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测井数据分维计算及其应用条件研究 总被引：6，自引：1，他引：5
分形几何已成功地应用于储层表征,分维是储层一征和随机建模的控制参数,为了准确表征储层,必须精确地估计分维值。本文介绍了利用测井数据计算储层分维值的三种方法：变尺度分析法（Ｒ／Ｓ分析）,变异函数分析法、功率谱分析法,研究发现分维计算中对数据的分级处理实际上就是对数据进行灰色累加生成。研究表明影响分维估计精度的主要因素有四种：数据点数、数据概率分布、数据平稳性,无标度区,研究认为,现有的３种方法不能用 相似文献
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宇宙分维构造及其数学基础 总被引：5，自引：4，他引：1
探讨了宇宙分维构造的形式,给出了分维微积分及分形测度的数学基础,包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程．作为诠释,探讨了原子核内中子与质子的趋势关系方程,以及其周期解和原子序数极限值。 相似文献
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断层泥粒度成分的分形研究 总被引：10，自引：3，他引：10
用分形理论分析了断层泥粒度成分的分形结构特征，其分维在２～３之间，平均值为２．８左右。分维可作为定量描述断层泥粒度成分的参数，分维值高的断层泥，自组织程度高，其形成演化处于高级阶段。探讨了断层泥的分维及其物理力学性质指标和断层运动特征的关系 相似文献
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本文从自仿射分形的角度探讨地震兆汾观测资料的分形处理方法。在对自仿射分形的分维量测方法进行对比分析的基础上，给出了处理地震前兆观测资料较为适用的分形方法和满足计算需要的样本点数，从对部分水氡和地电阻率资料进行了处理分析中，得到了有益的启示：地震前兆时序观测资料可用分形方法处理分析，分维值可反映观测资料的结构变化特征，其作为一个无量纲量为综合对比分析各类前兆现象，探讨地震前兆场的复杂性特征提供了有效 相似文献
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I. Lerche 《Pure and Applied Geophysics》1993,140(3):503-517
In order to assess the degree of uncertainty of fractal dimensionality, a procedure is given which provides a cumulative probability measure of uncertainty of fractal dimensionality in terms of assessments of range and most likely value. The procedure allows for a variation of the model proposed (i.e., variability of the parameters involved in the fractal relation) and leads to a relevant estimate of the uncertainty. The procedure is simple to apply and useful in providing a statistically valid comparison of results.As an illustration, the procedure was used on the fractal dimensions of faults measured from shear zones of different scale magnitudes. Results suggest that these shear zones are indeed quantitatively similar with a fractal dimension around 1.5. It is also shown that the range of uncertainty of the fractal dimensionality (90% likelihood range) is sensitive to the amount of data used to calculate the fractal dimension of the faults. 相似文献
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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. 相似文献
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Shi Xingjue Xu Heming Niu Zhiren Fan ZengjieUniversity of Science Technology of China Hefei China Seismologicai Bureau of Shanxi Xi'an China 《中国地震研究》1994,(3)
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 相似文献
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Specific features of the geomorphology and hydrology of Selenga River delta are considered. Fractal theory is used to evaluate the fractal dimension of the river delta as a branched structure. The fractal dimension of the planar pattern of the Selenga and Volga deltas are evaluated for the first time using three independent methods. The obtained values are 1.38 and 1.72, respectively. 相似文献
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Ｓｅｌｆ－ａｆｆｉｎｅｆｒａｃｔａｌｆｅａｔｕｒｅｓｏｆｅａｒｔｈｑｕａｋｅｔｉｍｅｓｅｒｉｅｓｂｅｆｏｒｅａｎｄａｆｔｅｒｍｏｄｅｒａｔｅｅａｒｔｈｑｕａｋｅｓＣｈａｎｇ－ＨａｔＬＩＵ（刘长海），Ｙｉ－ＧａｏＬＩＵ（刘义高）ａｎｄＪｕｎＺＨＡＮＧ（... 相似文献
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The fractal properties of topography as controlled by the interactions of tectonic,lithological, and geomorphological processes 
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下载免费PDF全文 Landscape topography widely exhibits fractal structure. Because of the complexity of relief geometry this structure is not homogeneous in space, and the study of its spatial characteristics represents a powerful method for investigating the interrelationships between landforms and underlying processes. We explore these interrelationships using the digital elevation model (DEM) of an area located in central Italy, where landscape topography is strongly linked to its geological evolution, being characterized by alternating intermountain basins and mountain ranges trending NW–SE. A modified version of the method based on the standard deviation of relief elevations is used to evaluate the fractal parameters of relief after tiling the DEM in spatial units characterized by homogeneous fractal geometry, and statistical methods in conjunction with spatial analysis techniques are applied to the resulting terrain datasets. Both the lowest and (to a lesser extent) the highest values of fractal dimension are found to follow the ridge‐and‐valley trend. Low fractal dimension is observed in the mountain ranges characterized by massive strata of limestone, and along the fault scarps defining the contact between the intermountain basins and the surrounding slopes, where sediment deposition prevails. High fractal dimension is observed in regions characterized by highly erodible terrigenous lithology, and in areas where tectonic activity favors erosional processes mainly by rivers. The analysis of the (fractal) power law parameters also suggests that each major lithological complex has its own characteristic fractal signature. These results provide new insights into the link between the fractal properties of topography and the tectonic, lithological, and geomorphological features of the area, and show that the analysis approach proposed is useful to depict key aspects about the geomorphological and geological setting of an area, using only a DEM. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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山西及邻区水系与黄土冲沟的分形几何学分析结果及其与构造活动的关系 总被引：9，自引：0，他引：9
