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Decorrelative Mollifier Gravimetry / Willi Freeden / Bâle (CHE) ; Boston, MA : Birkhäuser (2021)
Titre : Decorrelative Mollifier Gravimetry : Basics, Ideas, Concepts, and Examples Type de document : document électronique Auteurs : Willi Freeden, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2021 Collection : Geosystems Mathematics, ISSN 2510-1544 Importance : XIX, 482 p. 196 illus., 168 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-69909-3 Langues : Anglais (eng) Tags : Potential theory (Mathematics) Numerical analysis Physical geography Gravitation Potential Theory Numerical Analysis Earth System Sciences Classical and Quantum Gravitation Relativity Theory Résumé : This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown. This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back. Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration. Note de contenu : Introductory Remarks -- Part I: Gravitation and Gravimetry -- Gravitation -- Gravimetry -- Part II: Potential Theory -- Classical Context -- Newton-Haar Mollifier Theory and Application -- Disturbing Potential -- Part III: Surface Decorrelation -- Space versus Frequency Surface Modeling -- Surface Applications -- Part IV: Inverse Potential Theory -- Gravimetry as an Ill-Posed Inverse Problem -- Part V: Volume Decorrelation -- Volume Methodology -- Volume Applications -- Part VI: Decorrelative Potential Methods -- Decorrelative Monopole Potential Based Gravimetry -- Decorrelative Dipole Potential Based Magnetometry -- Decorrelative Acoustic Potential Based Exploration -- Decorrelative Elastic Potential Based Exploration -- Concluding Remarks Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166358 Decorrelative Mollifier Gravimetry : Basics, Ideas, Concepts, and Examples [document électronique] / Willi Freeden, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2021 . - XIX, 482 p. 196 illus., 168 illus. in color : online resource. - (Geosystems Mathematics, ISSN 2510-1544) .
ISBN : 978-3-030-69909-3
Langues : Anglais (eng)
Tags : Potential theory (Mathematics) Numerical analysis Physical geography Gravitation Potential Theory Numerical Analysis Earth System Sciences Classical and Quantum Gravitation Relativity Theory Résumé : This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown. This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back. Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration. Note de contenu : Introductory Remarks -- Part I: Gravitation and Gravimetry -- Gravitation -- Gravimetry -- Part II: Potential Theory -- Classical Context -- Newton-Haar Mollifier Theory and Application -- Disturbing Potential -- Part III: Surface Decorrelation -- Space versus Frequency Surface Modeling -- Surface Applications -- Part IV: Inverse Potential Theory -- Gravimetry as an Ill-Posed Inverse Problem -- Part V: Volume Decorrelation -- Volume Methodology -- Volume Applications -- Part VI: Decorrelative Potential Methods -- Decorrelative Monopole Potential Based Gravimetry -- Decorrelative Dipole Potential Based Magnetometry -- Decorrelative Acoustic Potential Based Exploration -- Decorrelative Elastic Potential Based Exploration -- Concluding Remarks Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=166358 Diffusion in Random Fields / Nicolae Suciu / Bâle (CHE) ; Boston, MA : Birkhäuser (2019)
Titre : Diffusion in Random Fields : Applications to Transport in Groundwater Type de document : document électronique Auteurs : Nicolae Suciu, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2019 Collection : Geosystems Mathematics, ISSN 2510-1544 Importance : XIV, 262 p. 111 illus., 96 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-15081-5 Langues : Anglais (eng) Tags : Distribution Probability theory Numerical analysis Physical geography Probability Theory and Stochastic Processes Numerical Analysis Geophysics Geodesy Geophysics and Environmental Physics Résumé : This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling. Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems Note de contenu : Introduction -- Preliminaries -- Stochastic simulations of diffusion processes -- Diffusion in random velocity fields -- Monte Carlo GRW simulations of passive transport in groundwater -- Probability and filtered density function approaches -- Model, scale, and measurement Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=145613 Diffusion in Random Fields : Applications to Transport in Groundwater [document électronique] / Nicolae Suciu, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2019 . - XIV, 262 p. 111 illus., 96 illus. in color : online resource. - (Geosystems Mathematics, ISSN 2510-1544) .
