Using bivariate multiple-point statistics and proximal soil sensor data to map fossil ice-wedge polygons

Abstract Multiple-point statistics (MPS) is a collection of geostatistical simulation algorithms that uses a multiple-point training image (TI) as structural model instead of a two-point variogram. MPS allows to simulate more complex random fields, like phenomena characterized by spatial connectivity. A very recent development is multivariate MPS in which an ensemble of variables can be simulated simultaneously using a multivariate TI. We investigated if multivariate MPS can be used for the processing of proximal soil sensor data, i.e. interpolating the sensor data and predicting the target variable. We measured a field with fossil ice-wedge polygons in the subsoil with an electromagnetic induction sensor and used these measurements to predict the location of wedge material in the subsoil. We built a bivariate TI with a categorical image of a random polygonal network as primary variable and a continuous image of the corresponding sensor values as secondary variable. Then, we performed a bivariate reconstruction with the recently developed Direct Sampling software. The resulting E-types provided an interpolated sensor data map and a probability map predicting the location of wedge material in the subsoil. This procedure was compared to the more traditional approach of interpolating the sensor data with ordinary kriging and performing a fuzzy k-means classification. Comparing the resulting maps with an aerial photograph revealing the location of the ice-wedges through polygonal crop marks, showed that MPS reconstructed the polygonal patterns much better. The local accuracy of the MPS maps was proven by an independent quantitative validation based on nine extra measurement lines and 94 bore hole samples. As a first application in soil science, our case study showed that multivariate MPS can be used for the processing of proximal soil sensor data. The flexibility of the technique opens perspectives for other new applications and therefore multivariate MPS can become a valuable part of the pedometrical toolbox.