Multifractality Method And Its Application Based On Multifractal Detrending Moving Average Analysis

Multifractal is a set of infinite number of scale indices defined on a fractal structure that describes different local conditions or special structural behaviors and characteristics caused by different levels in the evolutionary process. Due to the long-term and multi-stage nature of the geological process, the mineralization process is often repeated with multiple repetitions. This multiple mineralization superposition leads the spatial distribution of elements to follow a nested law,resulting in a variety of geochemical elements. The gradual enrichment or depletion of the geologic body reflects the heterogeneity and singularity of the distribution of geochemical elements in rocks and so on. Therefore, multifractal methods are suitable to analyze the above issues. Multifractal detrending moving average analysis(MFDMA) is a useful method to study the multifractal features of fractal sequences using sliding window technology. It is widely used in biomedical,economics and computer science. In this paper, firstly we study the influence of data volume and positional parameters on the MFDMA of the de-sliding mean trend by means of the typical binomial fractal model. Secondly, we analyze the Multifractal detrending moving average analysis and Multifractal Detrended Fluctuation Analysis(MFDFA) in different condition of noise, and then the sensitivity analysis of the obtained Hurst index is carried out. Finally, the singularity of the ore-forming elements in the Shang-zhuang is studied by using the MFDMA. The main results are as follows:(1) Analyze the effect of positional parameters on the results of MFDMA algorithm, select the parameters of the MFDMA algorithm as 0,0.5,1, and analyze the difference between the Hurst index and the theoretical value. The results show that the Hurst exponent curve calculated by MFDMA algorithm is the most fitted and the root mean square error is the smallest when the position parameter is zero.(2) Analyze the influence of data capacity on MFDMA algorithm. The three sets of data with capacity of 256, 512, 1024 in binomial fractal model are selected,and the influence of data capacity N on MFDMA is analyzed. The results show that with the increase of data capacity, the Hurst exponent curve calculated by MFDMA quickly approximates to the theoretical curve, and the root mean square error decreases gradually, indicating that the higher data capacity, the higher accuracy of the calculation results.(3) Analyze the effect of noise on MFDMA. The effects of noise and intensity on the Hurst estimation of MFDMA are analyzed by adding the Gaussian noise,white noise and spike noise through the binomial fractal model, and compared with MFDFA. The results show that the enhancement of Gaussian noise and white noise intensity has an interference effect on MFDMA. With the increase of the parameters of binomial fractal model, the influence of noise is reduced and the anti-noise ability is enhanced. The ability of MFDFA to distinguish noise data is weak and easy which is affected by noise and its intensity. In addition, the peak noise is easy to interfere with the analysis results of MFDMA and MFDFA method. It is found that the peak error of the MFDMA method is lower than that of the MFDMA method. As the root mean square error before noise reduction, therefore, MFDMA has a stronger robustness than MFDFA.(4) Analyze the multifractal fractal characteristics of mineral elements in Shangzhuang Gold Mine which is province in shandong using MFDMA Algorithm.The results show that the multifractal characteristics of Cu and Au are the most predominant, followed by the elements Hg, Zn and Pb, and the elements Ag, As and Sb are the weakest. The morphological differences of the multifractal spectra can provide the basis for the identification of mineralization intensity.