本文用分形几何理论,对山西及邻区水系与黄土冲沟作了分析,发现水系与冲沟分维值的大小反映了该区构造活动性的强弱,分维值的分布定量地反映了区域构造活动的背景及各区域构造活动性的差异,在构造活动强的区域,分维值高,反之则低。按分维值的大小山西断陷带分成南中北三段,以中段介休-临汾一带的分维值及反映的构造活动性最强。该区分维值的分布及反映的构造活动性有从四周向中间增强的特点,增强区与强震的发生有关 相似文献
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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. 相似文献
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中国湖泊分形特征初探 总被引：10，自引：1，他引：9
本文分形概念入手,介绍自然界（水系,云,雪,树木）普遍存在分形特征,继而用偏差法求解中国湖泊分布的分形特征,并对其进行地理意义的解释,为湖泊信息分类和湖泊数据库建设服务。 相似文献
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The concept of fractals is used here for the identification of seismic reflectors with special emphasis on thin‐bed delineation, which is generally overlooked during standard data processing. A new fractal analysis scheme is applied to both synthetic and real field seismic data. The fractal dimensions of the three seismic attributes – amplitude, phase, and instantaneous frequency – have been analysed and evaluated. A change in fractal dimension is found to occur whenever there is a reflection. However, the resolution in the delineation of reflectors varies, depending on the attribute under consideration and the method of fractal dimension estimation used. Fractal analysis is performed on both noise‐free and noisy synthetic data to establish the noise tolerance limit for both the ‘divider method’ and the ‘Hurst method’. It is then tested with different peak frequencies of the source wavelet to establish the criteria for using the divider method and the Hurst method. The divider method is found to be suitable for high peak frequency source wavelets (> 25 Hz), while the Hurst method is best suited for low peak frequency source wavelets (< 25 Hz). Finally, when applied to the digitally processed and migrated field seismic data, it could even delineate reflectors which otherwise went undetected on the migrated time section. 相似文献
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L. Telesca V. Cuomo V. Lapenna M. Macchiato C. Serio 《Pure and Applied Geophysics》1999,156(3):487-501
—We use advanced methods to extract quantitative time dynamics from geomagnetic signals. In particular we analyse daily geomagnetic time series measured at three stations in Norway. The dynamics of geomagnetic measurements has been investigated using autoregressive models. The procedure is based on two forecasting approaches: the global autoregressive approximation and the local autoregressive approximation. The first technique views the data as a realisation of a linear stochastic process, whereas the second considers them as a realisation of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a strong test to discriminate between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical system governing the phenomena is characterised by a stochastic dynamics, and the process could be described by numerous degrees of freedom. We also investigated the kind of stochasticity of the geomagnetic signals, analysing the power spectrum density. We identify a power law P(?)∝?-α, with the scaling exponent α which is a typical fingerprint of irregular processes. In this analysis we use the Higuchi method, which presents an interesting relationship between the fractal dimension D and the spectral power law scaling index α. 相似文献
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Alberto Malinverno 《Pure and Applied Geophysics》1989,131(1-2):139-155
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. 相似文献
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SPATIAL DISTRIBUTION AND FRACTAL STRUCTURE OF AE FOCUSES OF INADA GRANITE UNDER TRIAXIAL COMPRESSION
An experimental study on the spatial distribution of the focuses of acoustic emissions of Inada granite (coarse grained granodiorite) under triaxial compression is reported in this paper. It is pointed out that AE locations is fractal with a dimension of 2.2 in average, lower than the result of Oshima granite (fine grained granodiorite), which is 2.7, under similar deformation condition. For Inada granite a band-limited fractal had been observed. Fractal dimension changed around grai 相似文献