Mathematical Geophysics
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Mathematical Geophysics
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Author : N.J. Vlaar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Geophysics written by N.J. Vlaar 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.
The contributions to this book follow a topical trend. In several geophysical fields evidence is accumulating concerning the deviation of the earth's structure from radial symmetry. Seismology provides the most adequate resolution for revealing the earth's lateral inhomogeneity on a global to local scale. Lateral structure in the density distribution is also manifest in the earth's gravity field and in the geoid. Asphericity in physical parameters, generally supposed only to vary with the vertical coordinate, has a profound influence on geodynamics. The effects of these deviations from spherical symmetry concern in particular convection theory, post-glacial rebound and the dynamics of the lithosphere and upper mantle in general. At the 16th International Conference on Mathematical Geophysics which was held in Oosterbeek, the Netherlands, in 1986, the need was felt to present the state of the art. Several prospective authors were found interested to contribute to the present book. This Oosterbeek conference was one in a long series of topical conferences starting with the Upper Mantle Project Symposia on Geophysical Theory and Computers in the 1960s, and thence their successors, the conferences on Mathematical Geophysics, until the present.
Mathematical Methods For Geophysics And Space Physics
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Author : William I. Newman
language : en
Publisher: Princeton University Press
Release Date : 2016-05-03
Mathematical Methods For Geophysics And Space Physics written by William I. Newman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-03 with Science categories.
Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors
Mathematical Geophysics
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Author : Jean-Yves Chemin
language : en
Publisher: Clarendon Press
Release Date : 2006-04-13
Mathematical Geophysics written by Jean-Yves Chemin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Science categories.
Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.
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 Geophysics
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Author : Jean-Yves Chemin
language : en
Publisher: Oxford University Press on Demand
Release Date : 2006-04-13
Mathematical Geophysics written by Jean-Yves Chemin and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Mathematics categories.
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
Mathematical And Computational Models Of Flows And Waves In Geophysics
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Author : Gerardo Hernández-Dueñas
language : en
Publisher: Springer Nature
Release Date : 2022-11-03
Mathematical And Computational Models Of Flows And Waves In Geophysics written by Gerardo Hernández-Dueñas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-03 with Mathematics categories.
This volume proposes an integral approach to studying the geophysics of Earth. It is motivated by a variety of phenomena from nature with deep and direct impacts in our lives. Such events may evolve across a large range of spatial and time scales and may be observed in the ocean, the atmosphere, the volcanic surface as well as underground. The physical laws dictating the evolution of such phenomena lead to the unifying theme of this manuscript, that is, the mathematical and computational modeling of flows and waves. Consequently, the underlying models are given in terms of Partial Differential Equations (PDEs) whose solutions are approximated using numerical methods, thus providing simulations of the aforementioned phenomena, as well as the appropriate geophysical validation and interpretation.
Geomathematics
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Author : Volker Michel
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-28
Geomathematics written by Volker Michel 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 2022-04-28 with Mathematics categories.
A comprehensive summary of the fundamental mathematical principles behind key topics in geophysics and geodesy. Each section begins with a problem in gravimetry, geomagnetics or seismology and analyses its mathematical features. With each chapter ending with a series of review questions, this is a valuable reference for students and researchers.
Theory And Practice Of Geophysical Data Inversion
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Author : Andreas Vogel
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2012-12-06
Theory And Practice Of Geophysical Data Inversion written by Andreas Vogel and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The contributions to this volume cover a wide spectrum of recent developments in geophysical data inversion, including basic mathematics and general theory, numerical methods, as well as computer implementation of algorithms. Most of the papers are motivated by problems arising from geophysical research and applications both on a global scale and with respect to local geophysical surveys, underlining the increasing importance of geophysical exploration methods in various fields, such as structural geology, prospecting for mineral and energy resources, hydro geology, geotechnology, environmental protection and archaeology. The first section of the book deals with basic mathematics and general theory underlying geophysical data inversion. Papers presented here are concerned with stabilization algorithms to solve ill-posed inverse problems, sensitivity of kernel function estimations to random data errors and reduction of errors in inverse modelling of response functions by linear constraints, numerical procedures for approximating the solution to boundary value problems, accuracy and stability of inverse ill-posed problems constituted by problems of moments, and fast Fourier transforms for solving potential field problems. The second section contains papers on gravity and magnetics, dealing with the solvability of the inverse gravimetric problem for sources represented by point masses and other elementary, solution of the inverse problem in cases of nonuniformly distributed data as obtained by palaeomagnetic studies, satellite observations, and surface projections of buried archaeological targets by inverse filtering of geomagnetic data.
Geophysical Data Inversion Methods And Applications
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Author : Andreas Vogel
language : de
Publisher: Springer-Verlag
Release Date : 2013-03-09
Geophysical Data Inversion Methods And Applications written by Andreas Vogel and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
Geomathematics Theory And Applications Volume I
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Author : Virginia Williams
language : en
Publisher: Clanrye International
Release Date : 2023-09-12
Geomathematics Theory And Applications Volume I written by Virginia Williams and has been published by Clanrye International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.
Geomathematics is the application of mathematical methods to solve problems in geosciences, including geology and geophysics. It is also called mathematical geophysics. There are several applications of geomathematics in different areas such as data assimilation, geophysics, terrestrial tomography, crystallography, geomorphology, glaciology and geophysical statistics. The field of geomorphology involves the application of geomathematics by using mathematical methods related to soil and water. It includes the application of various mathematical concepts such as Darcy's law, Stoke's law, stream power and differential equations. Seismic tomography, a technique used for the imaging of the subsurface of the Earth by using seismic waves, also makes extensive use of geomathematics. This book provides a detailed explanation of geomathematics. Its extensive content provides the readers with a thorough understanding of the theory and applications of this field. Coherent flow of topics, student-friendly language, and extensive use of examples make this book an invaluable source of knowledge.