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.     

求解活断层滑动速率的分形方法及其初步应用

断层平均滑动速率是描述和衡量断层活动强度的一个重要指标。破裂过程的分形结构决定了断层能量结构和几何结构都存在自相似性,断层系的尺度无关性对于断层活动性的定量化研究有着重要的理论价值和实用价值。本文以破裂发展的分形理论为基础,发展了求解活断层现代滑动速率的分形方法,导出了一个便于应用的分形公式。并以川西鲜水河断裂带为例对其中的活动断层的现代滑动速率作了计算,结果表明分形方法是研究断层活动强度的有效捷径。     

依兰-伊通断裂北段地震活动性研究

依据地质构造背景，应用测震学的基本方法，讨论依兰-伊通断裂北段的地震活动特征，由地震活动在时空强显示的一些规律性，认为近期该区域中强地震活动可能处于较弱势状态。     

Fractal interrelationships between topography and structure

Factal interrelationships between topography and structure are investigated in two areas of the North American central Appalachian Mountains: one in the intensely deformed Valley and Ridge province and the other in the relatively undeformed foreland area of the Appalachian Plateau province. In the Valley and Ridge province the fractal dimensions of topographic and structural relief vary systematically along the strike of major folds following a second-order polynominal trend. Cross-correlation of the fractal dimensions of topography to structure indicates that there is a significant positive correlation between the two. Fractal analysis of topography in the relatively undeformed foreland area of the Appalachian Plateau revealed no significant variation in the fractal characteristics of topography across the study area, consistent with the lack of near-surface structure. However, fractal analysis of deeper structures beneath the Plateau area undertaken using reflection seismic data revealed step-wise increases in fractal dimension from the deeply buried Precambrian basement to the near-surface. These vertical changes in fractal dimension can be related to the tectonic history of the area. Taken together, these studies indicate that fractal analysis provides a means to quantify and compare the influence of near-surface structure on topographic development and lateral and vertical structural variability. Fractal analysis provides a means to characterize the systematic changes in the complex patterns formed by topography and structure and the interrelationships between them. Similarity in their fractal characteristics implies similarity in the relative amplitude and abundance of different wavelength features in the topographic or structural profile. © 1998 John Wiley & Sons, Ltd.     

地震主压应力轴分布的分形特征研究

本文通过对全国许多地区大量的小震及中、强地震主压应力轴分布情况的详细研究，发现地震主压应力轴的分布具有分形结构特征，并满足幂函数关系式ｌｇＮ＝ａ＋ｂＪ，其特征值ｂ与分数维大致成反比，无标度区约为２°－８°。中强以上地震的前震序列的地震主压应力轴分布的特征值似乎明显比小震群活动的地震主压应力轴分布的特征值大。     

云南10次大震前地震活动分形研究

本文通过１９６５－１９９３年发生在云南及邻区８组１０次６．８≤Ｍ≤７．７大震前空间容量维、关联维、信息熵等多种参数系统的计算研究，发现１０次大震前降维减熵异常十分显著。     

The Fractal Feature of Granulometric Composition in Fault Gouges from the Yishu Fault Zone and Adjacent Northwest-Trending Faults and Its Seismo-geological Implications

In this work,the fractal dimension of granulometric composition in the fault gouge from the Yishu fault zone and northwest-trending faults on its west side is calculated and studied based on the fractal theory of rock fragmentation.The seismo-geological implications of the fractal dimension of granulometric composition in fault gouges are also discussed.The results show that the Yishu fault zone is more active than the northwest-trending faults and the Anqiu-Juxian fault is the most active in the Yishu fault zone.The fractal dimension of fault gouge is a parameter describing the relative active age and rupture mode of the fault and forming age of the fault gouge.The fractal dimension value is also related to the parent rock,thickness,structural position,and clay content of the fault gouge.     

基于分形理论的地裂缝成因机制研究.

依据分形理论分析了清徐境内交城断裂带、地裂缝以及地貌的分形结构特征.同时根据分析结果讨论了地裂缝、断裂以及地貌之间的内在联系,并对清徐地裂缝的成因机制进行了研究.     

