The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size. This paper shows that a number of distributions, including power-function, Pareto, lognormal, and Zipf, display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal models for data exhibiting such distributions. The summation method is developed on the basis of fractal models to determine thresholds for Au data in Shandong Province, China. The anomalous area is enclosed by contours which have contour values greater than or equal to threshold （200 × 10^- 9） and contains known large-sized and super large-sized gold mineral deposits.
It is generally acknowledged that geomagnetic polarity has reversed many times in geological history and an abnormal geologic phenomenon is the Cretaceous normal superchron. However, the causes have been unknown up to now. The nonlinear theory has been applied to analyze the phenomenon in geomagnetic polarity reversal and the Cretaceous normal superchron. The Cretaceous normal superchron implies that interaction of the Earth＇s core-mantle and liquid movement in the outer core may be the lowest energy state and the system of Earth magnetic field maintains a sort of temporal or spatial order structure by exchanging substance and energy in the outside continuously. During 121-83 Ma, there was no impact of a celestial body that would result in a geomagnetic polarity reversal, which may be a cause for occurrence of the Cretaceous normal superchron.The randomness of geomagnetic polarity reversal has the self-reversion characteristic of chaos and the chaos theory gives a simple and clear explanation for the dynamic cause of the geomagnetic polarity reversal.
