Download or read book Wavelt Analysis and Spline Modeling of Geophysical Data on the Sphere written by Michael Hayn and published by . This book was released on 2010 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavelets in the Geosciences written by Roland Klees and published by Springer Science & Business Media. This book was released on 2000-03-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.
Download or read book Wavelets in Geophysics written by Efi Foufoula-Georgiou and published by Elsevier. This book was released on 2014-06-28 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of wavelet analysis to the geophysical sciences grew from Jean Morlet's work on seismic signals in the 1980s. Used to detect signals against noise, wavelet analysis excels for transients or for spatiallylocalized phenomena. In this fourth volume in the renown WAVELET ANALYSIS AND ITS APPLICATIONS Series, Efi Foufoula-Georgiou and Praveen Kumar begin with a self-contained overview of the nature, power, and scope of wavelet transforms. The eleven originalpapers that follow in this edited treatise show how geophysical researchers are using wavelets to analyze such diverse phenomena as intermittent atmospheric turbulence, seafloor bathymetry, marine and other seismic data, and flow in aquifiers. Wavelets in Geophysics will make informative reading for geophysicists seeking an up-to-date account of how these tools are being used as well as for wavelet researchers searching for ideas for applications, or even new points of departure. Includes twelve original papers written by experts in the geophysical sciences Provides a self-contained overview of the nature, power, and scope of wavelet transforms Presents applications of wavelets to geophysical phenomena such as: The sharp events of seismic data, Long memory processes, such as fluctuation in the level of the Nile, A structure preserving decomposition of turbulence signals
Download or read book Wavelet Analysis on the Sphere written by Sabrine Arfaoui and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.
Download or read book Wavelets in the Geosciences written by Roland Klees and published by Springer. This book was released on 2014-03-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.
Download or read book Wavelets and Fractals in Earth System Sciences written by E. Chandrasekhar and published by Taylor & Francis. This book was released on 2013-11-20 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of wavelet analysis and fractal analysis is fast developing and has drawn a great deal of attention in varied disciplines of science and engineering. Over the past couple of decades, wavelets, multiresolution, and multifractal analyses have been formalized into a thorough mathematical framework and have found a variety of applications w
Download or read book Wavelets in Geodesy and Geodynamics written by Wolfgang Keller and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many years, digital signal processing has been governed by the theory of Fourier transform and its numerical implementation. The main disadvantage of Fourier theory is the underlying assumption that the signals have time-wise or space-wise invariant statistical properties. In many applications the deviation from a stationary behavior is precisely the information to be extracted from the signals. Wavelets were developed to serve the purpose of analysing such instationary signals. The book gives an introduction to wavelet theory both in the continuous and the discrete case. After developing the theoretical fundament, typical examples of wavelet analysis in the Geosciences are presented. The book has developed from a graduate course held at The University of Calgary and is directed to graduate students who are interested in digital signal processing. The reader is assumed to have a mathematical background on the graduate level.
Download or read book Lectures on Constructive Approximation written by Volker Michel and published by Springer Science & Business Media. This book was released on 2012-12-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.
Download or read book Integration and Cubature Methods written by Willi Freeden and published by CRC Press. This book was released on 2017-11-22 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.
Download or read book Wavelet Domain Inversion and Joint Deconvolution interpolation of Geophysical Data written by Jonathan Andrew Kane and published by . This book was released on 2003 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) A third issue is also addressed, somewhat separate from the first two: the correct manipulation of discrete geophysical data. The theory of fractional splines is introduced, which allows for optimal approximation of real signals on a digital computer. Using splines, it can be shown that a linear operation on the spline can be equivalently represented by a matrix operating on the coefficients of a certain spline basis function. The form of the matrix, however, depends completely on the spline basis, and incorrect discretization of the operator into a matrix can lead to large errors in the resulting matrix/vector product.
Download or read book Spectral Methods in Geodesy and Geophysics written by Christopher Jekeli and published by CRC Press. This book was released on 2016-02-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a rigorous treatment of spectral analysis using Fourier-based techniques in the geosciences, specifically geodesy and geophysics that deal with global and regional spatial data. It emphasizes spatial -frequency analysis for data on the plane and sphere. It includes applications to stochastic processes on the plane and sphere, which are important for many estimation problems that are based on some kind of stochastic constraints in inverse theory. It also briefly outlines wavelet analysis, although unusual, it is included to illustrate the contrast to traditional spectral analysis, going more toward a time-frequency analysis.
Download or read book Spherical Functions of Mathematical Geosciences written by Willi Freeden and published by Springer Nature. This book was released on 2022 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2000 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 International Reference Ionosphere and Solar Activity Variations written by D. Bilitza and published by . This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat and published by Elsevier. This book was released on 1999-09-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
Download or read book Modeling the Ionosphere Thermosphere written by J. D. Huba and published by John Wiley & Sons. This book was released on 2014-03-17 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 201. Modeling the Ionosphere-Thermosphere System brings together for the first time a detailed description of the physics of the IT system in conjunction with numerical techniques to solve the complex system of equations that describe the system, as well as issues of current interest. Volume highlights include discussions of: Physics of the ionosphere and thermosphere IT system, and the numerical methods to solve the basic equations of the IT system The physics and numerical methods to determine the global electrodynamics of the IT system The response of the IT system to forcings from below (i.e., the lower atmosphere) and from above (i.e., the magnetosphere) The physics and numerical methods to model ionospheric irregularities Data assimilation techniques, comparison of model results to data, climate variability studies, and applications to space weather Providing a clear description of the physics of this system in several tutorial-like articles, Modeling the Ionosphere-Thermosphere System is of value to the upper atmosphere science community in general. Chapters describing details of the numerical methods used to solve the equations that describe the IT system make the volume useful to both active researchers in the field and students.