沂沭断裂带及其附近断裂的断层泥分形特征及其地震地质意义

利用岩石碎裂数目的分形理论，分析，计算了沂沭断裂带及其西侧北西向断裂的断层泥粒度成分的分维值，讨论了断层泥粒度成分分维的地震地质意义，研究结果表明，沂沭断裂带内的断裂活动的强度大于北西向断裂活动强度；Ｆ２是沂沭断裂带中活动最强的一条断裂，断层泥粒度成分分维值可作为表征断裂活动时代，破裂形式和断层泥形成斫代等的参量；分维值还与断层泥的母岩，厚度，粘土矿物含量和所处的断裂部位等相关。     

Remote measurement of river morphology via fusion of LiDAR topography and spectrally based bathymetry

This study developed and evaluated a hybrid approach to remote measurement of river morphology that combines LiDAR topography with spectrally based bathymetry. Comparison of filtered LiDAR point clouds with surveyed cross‐sections indicated that subtle features on low‐relief floodplains were accurately resolved by LiDAR but that submerged areas could not be detected due to strong absorption of near‐infrared laser pulses by water. The reduced number of returns made the active channel evident in a LiDAR point density map. A second dataset suggested that pulse intensity also could be used to discriminate land from water via a threshold‐based masking procedure. Fusion of LiDAR and optical data required accurate co‐registration of images to the LiDAR, and we developed an object‐oriented procedure for achieving this alignment. Information on flow depths was derived by correlating pixel values with field measurements of depth. Highly turbid conditions dictated a positive relation between green band radiance and flow depth and contributed to under‐prediction of pool depths. Water surface elevations extracted from the LiDAR along the water's edge were used to produce a continuous water surface that preserved along‐channel variations in slope. Subtracting local flow depths from this surface yielded estimates of the bed elevation that were then combined with LiDAR topography for exposed areas to create a composite representation of the riverine terrain. The accuracy of this terrain model was assessed via comparison with detailed field surveys. A map of elevation residuals showed that the greatest errors were associated with underestimation of pool depths and failure to capture cross‐stream differences in water surface elevation. Nevertheless, fusion of LiDAR and passive optical image data provided an efficient means of characterizing river morphology that would not have been possible if either dataset had been used in isolation. Copyright © 2011 John Wiley & Sons, Ltd.     

分形几何在岩土力学研究中的过去、现在与未来

首先简略地介绍了分形几何理论及其方法。从岩土材料结构的定量描述、流体在岩土体中的渗流问题、岩土材料强度的分形模型和分形空间的力学特征四个方面叙述了分形理论在岩土力学研究中取得的成果及应用。指出只有将岩土力学系统在欧氏空间的各种基本变量、原理和方法向分形空间推广和拓展,才能产生对岩土材料非线性力学行为的新认识,这也是分形理论在岩土力学研究中进一步深化的基础。     

陆态网络重力测网的分形特征与地震监测能力分析

介绍了“中国大陆构造环境监测网络”（简称“陆态网络”）重力观测体系。从分形几何学角度研究了陆态网络重力测网的分形特征,计算得到测网分维数D_f=1.5598、最佳网格化间距r=139km。综合测网分维数与重力时变距、重力异常范围、测网范围等量化指标,对陆态网络重力测网的地震监测能力进行分析,结果表明,测网最佳网格化间距等特征值与M_S6.0地震引发的重力场变化区域的特征异常区半径等统计量化指标接近,具备监测我国除边界及藏北无人区以外大陆区域的M_S6.0及以上地震的能力。     

分数维约束下的自适应对消技术研究

介绍了自适应对消技术的基本原理,分析了自适应对消技术的优缺点,针对一些缺点提出了相应的改进方法。由于常规自适应对消技术是通过迭代技术实现的,需要迭代一定次数后才能确定最佳参数,所以在信号起始位置和有效信号尾部收敛效果不好,从而影响滤波效果。引入hausdorff维数来约束地震信号,首先求取原始地震信号的hausdorff维数谱,利用有效信号与随机噪音维数的不同,将有效信号以外的随机噪音滤除,并将自适应对消中的参考噪声对应位置的随机噪音去除;然后将更新后的地震信号和参考噪声进行自适应滤波,从而得到一个优化的自适应对消滤波器。     

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。     

地震活动性的层次模型及推导的地震活动经验公式和分维性质

文章从一个简单的地震活动层次模型出发，推导地震活动性中几个经验公式以及地震活动的时、空和震源大小分维性质。研究结果表明：（１）震级和频度关系式即Ｇｕｔｅｎｂｅｒｇ－Ｒｉｃｈｔｅｒ公式中的比例系数ｂ值等于震级和平均震中距关系式中的比例系数ｂ１的２倍，并且ｂ值也等于震级和平均时间间隔关系式中的比例系数ｂ２。（２）平均震中距分维值为２，平均时间间隔分维值为１，震源大小分布的分维值的２ｂ。     

