Download or read book A Mathematical Approximation to the Geomagnetic Field written by Robert Earl Wiley (1LT, USAF.) and published by . This book was released on 1966 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Mathematical Approximation to the Geomagnetic Field written by Robert Earl Wiley and published by . This book was released on 1966 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attempt was made to form a mathematical model for calculating the geomagnetic field using fewer terms than presently used in spherical harmonic expansion models. The model was to be made up of pairs of magnetic monopoles. It was found that at least four pairs of monopoles would be needed to produce a satisfactory model. The initial data used for fitting the four pair of monopoles was the geomagnetic field as calculated by a spherical harmonic expansion using the Jensen and Cain coefficients. Emphasis was given to fitting the South Atlantic Anomaly. The root-mean-square error for this region was 1.3 x 10 to the -2 gauss while the overall root-mean-square error was 3.4 x 10 to the -2 gauss. Comparison of the errors of the monopole model with the errors of the Jensen and Cain coefficients indicates that the root-mean-square error for the monopole model is larger than that of the Jensen and Cain coefficients. Additionally, it was found that the monopole model calculations were only 1/3 faster than the spherical harmonic expansion instead of the desired 1/2 or more reduction in calculation time. (Author).
Download or read book Foundations of Geomagnetism written by George Backus and published by Cambridge University Press. This book was released on 1996-02-23 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth's core, and how it changes in time requires a variety of mathematical and physical tools. This book presents the foundations of geomagnetism, in detail and developed from first principles. The book is based on George Backus' courses for graduate students at the University of California, San Diego. The material is mathematically rigorous, but is logically developed and has consistent notation, making it accessible to a broad range of readers. The book starts with an overview of the phenomena of interest in geomagnetism, and then goes on to deal with the phenomena in detail, building the necessary techniques in a thorough and consistent manner. Students and researchers will find this book to be an invaluable resource in the appreciation of the mathematical and physical foundations of geomagnetism.
Download or read book Inverse Magnetometry written by Christian Blick and published by Springer Nature. This book was released on 2021-09-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the geoscientific context arising in decorrelative geomagnetic exploration. First, an insight into the current state of research is given by reducing magnetometry to mathematically accessible, and thus calculable, decorrelated models. In this way, various questions and problems of magnetometry are made available to a broad scientific audience and the exploration industry. New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown. Potential data sets primarily of terrestrial origin constitute the main data basis in the book. For deep geology, the geomathematical decorrelation methods are designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Overall, this book provides pioneering and ground-breaking innovative mathematical knowledge as a transfer methodology from the “reality space” of magnetometric measurements into the “virtual space” of mathematical-numerical modeling structures and mollifier solutions with novel geological application areas. It pursues a double goal: On the one hand, it represents a geoscientific set of rules for today's geoengineering, interested in the application of innovative modelling and simulation techniques to promising data sets and structures occurring in geomagnetics. On the other hand, the book serves as a collection of current material in Applied Mathematics to offer alternative methodologies in the theory of inverse problems.
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 Geomathematically Oriented Potential Theory written by Willi Freeden and published by CRC Press. This book was released on 2012-10-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.
Download or read book The Geomagnetic Field written by David J. Knecht and published by . This book was released on 1972 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Geophysics and Space Environments written by Air Force Cambridge Research Laboratories (U.S.) and published by . This book was released on 1965 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is a comprehensive collection of data, formulas, definitions, and theories concerning the natural environment. It was written by scientists of the Air Force Cambridge Research Laboratories (AFCRL) which, in 1976, became the Air Force Geophysics Laboratory (AFGL). It was designed to serve a broad spectrum of users: the planner, designer, developer, and operator of aerospace systems; the scientist who will find the tables and figures a convenient reference in his own field; the specialist who needs environmental data in another discipline; and science minded people who seek a summary of space-age environmental research. Revisions of individual chapters and sections of this handbook will be published as additional environmental research efforts pay off in new knowledge.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1976 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Paleomagnetic Principles and Practice written by L. Tauxe and published by Springer Science & Business Media. This book was released on 2005-12-17 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paleomagnetic data are useful in many applications in Earth Science from determining paleocurrent directions to analyzing the long-term behavior of the geomagnetic field. In this book, an attempt has been made to draw together the various principles and practices within paleomagnetism in a consistent and up-to-date manner. It includes many practical examples that illustrate various applications of paleomagnetism. A companion software package implements the theory explained in the text. Audience: This volume is aimed at professional Earth Scientists using paleomagnetic data for their research. It is also suitable for use as a text book for students in courses with a paleomagnetic content. In addition, this volume will be of value to other professionals with an interest in the analysis of vector and tensor data in general.
Download or read book Mathematical Methods for Geo electromagnetic Induction written by John Trevor Weaver and published by Taunton, Somerset, England : Research Studies Press ; New York : Wiley. This book was released on 1994 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Magnetic Field of the Earth written by Ronald T. Merrill and published by Academic Press. This book was released on 1998 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics involved in studies of the Earth's magnetic field and its secular variation range from the intricate observations of geomagnetism, to worldwide studies of archeomagnetism and paleomagnetism, through to the complex mathematics of dynamo theory. Traditionally these different aspects of geomagnetism have in the main been studied and presented in isolation from each other. This text draws together these lines of inquiry into an integrated framework to highlight the interrelationships and thus to provide a more comprehensive understanding of the geomagnetic field.
Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 1371 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Download or read book Magnetoconvection written by N. O. Weiss and published by Cambridge University Press. This book was released on 2014-10-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last thirty years have seen great leaps forward in the subject of magnetoconvection. Computational techniques can now explain exotic nonlinear behaviour, transition to chaos and the formation of structures that can be observed on the surface of the Sun. Here, two leading experts present the current state of knowledge of the subject. They provide a mathematical and numerical treatment of the interactions between electrically conducting fluids and magnetic fields that lead to the complex structures and rich behaviour observed on the Sun and other stars, as well as in the interiors of planets like the Earth. The authors' combined analytical and computational approach provides a model for the study of a wide range of related problems. The discussion includes bifurcation theory, chaotic behaviour, pattern formation in two and three dimensions, and applications to geomagnetism and to the properties of sunspots and other features at the solar surface.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1963 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Potential Theory in Gravity and Magnetic Applications written by Richard J. Blakely and published by Cambridge University Press. This book was released on 1996-09-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
