How different data supports affect geostatistical modelling: the new aggregation method and comparison with the classical regularisation and the theoretical punctual model

ABSTRACT

In geostatistical analysis, often the data have different support (volume). Data with different supports can be treated separately or together but in a consistent way. In many applications, data are considered as point variable averaged over the sample volume. Regularisation of data has a significant impact on variograms and geostatistical estimations. Two methods of managing data with different supports (“integrating”) are compared: regularisation and aggregation. This paper examines the consequences of the regularisation on sample variograms and proposes another procedure to integrate samples called “aggregation”. The variogram models of integrated data are compared with the theoretical punctual model. The point-support variogram presents some advantages, such as the possibility of utilizing samples without compositing their values. But, this implies to modify the classical kriging system. The ways of managing data with different supports are applied to a complex dataset of an iron ore body. The spatial variable analysis from the composited borehole samples demonstrates the impact of the integrating methods through cross validation. Results show the effect of the variogram model in the kriging system and the accuracy of the evaluation. Also evidenced are the sensitivity to the integration method, the selected parameters and the benefits of the theoretical punctual variogram.

KEYWORDS:

• Geostatistics
• Compositing data
• regularisation
• aggregation
• theoretical punctual variogram

Acknowledgements

The authors would like to thank Professor Jacques Rivoirard and Professor Helen Beucher from Mines ParisTech for their help and their suggestions regarding the methodology and how to improve results.

Disclosure statement

No potential conflict of interest was reported by the authors.