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Type: Journal article
Title: Geostatistics in the Presence of Multivariate Complexities: Comparison of Multi-Gaussian Transforms
Author: Abulkhair, S.
Dowd, P.A.
Xu, C.
Citation: Mathematical Geosciences, 2023; 55(6):713-734
Publisher: Springer
Issue Date: 2023
ISSN: 1874-8961
Statement of
Sultan Abulkhair, Peter A. Dowd, Chaoshui Xu
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.
Keywords: Rotation based iterative Gaussianisation
Projection pursuit multivariate transform
Flow transformation
Minimum/maximum autocorrelation factors
Complex bivariate relationships
Description: Published 05 April 2023.
Rights: © The Author(s) 2023. Open Access. This article is licensed under a Creative Common sAttribution 4.0 International License,which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
DOI: 10.1007/s11004-023-10056-y
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Appears in Collections:Civil and Environmental Engineering publications

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