Fractal Dimension Analysis For Earth Surface And Its Implication To Geological Process

The theory of fractal has brought a new perspective to geologists on understanding the geologic world. It is the first time to measure and analyze the geometric feature of geologic object quantitatively in the aspect of complexity, and these geometric features are seems correlated to the evolution of geologic object. Fractal is characterized by power function for geometric feature, which can be used to describe many complicated geologic cases, such as the distribution of minerals with different reserves and the heterogeneous distribution of elements, and so on. However, a fractal in nature is often composed of several independent events and each of them could be treated as an independent fractal. In other words, an actual fractal in nature is superposed by many fractals, so called multifractal, and it has been the greatest challenge for fractal application.The two problems encountered in dimension calculation of a natural multifractal lie in: 1. the dimension would change as the yardstick changes; 2. the dimension would change as the measurement range changes. Even only the starting point has a little shift would lead to an obvious change in fractal dimension. Scientists have done their best to achieve a stable dimension of multi-fractal: Mathematician adopted high-order general dimension corresponding to the multi-time effect mechanism of a multi-fractal, and gelogists used block sub segmentation to study the spatial dimension variation. Though there is some improvements, the multifractal in nature is still a basic problem when the fractal method are applicated for nature feature. This paper does not use the previous methods for multifractal which focus on pursuing an unified dimension by eliminating the dimension discrepancy among different regions. The general dimension is instead of a fractal dimension series derived from Successive Shift Divider (SSD) method. The fractal dimension series can show the variation of multifractal clearly.Main developments and conclusions of this study are listed below:1. A fractal dimension series is proposed to describe the geometric characteristics of a natural multifractal. The Successive Shift Method is developed to calculate fractal dimension series , which includes three methods for different natural features of dimension series respectively: one is suitable to a lineal object, another is for a planar object and the other is for a three dimensions object.2. In the previous studies, the change either of the starting point or the yardstick would influence the result of fractal dimension. Due to the independence of the fractal dimension series and the starting point, it is possible to study the dimension variation caused only by the varied yardstick and discuss the relationship between them. Furthermore, the specific scale of geologic process and geologic object could be elucidated.3. The fractal dimension series of the mainstream of the Yellow River demonstrates that the fractal dimension is related to the activity time and the evolution state of the tectonic unit it flowing through. Compared to the fractal dimension of a channel located in the interior region of a plate, the fractal dimension of channel located in the orogenic belt is higher. For a channel located in an orogenic belt, the newer the activity time of the orogenic belt, the higher the fractal dimension. For a channel located in an interior region of a plate, fractal dimension would increase significantly when the channel is flowing into the reactive zone of Mesozoic-Cenozoic.4. The fractal dimension series of the coastline in Zhejiang displays that the fractal dimension of the coastline with quaternary sedimentary near an estuary is relatively low while the fractal dimension of the coastline with eroded rock is relatively high. High fractal dimensions of coastline might be correlated with the activity of Cenozoic_nearshore fault basin. The comparison and analysis of the fractal dimension series of the coastline in 50 years indicates that the range of low fractal dimension has little variation while the range of high fractal dimension has more variation. However, the fractal dimension was going to decrease in 50 years, which likely be caused by the more and more man-made seawalls in costal zone.5. The fractal dimension series of DEM (digital elevation model) of the region of Santanghui in Zhejiang province shows that the fractal dimension in intersect zone of faults or intersect zone of fault and strata boundary is relatively high, implying the stress concentration may be occurred on these rocks in these zones when effected by a stress which results in fragmented rocks and complicated topography. It could be a new view for fault recognition based on the terrain morphology.6. The construction of urban usually started on natural physiognomy and is the best product of human and nature. The fractal dimension series of the remote sensing image of Shaoxing indicates that the fractal dimensions in old urban area are relatively high and the fractal dimensions in new urban area are relatively low. The extension of new urban is seems relative to the distribution of river network.7. According to the above production, the chang of fractal dimension reflect the chang of type of geologe process , the chang of degree of geologe process don't bring chang of fractal dimension. According to the statisticas of fractal dimension series, the dimension distribution of natural multifractal feature would be deteced. Take the main channel of the Yellow River as an example, the historgram of the fractal dimension series of it reveals that there are several crests for one tectonic unit and the crest amount is related close to the evolution process in that more crests appear in older tectonic unit.