Page 284 - Modern Spatiotemporal Geostatistics

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A CALL NOT TO ARMS, BUT TO RESEARCH

"What an interior strength a man can summon if he devotes himself
entirely to knowledge and creation, rather than to a vain search

for honors and celebrity! What a lesson!" B . Russell for G. Frege
Unification and Distinction

A careful study of the developments in geostatistics reveals that the latter
continuously undergoes two major processes of growth and advancement:
1. A unification process with respect to its methods.
2. A distinction process with respect to its mathematical structure and the
way it relates to experience.
These two processes may seem to follow opposite paths, but in essence they
complement each other, and are equally important for the growth of the field.
As the methods of modern spatiotemporal geostatistics lay claim to
broader domains of space/time data analysis, they also become increasingly
unified. For example, as we saw in Chapter 12, generalized random fields
unite previously separate classes of fractal and wavelet random fields; also,
BME mapping incorporates the interpolation methods of traditional geostatis-
tics and spatial statistics as special cases. At the basis of the unified frame-
work lies a physical geometry in which space and time constitute an integrated
whole. The choice of an appropriate geometry depends on the local properties
of space/time and on the physical constraints imposed by the phenomenon of
interest (Chapter 2). Within the unified framework, useful classifications of the
geostatistical techniques are possible, which depend on the physical knowledge
sources processed, the information functions assumed, the conditionalization
rules used, etc. (Chapters 3-8).
Considered as a theory of physical model-based estimation, geostatisti-
cal mapping has two distinct parts: a formal part and an interpretive part.

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