MULTIFRACTAL-KRIGE INTERPOLATION METHOD

Abstract

The Multifractal-Krige method developed in this study can not only interpolate irregular distributed values into regular distributed grids, but also extract the high frequency, local and weak signals, which are useful in feature retrieval or pattern recognition, from temporal-spatial signals. The signal from observing science is often distributed irregularly and it is often critical to interpolate irregular distributed signal into regular grids or estimate values at some points. For examples, in reservoir, coal bed and mineral tonnage estimations or in engineering parametric estimations, regional harmonious insects inspections, the interpolation is necessary. The Krige method had been widely used even though it is a low-pass filter and can not construct the high frequency, local and weak signals which are often play more important role in related study. The low-pass filtering property of Krige method is studied from the filtering points of view in frequency domain and it was found that Krige method is a low pass filters. In contrary, Multifractal interpolation method can reconstruct part of these signals. To implement the fractal interpolation, which keeps more high frequency information, the measure and scale pairs are defined, formula and procedures are studied in this study. The integration of Krige and Multifractal method produced Multifractal-Krige method that keeps benefits of both Krige and Multifractal interpolations. The core density data from Hole 1143A of Ocean Drilling Program (ODP) 184th cruise is used to test the algorithm. The interpolated results and power spectra are compared to show the benefits of Multifractal interpolation and Krige-Multifractal method. The results proved that the Multifractal-Krige interpolation approximates known points better and had richer high frequency frequencies than other methods. Factors that affect the method, such as uncertainty in the value estimation problems, had also been studied quantitatively. Further more, the local singularities, regression index and standard errors got from the interpolation procedure are good approximation of the high frequency, local and weak signals. So, Krige-Multifractal interpolation method can also be used in other kinds of applications, such as information retrieval, enhancement and pattern recognition.