Distance gradient based variogram and Kriging to evaluate cobalt rich crust deposits on seamounts
Abstract The spatial distribution of cobalt rich crust thicknesses on seamounts is partly controlled by water depth and slope gradients. Conventional distance direction based variogram have not effectively expressed the spatial self correlation or anisotropy of the thicknesses of cobalt rich crusts. To estimate resources in cobalt rich crusts on seamounts using geostatistics, we constructed a new variogram model to adapt to the spatial distribution of the thicknesses of the cobalt rich crusts. In this model, we defined the data related to cobalt rich crusts on seamounts as three dimensional surface random variables, presented an experimental variogram process based on the distance gradient or distance "relative water depth," and provided a theoretical variogram model that follows this process. This method was demonstrated by the spatial estimation of the thicknesses of cobalt rich crusts on a seamount, and the results indicated that the new variogram model reflects the spatial self correlation of the thicknesses of cobalt rich crusts well. Substituted into the Kriging equation, the new variogram model successfully estimated the spatial thickness distribution of these cobalt rich crusts.