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.

翻译：多元地质统计学最具挑战性的方面之一在于处理变量间的复杂关系。常用于多变量建模的地质统计协同模拟与空间去相关方法在面临多元复杂性时效果有限。而多高斯变换方法专门针对非线性、异方差性和地质约束等复杂多元关系设计，通过将原始变量转化为可独立模拟的多高斯因子来解决这一问题。本研究系统比较了以下三种多高斯变换方法的性能：基于旋转的迭代高斯化、投影寻踪多元变换和流形变换。通过含二元复杂性的案例研究，从变换后变量的实现值出发，运用地质统计验证的通用指标（包括多元正态性检验、二元关系再现度、直方图与变异函数验证）进行评价。多数指标显示三种方法生成的结果质量相近，其中最显著的差异体现在正反变换的执行速度上——流形变换的运行速度明显慢于其他两种方法。