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Wavefronts And Rays As Characteristics And Asymptotics Third Edition
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Author : Andrej Bona
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-09-14
Wavefronts And Rays As Characteristics And Asymptotics Third Edition written by Andrej Bona 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 2020-09-14 with Mathematics categories.
Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research. 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 senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
On Foundations Of Seismology Bringing Idealizations Down To Earth
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Author : James Robert Brown
language : en
Publisher: World Scientific
Release Date : 2017-04-27
On Foundations Of Seismology Bringing Idealizations Down To Earth written by James Robert Brown and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-27 with Science categories.
'I can wholeheartedly recommend this book students, researchers, college and university science professors, and readers of The Leading Edge. I also recommend it to all those who want to enrich their own experience of practicing and teaching science with some carefully considered soul searching on how it all fits together in the human story of ‘figuring things out’ … It is written throughout with precise and careful language: prudently paced, carefully crafted, eloquently enunciated, and playfully illuminated.'The Leading EdgeThis remarkable collaboration between a mathematical physicist and a science philosopher concerns foundational and conceptual issues in seismology. Their aim is to present mathematical, physical and philosophical topics in a clear and concise manner. They provide an extensive philosophical discussion of the methods of science and show how seismology fits in. They explain with care and precision the basic structure of seismology, which is built on classical continuum mechanics. Not only do they explain how various models work in seismology, they also include an extensive discussion of the nature of models and idealizations.
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.
Introduction To Petroleum Seismology Second Edition
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Author : Luc T. Ikelle
language : en
Publisher: SEG Books
Release Date : 2018-03-26
Introduction To Petroleum Seismology Second Edition written by Luc T. Ikelle and has been published by SEG Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Science categories.
Introduction to Petroleum Seismology, second edition (SEG Investigations in Geophysics Series No. 12) provides the theoretical and practical foundation for tackling present and future challenges of petroleum seismology especially those related to seismic survey designs, seismic data acquisition, seismic and EM modeling, seismic imaging, microseismicity, and reservoir characterization and monitoring. All of the chapters from the first edition have been improved and/or expanded. In addition, twelve new chapters have been added. These new chapters expand topics which were only alluded to in the first edition: sparsity representation, sparsity and nonlinear optimization, near-simultaneous multiple-shooting acquisition and processing, nonuniform wavefield sampling, automated modeling, elastic-electromagnetic mathematical equivalences, and microseismicity in the context of hydraulic fracturing. Another major modification in this edition is that each chapter contains analytical problems as well as computational problems. These problems include MatLab codes, which may help readers improve their understanding of and intuition about these materials. The comprehensiveness of this book makes it a suitable text for undergraduate and graduate courses that target geophysicists and engineers as well as a guide and reference work for researchers and professionals in academia and in the petroleum industry.