Multi-fractal Detrended Analysis Method And Its Application In Geological Statistics

In the real world,complex system is ubiquitous,with typical characteristics of self-organization,nonlinearity,multi-level and multi-scale.Analyzing the complexity of the system itself and the correlation between system elements is one of important measures to study its internal mechanism and operation mechanism.Fractal and multi-fractal theory is an important research branch of nonlinear science,and it analyzes the complexity characteristics of the system through the parameter such as dimension,multi-fractal spectrum and scaling exponent.With the development of fractal theory,it was introduced in the geological research in the late1980s.Due to the long-term and multi-period of geological processes,the mineralization process is often multi-stage repeated mineralization,resulting in the extremely complex spatial and temporal distribution structures of ore-forming elements.Quantitative description of the distribution of ore-forming elements is an important basis for scientifically estimating the potential of ore deposits.In this dissertation,the detrended pattern of Multi-Fractal Detrended Fluctuation Analysis(MFDFA)method and Multi-Fractal Detrended Moving Average(MFDMA)method are modified,and two new algorithms are obtained.The applicability and stability of the algorithm are verified by the classical Binomial Multi-fractal Sequence(BMS)model,and compared with the traditional method to provide support for practical application.The two new algorithms are further applied to geological statistical analysis to explore the singularity characteristics of ore-forming element grade sequence and reveal the regularity between mineralization grade and mineralization elements.The main research conclusions are as follows:(1)Using the fractal interpolation fitting to replace the polynomial fitting in MFDFA,Fractal Interpolation based Multi-Fractal Detrended Fluctuation Analysis(FI-MFDFA)method is proposed.Furthermore,the influence of the number of interpolation points M on FI-MFDFA analysis results and the recognition effect of the multi-fractal feature are studied.The result shows that when M is 5,the results of FI-MFDFA are closer to the theoretical value;and FI-MFDFA can effectively identify the degree of multiple distribution singularity of sequences;the method is extended to two-dimensional case.(2)Using the exponential weighted average to replace the average in MFDMA,Multi-Fractal Detrending Exponential Smoothing(MFDES)method is proposed.The influence of smoothing index w on MFDES analysis results and the recognition effect of the multi-fractal feature are studied.The result shows that when w is 0.9,the parameter error of MFDES is small,and the results are close to the theoretical value.MFDES can effectively identify the degree of multiple distribution singularity of sequences;the method is extended to two-dimensional case.(3)The comparative analysis of FI-MFDFA and MFDFA,MFDES and MFDMA from the four aspects:algorithm steps,statistical accuracy of parameters,sensitivity of sample size and sensitivity of selected scale-free interval.The result shows that FI-MFDFA is superior to MFDFA,and the influence of the selection of fitting order on the calculation results of multiple parameters is avoided.MFDES is better than MFDMA,and can take into account the influence of position factors on the overall fluctuation of the sequence.(4)The applicability of FI-MFDFA and MFDES under different trends was analyzed.The result shows that FI-MFDFA is suitable for the analysis of sequences with linear trend and polynomial trend,and MFDES is suitable for the analysis of sequences without trend,with periodic trend and with exponential trend.(5)Taking the metallogenic element grade sequence of Jiama copper deposit in Tibet as the research object,the complexity of the distribution structure of Cu grade sequence under different mineralization levels was analyzed by using FI-MFDFA and MFDES.The result shows that the Cu grade sequence of all drifts have multifractal characteristics,and there are differences in the multiple parameters of element distribution under different mineralization levels.?_a_L??_a_R in Intensely and Moderately mineralized drifts and?_f?0;?_a_L??_a_Rin Barely mineralized drifts and?_f?0.The long-term correlation of Cu grade distribution under different mineralization levels is as follow:Intensely mineralized drifts>Moderately mineralized drifts>Barely mineralized drifts,indicating that the Cu element in intensely mineralized drifts is relatively concentrated with high grade and has metallogenic potential.FI-MFDCCA and ES-MFDCCA are used to discuss the cross correlation between metallogenic elements at different mineralization levels.The result shows that the long-term correlation between Cu,Pb,Zn and Au,Ag in barely mineralized drifts,Pb,Zn and Au,Ag in moderately mineralized drifts are reverse,while there is a strong long-term correlation among metallogenic elements.This result provides a new quantitative method for further delineating metallogenic target areas and characterizing the enrichment degree of ore deposits.