Spatial interpolation of coal properties using geographic quantile regression forest

Abstract

Inaccuracies in spatial modelling of coal properties can impact coal resource and reserve estimates. Geostatistical methods which account for compositional data have previously been recommended as a preferred method for modelling of coal properties. These methods can quantify uncertainty, can use auxiliary information to improve estimates, and ensure that compositional data (such as coal proximate analysis) is modelled in a mathematically consistent way. However, geostatistical methods have drawbacks in that have rigid statistical assumptions about the distribution and stationarity of the target variable and require variogram interpretation which can be onerous when then number of domains and target variables are numerous. Due to these drawback, inverse distance weighting (a simple deterministic method) remains the most popular method for modelling coal properties in Australian resource estimates. To address the drawbacks of geostatistical methods, a machine learning approach based on the quantile regression forest algorithm is proposed as an alternative method to spatially model coal properties. This newly proposed method, accounts for spatial arrangement of data, requires minimal pre-processing steps, can quantify uncertainty and can easily incorporate auxiliary information of various types. To evaluate the performance of this method, the accuracy of predictions of coal proximate analysis properties, and coal density are compared to the predictions of inverse distance weighting and regression kriging. All methods incorporate isometric log ratio transform and back-transform of data in order to account for the compositional nature of coal proximate analysis. Data from an active coal mine in the Bowen Basin, Queensland Australia was used as basis of the results. A unique feature of the mine site in this basin is the presence of intrusion which impacts coal quality properties to various degrees. Using evaluation metrics from leave-one-out cross-validation, this paper demonstrates that quantile regression forest has higher accuracy, lower bias and higher precision than inverses distance weighting across all coal properties. The paper also shows that results of the new method are very similar or better than regression kriging. It is also demonstrated that the prediction maps produced by quantile regression forest could be used to more accurately map out coal impacted by intrusion compared to inverse distance weighting, and that inverse distance weighting overestimates the impact of intrusion and intrusion extent. A drawback of the method compared to inverse distance weighting, is that it is more computationally demanding, less intuitive and is currently not available in existing geological packages.