Geomathematically Oriented Potential Theory
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Geomathematically Oriented Potential Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2012-10-30
Geomathematically Oriented Potential Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
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.
Geomathematically Oriented Potential Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2012-10-30
Geomathematically Oriented Potential Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
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 Orien
Multiscale Potential Theory
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Author : Willi Freeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiscale Potential Theory written by Willi Freeden 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 Mathematics categories.
This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.
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.
An Invitation To Geomathematics
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Author : Willi Freeden
language : en
Publisher: Springer
Release Date : 2019-05-17
An Invitation To Geomathematics written by Willi Freeden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Mathematics categories.
The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.
Handbook Of Mathematical Geodesy
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Author : Willi Freeden
language : en
Publisher: Birkhäuser
Release Date : 2018-06-11
Handbook Of Mathematical Geodesy written by Willi Freeden and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.
Integration And Cubature Methods
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Integration And Cubature Methods written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.
Exploratory Potential Methods In Geothermal Power Generation
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Author : Willi Freeden
language : en
Publisher: Springer Nature
Release Date : 2024
Exploratory Potential Methods In Geothermal Power Generation written by Willi Freeden and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Geology categories.
The book provides the geoscientific context, that arises in gravimetric/magnetometric exploration. It essentially uses mathematics as a key technology for modeling issues on the basis of analysis and interpretation according to dense and precise gravitational/magnetic measurements. It is dedicated to surface and deep geology with potential data primarily of terrestrial origin. The book spans the interdisciplinary arc from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back again. It presents the recently published pioneering and groundbreaking multiscale mollifier methodologies realizing the bridging transfer from gravitational/magnetic measurements to approximative/numerical mollifier wavelet decorrelations with novel geologic prospects and layer-structure determination as outcome. Using the specific example of the German Saarland region, new important fields of application, especially for areas with mining-related cavities, will be opened up and subjected to an in-depth geologic detection.
Ix Hotine Marussi Symposium On Mathematical Geodesy
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Author : Pavel Novák
language : en
Publisher: Springer Nature
Release Date : 2020-09-16
Ix Hotine Marussi Symposium On Mathematical Geodesy written by Pavel Novák and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-16 with Science categories.
This volume gathers the proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy, which was held from 18 to 22 June 2018 at the Faculty of Civil and Industrial Engineering, Sapienza University of Rome, Italy. Since 2006, the Hotine-Marussi Symposia series has been produced under the auspices of the Inter-Commission Committee on Theory (ICCT) within the International Association of Geodesy (IAG). The ICCT has organized the last four Hotine-Marussi Symposia, held in Wuhan (2006) and Rome (2009, 2013 and 2018). The overall goal of the ICCT and Hotine-Marussi Symposia has always been to advance geodetic theory, as reflected in the 25 peer-reviewed research articles presented here. The IX Hotine-Marussi Symposium was divided into 10 topical sessions covering all aspects of geodetic theory including reference frames, gravity field modelling, adjustment theory, atmosphere, time series analysis and advanced numerical methods. In total 118 participants attended the Symposium and delivered 82 oral and 37 poster presentations. During a special session at the Accademia Nazionale deiLincei, the oldest scientific academy in the world, six invited speakers discussed interactions of geodesy with oceanography, glaciology, atmospheric research, mathematics, Earth science and seismology.
Spherical Sampling
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Author : Willi Freeden
language : en
Publisher: Birkhäuser
Release Date : 2018-05-03
Spherical Sampling written by Willi Freeden and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-03 with Mathematics categories.
This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.