Page 236 - Modern Spatiotemporal Geostatistics

11

MULTIPOINT ANALYTICAL
FORMULATIONS

"Science begins with myths and with the criticism of myths."
K. Popper

The Basic Multipoint BME Equations

The modern spatiotemporal geostatistics model is built upon three fundamen-
tal postulates that may be termed the spatiotemporal physical geometry rela-
tionships, the epistemic (observer-observed) paradigm, and the ontological
(context-dependent) knowledge bases. Before our image of the BME concept
becomes clouded with more analytical and computational formulations in the
remaining sections, it is worth summarizing its main stages. In a nutshell, the
main stages of the BME conception of scientific mapping are as follows:
1. We set up the basic BME equations using whatever sources of knowledge
(general and specificatory) are available.
2. We solve the BME equations and see if they lead to experimentally verified
predictions. If the predictions are verified, this means that our knowledge
bases that led to these predictions were sufficiently accurate and detailed
enough for our purposes.
3. If the predictions are not verified, this means that there may be unknown
physical influences which are relevant and which should be sought at the
ontological level.
Working along the lines of scientific reasoning proposed by modern spatio-
temporal geostatistics, in this chapter we derive analytical results for various
multipoint BME mapping scenarios. The basic BME equations of multipoint
spatiotemporal mapping are summarized in Table 11.1 (equation numbers used
in previous chapters are included in the table; parameters and the operators
A, B, D, and E, s are defined in Table 6.1 on p. 133). These equations offer

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