Willi Freeden, Volker Michel

Multiscale Potential Theory

With Applications to Geoscience

• Gebundenes Buch

Produktbeschreibung

This self-contained book provides a basic foundation for students, practitioners, and researchers interested in some of the diverse new areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled and analyzed using a continuous flow of observations from land or satellite devices. Harmonic wavelet methods are introduced, as well as fast computational schemes and various numerical test examples.

Topic and key features:

- 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

Produktdetails

• Applied and Numerical Harmonic Analysis
• Verlag: Springer, Basel
• Artikelnr. des Verlages: 10700246
• 2004
• Seitenzahl: 532
• Erscheinungstermin: 21. September 2004
• Englisch
• Abmessung: 241mm x 160mm x 33mm
• Gewicht: 856g
• ISBN-13: 9780817641054
• ISBN-10: 081764105X
• Artikelnr.: 13305974

Autorenporträt

Willi Freeden, Technische Universität Kaiserslautern, Germany / Volker Michel, Technische Universität Kaiserslautern, Germany

Inhaltsangabe

Preface.
- Introduction.
- Preliminary Tools.

- Part I: Well-Posed Problems.
- Boundary-Value Problems of Potential Theory.
- Boundary-Value Problems of Elasticity.

- Part II: Ill-Posed Problems.
- Satellite Problems.
- The Gravimetry Problem.
- Conclusion.
- Hints for the Solutions of the Exercises.
- References.
- Index.

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1 Introduction.- 2 Preliminary Tools.- 2.1 Basic Settings.- 2.2 Spherical Nomenclature.- 2.3 Sphere Oriented Potential Theory.- 2.4 Exercises.- I Well-Posed Problems.- 3 Boundary-Value Problems of Potential Theory.- 4 Boundary-Value Problems of Elasticity.- II Ill-Posed Problems.- 5 Satellite Problems.- 6 The Gravimetry Problem.- 7 Conclusion.- 8 Hints for the Solution of the Exercises.- References.

Rezensionen

"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