Spatial prediction of river channel topography by kriging

Topographic information is fundamental to geomorphic inquiry, and spatial prediction of bed elevation from irregular survey data is an important component of many reach‐scale studies. Kriging is a geostatistical technique for obtaining these predictions along with measures of their reliability, and this paper outlines a specialized framework intended for application to river channels. Our modular approach includes an algorithm for transforming the coordinates of data and prediction locations to a channel‐centered coordinate system, several different methods of representing the trend component of topographic variation and search strategies that incorporate geomorphic information to determine which survey data are used to make a prediction at a specific location. For example, a relationship between curvature and the lateral position of maximum depth can be used to include cross‐sectional asymmetry in a two‐dimensional trend surface model, and topographic breaklines can be used to restrict which data are retained in a local neighborhood around each prediction location. Using survey data from a restored gravel‐bed river, we demonstrate how transformation to the channel‐centered coordinate system facilitates interpretation of the variogram, a statistical model of reach‐scale spatial structure used in kriging, and how the choice of a trend model affects the variogram of the residuals from that trend. Similarly, we show how decomposing kriging predictions into their trend and residual components can yield useful information on channel morphology. Cross‐validation analyses involving different data configurations and kriging variants indicate that kriging is quite robust and that survey density is the primary control on the accuracy of bed elevation predictions. The root mean‐square error of these predictions is directly proportional to the spacing between surveyed cross‐sections, even in a reconfigured channel with a relatively simple morphology; sophisticated methods of spatial prediction are no substitute for field data. Copyright © 2007 John Wiley & Sons, Ltd.     

Fractal analysis of flow of the river Warta

A long time series (170 years) of daily flows of the river Warta (Poland) are subject to fractal analysis. A binary variable (renewal stream) illustrating excursions of the process of flow is examined. The raw series is subject to de-seasonalization and normalization. Fractal dimensions of crossings of Warta flows are determined using a novel variant of the box-counting method. Temporal variability of the flow process is studied by determination of fractal dimensions for shifted horizons of 10 or 30 years length. Spectral properties are compared between the time series of flows, and the fractional Brownian motion which describes both the fractal structure of the process and the Hurst phenomenon. The approach may be useful in further studies of non-stationary of the process of flow, analysis of extreme hydrological events and synthetic flow generation.     

Self-Affine Fractals and the Fractal Dimension of Fractured Rock Profiles

The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same res     

Effect of transect location,transect spacing and interpolation methods on river bathymetry accuracy

Digital elevation models (DEMs) of river channel bathymetries are developed by interpolating elevations between data collected at discrete points or along transects. The accuracy of interpolated bathymetries depends on measurement error, the density and distribution of point data, and the interpolation method. Whereas point measurement errors can be minimized by selecting the most efficient equipment, the effect of data density and interpolation method on river bathymetry is relatively unknown. Thus, this study focuses on transect‐based collection methods and investigates the effects of transect location, the spacing between transects, and interpolation methods on the accuracy of interpolated bathymetry. This is accomplished by comparing four control bathymetries generated from accurate and high resolution, sub‐meter scale data to bathymetries interpolated from transect data extracted from the control bathymetries using two transect locating methods and four interpolation methods. The transect locating methods are a morphologically‐spaced and an equally‐spaced model. The four interpolation methods are Ordinary Kriging, Delaunay Triangulation, and Simple Linear, which are applied in curvilinear coordinates (Delaunay Triangulation is also applied in Cartesian coordinates), and Natural Neighbor only in Cartesian Coordinates. The bathymetric data were obtained from morphologically simple and complex reaches of a large (average bankfull width = 90 m) and a small (average bankfull width = 17 m) river. The accuracy of the developed DEMs is assessed using statistical analysis of the differences between the control and interpolated bathymetries and hydraulic parameters assessed from bankfull water surface elevations. Results indicate that DEM accuracy is not influenced by the choice of transect location method (with same averaged cross‐section spacing) or a specific interpolation method, but rather by the coordinate system for which the interpolation method is applied and the spacing between transects. They also show negligible differences between the mean depths and surface areas calculated from bathymetries with dense or coarse spacing. Copyright © 2016 John Wiley & Sons, Ltd.