Modeling local scaling properties for multiscale mapping

Mapping surface soil properties and estimating soil parameters with multiresolution data has been significantly advanced by newly developed multiscale mapping technologies, which incorporate the concept and models of scaling analysis in data processing. This study was conducted to develop a new multiscale mapping technique on the basis of a power-law model characterizing local singularity of exploratory data for mapping surface soil properties. A field with singularity due to self-organization or self-similarity properties of the underlying processes can be modeled by multifractal models. These types of data may not have the statistical stationary property required by ordinary geostatistical mapping techniques. The new mapping technique utilizes a scaling property for data interpolation and for downscaling image processing. The inputs, either point data or an image, can be separated into a nonsingular background component for estimation purposes and an anomalous component of singularity for multiscale high-pass filtering purposes. When used for the purpose of data interpolation, this new method assigns weights for data interpolation by taking into account not only the distance between neighborhood points but also local structures and singularity of the field. The results of application of the method to a data set of geochemical concentration values of Ag from 1172 lake sediments in the Gowganda area of Ontario, Canada, have delineated favorable target areas with strong singularity of Ag concentrations caused by mineralization in lake sediments.