Page 280 - Modern Spatiotemporal Geostatistics

Popular Methods in the Light of Modern Geostatistics 261

of such developments will be the emergence of a powerful computational view-
point in modern spatiotemporal geostatistics that may be called computational
BME. With the aid of computers, the rigorous mathematical structure of the
BME model can distill the complexity of physical knowledge bases into hu-
manly manageable amounts of information in the form of space/time maps,
to which scientists and engineers can apply their intuition to produce a real-
istic picture of the phenomenon under consideration. Computational BME is,
therefore, a theme of the modern geostatistics paradigm that involves com-
bining actual observations of real phenomena with computer simulations of
the phenomena. These simulations (the computer's way of "experimenting")
are, of course, physical model-based simulations rather than merely graphical
displays of data or model-free, fuzzy-system representations.
Computational BME involves a wide range of numerical techniques, includ-
ing deterministic (linear algebra, finite differences, etc.) and stochastic schemes
of various forms (Monte Carlo, Brownian dynamics, etc.). In the context of
BME analysis, the implementation of these techniques has two main goals, to
• solve integrodifferential and integrodifference equations with respect to
the BME coefficients at the prior stage, and
• evaluate multidimensional integrals of functions of the pdf at the posterior
stage.
Systematic applications of the above techniques—together with analytical
methods—seek to incorporate a part of physical reality as large as possible
into BME mapping. For computational BME, abstraction and construction
become close partners in mapping investigations. Because of its capacity to
manage large amounts of knowledge and solve large systems of mathematical
equations, computational BME will divulge new aspects of BME theory and
will even lead to theoretical improvements.

Modern Spatiotemporal Geostatistics and
CIS Integration Technologies

Geostatistical analysis and modeling of natural processes is not merely an issue
of inserting data bases into a library of "black box"-type computer programs.
In many practical applications, a major challenge faced by geostatistical prac-
titioners is how to integrate, rigorously and effectively, two aspects of the
information (see Fig. 12.18) upon which they draw:
(i.) the powerful theoretical tools and conceptual models (mathematical
equations expressing physical laws, scientific theories, phenomenological
relationships, optimal estimators, etc.) which have usually been devel-
oped for well-defined conceptual environments', and
(ii.) the site-specific details of the real environment under consideration;
in the case of a hazardous waste site, e.g., these details may include
the specific hydrogeological characteristics of the site (local drainage
catchment basins, stratigraphy, faults, dikes, sills, zones of alteration,