【作者】 李锰；

【导师】 朱令人；

【作者基本信息】 中国地震局地球物理研究所 ， 固体地球物理学， 2002， 博士

【摘要】 以分形理论为基础．从不同层次、不同维度和用不同方法研究了天山地区地貌系统的分形与多重分形特征．并结合地貌形态所表现出来的分形特征对地貌形成发展的动力学机制进行了探讨。此外，利用强震前后不同时期地震垂直形变场的图象，分析了其多重分形谱异常特征与强震孕育发生的关系。 地形等高线的分形研究结果表明．不同地貌类型在不同标度范围内表现出不同的分形特点。在0.1-10km标度范围内，等高线分维值总体表现为最新隆起区(中低山区)>强烈隆起区(高山区)＞沉积凹陷区(盆地区)；在5-200km标度范围内则表现出强烈隆起区＞最新隆起区＞沉积凹陷区。等高线复杂性产生的直接原因主要是侵蚀作用和不均匀沉积作用造成的。等高线分维可作为区分不同地貌作用类型和作用强度的一个指标，并可借助不同标度下等高线的多分维特点，估计地貌的相对发展速度和阶段。 对不同构造地貌类型剖线的自仿射分形和多重分形特征的研究认为：在研究的标度范围内。地形剖线具有较好的自仿射分形性质，地形剖线并不是完全随机的布朗曲线，而是分形布朗曲线：不同地貌区分维值总体表现出高山区＞中低山区＞盆地区：同一地貌形态具有不同程度的各向异性。与构造地貌方向(斜坡)平行的剖线的分维值和渡越长度多大于与其垂直方向剖线的分维值和渡越长度。表明了构造运动与重力侵蚀作用的方向性。 在所研究标度范围内．隆起区分维值所表现出一般特点是大于1.5的类似于准周期运动的负反馈机制。侵蚀作用的强度越大。负反馈机制表现的越明显；对于以构造沉降作用为主的盆地区而言，各个方向的地形剖线的分维值均显示出小于1.5的正反馈机制。分维值的大小反映了外营力侵蚀作用的强度，也表明了内力构造作用的系统性、稳定性以及外营力地貌作用随机性、不稳定性：渡越长度是自仿射分形研究中的另一个重要参数。 对大型地貌组合形态剖线分形特征的研究认为．分维与测量的标度有关，表现出多度域分形特点，一定度域范围内的分维值表征了特定地质作用机制的方式和强度，不同度域范围的标度分界点有着特别意义，根据内、外营力地貌作用各自在宏观上的系统性和在微观上的不稳定性。提出以地貌分形特点和渡越长度为依据的地貌层次界定方案，研究指出了5Km左右应为宏观临界点：不同构造地貌区、不同取向的剖线的多重分形谱值域范围宽窄表现出中低山区＞高山区＞盆地区，垂直构造地貌斜坡方向＞斜交方向＞平行方向的特点，表明了内外营力作用的不均匀性和方向性。 不同类型地貌区二维地貌表面也表现出多度域分形特征，而且随着观测尺度的增加，每个区间的分维值均表现为依次减小，表明外营力作用的影响逐渐被内营力作用所取代：不同类型地貌区在相应区间的分维值表现为高山区＞中低山区＞盆地区，体现了不同类型地貌表面粗糙性或复杂性的差异，因此分维值大小可作为地貌表面外营力侵蚀作用强度的重要指标： 利用标度区的间断点和各种地貌类型表面分维值或宏观效应趋于一致，提出5-6Km左右可作为地貌的宏观临界点，并且与利用地貌剖线研究所得到的5Km这一数值是基本吻合的。该结果对理论地貌研究具有重要意义：不同地貌类型表面的多重分形谱值域表现为高山区＞中低山区＞盆地区的总体特征，地貌表面多重分形谱特征表明了内外营力地貌作用类型和强度在空间上分布的不均匀程度。 对分形地貌研究中遇到的问题进行了分析，并对多度域分形、物理场多重分形谱和外营力随机特性进行了数值模拟研究，结果表明：单一分维值并不表示只有一种分形结构：多重分形谱值域的宽窄表明了分形结构的非均匀或复杂程度；外营力地貌作用具有相对稳定性。 对不同时段地震形变场图象多重分形特征的研究表明，震源区及近震源区强震前垂直形变图象都出现信息维降低，多重分形谱曲线Dq变陡，值域范围变宽的特征，说明在强震前地壳垂直形变出现了局部化、不均匀性增强的行为，这些对地震预报都有重要的实际意义。更多还原

【Abstract】 Based on the fractal theory, fractal and multifractal properties of landform system in Tianshan area, Xinjiang, China, are studied from different aspects and hieracies and by using different computing methods. Furthermore, the dynamic mechanisms of geomorphological formation and evolution are discussed. In addition, the pattern fractal and multifractal features of different periodical sesmic deformation fields are analysed.The fractal dimensions of elevation isolines in 6 studying sections from 3 different types of geomorphological zones, including high mountain, low-moderate mountain and catchment basin,are computed by using successive coarsening method. The results show that all the studied isolines are statistical fractals, and the fractal dimensions take on different characters for different geomorphological types and scale ranges. It can be inferred that the fractional dimension values are closely dependent on the erosional intensities, and it can be a very important parameter for dynamic geomorphological researches.By using the standard deviation method, the scaling properties described by the local fractal dimension D and crossover length tc of 48 measured landform profiles in different direction of 6 different studied landform sections are calculated . After that, the multifractal spectra Dq-q are computed by fixed-mass method. The results show that in the studied scaling range different types of landscapes and profiles in different directions perform different fractal properties, that is, the D value and crossover length ^ decrease in turns with the landform type from high-moutain, mid-low mountain to basin , and the profile parallel to wear grooves often has lower D values(<1.5) than those perpendicular to wear grooves do(1.5) in the same section. Furthermore, the Dq value ranges of profile multifarctal spectra in different landform types and in different directions of the same sections perform different properties and anisotrpies. It can be concluded that the landscape fractal properties depends closely on the intensity, manner and inhomogenity of exogenic and inogenic processess,and with the properties, we can study quantatively the dynamic geomorphic process.By using the same methods just above, local fractal dimensions D , crossover length tc and the multifractal spectra Dq-q of two large-scale landform profiles (across and along Tianshan mountain ranges respectively) are calculated .The results show that in the studied scaling range the two profiles perform different scaling properties ,and both of them can be divided to three evident different linear scaling subsections. In addition,the Dq-q curves behave in different shapes. It can be concluded that the scaling properties depend colsely on the way, intensity .acting scale and distribution in space of inogenic and exogenic processes. According to the scaling natures of the two landform profiles , it is proposed that the 5Km scale is the low limit of the inogenic process effects which begin to dominate landscape patterns in landform systems.By using the projective covering method and projective covering probability, fractal and multifractal dimensions of different types of landform sueface above are computed. Results show that all the studied landform surface are not simple fractals, but multi-range scaling fractals, and the fractal dimensions increase with the landform type from basin to mid-low mountain and highmountain. Nevertheless, different type landscapes perform different Dq-q curve shapes.which the Dq value has the widest range in the high mountain type, the second one is the mid-low mountain type, and then the basin type. It suggests that the fractal dimension value mainly depends on the exogenic process intensity and its processing scale range, and the Dq value range indicates inhomogenous distribution of the exogenic process intensity. According to the scaling natures of different type landform, it can be concluded that 5-6Km scale is the high limit of exogenic process effects which dominate landscape patterns.Usin更多还原