Complexity of the Geological Framework and Use of Mathematics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 9

Fig. 1.3 Schematic sections originally compiled by Nieuwenkamp ( 1968 ) showing that a good
conceptional understanding of time-dependent geological processes is required for downward
extrapolation of geological features observed at the surface of the Earth. Sections a and b are
modified after von Buch ( 1842 ) illustrating his genetic interpretation that was based on combining
Abraham Werner's theory of Neptunism with von Buch's own firsthand knowledge of volcanoes
including Mount Etna in Sicily with a basaltic magma chamber. Section c is after Westerg ˚ rd
et al. ( 1943 ) (Source: Agterberg 1974 , Fig. 1)
granite became active later changing sediments into gneisses, while the primeval
basalt became a source for hypothetical volcanoes.
1.2.3 Scientific Method in the Geosciences
According to van Bemmelen ( 1972 , p. 8), the computerization and adoption of
mathematics in geoscience presents a wide-ranging and challenging field of future
developments but is fraught with organizational, educational and technical diffi-
culties. The usage of mathematics has progressed further in geophysics and geo-
chemistry than in geology because of differences in the nature of the data and other
sampling methods. The relative weights to be assigned to data collected from
geological observations at the surface of the Earth are often unknown. A fact can
be important and applicable at other places; frequently at great distances from the
original observation point, or it may be unique and unimportant ( cf . Agterberg
1979a ). Most geological facts are not unique but greatly influenced by other
observations and by deductions from specific concepts on geological processes.
Basic measurements, such as chemical analysis of a rock sample or determination
of the strike and dip of a structural plane, might represent local exceptions and their
importance can be evaluated only against a background of regional data. Satisfac-
tory statistical averaging may not be possible due to lack of exposure.