数字高程模型的随机分形算法研究

本文研究了基于随机分形的数字高程模型算法。实践证明，用此方法进行形状逼近内插，所需数据量小，可节省大量内存及计算时间，较容易获得所需要的分辨率。     

The fractal geometry of the soil—covered landscape

The soil-covered landscape surface can be idealized from two viewpoints. The intuitive view is of a smooth, absolutely continuous surface with continuous contour lines and measurable in integral dimensions. The alternative view emphasizes the roughness, a surface of little regularity and at the limit of no contours, the appropriate measure being that of fractional Hausdorff dimension. Regularity is a local property and both idealizations need to stop far short of the limit to avoid awkward consequences. The dichotomy of viewpoint can be matched in the theory of Gaussian random fields. These, if they are smooth, are very smooth but if they are irregular they are highly irregular (erratic); there is no middle ground. This Belayev dichotomy is defined and both modes applied to the soil-covered landscape. On the one hand, if the landscape is subject to a general diffusive type degradation or more generally a Davisian downwasting regime then the curvature of the landscape surface is progressively straightened and the distribution of gradient (increments) along a typical traverse will eventually adopt a Gaussian form. Then from the irregular viewpoint the surface is ultimately well represented by a fractional Brownian surface of low Hausdorff dimension (2·0 < dim < 2·3). The Hausdorff dimension is directly related to the entropy of the landscape and as degradation proceeds both quantities decrease in value. On the other hand, if the surface is regarded as smooth and well represented by an absolutely continuous Gaussian field then the mean value of the number of upcrossings of a level or the extent of an excursion set will also be Gaussian. This analysis is restricted to one dimension; the number of times a profile curve crosses or the amount of time it spends above any given level. Predictions from both viewpoints are substantially corroborated in a map analysis of 15 sites on varied terrains in Southern England and the map analysis checked against one based upon digital tape data for one of the sites.     

广义生态水利的内涵及其过程与维度

总结中国工程水利、环境水利、资源水利、生态水利发展沿革，分析国内外生态水利研究进展、发展趋势及其特点，指出生态水利是人类社会发展到生态文明时代水资源利用的一种新途径和方式，以尊重和维护生态环境为主旨，开发水利、发展经济，为人类社会可持续发展服务。阐述了广义生态水利的内涵、定义和发展模式及其过程和维度，并提出以下结论和观点：①生态水利将水资源和水循环调控作为重要生态要素，从流域生态系统能量交换、生物链接、结构平衡、循环转化全视角开展研究，探索既能满足人类社会需求，又能兼顾水生态系统健康和良性发展的生态水利措施和方法。②建立了水利工程"规划设计—建设管理—运行调度"全过程、全生命周期的工程安全和生态安全保障体系，特别是将生态调度纳入水利工程全"服役期"，其中"后坝工时代"实施全流域大尺度生态调度，是生态保护和恢复最有效的措施。③从"生态环境-社会经济-水循环调控"三个维度，在生态文明视野下的国土空间规划治理体系中，科学把控生态水利的空间定位，促进"三生空间"优化布局，保障"三生用水"合理配置，优化"三生关系"耦合协调，实现生态保护和高质量发展，推动生态水利事业创新发展。     

地震活动的分形特征及其对地震预测的意义

岩石破裂是一个自相似过程,地震作为地壳岩石破裂的结果,它在时间和空间上的分布具有分形结构。基于系统科学和分形几何学的观点,本文采用标度变换法和嵌入空间法,分别研究了唐山7.8级、海城7.3级和松潘7.2级地震前后地震活动时、空分布的分维数,同时分析了宁夏灵武5.5级震群和澜沧5.0级前震序列的时间分维随时间的变化特征。初步结果表明:大震后余震的分维数明显增大,无标度区范围减小,展示了震后地震活动随机干扰背景增强！前兆性地震序列的时间分维数相对偏低,有序性增加。此外,文中还研究了单轴压缩下岩石破裂声发射序列的分形特征,结果表明,声发射序列亦具有自相似性,在岩石破坏过程中,声发射序列的分线数随时间的变化不是单调的。最后,籍助于“耗散结构理论”的基本概念,简要地探讨了地震时间、空间分维与地震活动熵的关系。提出了地震时、空分维作为表征地震孕育系统演化过程的序参量之一,应用于地震预测的可能途径及需要进一步研究的若干问题。     

新疆近期两次地震序列的时间信息维特征

本文以新疆两次中强地震的余震序列为例,探讨地震序列不均勻时间分布的分形特征。对其信息维的测算表明,无标度区范围基本稳定,同一时间段内信息维数随震级下限的升高略有降低;而对相同震级下限的样本群而言,不同时段的信息维数具有一定的差异。通常是强余震活动结束之后的信息维数略高于强余震活动期间的信息维数。这一特点对大震后地震趋势的合理估计具有积极意义。     

低位数线阵CCD高精度非接触尺寸测量

从提高测量精度、增大测量范围、经济、实用的角度出发,本文分析了常用的两种线阵CCD非接触尺寸测量方式存在的问题,提出了“单眼”单端扫描测量方式,并设计出了适合测量应用的线阵CCD驱动电路和计算机通用接口。通过实验,证明此方法是行之有效的。     

Multifractal measures,especially for the geophysicist

This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function (), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity is called Hölder exponent. In terms of the alternative functionf() used in the approach of Frisch-Parisi and of Halseyet al., one has ()=f()–E for measures supported by the Euclidean space of dimensionE. Whenf()0,f() is a fractal dimension. However, one may havef()<0, in which case is called latent. One may even have <0, in which case is called virtual. These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD _q, which is shown forq>1 to be a critical dimension for the cuts. An enhanced multifractal diagram is drawn, includingf(), a function called (q) andD _q.This text incorporatesand supersedes Mandelbrot (1988). A more detailed treatment, in preparation, will incorporateMandelbrot (1989).     

地震学中的某些非线性现象的初步分析

本文对地震中的一些现象,如小震调制、共维时间、共维面积以及嵌套调制和混沌的预报尺度进行了初步的分析和探讨,对我们关于前兆的复杂性以及对地震预报的进一步认识有一定的参考价值。     

云南地区强震前时空强分维特征

本文以标度变换法、相关函数法、最小二乘法分别计算时间分维D_t、空间分维D_s、强度分维D_m(b值),系统清理了云南地区1976年以来6级以上强震前时空强分维的变化特征,表明强震前的降维现象是普遍存在的,但各次强震前的异常三要素又表现出复杂的多样性。结果还表明,强震前小震活动在时间分布上的明显不均匀性主要表现在强震孕育地区,而在空间分布上的明显不均匀性却主要表现在强震孕育的外围地区。