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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.
Mathematics. --- Geophysics. --- Harmonic analysis. --- Partial differential equations. --- Abstract Harmonic Analysis. --- Geophysics/Geodesy. --- Partial Differential Equations. --- Geodesy --- Physical geography. --- Differential equations, partial. --- Partial differential equations --- Geography --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics
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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 space borne 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 of Geomathematics’ deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific 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.
Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Earth sciences. --- Mathematics, general. --- Earth Sciences, general. --- Geosciences --- Environmental sciences --- Physical sciences --- Math --- Science --- Geography. --- Cosmography --- Earth sciences --- World history --- Geology
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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.
Mathematics. --- Geophysics. --- Partial differential equations. --- Special functions. --- Information theory. --- Numerical analysis. --- Mathematics --- Special Functions. --- Partial Differential Equations. --- Numerical Analysis. --- Geophysics/Geodesy. --- Information and Communication, Circuits. --- Mathematics Education. --- Study and teaching. --- Functions, special. --- Differential equations, partial. --- Physical geography. --- Geography --- Partial differential equations --- Mathematical analysis --- Math --- Science --- Special functions --- Mathematics—Study and teaching . --- Communication theory --- Communication --- Cybernetics --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics
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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.
Geology --- Mathematics. --- Geomathematics --- Mathematical geology --- Differential equations, partial. --- Integral equations. --- Potential theory (Mathematics). --- Partial Differential Equations. --- Integral Equations. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Equations, Integral --- Functional equations --- Functional analysis --- Partial differential equations --- Partial differential equations. --- Potential theory (Mathematics)
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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.
Applied mathematics. --- Engineering mathematics. --- Earth sciences. --- Applications of Mathematics. --- Earth Sciences, general.
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Das vorliegende Handbuch stellt erstmalig in deutscher Sprache umfassend alle Themen im Bereich Tiefe Geothermie vor: Prospektion, Exploration, Realisierung und Nutzung. In zwei abschließenden Kapiteln werden Zukunft und Perspektiven von Tiefer Geothermie vorgestellt und diskutiert. Die von anerkannten Spezialisten verfassten Artikel sind so konzipiert und geschrieben, dass alle an der Konzeption und Erschließung tiefengeothermischer Ressourcen Beteiligten einen direkten Nutzen für ihre Arbeit daraus ziehen können.
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Die durch das Reaktorunglück in Fukushima forcierte Energiewende hin zu einer Stromversorgung mit primär erneuerbaren Energien konzentriert sich in der aktuellen Wahrnehmung nur auf den Ausbau von Solar und Windkraftenergie. Dabei wird vergessen, dass aufgrund fehlender Stromspeichertechnologien und Überlandstromtrassen eine erneuerbare Energie benötigt wird, die konstant Strom liefern und so Erzeugungsschwankungen bei Solar- und Windkraftenergie ausgleichen kann. Tiefe Geothermie, also Energie, die aus der Erde kommt, kann diese Aufgabe leisten, da sie die einzige erneuerbare Energie ist, die nicht klimatischen oder wetterbedingten Schwankungen unterliegt. Mit einem durch Wissenschaftlern und Praktikern erstellten Normenkatalog für tiefengeothermische Bohrungen, würde hier ein höchstmöglichen Sicherheitsstandard erreicht, und die wirtschaftlichen wie geologischen Risiken jedes Projektes minimiert werden. Der Inhalt Der aktuelle Energiemix in Deutschland Der zukünftige Energiemix Das thermische Regime der Erde und Geothermie Schlussfolgerung und Nachklang Die Zielgruppen Praktiker aus dem Bereich der Geowissenschaft Praktiker aus dem Bereich Energiewirtschaft Politiker Die Autoren Prof. Dr.-Ing. Dr. h.c. Mathias Bauer, CBM Gesellschaft für Consulting, Business und Management mbH, Bexbach. Prof. Dr. Willi Freeden, Technische Universität Kaiserslautern, Geomathematics Group. Prof. Dr. Hans Jacobi, Jacobi & Partner Industrieberatung GmbH, Essen. Dipl.-Ing. Thomas Neu, proG.E.O. Ingenieurgesellschaft mbH, Saarbrücken.
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