Testing linear models of sea-floor topography

Stochastic models can generate profiles that resemble topography by taking uncorrelated, zero-average noise as input, introducing some correlation in the time series of noise, and integrating the resulting correlated noise. The output profile will depict a nonstationary, randomly rough surface. Two models have been chosen for comparison: a fractal model, in which the noise is correlated even at large distances, and an autoregressive model of order 1, in which the correlation of the noise decays rapidly. Both models have as an end-member a random walk, which is the integration of uncorrelated noise. The models have been fitted to profiles of submarine topography, and the sample autocorrelation, power spectrum and variogram have been compared to the theoretical predictions. The results suggest that a linear system approach is a viable method to model and classify sea-floor topography. The comparison does not show substantial disagreement of the data with either the autoregressive or the fractal model, although a fractal model seems to give a better fit. However, the amplitudes predicted by a nonstationary fractal model for long wavelengths (of the order of 1000 km) are unreasonably large. When viewed through a large window, ocean floor topography is likely to have an expected value determined by isostasy, and to be stationary. Nonstationary models are best applied to wavelengths of the order of 100 km or less.     

矿产勘查中化探异常下限的多重分形计算方法

化探异常下限计算方法在矿产勘查和资源预测中非常重要。传统的计算方法存在依据不充分的问题。这里在研究地球化学场数据分布的基础上,提出了多重含量～频数分形计算方法。研究表明,多重分形异常下限计算方法较之传统的方法具有理论基础扎实、适用性较广的特点。     

The problem of scaling in grid-related hydrological process modelling

This article shows some important scaling aspects that exist in hydrological process grid modelling with GIS, with respect to selecting the optimal grid width. Hydrologically relevant space parameter fields should often be regarded as self-similar fractals for which certain invariance characteristics are applied. These characteristics are especially important if there is an extensive change in the model grid width. The self-similarity generates simple scaling laws, which can be used for rescaling procedures. © 1997 John Wiley & Sons, Ltd.     

Applied Geography and New Geographies

Scale and resolution have long been key issues in geography. The rapid development of analytical cartography, GIS, and remote sensing (the mapping sciences) in the last decade has forced the issues of scale and resolution to be treated formally and better defined. This paper addresses the problem of scale and resolution in geographical studies, with special reference to the mapping sciences. The fractal concept is introduced, and its use in identifying the scale and resolution problem is discussed. The implications of the scale and resolution problem on studies of global change and modeling are also explored.     

大气边界层风速脉动的分形模拟

应用曲线分数维计算方法计算大气边界层实际风速观测资料的分数维值,并根据分形理论构造出一个理论模型来模拟真实的大气边界层风速时间序列。将模拟和真实数据的一些重要的统计特征,例如方差、风速概率分布、谱密度函数和自相关函数等,进行了比较,结果表明二者具有很好的一致性。     

高应力下颗粒材料一维力学特性研究(Ⅱ):蠕变性质

现场和试验观测表明,高应力下砂土的蠕变过程伴随着颗粒破碎现象。通过开展砂土的一维蠕变试验发现,试样的颗粒破碎量随时间增加而增加,且蠕变速率与颗粒破碎速率成正比。在此基础上,分析了蠕变过程中能量转化关系,利用表面物理学和分形几何学理论,得到了一维蠕变条件下颗粒破碎速率与宏观蠕变速率之间的关系表达式。研究结果表明,高应力一维蠕变条件下颗粒材料的宏观蠕变速率与颗粒破碎速率成正比。最后,对该研究采用的等效化方法进行了讨论。     

沈阳经济区城市体系空间结构的分形研究

以沈阳经济区城市体系为研究对象,利用聚集维数、关联维数及计盒维数的基本模型对该城市体系的空间结构进行了分析,认为沈阳经济区城市体系结构具有分形特征,测算结果表明:沈阳经济区城市体系的空间分布呈现围绕中心城市-沈阳的向心式聚集,城市之间交通网络通达性好,空间形态较辽宁省城市体系紧凑。沈阳经济区城市体系的划分相对合理,但仍需优化。建议充分发挥沈阳作为中心城市的强辐射与带动作用,并通过打造沈抚、沈本、沈铁、沈辽鞍营和沈阜5条城际连接带,推动城镇化、加速区域一体化进程;通过产业整合和产业集群化促进资源优化配置,提高城市之间的相互作用,促进沈阳经济区形成联系紧密的"区域经济共同体"。