Page 44 - Modern Spatiotemporal Geostatistics

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SPATIOTEMPORAL GEOMETRY

"The basis of metrical determination must be sought outside the
manifold in the binding forces which act upon it." G.F.B. Riemann

A More Realistic Concept

As geostatistics expands its domain in search of new concepts and applications,
the return to its foundations will continue, each process nourishing the other.
The complete understanding of any line of scientific reasoning calls for exam-
ining the underlying hypotheses and exposing fallacies, whether of the factual
or conceptual sort. Chapter 1 discusses the goals of the epistemic analysis that
lies at the heart of modern spatiotemporal geostatistics. Among the goals are
the exposition and correction of three fallacies of classical geostatistics:
1. Spatiotemporal structure is a purely geometrical affair.
2. The data always speak for themselves.
3. Estimation is an exercise of mathematical optimization.
These fallacies exist as a set of hidden assumptions implicitly held for a
number of years by many classical geostatisticians. Epistemic analysis can ad-
vance the state of geostatistics by removing misconceptions that have blocked
its path. This chapter demonstrates how modern geostatistics succeeds in cor-
recting the fallacy that spatiotemporal structure is purely geometrical. This
is accomplished by promoting a more realistic concept involving knowledge
of the underlying physical processes. The geometry placed upon space/time
should establish a structure within which physical data, laws, theories, etc.
make sense and can be represented with consistency, free of contradiction, and
can be tested and used to make predictions in space/time.
The response of modern spatiotemporal geostatistics to the other miscon-
ceptions listed above is the subject of later chapters. As we shall see in Chapter
3, the second fallacy is corrected by demonstrating the importance of scientific

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