Journal of the Southern African Institute of Mining and Metallurgy
On-line version ISSN 2411-9717
Print version ISSN 0038-223X
CHENG, Q.. Multifractal interpolation method for spatial data with singularities. J. S. Afr. Inst. Min. Metall. [online]. 2015, vol.115, n.3, pp.235-240. ISSN 2411-9717.
This paper introduces the multifractal interpolation method (MIM) developed for handling singularities in data analysis and for data interpolation. The MIM is a new moving average model for spatial mapping and interpolation. The model decomposes the raw data into two components: singular and nonsingular components. The former can be characterized by a localized singularity index that quantifies the scaling invariance property of measures from a multifractal point of view. The latter is a smooth component that can be estimated using ordinary kriging or other moving average models. The local singularity index characterizes the concave/convex properties of the neighbourhood values. The paper utilizes a binomial multiplicative cascade model to demonstrate the generation of one- and two-dimensional data with multi-scale singularities which can be modelled by asymmetrical multifractal distribution. It then introduces a generalized moving average mathematical model for analysing and interpolating data with singularities. Finally, it is demonstrated by a one-dimensional case study of de Wijs' data from a profile in a zinc mine, that incorporation of spatial association and singularity can improve the interpolation result, especially for observed values with significant singularities.
Keywords : data analysis; spatial mapping; moving average models; multrifractal interpolation.