Multiscale Potential Theory

Author : Willi Freeden,Volker Michel
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220480

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Multiscale Potential Theory by Willi Freeden,Volker Michel Pdf

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.

Author : Fabio Trovato,Peter J. Bond,Joanna Trylska,Peter Guy Wolynes
Publisher : Frontiers Media SA
Page : 322 pages
File Size : 50,9 Mb
Release : 2022-01-11
Category : Science
ISBN : 9782889740253

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Combining Simulations, Theory, and Experiments into Multiscale Models of Biological Events by Fabio Trovato,Peter J. Bond,Joanna Trylska,Peter Guy Wolynes Pdf

Author : Willi Freeden,Christian Gerhards
Publisher : CRC Press
Page : 468 pages
File Size : 55,8 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9781439895436

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Geomathematically Oriented Potential Theory by Willi Freeden,Christian Gerhards Pdf

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

Author : Willi Freeden,M. Zuhair Nashed
Publisher : Birkhäuser
Page : 932 pages
File Size : 47,9 Mb
Release : 2018-06-11
Category : Mathematics
ISBN : 9783319571812

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Handbook of Mathematical Geodesy by Willi Freeden,M. Zuhair Nashed Pdf

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.

Author : Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner
Publisher : Springer Nature
Page : 114 pages
File Size : 53,5 Mb
Release : 2021-09-08
Category : Mathematics
ISBN : 9783030795085

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Inverse Magnetometry by Christian Blick,Willi Freeden,M. Zuhair Nashed,Helga Nutz,Michael Schreiner Pdf

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.

Author : Willi Freeden,Helga Nutz
Publisher : Springer Nature
Page : 224 pages
File Size : 53,9 Mb
Release : 2024
Category : Geology
ISBN : 9783031544125

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Exploratory Potential Methods in Geothermal Power Generation by Willi Freeden,Helga Nutz Pdf

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.

Author : Pavel Novák,Mattia Crespi,Nico Sneeuw,Fernando Sansò
Publisher : Springer Nature
Page : 256 pages
File Size : 45,5 Mb
Release : 2020-09-16
Category : Science
ISBN : 9783030542672

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IX Hotine-Marussi Symposium on Mathematical Geodesy by Pavel Novák,Mattia Crespi,Nico Sneeuw,Fernando Sansò Pdf

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.

Author : Roland Klees,Roger Haagmans
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 42,7 Mb
Release : 2000-03-06
Category : Science
ISBN : 3540669515

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Wavelets in the Geosciences by Roland Klees,Roger Haagmans Pdf

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.

Author : Willi Freeden,Christian Gerhards
Publisher : CRC Press
Page : 470 pages
File Size : 46,9 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9781439895429

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Geomathematically Oriented Potential Theory by Willi Freeden,Christian Gerhards Pdf

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.

Author : Leonid Berlyand,Volodymyr Rybalko
Publisher : Springer
Page : 178 pages
File Size : 50,5 Mb
Release : 2018-11-22
Category : Computers
ISBN : 9783030017774

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Getting Acquainted with Homogenization and Multiscale by Leonid Berlyand,Volodymyr Rybalko Pdf

The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Author : Volker Michel
Publisher : Cambridge University Press
Page : 467 pages
File Size : 44,9 Mb
Release : 2022-04-28
Category : Mathematics
ISBN : 9781108419444

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Geomathematics by Volker Michel Pdf

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.

Author : Matthias Albert Augustin
Publisher : Birkhäuser
Page : 235 pages
File Size : 50,9 Mb
Release : 2015-07-15
Category : Mathematics
ISBN : 9783319170794

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A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs by Matthias Albert Augustin Pdf

This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth’s crust, which is harnessed by so-called geothermal facilities. Scientists from fields like geology, geo-engineering, geophysics and especially geomathematics are called upon to help make geothermics a reliable and safe energy production method. One of the challenges they face involves modeling the mechanical stresses at work in a reservoir. The aim of this thesis is to develop a numerical solution scheme by means of which the fluid pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling and during production. For this purpose, the method should (i) include poroelastic effects, (ii) provide a means of including thermoelastic effects, (iii) be inexpensive in terms of memory and computational power, and (iv) be flexible with regard to the locations of data points. After introducing the basic equations and their relations to more familiar ones (the heat equation, Stokes equations, Cauchy-Navier equation), the “method of fundamental solutions” and its potential value concerning our task are discussed. Based on the properties of the fundamental solutions, theoretical results are established and numerical examples of stress field simulations are presented to assess the method’s performance. The first-ever 3D graphics calculated for these topics, which neither requiring meshing of the domain nor involving a time-stepping scheme, make this a pioneering volume.

Author : Simon Hubbert,Quôc Thông Le Gia,Tanya M. Morton
Publisher : Springer
Page : 143 pages
File Size : 50,5 Mb
Release : 2015-05-13
Category : Mathematics
ISBN : 9783319179391

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Spherical Radial Basis Functions, Theory and Applications by Simon Hubbert,Quôc Thông Le Gia,Tanya M. Morton Pdf

This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.

Author : Willi Freeden
Publisher : CRC Press
Page : 467 pages
File Size : 49,7 Mb
Release : 2011-05-09
Category : Mathematics
ISBN : 9781439861851

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Metaharmonic Lattice Point Theory by Willi Freeden Pdf

Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of

Author : Horst J. Neugebauer
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 48,7 Mb
Release : 2003-04-07
Category : Science
ISBN : 9783540417965

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Dynamics of Multiscale Earth Systems by Horst J. Neugebauer Pdf

Today, earth and life scientists are increasingly confronted with the puzzling complexity of phenomena enmeshed in a seemingly boundless web of interrelations. To deal with this complexity and to further our ability to analyze and predict system behavior, science is learning to transcend reliance on averages and ‘permanence’ and to consider the fundamental multiple-scale character of phenomena. The contributions collected here detail techniques of multi-scale and fractal analysis that enhance the study of geo-complexity. They represent a multi-disciplinary approach to understanding the geological history of a section of the Lower Rhine River. They have in common the underlying question of how our qualitative modelling of natural phenomena do or do not prove the existence of representative averages.