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Birkhäuser

Multiscale Potential Theory

With Applications to Geoscience

  • Textbook
  • © 2004

Overview

Authors:
  1. Willi Freeden

    1. Department of Mathematics Geomathematics Group, Technical University of Kaiserslautern, Kaiserslautern, Germany

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  2. Volker Michel

    1. Department of Mathematics Geomathematics Group, Technical University of Kaiserslautern, Kaiserslautern, Germany

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    You can also search for this author in PubMed   Google Scholar

  • New mathematical methods are developed enabling the gravitational potential of a planetary body (the Earth) to be modeled and analyzed using a continuous flow of observations from land or satellite devices
  • Comprehensive coverage of topics which, thus far, are only scattered in journal articles and conference proceedings
  • Important applications and developments for future satellite scenarios; new modelling techniques involving low-orbiting satellites
  • Multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling
  • Exercises at the end of each chapter and an appendix with hints to their solutions
  • Accessible to a broad audience of grad students, geoscientists, applied mathematicians, and engineers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Introduction

    1. Introduction

      • Willi Freeden, Volker Michel
      Pages 1-3

    2. Preliminary Tools

      • Willi Freeden, Volker Michel
      Pages 5-67

  3. Well-Posed Problems

    1. Front Matter

      Pages 69-69
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    2. Boundary-Value Problems of Potential Theory

      • Willi Freeden, Volker Michel
      Pages 71-266

    3. Boundary-Value Problems of Elasticity

      • Willi Freeden, Volker Michel
      Pages 267-329

  4. Ill-Posed Problems

    1. Front Matter

      Pages 331-331
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    2. Satellite Problems

      • Willi Freeden, Volker Michel
      Pages 333-399

    3. The Gravimetry Problem

      • Willi Freeden, Volker Michel
      Pages 401-471

    4. Conclusion

      • Willi Freeden, Volker Michel
      Pages 473-475

    5. Hints for the Solution of the Exercises

      • Willi Freeden, Volker Michel
      Pages 477-482

  5. Back Matter

    Pages 483-509
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Keywords

About this book

During the last few decades, the subject of potential theory has not been overly popular in the mathematics community. Neglected in favor of more abstract theories, it has been taught primarily where instructors have ac­ tively engaged in research in this field. This situation has resulted in a scarcity of English language books of standard shape, size, and quality covering potential theory. The current book attempts to fill that gap in the literature. Since the rapid development of high-speed computers, the remarkable progress in highly advanced electronic measurement concepts, and, most of all, the significant impact of satellite technology, the flame of interest in potential theory has burned much brighter. The realization that more and more details of potential functions are adequately visualized by "zooming­ in" procedures of modern approximation theory has added powerful fuel to the flame. It seems as if, all of a sudden, harmonic kernel functions such as splines and/or wavelets provide the impetus to offer appropriate means of assimilating and assessing the readily increasing flow of potential data, reducing it to comprehensible form, and providing an objective basis for scientific interpretation, classification, testing of concepts, and solutions of problems involving the Laplace operator.

Reviews

"The book is devoted to well-posed and ill-posed boundary-value problems arising in geoscience, elasticity, gravimetry and other areas, including satellite problems. New mathematical methods and fast computational schemes based on harmonic analysis and wavelet transforms are developed…. The book may be used for graduate-level courses in geomathematics, applied mathematics, and geophysics. It is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers."   —Zentralblatt MATH

"Potential theory is a classical area in mathematics which for over 200 years has attracted and still attracts attention. Famous mathematicians have contributed. At the beginning of the 19th century it was Laplace, Poisson, Gauss, Green, both F. and C. Neumann, Helmholtz, Dirichlet and others. In the last century axiomatic, fine, probabilistic, discrete, and nonlinear potential theory arose.

The present book is written for applications in geodesy and geophysics and is hence devoted to classical potential theory with particular attention to wavelet approximation.... Each chapter is concluded with exercises which have solution hints at the end of the book.... The book is a self-contained and unique presentation of multiscale potential theory, interesting for applied mathematicians, geophysicists, etc. and proper even for students."   —Mathematical Reviews

 

Authors and Affiliations

  • Department of Mathematics Geomathematics Group, Technical University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden, Volker Michel

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