共查询到20条相似文献，搜索用时 31 毫秒
1.
Apparent multifractality and scale‐dependent distribution of data sampled from self‐affine processes
Shlomo P. Neuman 《水文研究》2011,25(11):1837-1840
It has been previously demonstrated theoretically and numerically by the author that square or absolute increments of data sampled from fractional Brownian/Lévy motion (fBm/fLm), or of incremental data sampled from fractional Gaussian/Lévy noise (fGn/fLn), exhibit apparent/spurious multifractality. Here, we generalize these previous development in a way that (a) rigorously subordinates (truncated) fLn to fGn or, in a statistically equivalent manner, (truncated) fLm to fBm; (b) extends the analysis to a wider class of subordinated self‐affine processes; (c) provides a simple way to generate such processes and (d) explains why the distribution of corresponding increments tends to evolve from heavy tailed at small lags (separation distances or scales) to Gaussian at larger lags. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
CHEN Zhaonan 《中国科学D辑(英文版)》2004,47(3)
Are human able to foresee the future? For thou-sands of years close attention has been paid to this issue. At the present day, in order to survive from competition and to predominate over the nature, hu-man抯 desire of forecasting things has become more and more intense. Compared to conquering space, more people yearn for being able to control the time. From ancient to the present, mankind always dream of contacting the past, governing the present and tran-scending the future. Recent years in… 相似文献
3.
Kuo-Chin Hsu Kuan-Chih Chen 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(7):1053-1065
This paper proposes a multiscale flow and transport model which can be used in three-dimensional fractal random fields. The
fractal random field effectively describes a field with a high degree of variability to satisfy the one-point statistics of
Levy-stable distribution and the two-point statistics of fractional Levy motion (fLm). To overcome the difficulty of using
infinite variance of Levy-stable distribution and to provide the physical meaning of a finite domain in real space, truncated
power variograms are utilized for the fLm fields. The fLm model is general in the sense that both stationary and commonly
used fractional Brownian motion (fBm) models are its special cases. When the upper cutoff of the truncated power variogram
is close to the lower cutoff, the stationary model is well approximated. The commonly used fBm model is recovered when the
Levy index of fLm is 2. Flow and solute transport were analyzed using the first-order perturbation method. Mean velocity,
velocity covariance, and effective hydraulic conductivity in a three-dimensional fractal random field were derived. Analytical
results for particle displacement covariance and macrodispersion coefficients are also presented. The results show that the
plume in an fLm field moves slower at early time and has more significant long-tailing behavior at late time than in fBm or
stationary exponential fields. The proposed fractal transport model has broader applications than those of stationary and
fBm models. Flow and solute transport can be simulated for various scenarios by adjusting the Levy index and cutoffs of fLm
to yield more accurate modeling results. 相似文献
4.
吴忠良 《地震学报(英文版)》2001,14(5)
It has been recognized for a long time that the b-value in the Gutenberg-Richters fre-quency-magnitude relation (Gutenberg, Richter, 1954) tends to decrease before some of the earth-quakes (LI, et al, 1979, and the references therein). Since the 1980s, study on b-value has caused much attention among seismologists and physicists when b-value was related to the fractal dimen-sion of an earthquake fault (Aki, 1981; King, 1983) and/or the scaling constant in the model of self-organized critical… 相似文献
5.
C.-C. P. Tsai 《Pure and Applied Geophysics》1997,149(4):689-706
—The characteristics of slip and stress drop distributions accompanying earthquakes are explored from the perspective of fractional Brownian motion (fBm). Slip and stress drop distributions are assumed to be processes of fBm.The Hurst exponent (H), which reveals the roughness of a random process of fBm, is first estimated from ten inferred slip maps for six crustal earthquakes occurring in California. The relationships between the Hurst exponents with respect to static slip (H u ),stress (H τ ), static stress drop (H δσ ) and slip velocity (H ú ) are then established following Andrews (1980). They are found to be H δσ = H τ = H u -1 = H ú -0.5. Empirically, H u is recognized as being about 1 which, according to the theory of fBm, implies that the static slip distribution of an earthquake is just on the margin between being and not being self-similar, depending on the individual case. Cases where H u is less than 1 (i.e., self-similar) suggest that H δσ < 0(i.e., the distribution of static stress drop diverges), which is, in light of fBm, invalid. One possible explanation for this paradox is that H u is less than 1 in crustal earthquake phenomena only over a certain specific bandwidth of wavenumbers, or it could be that the relation H δσ = H u -1 is not valid, which implies that static stress drop in the wavenumber domain is not the product of stiffness and slip as described in Andrews (1980). It could be that some different physics apply over this particular bandwidth. In such cases, multi-fractals may be a better way to explore the characteristics of the Hurst exponents of slip. In general, static stress drop and stress distributions are more likely to be self-similar than static slip distribution. H u ≌ 1 and H δσ ≌ 0 are good first approxima tions for the slip and stress drop distributions. The spectrum of ground motion displacement falls off as ω -(Hδσ + 2) with H δσ ≌ 0, consistent with an ω-2 model of the earthquake source. 相似文献
6.