ISBN : 978-3-030-15081-5
Langues : Anglais (eng)
Tags : Distribution Probability theory Numerical analysis Physical geography Probability Theory and Stochastic Processes Numerical Analysis Geophysics Geodesy Geophysics and Environmental Physics Résumé : This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling. Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems Note de contenu : Introduction -- Preliminaries -- Stochastic simulations of diffusion processes -- Diffusion in random velocity fields -- Monte Carlo GRW simulations of passive transport in groundwater -- Probability and filtered density function approaches -- Model, scale, and measurement Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=145613 Handbook of Mathematical Geodesy / Willi Freeden ; SpringerLink (Online service) ; M. Zuhair Nashed / Bâle (CHE) ; Boston, MA : Birkhäuser (2018)
Titre : Handbook of Mathematical Geodesy : Functional Analytic and Potential Theoretic Methods Type de document : document électronique Auteurs : Willi Freeden, ; SpringerLink (Online service) ; M. Zuhair Nashed, Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2018 Collection : Geosystems Mathematics, ISSN 2510-1544 Importance : XIV, 932 p. 155 illus., 76 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-319-57181-2 Langues : Anglais (eng) Tags : Harmonic analysis Physical geography Differential equations partial Abstract Harmonic Analysis Geophysics Geodesy Partial Differential Equations Résumé : 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 Note de contenu : Introduction -- Gauss as Scientific Mediator between Mathematics and Geodesy from the Past to the Present -- An Overview on Tools from Functional Analysis -- Operator-Theoretic and Regularization Approaches to Ill-Posed Problems -- Geodetic Observables and Their Mathematical Treatment in Multiscale Framework -- The Analysis of Geodetic Boundary Value Problem: State and Perspectives -- Oblique Stochastic Boundary Value Problem -- About the Importance of the Runge-Walsh Concept for Gravitational Field Determination -- Geomathematical Advances in Satellite Gravity Gradiometry -- Parameter Choices for Fast Harmonic Spline Approximation -- Gravimetry as an Ill-Posed Problem in Mathematical Geodesy -- Gravimetry and Exploration -- On the Non-Uniqueness of Gravitational and Magnetic Field Data Inversion -- Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods -- Spherical Potential Theory: Tools and Applications -- A combination of Downward Continuation and Local Approximation for Harmonic Potentials -- Joint Inversion of Multiple Observation Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=143649 Handbook of Mathematical Geodesy : Functional Analytic and Potential Theoretic Methods [document électronique] / Willi Freeden, ; SpringerLink (Online service) ; M. Zuhair Nashed, . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2018 . - XIV, 932 p. 155 illus., 76 illus. in color : online resource. - (Geosystems Mathematics, ISSN 2510-1544) .
ISBN : 978-3-319-57181-2
Langues : Anglais (eng)
Tags : Harmonic analysis Physical geography Differential equations partial Abstract Harmonic Analysis Geophysics Geodesy Partial Differential Equations Résumé : 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 Note de contenu : Introduction -- Gauss as Scientific Mediator between Mathematics and Geodesy from the Past to the Present -- An Overview on Tools from Functional Analysis -- Operator-Theoretic and Regularization Approaches to Ill-Posed Problems -- Geodetic Observables and Their Mathematical Treatment in Multiscale Framework -- The Analysis of Geodetic Boundary Value Problem: State and Perspectives -- Oblique Stochastic Boundary Value Problem -- About the Importance of the Runge-Walsh Concept for Gravitational Field Determination -- Geomathematical Advances in Satellite Gravity Gradiometry -- Parameter Choices for Fast Harmonic Spline Approximation -- Gravimetry as an Ill-Posed Problem in Mathematical Geodesy -- Gravimetry and Exploration -- On the Non-Uniqueness of Gravitational and Magnetic Field Data Inversion -- Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods -- Spherical Potential Theory: Tools and Applications -- A combination of Downward Continuation and Local Approximation for Harmonic Potentials -- Joint Inversion of Multiple Observation Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=143649 Modern Solvers for Helmholtz Problems / Domenico Lahaye ; SpringerLink (Online service) ; Jok Tang ; Kees Vuik / Bâle (CHE) ; Boston, MA : Birkhäuser (2017)
