Geostatistics in the presence of multivariate complexities: comparison of multi-Gaussian transforms

TL;DR

This paper compares three multi-Gaussian transform methods used in multivariate geostatistics to handle complex variable relationships, evaluating their performance and computational efficiency through case studies.

Contribution

It provides a comparative analysis of rotation based iterative Gaussianisation, projection pursuit, and flow transformation methods for multivariate geostatistical modeling.

Findings

All three methods produce similar quality results across most metrics.

Flow transformation is significantly slower in execution.

Transform methods effectively handle non-linearity and heteroscedasticity in variables.

Abstract

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.