Multivariate geostatistical modelling with dimension reduction techniques

Overview

Multivariate geostatistical modelling aims at modelling the complex relationships between multiple attributes in space. Several challenges arise during this process, due to the non-linear features in the relationships, the heteroscedastic behavior of the variables or the presence of mineralogical constraints.

Traditional multivariate modelling relies on the Linear Model of Corregionalization and in most cases, on the multigaussian assumption, which is limited and generates models that do not properly reproduce the features of the original multivariate samples.

In this research, we investigate dimensionality reduction techniques to capture linear and non-linear features in the multivariate distribution. We explore how these techniques impact the reproduction of spatial continuity of each variable and between variables, through direct and cross-variograms.

Application to a nickel laterite deposite shows the workflow required to apply these approaches.

Starting with the samples, a log-ratio transformation is performed to ensure closure in the simulation results. Then, the relationships are investigated through a scatterplot matrix.

A dimensionality reduction technique is applied (in this case, PCA) and the factors are simulated through sequential Gaussian simulation. Results need to be back-transformed to obtain the simulated grades, where the relationships are compared with those of the original sample data.

Results show a good reproduction of the univariate histograms, spatial continuity (direct and cross variograms) and linear correlations. Some non-linear features are not properly reproduced, as expected.

Future work

Research is currently ongoing, looking at other dimensionality reduction techniques, and analyzing possible modifications to work under the conditions imposed by spatial data.

References

  • Bolgkoranou M, Ortiz JM (2019) Multivariate geostatistical simulation of compositional data using Principal Component Analysis – Application to a Nickel laterite deposit, in preparation.
  • Ortiz JM, Kracht W, Townley B, Lois P, Cardenas E, Miranda R, Alvarez M (2015) Workflows in geometallurgical prediction: challenges and outlook, 17th Annual Conference IAMG 2015, September 5-13, 2015, Freiberg, Germany.