Where data is available, it is desirable in geostatistical modelling to make use of additional covariates, for example terrain data, in order to improve prediction accuracy in the modelling task. While elevation itself may be important, additional explanatory power for any given problem can be sought (but not necessarily found) by filtering digital elevation models to extract higher-order derivatives such as slope angles, curvatures, and roughness. In essence, it would be beneficial to extract as much task-relevant information as possible from the elevation grid. However, given the complexities of the natural world, chance dictates that the use of 'off-the-shelf' filters is unlikely to derive covariates that provide strong explanatory power to the target variable at hand, and any attempt to manually design informative covariates is likely to be a trial-and-error process -- not optimal. In this paper we present a solution to this problem in the form of a deep learning approach to automatically deriving optimal task-specific terrain texture covariates from a standard SRTM 90m gridded digital elevation model (DEM). For our target variables we use point-sampled geochemical data from the British Geological Survey: concentrations of potassium, calcium and arsenic in stream sediments. We find that our deep learning approach produces covariates for geostatistical modelling that have surprisingly strong explanatory power on their own, with R-squared values around 0.6 for all three elements (with arsenic on the log scale). These results are achieved without the neural network being provided with easting, northing, or absolute elevation as inputs, and purely reflect the capacity of our deep neural network to extract task-specific information from terrain texture. We hope that these results will inspire further investigation into the capabilities of deep learning within geostatistical applications.