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Geomathematics: Its Role, Its Aim, and Its Potential

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Handbook of Geomathematics

Abstract

During the last decades, geosciences and geoengineering were influenced by two essential scenarios: First, the technological progress has completely changed the observational and measurement techniques. Modern high-speed computers and satellite-based techniques are more and more entering all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, and 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 spaceborne data of better and better quality, explain the strong need of new mathematical structures, tools, and methods, i.e., geomathematics.

This paper deals with geomathematics, its role, its aim, and its potential. Moreover, the “circuit” geomathematics is exemplified by three problems involving the Earth’s structure, namely, gravity field determination from terrestrial deflections of the vertical, ocean flow modeling from satellite (altimeter measured) ocean topography, and reservoir detection from (acoustic) wave tomography.

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Acknowledgements

This introductory chapter is based on the German note “W. Freeden (2009):Geomathematik, was ist das überhaupt?, Jahresbericht der DeutschenMathematiker Vereinigung (DMV), JB.111, Heft 3, 125–152.” I am obliged to thepublisher Vieweg+Teubner for giving the permission for an English translation ofessential parts of the original version.

Particular thanks go to Dr. Helga Nutz for reading an earlier version and eliminating some inconsistencies.

Furthermore, I would like to thank my Geomathematics Group, Kaiserslautern, for the assistance in numerical calculation as well as graphical illustration concerning the three exemplary circuits.

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  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

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  1. Willi Freeden
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Correspondence to Willi Freeden .

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  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

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Freeden, W. (2015). Geomathematics: Its Role, Its Aim, and Its Potential. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_1

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