Abstract

Multifractal interpolation method for spatial data with singularities

Highlights

  • Since the term ‘kriging’ was coined by Georges Matheron in the early 1960s on the basis of Krige’s master’s thesis dealing with interpolation of point samples, geostatistics has been rapidly developed as a branch of science and relevant techniques have been commonly applied in many fields of science for mapping, estimation, simulation, and prediction (Journel and Huijbregts, 1978; Goovaerts, 1997)

  • Kriging and other geostatistical techniques have been widely applied outside of geosciences, where users unaware of its origins and mathematical evolution refer to it as a type of spatial analysis

  • This paper introduces a generalized binomial multiplicative cascade process to demonstrate the generation of one- and two-dimensional data with multi-scale singularities which can be modelled by asymmetrical multifractal distribution

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Summary

Introduction

Since the term ‘kriging’ was coined by Georges Matheron in the early 1960s on the basis of Krige’s master’s thesis dealing with interpolation of point samples, geostatistics has been rapidly developed as a branch of science and relevant techniques have been commonly applied in many fields of science for mapping, estimation, simulation, and prediction (Journel and Huijbregts, 1978; Goovaerts, 1997). Interpolation algorithms have been developed for a variety of simple, indicator, and higher-order kriging as well as kriging with transformed and compositional data. Chiles and Delfiner, 1999), mixed categorical and/or continuous data (Journel and Huijbregts, 1978; Goovaerts, 1997), and compositional data (Pawlowsky-Glahn and Olea, 2004), have been created. Case studies comparing these methods are available in the literature Application of kriging depends heavily on stationarity of the mean and second-order moments involving the variogram and standard deviation of a regionalized random variable. The real data, especially exploratory data involved in characterizing mineralization and hazardous events, often does not meet stationarity requirements because of singularities

Multifractal interpolation method for spatial data with singularities
Multiplicative cascade processes and multifractal distributions
MIM incorporating spatial association and singularity
Discussion and conclusions
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