This paper proposes a numerical method to simulate oil spill trajectories, which are affected by the combination of advection, turbulent diffusion and mechanical spreading process, based on a particle tracking algorithm. Recent studies have shown that the trajectories of drifters on the ocean surface have a fractal structure that is far from being described using ordinary Brownian motion. Thus, in modeling the diffusion process, a discrete method has been employed for the generation of fractional Brownian motion (fBm) to illustrate superdiffusive transport. The algorithm is implemented to predict oil slick trajectories following the “Arteaga” oil spill accident that occurred near the Dalian coastal region in 2005. When compared with the observed data and the results of traditional diffusion modeling, the numerical results based on the fBm model are encouraging. 相似文献
7.
Temporal variations of the main hydrological variables over 16 years were systematically investigated based on the results from an integrated hydrological modeling at the Sagehen Creek watershed in northern Sierra Nevada. Temporal scaling of these variables and damping effects of the hydrological system as well as its subsystems, i.e., the land surface, unsaturated zone, and saturated zone, were analyzed with spectral analyses. It was found that the hydrological system may act as a cascade of hierarchical fractal filters which sequentially transfer a non-fractal or less correlated fractal hydrological signal to a more correlated fractal signal. The temporal scaling of simulated infiltration (SI), simulated actual evapotranspiration (SET), simulated recharge (SR), measured baseflow (MBF), measured streamflow (MSF) exist and the temporal autocorrelation of these variables increase as water moves through the system. The degree of the damping effect of the subsystems is different and is strongest in the unsaturated zone compared with that of the land surface and saturated zone. The temporal scaling of the simulated groundwater levels (Sh) also exists and is strongly affected by the river: the temporal autocorrelation of Sh near the river is similar to that of the river stage fluctuations and increases away from the river. There is a break in the temporal scaling of Sh near the river at low frequencies due to the effect of the river. Temporal variations of the simulated soil moisture (Sθ) is more complicated: the value of the scaling exponent (β) for Sθ increases with depth as water moves downwards and its high-frequency fluctuations are damped by the unsaturated zone. The temporal fluctuations of measured precipitation and SI are fractional Gaussian noise, those of SET, SR, MBF, and MSF are fractional Brownian motion (fBm), and those of Sh away from the river are 2nd-order fBm based on the values of β obtained in this study. 相似文献
8.
The highest response of multi-supported structures subjected to partially specified multi-component earthquake support motions is considered. The seismic inputs are modelled as incompletely specified vector Gaussian random processes with known autospectral density functions but unknown cross spectral densities and these unknown functions are determined such that the steady state response variance of a given linear system is maximized. The resulting cross power spectral density functions are shown to be dependent on the system properties, autospectra of excitation and the response variable chosen for maximization. It emerges that the highest system response is associated neither with fully correlated support motions, nor with independent motions, but, instead, specific forms of cross power spectral density functions are shown to exist which produce bounds on the response of a given structure. Application of the proposed results is demonstrated by examples on a ground based extended structure, namely, a 1578 m long, three span, suspension cable bridge and a secondary system, namely, an idealized piping structure of a nuclear power plant. 相似文献
9.
Lin Yuan HongGuang Sun Yong Zhang YouKuan Zhang Xiufen Gu Shawn Dawley 《Ground water》2019,57(3):485-491
Natural dynamics such as groundwater head fluctuations may exhibit multi-fractionality, likely caused by multi-scale aquifer heterogeneity and other controlling factors, whose statistics requires efficient quantification methods. As a scaling exponent, the Hurst exponent can describe the temporal correlation or multifractal behavior in groundwater level fluctuation processes. However, the scaling behavior may change with time under natural conditions, likely due to the non-stationary evolution of internal and external conditions, which cannot be characterized by traditional methods using a single or several scaling exponents for the complex features of the overall process. This methods note quantifies the multi-fractionality using the timescale local Hurst exponent (TS-LHE) and then proposes a systematic statistical method to analyze groundwater head fluctuations. Time series of daily groundwater level fluctuations from three wells located in the lower Mississippi valley are analyzed, after removing the seasonal cycle, which leads to transient TS-LHE, implying multi-fractionality and multifractal-scaling behavior that changes with time and location. Therefore, the temporal scaling analysis proposed here may provide useful and quantitative information to understand the nature of dynamic hydrologic systems. 相似文献
10.
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
11.
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
12.
ABSTRACTTurbulence is considered to generate and drive most geophysical processes. The simplest case is isotropic turbulence. In this paper, the most common three-dimensional power-spectrum-based models of isotropic turbulence are studied in terms of their stochastic properties. Such models often have a high order of complexity, lack stochastic interpretation and violate basic stochastic asymptotic properties, such as the theoretical limits of the Hurst coefficient, when Hurst-Kolmogorov behaviour is observed. A simpler and robust model (which incorporates self-similarity structures, e.g. fractal dimension and Hurst coefficient) is proposed using a climacogram-based stochastic framework and tested over high-resolution observational data of laboratory scale as well as hydro-meteorological observations of wind speed and precipitation intensities. Expressions of other stochastic tools such as the autocovariance and power spectrum are also produced from the model and show agreement with data. Finally, uncertainty, discretization and bias related errors are estimated for each stochastic tool, showing lower errors for the climacogram-based ones and larger for power spectrum ones. 相似文献
13.
