ABSTRACT
Spatial association indexes (autocorrelation, covariance, and variogram) have been commonly used to characterize the local structure of surfaces and for data interpolation in kriging. Singularity is another index representing the scaling invariant property of measures from a multifractal point view. Spatial association and scaling invariant are two different aspects of local structure of surfaces. Both must be taken into account in data interpolation and surface construction. Kriging as one of the sophisticated mapping techniques is based on the spatial association of neighborhood values through semivariogram. Recent study of multifractal modeling has shown that the local singularity exponent involved in multifractal modeling can quantify the local scaling invariant property characterizing the concave/convex properties of the neighborhood values. The method proposed in this paper incorporates both the singularity and spatial association in data interpolation. It has been shown by a case study of As geochemical values of sediment samples from southwestern Nova Scotia, Canada, that incorporation of spatial association and singularity can improve the interpolation result significantly, especially for observed values with significant singularity.
