地表分形与地质作用
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摘要
分形理论给地质学家认识地质世界带来了新的视角,地质学家们第一次从复杂性入手定量地测算和分析地质对象的几何特征,这些几何特征似乎与地质对象的形成演化存在某种联系,这种以幂率表征的几何特征的函数关系可以推广到诸如不同储量矿体的分布,元素的不均匀分布等复杂地质对象的描述。然而,在实际应用中面临的最大问题是自然界的分形对象常常是由多组独立的事件叠加作用而成,每一组独立事件可形成相应的分形对象,也就是说自然界的实际分形对象常常是由多个分形叠加合成,即重分形。自然界的重分形对象在维数的测算时面临二大问题,一是维数的测量随码尺的改变而变化,二是维数随测量的范围变化而改变,即便是测量的起点有很小的移动,大部分范围重叠,维数也可能发生明显改变。为了能求得重分形对象的稳定维数,科学家作了大量的努力,数学家采用了高阶广义维来对应多次的作用机制,地学家采用了细化区块的方法来了解维数的空间变化,尽管这些努力取得一些的改进,但没有从根本上解决问题,自然对象的重分形成为分形理论应用于自然对象的一个长期没有很好解决的难点。本文改变了以往对重分形所用的尽量消除维数的局域差异追求统一维数的做法,用连续叠移法求得的分形维数谱代替一般维数,充分地表达重分形对象的维数变化规律。取得了以下认识:
1、提出了分形维数谱的概念,建立了测算分形维数谱的连续叠移法,并将连续叠移法系统地扩展为针对线性对象,平面对象,空间对象的完整算法。
2、由于分形维数谱与测量起点无关,使得原来测量起点与测量码尺二个相互影响相互关联的变量,减少为一个。这样可以通过不同尺码的试算了解尺码的变化引起的维数变化,讨论测量尺码变化与分形维数谱变化之间的关系,进而讨论地质事件和地质对象的特征尺度。
3、黄河河道分形维数谱显示了河道几何形态的分形维数与河流流经的构造单元的活动时期及演化历程有关,造山带与板块相比总体上造山带上的河道几何形态的分形维数大于板块内部河道几何形态的分形维数;对于造山带上流经的河流,造山带活动时期越新则河道几何形态的分形维数越大;对于板块内部流经的河段,分形维数在普遍低维的基础上,经过新生代重新活动的区段时,河道几何形态的分形维数将会明显提高。
4、浙江省海岸线分形维数谱显示了河口附近的第四纪沉积区岸线分形维数较低,而侵蚀的岩石岸线分形维数谱相对较高,近岸中新生代断陷盆地的活动与岸线的高分形维有一定的相关性。近50年浙江省海岸线的分维数谱的对比显示,低维段相对变化较小,高维段变化较大,总体上显示维数降低的趋势,可能与越来越多的人工海塘修建有关。
5、浙江省三塘汇地区地形高程模型的分形维数谱显示了断层相交部位,断层与地层界线的相交部位的分形维数较高,可能与这些位置岩石受力时易产生应力集中,岩石相对较破碎,风化侵蚀后地形形态较为复杂有关,这一现象的发生为从地形的形态特征识别断层提供了新的思路。
6、城市的建设是在自然地貌的基础上进行的,是人与自然结合的最好产物,绍兴的城市遥感影像分形维数谱显示新城区维数较高老城区维数较低,新城区的扩展与河网的分布具有某种联系。
7、以上研究显示分形维数是对地质作用类型的表述,作用力的大小与作用程度并不能明显地改变维数。通过分形维数谱中维数的统计,可以求得自然界重分形对象的维数分布特征。以黄河河道分形维数谱的统计为例,直方统计图显示一个构造单元内河道分形维数常出现多峰分布,而峰的多少与单元的演化的历程有关,越老的单元演化历程越复杂峰的个数越多。
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.
1、提出了分形维数谱的概念,建立了测算分形维数谱的连续叠移法,并将连续叠移法系统地扩展为针对线性对象,平面对象,空间对象的完整算法。
2、由于分形维数谱与测量起点无关,使得原来测量起点与测量码尺二个相互影响相互关联的变量,减少为一个。这样可以通过不同尺码的试算了解尺码的变化引起的维数变化,讨论测量尺码变化与分形维数谱变化之间的关系,进而讨论地质事件和地质对象的特征尺度。
3、黄河河道分形维数谱显示了河道几何形态的分形维数与河流流经的构造单元的活动时期及演化历程有关,造山带与板块相比总体上造山带上的河道几何形态的分形维数大于板块内部河道几何形态的分形维数;对于造山带上流经的河流,造山带活动时期越新则河道几何形态的分形维数越大;对于板块内部流经的河段,分形维数在普遍低维的基础上,经过新生代重新活动的区段时,河道几何形态的分形维数将会明显提高。
4、浙江省海岸线分形维数谱显示了河口附近的第四纪沉积区岸线分形维数较低,而侵蚀的岩石岸线分形维数谱相对较高,近岸中新生代断陷盆地的活动与岸线的高分形维有一定的相关性。近50年浙江省海岸线的分维数谱的对比显示,低维段相对变化较小,高维段变化较大,总体上显示维数降低的趋势,可能与越来越多的人工海塘修建有关。
5、浙江省三塘汇地区地形高程模型的分形维数谱显示了断层相交部位,断层与地层界线的相交部位的分形维数较高,可能与这些位置岩石受力时易产生应力集中,岩石相对较破碎,风化侵蚀后地形形态较为复杂有关,这一现象的发生为从地形的形态特征识别断层提供了新的思路。
6、城市的建设是在自然地貌的基础上进行的,是人与自然结合的最好产物,绍兴的城市遥感影像分形维数谱显示新城区维数较高老城区维数较低,新城区的扩展与河网的分布具有某种联系。
7、以上研究显示分形维数是对地质作用类型的表述,作用力的大小与作用程度并不能明显地改变维数。通过分形维数谱中维数的统计,可以求得自然界重分形对象的维数分布特征。以黄河河道分形维数谱的统计为例,直方统计图显示一个构造单元内河道分形维数常出现多峰分布,而峰的多少与单元的演化的历程有关,越老的单元演化历程越复杂峰的个数越多。
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.
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