Titre : Modern Solvers for Helmholtz Problems Type de document : document électronique Auteurs : Domenico Lahaye ; SpringerLink (Online service) ; Jok Tang ; Kees Vuik Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2017 Collection : Geosystems Mathematics, ISSN 2510-1544 Importance : XII, 243 p. 54 illus., 39 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-319-28832-1 Langues : Anglais (eng) Tags : Mathematics Matrix theory Algebra Difference equations Functional equations Partial differential equations Numerical analysis Numerical Analysis Partial Differential Equations Linear and Multilinear Algebras Matrix Theory Difference and Functional Equations Résumé : This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra Note de contenu : I Algorithms: new developments and analysis -- II Algorithms: practical methods and implementations -- III Industrial applications. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128281 Modern Solvers for Helmholtz Problems [document électronique] / Domenico Lahaye ; SpringerLink (Online service) ; Jok Tang ; Kees Vuik . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2017 . - XII, 243 p. 54 illus., 39 illus. in color : online resource. - (Geosystems Mathematics, ISSN 2510-1544) .
ISBN : 978-3-319-28832-1
Langues : Anglais (eng)
Tags : Mathematics Matrix theory Algebra Difference equations Functional equations Partial differential equations Numerical analysis Numerical Analysis Partial Differential Equations Linear and Multilinear Algebras Matrix Theory Difference and Functional Equations Résumé : This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra Note de contenu : I Algorithms: new developments and analysis -- II Algorithms: practical methods and implementations -- III Industrial applications. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=128281 Spherical Sampling / Willi Freeden / Bâle (CHE) ; Boston, MA : Birkhäuser (2018)
Titre : Spherical Sampling Type de document : document électronique Auteurs : Willi Freeden, ; M. Zuhair Nashed, ; SpringerLink (Online service) ; Michael Schreiner, Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2018 Collection : Geosystems Mathematics, ISSN 2510-1544 Importance : XV, 596 p Présentation : online resource ISBN/ISSN/EAN : 978-3-319-71458-5 Langues : Anglais (eng) Tags : Functions special Differential equations partial Numerical analysis Physical geography Mathematics Special Functions Partial Differential Equations Numerical Analysis Geophysics Geodesy Information and Communication Circuits Mathematics Education Résumé : 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 Note de contenu : Preliminaries -- Function Systems -- Shannon Sampling Variants -- Bandlimited Sampling -- Spline Sampling -- Bandlimited Fourier Expansion Sampling -- Spacelimited Multi-Scale Approximate Identity Sampling -- Spacelimited Multi-Resolution Up-Function Sampling -- Spacelimited Multi-Scale Regularized Green Function Sampling -- Non-Spacelimited Wavelet Sampling -- Inverse Wavelet Sampling -- Conclusion -- Appendices Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=143605 Spherical Sampling [document électronique] / Willi Freeden, ; M. Zuhair Nashed, ; SpringerLink (Online service) ; Michael Schreiner, . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2018 . - XV, 596 p : online resource. - (Geosystems Mathematics, ISSN 2510-1544) .
ISBN : 978-3-319-71458-5
Langues : Anglais (eng)
Tags : Functions special Differential equations partial Numerical analysis Physical geography Mathematics Special Functions Partial Differential Equations Numerical Analysis Geophysics Geodesy Information and Communication Circuits Mathematics Education Résumé : 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 Note de contenu : Preliminaries -- Function Systems -- Shannon Sampling Variants -- Bandlimited Sampling -- Spline Sampling -- Bandlimited Fourier Expansion Sampling -- Spacelimited Multi-Scale Approximate Identity Sampling -- Spacelimited Multi-Resolution Up-Function Sampling -- Spacelimited Multi-Scale Regularized Green Function Sampling -- Non-Spacelimited Wavelet Sampling -- Inverse Wavelet Sampling -- Conclusion -- Appendices Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=143605