  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.
