Table of contents

  1. Front Matter
    Pages i-xxviii
  2. General Issues, Historical Background, and Future Perspectives

  3. Observational and Measurement Key Technologies

    1. Front Matter
      Pages 145-145
    2. Henri Laur, Volker Liebig
      Pages 147-170
    3. Nils Olsen, Gauthier Hulot, Terence J. Sabaka
      Pages 227-249
  4. Modeling of the System Earth (Geosphere, Cryosphere, Hydrosphere, Atmosphere, Biosphere, Anthroposphere)

    1. Front Matter
      Pages 251-251
    2. Helmut Moritz
      Pages 253-289
    3. F. Sansò
      Pages 291-319
    4. Willi Freeden, Michael Schreiner
      Pages 339-379
    5. Erik W. Grafarend, Matthias Klapp, Zdeněk Martinec
      Pages 381-496
    6. Luciana Fenoglio-Marc, Erwin Groten
      Pages 519-544
    7. Julian Kuhlmann, Maik Thomas, Harald Schuh
      Pages 545-565
    8. Sergey Danilov, Jens Schröter
      Pages 567-599

About this book


During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as space borne data of better and better quality explain the strong need of new mathematical structures, tools and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important.

The ‘Handbook of Geomathematics’ deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.


Constructive approximation Differential equations Geomathematics Inverse problems Mathematical modeling

Editors and affiliations

  • Willi Freeden
    • 1
  • M. Zuhair Nashed
    • 2
  • Thomas Sonar
    • 3
  1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  3. 3.Computational MathematicsTechnische Universität BraunschweigBraunschweigGermany

About the editors

Prof. Dr. Willi Freeden is working at the Technische Universität Kaiserslautern. His Subjects of Research are:
special functions of mathematical (geo)physics (in particular orthogonal polynomials, (scalar, vectorial, tensorial) spherical harmonics, Bessel and Hankel functions, etc.)partial differential equations (potential theory, elasticity, electromagnetism, fluid dynamics, refraction, geothermal flow)constructive approximation (in particular radial basis functions, finite elements, splines, wavelets etc.), integral transformsnumerical methods ("scientific computing", particularly of georelevant problems in potential theory, elasticity and electromagnetic theory)inverse problems in geophysics, geodesy and satellite technology (e.g., geomagnetics, gravimetry, satellite to satellite tracking, satellite gradiometry, seismics, etc.)mathematics in industry: transfer of mathematical know how into (geo)practice, in particular in geothermal research.

M. Zuhair Nashed is professor of Mathematics at the University of Central Florida. His research interests include:  
Integral and Operator Equations, Inverse and Ill-posed Problems, Numerical and Nonlinear Functional Analysis, Optimization and Approximation Theory, Operator Theory, Optimal Control Theory, Signal Analysis and Signal Processing.

Thomas Sonar is professor of Mathematics and head of the Institute of Computational Mathematics at Technische Universität Braunschweig.


Bibliographic information

Industry Sectors
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“The second edition has greatly expanded the scope of topics beyond those in the first edition. … the chapters are well written, and even the casual readers will find much descriptive material to enjoy. Indeed, the editors have performed a great service to the geomathematics community (and beyond) in this major update of the first edition of the Handbook.” (John Adam, Mathematical Reviews, August, 2017)