ABSTRACT

Multifractals techniques are mainly used to characterize the scaling behaviour of a system. This chapter provides some examples of how multifractals analysis and geostatistics are related. It applies the generalized structure function to data on soil properties along a transect of arable fields, compares and evaluates the results obtained for characterizing their structure and variability. Multifractal models are related to specific probability distributions and geostatistics. For example, Cheng showed the links between multifractal parameters and semivariogram and autocorrelation. Mapping of singularities in multifractal analysis has been proved to be a very effective tool to delineate areas with anomalies in measure distributions. The aim of the multifractal analysis (MFA) is to study how a normalized probability distribution of a variable varies with scale. Geostatistical methods and, more recently, multifractal/wavelet techniques have been used to characterize the scaling and heterogeneity of soil properties along with other methods originating from complexity science.