Properties and limitations of sequential indicator simulation

The sequential indicator algorithm is a widespread geostatistical simulation technique that relies on indicator (co)kriging and is applicable to a wide range of datasets. However, such algorithm comes up against several limitations that are often misunderstood. This work aims at highlighting these limitations, by examining what are the conditions for the realizations to reproduce the input parameters (indicator means and correlograms) and what happens with the other parameters (other two-point or multiple-point statistics). Several types of random functions are contemplated, namely: the mosaic model, random sets, models defined by multiple indicators and isofactorial models. In each case, the conditions for the sequential algorithm to honor the model parameters are sought after. Concurrently, the properties of the multivariate distributions are identified and some conceptual impediments are emphasized. In particular, the prior multiple-point statistics are shown to depend on external factors such as the total number of simulated nodes and the number and locations of the samples. As a consequence, common applications such as a flow simulation or a change of support on the realizations may lead to hazardous interpretations.