The authors introduce geomathematics as an active research area to
a wider audience. Chapter 1 presents an introduction to the Earth
as a system to apply scientific methods. Emphasis is laid on
transfers from virtual models to reality and vice versa. In the
second chapter geomathematics is introduced as a new scientific
area which nevertheless has its roots in antiquity. The modern
conception of geomathematics is outlined from different points of
view and its challenging nature is described as well as its
interdisciplinarity. Geomathematics is shown as the bridge between
the real world and the virtual world. The complex mathematical
tools are shown from a variety of fields necessary to tackle
geoscientific problems in the mathematical language. Chapter 3
contains some exemplary applications as novel exploration methods.
Particular importance is laid on the change of language when it
comes to translate measurements to mathematical models. New
solution methods like the multiscale mollifier technique are
presented. Further applications discussed are aspects of reflection
seismics. Chapter 4 is devoted to the short description of recent
activities in geomathematics. The Appendix (Chapter 5) is devoted
to the GEM - International Journal on Geomathematics founded ten
years ago. Besides a detailed structural analysis of the editorial
goals an index of all papers published in former issues is given.
General
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