On Foundations Of Seismology Bringing Idealizations Down To Earth

'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.

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.

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

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.

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.

Volume compiles studies of the production and reproduction of market-supporting social infrastructures through the prism of knowledge commons.

Modern Global Seismology, Second Edition, is a complete, self-contained primer on seismology, featuring extensive coverage of all related aspects-from observational data through prediction-and emphasizing the fundamental theories and physics governing seismic waves, both natural and anthropogenic. Based on thoroughly class-tested material, the text provides a unique perspective on Earth's large-scale internal structure and dynamic processes, particularly earthquake sources, and the application of theory to the dynamic processes of the earth's upper layer. This insightful new edition is designed for accessibility and comprehension for graduate students entering the field. Exploration seismologists will also find it an invaluable resource on topics such as elastic-wave propagation, seismic instrumentation, and seismogram analysis. Includes more than 400 illustrations, from both recent and traditional research articles, to help readers visualize mathematical relationships, as well as boxed features to explain advanced topics Offers incisive treatments of seismic waves, waveform evaluation and modeling, and seismotectonics, as well as quantitative treatments of earthquake source mechanics and numerous examples of modern broadband seismic recordings Covers current seismic instruments and networks and demonstrates modern waveform inversion methods Includes extensive, updated references for further reading new to this edition Features reorganized chapters split into two sections, beginning with introductory content such as tectonics and seismogram analysis, and moving on to more advanced topics, including seismic wave excitation and propagation, multivariable and vector calculus, and tensor approaches Completely updated references and figures to bring the text up to date Includes all-new sections on recent advancements and to enhance examples and understanding Split into shorter chapters to allow more flexibility for instructors and easier access for researchers, and includes exercises

1. What is geophysics? -- 2. Planet Earth -- 3. Seismology and the Earth's internal structure -- 4. Siesmicity--the restless Earth -- 5. Gravity and the figure of the Earth -- 6. The Earth's heat -- 7. The Earth's magnetic field -- 8. Afterthoughts