Terracing of potential fields by clustering methods

We propose to use clustering techniques to the terracing of potential fields. We show how k-means clustering or a simple reclassification of the field values based on the minimum Euclidean distance from a set of cluster centers, can produce a nicely terraced potential field map, with the degree of simplification of the original map controlled by the clusters number. We describe a method to automatically define both the number and the center value of the clusters. The gravity or magnetic maps terraced by clustering techniques present no smooth transitions and each terrace has a perfectly constant field value. Such a terraced map is thus suitable for computing an apparent physical property distribution. To obtain even better results it is possible to combine clustering techniques with edge-preserving filters. We tested our method on simple and complex synthetic fields and finally applied it to the real gravity data of a mining region in Canada, finding a good correspondence between the resulting apparent density distribution and a simplified geological map.