Download or read book Mathematical Problems in Seismology written by William J. Byatt and published by . This book was released on 1961 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Aspects of Seismology written by Markus Båth and published by Elsevier. This book was released on 2013-09-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics for Seismic Data Processing and Interpretation written by A.R. Camina and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the growth of modern computing power it has become possible to apply far more mathematics to real problems. This has led to the difficulty that many people who have been working in various jobs suddenly find themselves not understanding the modern processing which is being applied to their own professional field. It also means that the people presently being trained in these subjects need to understand a much wider range of mathe matics than in the past. It is to both of these groups that this book is addressed. The major objective is to present the reader with the basic mathematical understanding to follow the new developments in their own field. The mathematics in this book is based on the need to understand signal process ing. The modern work in this area is mathematically very sophisticated and our purpose is not to train professional mathematicians but to make far more of the literature accessible. Since this book is based on courses devised for Racal Geophysics there is clearly going to be a bias towards the applications in that area, as the title implies. It is also true that the bibliogra phy has been chosen in order to aid the reader in that field by pointing them in the direction of recent applications in geophysics.
Download or read book Mathematics of Multidimensional Seismic Imaging Migration and Inversion written by N. Bleistein and published by Springer Science & Business Media. This book was released on 2000-12-15 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.
Download or read book Geomathematics written by Volker Michel and published by Cambridge University Press. This book was released on 2022-04-28 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter ends with review questions, with solutions for instructors available online, providing a valuable reference for graduate students and researchers.
Download or read book Inverse Problems of Mathematical Physics written by V. G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Inverse Problems of Mathematical Physics".
Download or read book On Foundations Of Seismology Bringing Idealizations Down To Earth written by James Robert Brown and published by World Scientific. This book was released on 2017-04-27 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Download or read book Waves And Rays In Seismology Answers To Unasked Questions Third Edition written by Michael A Slawinski and published by World Scientific. This book was released on 2020-11-20 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics of Multidimensional Seismic Imaging Migration and Inversion written by N. Bleistein and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.
Download or read book Mathematical Aspects of Seismology written by Markus Bath and published by . This book was released on 1968 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Waves And Rays In Seismology Answers To Unasked Questions Third Edition written by MICHAEL A. SLAWINSKI and published by World Scientific Publishing Company. This book was released on 2020-11-13 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Aspects of Seismology written by Markus Båth and published by . This book was released on 1984 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seismology Surface Waves and Earth Oscillations written by Bruce Bolt and published by Elsevier. This book was released on 2012-12-02 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Computational Physics, Volume 11: Seismology: Surface Waves and Earth Oscillations is a five-chapter text that deals with the computational analysis of surface waves and the eigenvibrations of the Earth. Chapter 1 describes the advances in the numerical modeling of geological structures where the appropriate partial differential equations with boundary conditions for heterogeneous materials are solved using an intricate finite difference scheme. Chapter 2 presents the computer techniques of processing seismograms to obtain information on the dispersion of seismic surface waves, while Chapter 3 explains the fast algorithms for computation of eigenvalues in surface wave and terrestrial eigenvibration problems. Chapter 4 presents a competing method, much used in structural engineering and soil mechanics. Chapter 5 is devoted to the propagation of surface waves in layered media, which indicate that density and elasticity vary only in the vertical direction. This chapter also provides the fundamentals and numerical aspects of the theory of seismic surface waves. This book is an invaluable source for seismologists, earthquake engineers, and graduate students.
Download or read book Waves And Rays In Seismology Answers To Unasked Questions Second Edition written by Slawinski Michael A and published by World Scientific. This book was released on 2018-05-04 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Inverse Problems of Mathematical Physics written by Vladimir Gavrilovich Romanov and published by BRILL. This book was released on 1987 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to the Theory of Seismology written by Keith Edward Bullen and published by Cambridge University Press. This book was released on 1985-11-14 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical revision of Professor Bullen's acclaimed and widely used text provides an introduction to modern seismological theory, with emphasis on both the physical models and the mathematical descriptions of earthquakes and their sources. The essential core of the earlier editions has been retained, particularly the tensor treatment of elasticity, seismic wave travel-time analysis and density in the Earth, although these parts of the text have been brought up to date and expanded. The new part of the book reflects on how the study of earthquakes, seismic waves and seismic risk has been broadened in the past two decades. Thus, this edition includes introductory theory of earthquake sources, seismic wave travel through complex geological zones and viscous and anisotropic media, vibrations of the whole Earth, strong-motion seismology and earthquake prediction and risk. There is an emphasis on statistical and numerical procedures and problems of resolution in inverse theory. Modern class exercises are to be found throughout. The book assumes some background in classical physics and mathematics, including simple differential equations, linear algebra and probability theory. It will be suitable for use in undergraduate courses in geophysics, applied mechanics and geotechnology and for graduate courses in seismology and earthquake engineering. In addition, it will serve as a reference text on seismological problems for professionals concerned with earthquakes, Earth structure and wave motion.
Download or read book Applied Mathematical Problems in Geophysics written by Massimo Chiappini and published by Springer Nature. This book was released on 2022-07-23 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes. This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.
