Nature often behaves in a very complicated way, and geology is no exception. In petro-leum applications, where we are dealing with reservoirs at depths of several kilometers that are recognized by only a few wells and some seismic, we need to simplify the description of these reservoirs by means of models. A model is a simplification of nature and should never be identified with the natural phenomenon it seeks to describe. However, a model has the advantage of reducing our understanding of the reservoir to the estimation of a few parameters. The best approach is to explain the concepts using a 1D example.

Fig. 2-1 shows, on the left, a variable that varies around a constant mean. At any location, the behavior of the variable, although complicated, can be qualified as “homo-geneously heterogeneous.” On the average, it behaves the same everywhere, in the sense that we would make the same kind of error at any location if we were to predict the value of the variable from the value of the horizontal line. This will be discussed later as the stationarity hypothesis.

Fig. 2-1 shows, on the left, a variable that varies around a constant mean. At any location, the behavior of the variable, although complicated, can be qualified as “homo-geneously heterogeneous.” On the average, it behaves the same everywhere, in the sense that we would make the same kind of error at any location if we were to predict the value of the variable from