Dionissios T. Hristopulos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):739-754
Random fields based on energy functionals with local interactions possess flexible covariance functions, lead to computationally efficient algorithms for spatial data processing, and have important applications in Bayesian field theory. In this paper we address the calculation of covariance functions for a family of isotropic local-interaction random fields in two dimensions. We derive explicit expressions for non-differentiable Spartan covariance functions in \({\mathbb{R}}^2\) that are based on the modified Bessel function of the second kind. We also derive a family of infinitely differentiable, Bessel-Lommel covariance functions that exhibit a hole effect and are valid in \({\mathbb{R}}^{d}\), where d > 2. Finally, we define a generalized spectrum of correlation scales that can be applied to both differentiable and non-differentiable random fields in contrast with the smoothness microscale. 相似文献
14.
Paul S ADDISION 《国际泥沙研究》2009,24(4):439-454
An accurate particle tracking method using FBMINC （new fractional Brownian motion） is outlined. It generates non-Fickian diffusion rather than Fickian diffusion as traditional particle tracking model does. The FBMINC model is based on fractional Brownian motion （fl3m） which is generalization of regular Brownian motion. The two models of fBms （FBM model and FBMINC model） were explored and the differences of the two models are compared from the three aspects： the standard deviation of each step, the small memory and the effect of the number of particles in the cloud. The results show the FBMINC model is a better model as it produces more accurate statistics. The effect of simple shear dispersion for both Brownian and fBm was investigated. The power law scaling of fBm shear dispersion was correctly identified. In addition, a scaling coettieient was found numerically. The FBMINC model is then used for producing both superdiffusive and subdiffusive particle paths, therefore, the non-Fickian diffusion of soil particle clouds can be modelled. The particle clouds represent soil contaminant are released in an idealised coastal bay and the fBm particle tracking method is used for simulation the particle cloud spreading in the bay. There is a noticeable increase in the spreading rate of the cloud. In addition, owning to the spreading rate of the cloud, a noticeable part of it has escaped the bay area and transported downstream. The variation of the Hurst exponent can lead to an area of the flow being affected by a contaminant cloud which is not picked up by the regular Brownian motion models. The purpose of this paper is to bring soil transport engineers a new angle on soil particle transport research in fluids. Using FBM1NC particle tracking model allows more flexibility in simulation of diffusion in soil contaminant spread in coastal bay or ocean surface. 相似文献
15.
Wu Zhong-liang 《地震学报(英文版)》2001,14(5):585-588
In the estimation of seismic tendency, using Gutenberg-Richter’sb-value and using Hurst exponent are two commonly used methods. Based on the fractal geometry of earthquake time series, we
point out that these two methods correlate to each other. In the perspective of fractional Brownian motion (FBM), an earthquake
sequence withb>3/4 and that withb<3/4 have different dynamic properties.
Foundation item: The MOST Project G1998040705.
Contribution No. 01FE2010, Institute of Geophysics, China Seismological Bureau. 相似文献
16.
本文利用随机介质模型对复杂岩性储层进行了非均质性描述.利用模型特征量即非均质纵横比、纵向谱指数、横向谱指数以及扰动标准差等来模拟不同的随机介质.在前人工作的基础上,由某油气田的两口井资料估计储层非均质性能谱,从能谱曲线上提取储层纵向大小尺度非均质谱指数.通过将二维随机介质模拟的合成井记录互相关系数与实际井记录互相关系数进行分析比较,分别得到大小尺度非均质情况下最佳拟合时的横向谱指数和非均质性纵横比.以上求得的各种特征量从不同角度定量分析了储层非均质性的纵横向变化,为储层横向预测提供了依据. 相似文献
17.
In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting. 相似文献
18.
D. L. Turcotte L. Greene 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(1):33-40
In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting. 相似文献
19.
20.
重标极差分析法（R/S,rescaled range analysis method）,是研究分数布朗运动及自然现象的自仿射分形的有力工具之一,对于所有时间序列分析都有着广泛的用途．通过对天水台绝对地磁观测Z分量数据序列R/S分析,计算分段数据序列的Hurst指数H发现,昆仑山口西MS8.1地震和汶川MS8.0地震震前2—3个月,H值减小,分维数D增大,相关系数C为负值．这一动态变化表明,地震前数据序列由持久性序列发展为反持久性序列,观测数据的成分发生了改变．这与地壳内部应力变化和岩石破裂实验结果相符．所以,这一动态变化过程可以看作是强震前的一种前兆信号． 相似文献