Joint geostatistical simulation of categorical and continuous variables

Various geostatistical techniques have been developed for several data scales, like: sequential Gaussian simulation or cumulants for continuous variables, SNESIM and extensions for binary and categorical variables, or lognormal geostatistics for positive variables. However, the same material can often be described at the same time by multiple aspects, like its facies, its composition or its grade in a certain value element. Typically, these different regionalized variables are stochastically mutually dependent, and often observed at different locations. It would thus be interesting to have a joint conditional simulation methodology of all random fields integrating all observations regardless of its scale. We have developed a multipoint-based conditional simulation technique, which allows to simulate dependent random fields of more than one scale. It fits generalized linear models to training images in order to predict the conditional distribution of prediction points to the observed or already simulated data. It then follows an iterative scheme to fill in more points until a complete simulation is obtained. For well-chosen combinations of generalized linear models for all scales we get a simulation system preserving the observations and various properties of the joint distribution in the training image. Training images need to have a separate layer for each of the regionalized variables and typically must be quite large to ensure enough variation of conditioning variables. Training images are sampled with space-filling sequences rather than systematically in order to get reasonable performance. The generalized linear modes are stabilized to avoid specific artifacts generated by complex dependence.