Geostatistics in the Presence of Multivariate Complexities: Comparison of Multi-Gaussian Transforms

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