Complexity of the Geological Framework and Use of Mathematics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 8

often with abrupt changes at the contacts between them. The heterogeneous nature
of the geological framework will be reflected or masked in these other variables.
Geologists, geophysicists and geochemists produce different types of maps for
the same region. Geophysical measurements are mainly indirect. They include
gravity and seismic data, variations in the Earth's magnetic field, and electrical
conductivity. They generally are averages of specific properties of rocks over large
volumes with intensities of penetration decreasing with distance and depth.
Remotely sensed data are very precise and can be subjected to a variety of filtering
methods. However, they are restricted to the Earth's surface. Geochemists mainly
work with element concentration values determined from chips of rocks in situ ,but
also from samples of water, mud, soil or organic material.
1.2.2 Geological Cross-Sections
The facts observed at the surface of the Earth must be correlated with one another; for
example, according to a stratigraphic column. Continually, trends must be established
and projected into the unknown. This is because rocks are 3-D media that can only be
observed in 2-D. The geologist can look at a rock formation but not inside it. Sound
geological concepts are a basic requirement for making 3-D projections.
During the past two centuries, after William Smith, geologists have acquired a
remarkably good capability of imagining 3-D configurations by conceptual
methods. This skill was not obtained easily. In Fig. 1.3 , according to Nieuwenkamp
( 1968 ), an example is shown of a typical geological extrapolation problem with
results strongly depending on initially erroneous theoretical considerations. In the
Kinnehulle area in Sweden, the tops of the hills consist of basaltic rocks; sedimen-
tary rocks are exposed on the slopes; granites and gneisses in the valleys. The
first two projections into depth for this area were made by a prominent geologist
(von Buch 1842 ). It can be assumed that today most geologists would quickly
arrive at the third 3-D reconstruction (Fig. 1.3c ) by Westerg˚rd et al. ( 1943 ). At the
time of von Buch it was not yet common knowledge that basaltic flows can form
extensive flows within sedimentary sequences. The projections in Figs. 1.3a, b
reflect A.G. Werner's pan-sedimentary theory of “Neptunism” according to
which all rocks on Earth were deposited in a primeval ocean. Nieuwenkamp
( 1968 ) has demonstrated that this theory was related to philosophical concepts of
F.W.J. Schelling and G.W.F. Hegel. When Werner's view was criticized by other
early geologists who assumed processes of change during geological time, Hegel
publicly supported Werner by comparing the structure of the Earth with that of a
house. One looks at the complete house only and it is trivial that the basement was
constructed first and the roof last. Initially, Werner's conceptual model provided an
appropriate and temporarily adequate classification system, although von Buch,
who was a follower of Werner, rapidly ran into problems during his attempts to
apply Neptunism to explain occurrences of rock formations in different parts of
Europe. For the Kinnehulle area (Fig. 1.3 ) von Buch assumed that the primeval