  One of the most challenging aspects of multivariate geostatistics is dealing
with complex relationships between variables. Geostatistical co-simulation and
spatial decorrelation methods, commonly used for modelling multiple variables,
are ineffective in the presence of multivariate complexities. On the other
hand, multi-Gaussian transforms are designed to deal with complex multivariate
relationships, such as non-linearity, heteroscedasticity and geological
constraints. These methods transform the variables into independent
multi-Gaussian factors that can be individually simulated. This study compares
the performance of the following multi-Gaussian transforms: rotation based
iterative Gaussianisation, projection pursuit multivariate transform and flow
transformation. Case studies with bivariate complexities are used to evaluate
and compare the realisations of the transformed values. For this purpose,
commonly used geostatistical validation metrics are applied, including
multivariate normality tests, reproduction of bivariate relationships, and
histogram and variogram validation. Based on most of the metrics, all three
methods produced results of similar quality. The most obvious difference is the
execution speed for forward and back transformation, for which flow
transformation is much slower.
