Sliding window multifractal detrended fluctuation analysis (W-MFDFA) and multifractal moving average detrended method (MFDMA) are two effective methods to study multifractal characteristics of nonstationary time series. Taking the typical BMS signal model as an example, the selection of parameters, calculation accuracy and noise effects of the two algorithms are analyzed and compared. The results show that the calculation accuracy of MFDMA is better than that of W-MFDFA, but the latter is not sensitive to the changes of parameters, and has stronger anti-interference ability to noise and better stability. It can provide valuable reference for the research of actual data and the selection of internal parameters of the algorithm.

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The effect of peak noise and white Gaussian noise on moving cut data-permutation entropy method is discussed by constructing the nonlinear ideal time series. The results show that the moving cut data-permutation entropy method can accurately detect the location of the mutational point, even if the time series with high noise level, which showed that the effect of peak noise and white Gaussian noise on the result of this method is small. The moving cut data-permutation entropy has strong anti-noise ability, which is beneficial to the application of this method in actual observation data.

Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.

The self-similarity of ore-forming elements is caused by long-term, multi-period characteristics and the abnormal fluctuation induced by emergency in geological process. In this study, the fractal jump model referred as a combination of fractional Brownian motion and Poisson distributed jumps was built to depict the fluctuation pattern of ore-forming elements and simulate the distribution of Au sequence for three different mineralization intensities in Dayingezhuang gold deposit in the Jiaodong gold province, China. By calculating the fitting error and drawing the comparison diagram between the simulated data and the actual data, the applicability and advantages of the model were verified. The results showed that the fractal jump model can be considered as a reliable and computationally efficient method through the comparison of the statistical characteristics between simulated and real data. In addition, this model can well depict the change of the Au element content sequence, and better simulation was achieved when the intensity of mineralization was higher. The present work provides a new insight on the prediction of mineralized levels in concealed orebody.