Geostatistical Analysis of Seabed Sediment Type: A Compositional Approach with Non-Euclidean Distance Metrics

Although geostatistics is increasingly used to characterize coastal habitats, its full potential cannot be achieved through the blind application of off-the-shelf methods. Tools need to be tailored to the characteristics of each site and parameter; in particular, (1) complex coastal geometries might require the use of nonlinear measures of spatial proximity, and (2) the compositional nature of the variables hampers the application of traditional multivariate and kriging techniques; for example, the variance-covariance matrix is singular, while there is no guarantee that predicted percentages sum to 100%. Approaches to tackle both issues are introduced and illustrated using a multivariate dataset that includes, for 170 stations, sediment grain size distribution. The matrix of over-water distances between each pair of stations underwent a multidimensional scaling to create a new data configuration where Euclidean distances between observations approximate the original over-water distances, allowing the sound application of variogram modeling and kriging prediction. Then, a compositional data analysis was conducted by first transforming each set of textural fractions into a set of log-ratios that underwent a geostatistical analysis, leading to coherent sediment texture maps. The interpolation of texture classes relied on residual kriging and a spatial trend model that was built using machine learning and geomorphometric variables derived from bathymetry data (water depth, slope, roughness). For this particular dataset, using non-Euclidean distances and log-ratios resulted in the most accurate predictions for texture classes.