基于DEM的活动构造地貌参数研究
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摘要
构造地貌是指受构造内动力作用控制,通过内外营力相互作用所奠定的能够反映一定构造特征的地貌形式。研究构造地貌的学科即为构造地貌学。构造地貌学经历了早期的静态构造地貌研究和20世纪60年代以后的动态构造地貌研究。20世纪80年代以后,由于新构造的蓬勃发展,不少学者强调构造地貌主要是新构造活动控制下的地貌。近二十年来伴随着活动构造研究的开展,活动构造地貌,尤其是与地震活动断层有关的构造地貌研究受到国内外学者广泛关注,形成了构造地貌研究的新领域。构造地貌的研究,从本质上说是通过研究各种地貌标志的变形和位错来判断地壳活动特征。在研究方法上,结构形态分析法是构造地貌研究最基本、最常用的方法。由于构造地貌的结构形态可以用很多参数来定量描述,随着高分辨DEM数据的出现以及计算机技术的不断发展,近年来越来越多学者通过定量分析相关地貌参数来研究构造活动,使构造地貌的研究迈上了新台阶。
     本论文试图选择区域性和小流域性两类参数,在活动块体的大尺度和单一断裂带的小尺度两个层次上开展地貌参数研究。在区域性地貌参数中,分形参数综合描述和反映了地貌特征,它能应用在任何类型、任何尺度上的地貌中,因此本论文利用分形参数分别分析大尺度的鄂尔多斯块体及其周边地区以及小尺度的霍山山前断裂带的分形特征,并根据两研究区的分形特征阐述分形参数的地形意义、地质意义与构造意义。在小流域性参数中,本论文根据霍山山前断裂带的倾滑活动性质以及横穿断裂的冲沟发育特征,选择了河流纵剖面数学拟合函数、基于河流水力侵蚀模型坡度-面积关系以及凹曲指数与陡峭指数、河流坡降指标与Hack剖面等描述河流纵剖面形态的参数来反映横穿断裂的冲沟其发育形态对断裂带活动的响应。
     1、地貌的分形参数与地貌分区
     分形理论为形态、分布或结构极其不规则,但具有自相似性的自然现象的定量描述提供了几何描述方法与数学模型。分形几何可以从整体性和科学性方面对地表形态的综合特征进行定量化描述。计算分形参数的方法很多,本论文采用能很好地适应地形起伏自相仿性以及DEM高程数据栅格格式的直接测量地表分形特征的优良方法—变差函数法,并采用能很好地识别地形空间差异的元分维模型。利用变差函数法和元分维模型分别计算了大空间尺度的鄂尔多斯块体及其周边地区(DEM空间分辨率为90 m)以及小空间尺度的霍山山前断裂地区(DEM空间分辨率为2.5 m)的分形参数—地表分维值与截距值。结果显示,无论是鄂尔多斯块体及其周边大空间尺度的区域还是霍山山前断裂带小空间尺度的地区,分形参数的分布均具有明显的空间差异性与区域分带性。通过K-Means聚类分析法对上述两种类型的研究区进行基于分形参数的地貌区自动划分,结果显示,两研究区所得的分形分区结果与地貌类型、地层分布以及构造特征都具有很好的一致性,而且每一分形分区都具有特征的分形参数值。
     通过地表分维值与截距值联合定量聚类,鄂尔多斯块体及其周边被群集成五个分形分区:河套盆地和银川盆地(Aa分形区)是地表分维值高值区和截距值低值区,分维值主要为2.8-3.0,截距值主要为0-1;鄂尔多斯块体南部陕北黄土高原区(Bc分形区)的地表分维值主要为2.5-2.7,截距值主要为2.5-3.5;吕梁山、贺兰山、乌拉山等山区(Cc分形区)也是截距值高值区,主要为2.5-3.5,但地表分维值较低,主要为2.4-2.6;鄂尔多斯块体北部库布齐、毛乌素等沙漠区(Db分形区)与渭河、山西盆地带(Dd分形区)都是地表分维值低值区,地表分维值大部分低于2.5,但两区域的截距值差异明显。沙漠区地形起伏较缓,截距值主要为0-1.5,而渭河盆地和山西盆地带的截距值没有明显的优势范围。
     霍山山前断裂带仅利用地表分维值就达到很好的分区结果,在该研究区本论文得到五个分形分区:霍山中北部地段(A分形区)是低分维值区,分维值主要为2.1-2.3;霍山南部地段(B分形区)的分维值比中北部地段高,主要为2.2-2.4;汾河沿岸的黄土台地(C分形区)具有中等大小的分维值,主要为2.3-2.5;山前洪积扇的地表分维值从后缘到前缘(D分形区)逐渐增大,主要为2.4-2.6,洪积扇的前缘平缓区与汾河冲积区(E分形区)具有全区域最高的分维值,主要为2.6-2.7。
     本论文从信号波的角度阐述了地表分形特征的地形意义,分形参数反映和描述了地形起伏的形态,地表分维值反映了地形起伏的频率特征,高分维值的地形表现出高频率的起伏,低分维值的地形表现为低频率的起伏,而截距值反映的是地形起伏的幅度大小。此外,本论文还阐述了地质作用与外力作用对地表分维值的影响。构造隆升作用能在长波长上影响地形,使地表分维值降低。侵蚀作用可使地形粗糙化,地表分维值增大。岩层性质是影响侵蚀作用强弱的重要因素,因此地表分维值与岩层性质具有紧密关系。扩散作用与堆积作用使地形趋于平滑,地表分维值变小。
     2、霍山山前断裂带水系纵剖面形态参数的构造响应
     本论文通过分析霍山山前断裂带上64条冲沟纵剖面形态的多种参数来反映冲沟发育对构造运动的响应。这些参数包括河流纵剖面的数学拟合函数,基于河流水力侵蚀模型的坡度-面积关系以及凹曲指数、陡峭指数,河流坡降指标与Hack剖面。
     河流在不同的构造环境以及不同的发育阶段会呈现出不同的数学函数形态特征,常见的为线性函数、指数函数、对数函数以及乘幂函数。霍山山前断裂带上的冲沟均呈现为线性函数形态或轻微下凹的指数函数形态。在分析了发育时间、地区气候特征、河床基岩性质以及构造运动等四个影响河流纵剖面形态发育的主要因素后,本论文认为上新世以来霍山山前断裂持续而强烈的隆升作用,尤其是全新世以来时间间隔较短的多次强烈活动是导致冲沟发育一直表现为幼年期的近直线的下凹程度很小的特征,而这种特征正是冲沟纵剖面形态发育对霍山山前断裂带隆升运动的明显响应。
     河流水力侵蚀模型能够反映构造隆升作用与河流下切侵蚀作用之间的关系。当基岩隆升速率与河流下切侵蚀速率达到均衡时,基于河流水力侵蚀模型的坡度-面积(S-A)双对数图呈现直线形态;当基岩隆升速率大于河流下切侵蚀速率时,S-A双对数图表现为上凸特征;相反,则表现为下凹特征。在所统计的横穿霍山山前断裂带的64条冲沟其S-A双对数图均一致地呈现为上凸特征。由河流水力侵蚀模型得到的凹曲指数θ值平均值仅为0.223,远远低于均衡河道的经验平均值(0.49)。S-A双对数图的上凸特征以及相当低的凹曲指数是其对霍山山前断裂带强烈的隆升作用远远大于河流下切侵蚀作用的响应。另外,由河流水力侵蚀模型得到的冲沟陡峭指数log(ks)值呈现出老爷顶一带最高,南北两侧低,而且北部比南部高的分布特征,这是冲沟纵剖面的陡峭指数对霍山山前断裂带地区老爷顶一带隆升速率最大,南北两侧较低,而且北部隆升速率比南部高这一隆升速率区域差异的响应。
     Hack剖面是用半对数的方程式来描述河流纵剖面形态,它常用于描述河流纵剖面整体上对构造运动的调整。河流坡降指标(SL值)则用来描述河流纵剖面局部坡度的变化。研究区内冲沟的Hack剖面均呈现为上凸特征,这是冲沟Hack剖面对构造隆升作用十分典型的响应。另外,部分冲沟其Hack剖面以断裂位置为拐点,断裂上游河段的Hack剖面明显呈现为上凸形态,而断裂下游河段则呈现为直线形态或轻微下凹形态,这表明了冲沟正处于受构造运动作用后往新均衡剖面演化的初期阶段。在河流坡降指标方面,部分冲沟在断裂附近出现明显异常高的河流坡降指标值(SL/k’),这是断裂运动在该处形成裂点的表现。
     上述冲沟纵剖面的形态特征都是对霍山山前断裂垂向上运动的响应,而断裂的每次垂直活动在沟床上都能以裂点形式记录下来,因此通过裂点序列来分析断裂活动事件序列是一个很好的途径。本论文在23条冲沟纵剖面上很好地识别出断裂活动诱发裂点,部分冲沟纵剖面形态和裂点位置得到野外测量数据的验证。其中有7条河流基本只有一级裂点,而且裂点均位于断裂位置上,高度达4-9 m,推测裂点自形成后并未向上游发生明显迁移,并接受了多次事件叠加。另外,在16条冲沟上分别识别出2-3级裂点,高度主要为2-6 m,最新的裂点向上游迁移了40-70 m,次新的裂点则主要分布在距断裂150-250 m的河段内,最老的裂点大致位于300-500 m的距离。裂点后退迁移的速率与断裂上游流域面积成正相关关系。本论文认为最新的裂点是1303年洪洞8级地震(事件Ⅲ)造成的,并假定全新世中晚期以来研究区内河流溯源侵蚀速率基本不变,以此推算出次新裂点对应的地震事件(事件Ⅱ)发生在距今3336-2269 a之间,最早一次事件(事件Ⅰ)发生在距今5618-4504 a之间,重复周期约为1500-2600 a之间,这与前人通过探槽揭露的古地震事件序列的年代及重复周期基本一致。
Tectonic geomorphology is the landscape that is controlled by tectonic processes and established by endogenic along with exogenic processes. Tectonic geomorphology has experienced two stages: the static tectonic geomorphology in the early period and the dynamic tectonic geomorphology after 1960s. After 1980s, many researchers emphasize that tectonic geomorphology mainly is the one controlled by neotectonics. With the study on active tectonics in recent twenty years, active tectonic geomorphology, especially tectonic geomorphology related with the active faults, has already attracted much attention of researchers and has become a new research field. Tectonic geomorphology, in essence, is to study the deformation and dislocation of a variety of landscapes with the aim to reveal the dynamics in the earth. Among the main analytical methods of tectonic geomorphology, the morphological analysis is the most basic and the most commonly used one. And the morphology of the landscape can be described quantitatively by many geomophologic indexes, thus, more and more studies on tectonic geomorphology are made through a series of geomophologic indexes as the high-resolution DEM data has been developed in recent years. Therefore, this progress makes the tectonic geomorphology to a new stage.
     This thesis attempts to carry out a study on tectonic geomorphology on the large-scale region -- the Ordos Block and surrounding areas and the small-scale region– the Huoshan Mts. piedmont fault area with geomophologic indexes. Two types of geomophologic indexes are selected in this work. One is the regional indexes, and the other is the watershed indexes. Fractal parameters which are the regional indexes can be used to describe all kinds of landscapes with different scales. This thesis adopts the fractal parameters to characterize the fractal features of the Ordos Block and surrounding areas as well as the Huoshan Mts. piedmont fault area. On the basis of the fractal features of the two study areas above, the topographic significance, geological significance and tectonic significance of the fractal parameters are discussed. According to the dip-slip movement of the Huoshan Mts. piedmont fault and the characteristics of gullies across the Huoshan Mts. piedmont fault, this thesis adopts the watershed indexes to characterize the responses of the gullies to the tectonic movement. The watershed indexes using in this thesis include the mathematical functions fitting the longitudinal profiles of the gullies, the slope-area (S-A) plot, the concavity index and the steepness index from the stream-power incision model, the stream length-gradient index (SL index) and Hack profile.
     1. Fractal parameters of the landscape and the geomophologic zonation
     Fractal theory provides a quantitatively descriptive way and a mathematical model to the phenomenon, of which morphology, distribution or structure is extremely irregular but self-similar. Fractal geometry describes the overall characteristics of the earth surface in a comprehensive and scientific way. From many methods available for calculating the fractal parameters, the variogram method is selected in this thesis. The variogram method has proved to be a more intuitive and better way to measure fractal dimensions of landscapes which are self-affine and can be used with the grid-based DEM data. The cellular model which is carried out in a moving window operation can be used to reveal the variation of the fractal feature over landscapes. The DEM data with the spatial resolution of 90 m and 2.5 m are employed to the Ordos Block and surrounding areas, and the Huoshan Mts. piedmont fault area, respectively. Such fractal parameters as the fractal dimension (D) and the ordinate-intercept (γ) of the Ordos Block and surrounding areas and the Huoshan Mts. piedmont fault area are obtained using the variogram method combined with the cellular model. The results show that in both the Ordos Block and surrounding areas and the Huoshan Mts. piedmont fault area, the distributions of the fractal parameter are region-dependent apparently. The zonation results achieved by K-Means clustering algorithm reveal that the quantitative geomorphic zones defined by the fractal parameters are consistent well with the landscape types, lithology and structural features in the both study areas, and each zone has characteristic fractal values.
     There are five fractal zones defined by the fractal dimension and the ordinate-intercept comprehensively in the Ordos Block and surrounding areas. The Hetao Basin and the Yinchuan Basin (Zone Aa) are characterized by high fractal dimensions and low ordinate-intercepts (D = 2.8-3.0,γ= 0-1) in contrast to the mountainous areas including the Lvliang Mts., the Helan Mts. and Wulaer Mts. (Zone Cc) where low fractal dimensions and high ordinate-intercepts (D = 2.4-2.6,γ= 2.5-3.5) are found. The other zones are defined by the following fractal parameters, respectively: the North Shaanxi Loess Plateau in the southern part of the Ordos Block (Zone Bc), D = 2.5-2.7 andγ= 2.5-3.5; the Kubuqi Desert and the Mu Us Desert in the northern part of the Ordos Block (Zone Db), D = 2.2-2.4 andγ= 0-1; the Shanxi Graben System and the Weihe Basin (Zone Dd), D = 2.2-2.4 and no predominant ordinate-intercept values.
     Similarly, there are five fractal zones defined by the fractal dimension in the Huoshan Mts. piedmont fault area. The northern and central sections of the Huoshan Mts. (Zone A) are characterized by low fractal dimensions of 2.1-2.3. The fractal dimensions in the southern section of the Huoshan Mts. (Zone B) are higher than that in the northern and central sections and mainly in the range of 2.2-2.4. The loess mesas along the Fenhe River (Zone C) have the intermediate fractal dimensions of 2.3 -2.5. The fractal dimensions increase from the back part to the frontal part of the alluvial fans. The fractal dimensions in the back parts of alluvial fans (Zone D) fall mainly in the range of 2.4-2.6. The frontal parts of alluvial fans and the flat area of the Fenhe River have the highest fractal dimensions of 2.6-2.7.
     Based on the fractal features of the Ordos Block and surrounding areas and the Huoshan Mts. piedmont fault area, the topographic significance of the fractal parameters are discussed with the perspective of signal waves. The fractal dimension reveals the frequency of variation in elevation of the landscape and the ordinate-intercept value reflects the amplitude of the relief. High fractal dimension implies a high frequency of variation in elevation, while a low fractal dimension implies a low frequency of variation in elevation. The high ordinate-intercept value reflects the high amplitude of the relief, while the slow one reflects the small amplitude of the relief. The relationships between the fractal dimension and the strata and geological processes are analyzed to reveal the geological significance and tectonic significance of the fractal dimension. The tectonics can bring the information into the topography at long wavelengths, thus tending to make the fractal dimension low. Erosional process roughens the earth surface and can make the fractal dimension high. The lithology is an important factor affecting the erosional roughening, therefore, the fractal dimension is related to lithology closely. The diffusive process and depositional process make the earth surface smooth and the fractal dimension trends to be low.
     2. Morphological indexes of longitudinal profiles of gullies and their responses to the tectonic movement
     This thesis analyzes several morphological indexes about the longitudinal profiles of 64 gullies across the Huoshan Mts. piedmont fault to characterize the responses of the gullies the tectonic movement. These indexes include the mathematical functions fitting to the longitudinal profiles of the gullies, the slope-area (S-A) plot, the concavity index and the steepness index from the stream-power incision model, the stream length-gradient index (SL index) and Hack profile.
