摘要
Multifractal spectrum, autocorrelation/semivariogram and power spectrum are three dif- ferent functions characterizing a field or measure from different aspects. These functions are interre- lated in such that the autocorrelation/semivariogram and power spectrum are related to the low order statistical moments (0 to 2 nd) which may determine the local multifractality (τ ″(1)) of a multifractal measure. A better understanding of the interrelationships among these three functions is important because, on one hand, the multifractal modelling characterizes a multifractal measure in a more de- tailed manner since it involves moments of all orders. On the other hand, the commonly used semivariogram and power spectrum functions can be used as alternatives to study the dominant mul- tifractal properties around the mean measure. Moreover, semivariogram and power-spectrum func- tions provide spatial and spectral information, which is highly valued in geological applications. A new fractal relation found between area and power-spectrum will be useful for investigation of new meth- ods of spatial-spectral analysis for pattern recognition, anomaly separation, classification, etc. These results have been demonstrated with the case study of modelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, Canada. The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possess monofractal properties whereas the ratios of these values show high multifractality. The values of the ratios U/K and U/Th show relatively large variances and may provide more information for distinguishing the distinct phases of the granites, country rocks as well as possible gold mineralization-associated regional hydrothermal alteration zones. In addition, the power spectra for U, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges of wave number 12≤ω ≤160 km and 0≤ω ≤12 km. These properties might provide useful thresholds for separating the power-spectrum values into two types of patterns to reflect different influences of possible geological processes such as hydrothermal altera- tion in the study area.
Multifractal spectrum, autocorrelation/semivariogram and power spectrum arethree different functions characterizing a field or measure from different aspects. These functionsare interrelated in such that the autocorrelation/semivariogram and power spectrum are related tothe low order statistical moments (0 to 2 nd) which may determine the local multifractality (τ''(1))of a multifractal measure. A better understanding of the interrelationships among these threefunctions is important because, on one hand, the multifractal modelling characterizes a multifractalmeasure in a more detailed manner since it involves moments of all orders. On the other hand, thecommonly used semivariogram and power spectrum functions can be used as alternatives to study thedominant multifractal properties around the mean measure. Moreover, semivariogram and power-spectrumfunctions provide spatial and spectral information, which is highly valued in geologicalapplications. A new fractal relation found between area and power-spectrum will be useful forinvestigation of new methods of spatial-spectral analysis for pattern recognition, anomalyseparation, classification, etc. These results have been demonstrated with the case study ofmodelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, Canada.The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possessmonofractal properties whereas the ratios of these values show high multifractality. The values ofthe ratios U/K and U/Th show relatively large variances and may provide more information fordistinguishing the distinct phases of the granites, country rocks as well as possible goldmineralization-associated regional hydrothermal alteration zones. In addition, the power spectra forU, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges ofwave number 12≤ω≤160 km and 0≤ω ≤12 km. These properties might provide useful thresholds forseparating the power-spectrum values into two types of patterns to reflect different influences ofpossible geological processes such as hydrothermal alteration in the study area.
作者
CHENG Qiuming1,2 1. State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China
2. Department of Earth and Space Science and Engineering, Department of Geography, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada
