Regionalized Variables

If a variable is distributed in space, it is said to be ``regionalized''. Such a variable is usually a characteristic of a certain phenomenon, as metal grades, for example, are characteristics of a mineralization. The phenomenon that the regionalized variable is used to represent is called a ``regionalization'', examples of which are:

(i)

the market price of a metal which can be seen as the distribution of the variable price in time (one-dimensional space);

(ii)

a geological phenomenon such as the thickness of a subhorizontal bed which can be regarded as the distribution in the two-dimensional space of the variable thickness;

(iii)

a mineralized phenomenon can be characterized by the distribution in the three-dimensional space of variables such as grades, densities, recoveries, granulometrics, etc.

Regionalized variables are not restricted to mining, and examples from other fields include population density in demography, rainfall measurements in pluviometry and harvest yields in agronomy. In fact, almost all variables encountered in the earth sciences can be regarded as regionalized.

The definition of a regionalized variable as a variable distributed in space is purely descriptive. From the mathematical point of view, we interpret this regionalized variable as a realization of the random function $Z=Z({/boma x})$. In this chapter, we discuss some properties of such a random function. $Z$ at a certain, fixed point ${/boma x}$ is considered as a usual random variable.