     Longitudinal profiles of the gullies in different tectonic settings and different developmental stages show different morphological forms which can be fitted by such mathematical functions as the linear function, the exponential function, the logarithmic function and the power function. The longitudinal profiles of the gullies across the Huoshan Mts. piedmont fault are fitted best by the linear forms or the exponential forms with slightly concave shape. After analyzing such main factors affecting the morphological forms of the gully longitudinal profiles as the time, the climate, the rock of the riverbed and the tectonic movement, this thesis concludes that the linear forms or the exponential forms with very small concavity on the gully longitudinal profiles show the very young gullies are caused mainly by the strong activities of the Huoshan Mts. piedmont fault since Pliocene. The characteristics of the gully longitudinal profiles above exhibit the response of the gullies to the uplift of the fault.
     The stream-power incision model describes the relationship between the tectonic uplift and fluvial incision. When the bedrock uplift rate and the fluvial incision rate are kept in equilibrium, the S-A plot obtained from the stream-power incision model presents a straight line. When the bedrock uplift rate is higher than the fluvial incision rate, the S-A plot exhibits a convex form. On the contrary, the S-A plot shows a concave form in the situation that the bedrock uplift rate is smaller than the fluvial incision rate. All of the S-A plots of 64 gullies across the Huoshan Mts. piedmont fault present a convex form, which is the response of the gullies to the strong uplift of the fault. The average value of the concavity index (θ) of 64 gullies is 0.223, which is much smaller than the empirical value (0.49) of the rivers in steady state. The very small value of the concavity index indicates that the response of the uplift of the fault is stronger than the fluvial incision. The steepness values of the gullies rising from the Laoyeding Mt. are highest, while they are lower in the gullies rising from the northern mountains and southern mountains. Moreover, the steepness values of the gullies in the northern mountains are higher than that of the gullies in the southern mountains. The distribution of the steepness values described above corresponds to the difference in the uplift rates of the Huoshan Mts. The Hack profile which is a semi-logarithmic plot is usually used to depict the overall adjustment of the river longitudinal profile to tectonic movement, while the stream length-gradient index (SL index) is used to describe the changes on the local slope of the river longitudinal profile. All of Hack profiles of 64 gullies are featured by the convex curves, which are the characteristic response to the uplift of the fault. In addition, some of Hack profiles have an inflexion in the position of the fault. On these Hack profiles, the upstream sections have the convex shapes, while the downstream sections are presented as the early stage of re-establishment of grade equilibrium after the fault displacement. In the analysis of SL index, there are extremely high SL / k' values appearing in the reaches near to the fault, which implies the knickpoints caused by the fault movement exist.
     All the features of the morphological indexes of the gulliy longitudinal profiles described above show the responses of the gullies to the fault movement. Each fault movement in vertical direction can be recorded by the knickpoints, therefore, it is a good way to know the fault movement event through the knickpoints. The knickpoints are identified in 23 gullies. Some knickpoints are testified by the field data. There are 7 gullies with one knickpoint. This kind of knickpoints, of which the heights range from 6-9 m lie on the fault, which implies that there are several knickpoints superposed together and the knickpoints have not migrated upstream. There are 16 gullies with 2-3 knickpoints whose heights range between 2 and 6 m. The latest knickpoints have been migrated upstream to the distance of 40-70 m from the fault. The knickpoints of intermediate ages are at a distance of 150-150 m upstream from the fault and the oldest ones at a distance of 300-500 m. The rates of headward erosion for the gullies have a distinctively positive trend with the upstream areas. Under the conditions that the latest knickpoints are associated with the 1303 Mw8.0 Hongdong earthquake (EventⅢ) and that the gullies keep the same rate of headward erosion during the Holocene, EventⅡis estimated to take place during 3336-2269 a B.P. and EventⅠis estimated to take place during is estimated to take place during 3336-2269a B.P., respectively. The recurrence of events is about 1500-2600 a. These results are consistent with that obtained through the trench investigations.
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