Multiscale Potential Theory

With Applications to Geoscience

  • Willi Freeden
  • Volker Michel

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Introduction

    1. Willi Freeden, Volker Michel
      Pages 1-3
    2. Willi Freeden, Volker Michel
      Pages 5-67
  3. Well-Posed Problems

    1. Front Matter
      Pages 69-69
    2. Willi Freeden, Volker Michel
      Pages 71-266
    3. Willi Freeden, Volker Michel
      Pages 267-329
  4. Ill-Posed Problems

    1. Front Matter
      Pages 331-331
    2. Willi Freeden, Volker Michel
      Pages 333-399
    3. Willi Freeden, Volker Michel
      Pages 401-471
    4. Willi Freeden, Volker Michel
      Pages 473-475
    5. Willi Freeden, Volker Michel
      Pages 477-482
  5. Back Matter
    Pages 483-509

About this book


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.

The work is divided into two main parts: Part I treats well-posed boundary-value problems of potential theory and elasticity; Part II examines ill-posed problems such as satellite-to-satellite tracking, satellite gravity gradiometry, and gravimetry. Both sections demonstrate how multiresolution representations yield Runge–Walsh type solutions that are both accurate in approximation and tractable in computation.

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

* Multilevel stabilization procedures for regularization

* Treatment of the real Earth’s shape as well as a spherical Earth model

* Modern methods of constructive approximation

* Exercises at the end of each chapter and an appendix with hints to their solutions

Models and methods presented show how various large- and small-scale processes may be addressed by a single geoscientific modelling framework for potential determination. Multiscale Potential Theory may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The book is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.


Potential Potential theory Wavelet approximations geomathematics geophysics mathematical geophysics model modeling multiresolution analysis multiscale methods

Authors and affiliations

  • Willi Freeden
    • 1
  • Volker Michel
    • 1
  1. 1.Department of Mathematics Geomathematics GroupTechnical University of KaiserslauternKaiserslauternGermany

Bibliographic information