The truncated pluri-Gaussian approach is a powerful method for modeling geology. Its main strength is its flexibility in representing complex lateral and vertical facies transitions with different anisotropies. In addition, it is easy to condition simulations to data points. This makes it an excellent method for modeling reservoirs with a complex architecture, such as carbonate bioconstructions or reservoirs affected by diagenesis.

This chapter presents a method for obtaining a tractable and mathematically consistent model for lithotype semivariograms and cross-semivariograms in complex cases. The method is illustrated using an example involving algal bioconstructions in the outcrops of the Paradox basin (Utah). Complex facies transitions, both vertically and laterally between the mound and intermound facies, together with the complex geometry of the algal mounds, make it virtually impossible to simulate these sorts of deposits using object-based models or classical pixel-based methods. The truncated pluri-Gaussian model is introduced to handle these complex facies transitions using the concept of a lithotype rule.

Such a rule, when expressed diagrammatically, can be a valuable tool for synthesizing geological information, and it can serve as one of the key inputs into the stochastic model. As illustrated here, combining the rule with proportion curves is a very effective way for analyzing and modeling geology in terms of facies sequences, even in complex depositional environments.