In this introduction, we would like to highlight what appear to be the important land-marks in the history of geostatistical applications in the petroleum industry. What do we mean by “geostatistics?” In this course, this term will cover the petroleum applications resulting from the pioneering work of Prof. Georges Matheron and his Research Group at the Centre de Géostatistique de l'Ecole des Mines de Paris. As far as this course is concerned, the main pillars of this work are the developments of variogram-based modeling applications.
Variogram-based modeling applications can be classified in two broad categories, the first of which can be called deterministic geostatistics and is essentially all the development around kriging. We will see later that this covers a very wide number of techniques, including external drift kriging, error cokriging, factorial kriging, and collo-cated cokriging. Although kriging is a technique based on a stochastic model, it generates one single model as a result, and it is deterministic in that sense.
The second category can be called stochastic geostatistics, and it covers the numer-ous techniques developed around the conditional simulation concept. Conditional sim-ulation is stochastic in the sense that, as with the Monte-Carlo simulation, it generates a family of “realizations” of 1D, 2D, or 3D models, all compatible with the a priori model and the existing data. With regard to kriging, conditional simulation includes several techniques, such as indicator simulation, collocated cosimulation, or geostatistical inversion. This explains why this one-day course is subdivided in two half-days, the first half-day presenting