Multifractal characterization of the spatial distribution of ulexite in a Bolivian salt flat

Understanding spatial patterns is a critical and under-explored aspect of remote sensing. This paper describes how multifractal theory can be applied to characterize these heterogeneous patterns in remotely sensed data as well as to determine the operational scale. An example based on the characterization of ulexite distribution on the world's largest salt flat (10000 km(2)), located in Bolivia, using a binarized Landsat Thematic Mapper (TM) 4/7 ratio image, is used to describe the step-by-step procedure. Distribution was well characterized by the multifractal parameters and expressed through the f-alpha, tau-q and D-q relationships. Moments from q=-2 to 5 showed a linear trend in scales from approximately 0.007 to 10000km(2). This implies that the attribute analysed could be measured at different scales, within defined boundaries, and up- and down-scaled using the multifractal parameters. In addition, the asymmetry shown by the f-alpha spectrum indicates the presence of clusters with high probability of finding ulexite, and large areas where the mineral might be found in small patches. The areas with a high probability of finding ulexite were mapped to guide any future field survey. Using the maximum entropy concept, the operational scale to determine the mineral was obtained at 1062 m.