New seismic attribute:Fractal scaling exponent based on gray detrended fluctuation analysis

Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition system, and noise interference, seismic attributes for seismic data interpretation have uncertainties. Especially, the antinoise ability of seismic attributes directly affects the reliability of seismic interpretations. Gray system theory is used in time series to minimize data randomness and increase data regularity. Detrended fluctuation analysis （DFA） can effectively reduce extrinsic data tendencies. In this study, by combining gray system theory and DFA, we propose a new method called gray detrended fluctuation analysis （GDFA） for calculating the fractal scaling exponent. We consider nonlinear time series generated by the Weierstrass function and add random noise to actual seismic data. Moreover, we discuss the antinoise ability of the fractal scaling exponent based on GDFA. The results suggest that the fractal scaling exponent calculated using the proposed method has good antinoise ability. We apply the proposed method to 3D poststack migration seismic data from southern China and compare fractal scaling exponents calculated using DFA and GDFA. The results suggest that the use of the GDFA-calculated fractal scaling exponent as a seismic attribute can match the known distribution of sedimentary facies.

Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.

SCALING EXPONENTS IN FULLY DEVELOPED ASYMMETRIC CHANNEL FLOW

Wavelet analysis is applied to study the global and local scaling exponents in fully developed asymmetric channel flow. Global exponents are calculated by orthogonal wavelets and Extended Scaling Similarity(ESS). The results show that the flow in an asymmetric channel flow exhibits different characteristics of intermittency from that in a symmetric flow. It is also shown that the intermittency property of the streamwise fluctuations is different from that of vertical fluctuations, and the intermittency does not decay with the increase of the distance from the wall. In addition, the Continuous Wavelet Transform(CWT) method is found to be unreliable to calculate the local scaling components. Finally, it is pointed out that the existence and the significance of negative local scaling components need further study.

Second-order relative exponent of isotropic turbulence

Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent Sis greater than the real or theoretical inertial range scaling exponentξ,which is attributed to an evident bump in the ESS range.

Multi-fractal Behaviors of Relative Humidity over China

The multi-fractal ity over China are studied behaviors of relative humid using the multi-fractal de trended fluctuation analysis （DFA） method. Three multi fractal parameters （the spectrum width Aa, the asymmetry Aaas, and the long-range correlation exponent a0） of the singularity spectrum are introduced to quantify the multi-fractal behaviors. The results show that multi-frac tality exists in daily humidity records over most stations in China and is mainly due to the broad distribution of the probability density of the sequence values. Strong multi fractal behaviors over some stations in the Yunnan, Guangdong, and Inner Mongolia provinces are obvious. These behaviors are mainly caused by different long range correlations between large and small fluctuations. The asymmetry of the singularity of relative humidity records is weak, except for a small number of stations in the far east and west of China, where the singularity spec trum is left-skewed. Finally, the long-range correlations in North China are stronger than those in South China, which indicates better predictability in North China. By studying the parameters of the multi-fractal spectrum, various data of long-range power law correlations of the relative humidity records are obtained, which may pro vide theoretical support for climate prediction.

一种新型Hopfield神经网络平衡解的全局指数稳定性

结合生物学最近的研究成果,提出一种具有动态突触和不同时间尺度的新型Hopfield神经网络模型.运用不动点定理、不等式技巧及Lyapunov泛函等方法,讨论了该人工神经网络在具有常时滞和变时滞两种情况下,其平衡解的存在性唯一性和全局指数稳定性.

The 2/3 scaling of twig nitrogen to phosphorus in woody plants

Background:Nitrogen(N)and phosphorus(P)are important elements for plant metabolism and growth.Therefore,the quantification of the scaling relationship of N to P in plant organs can help us understand many fundamental ecological processes.The general scaling relationships between N and P in leaves and in fine roots have been reported.As compared to leaves and fine roots,however,little information is available on the N versus P scaling relationship in the stems of woody plants,especially for twigs.In this study,a comprehensive dataset comprising 2,038 N=P paired observations for a total of 536 woody species was compiled and analyzed to determine whether a general scaling relationship exists.Results:The global mean values of twig N and P concentrations and N:P ratios were 9.33 mg⋅g^(-1),1.12 mg⋅g^(-1) and 10.16,respectively.Twig N and P concentrations and N:P ratios differed significantly within and across functional groups and biomes.Across all of the species,a uniform 0.67 scaling exponent of twig N to P was observed across different functional groups and biomes,i.e.,a 2/3-power scaling relationship was observed.However,this numerical value differed across different sites,albeit converging onto 0.67 with increasing sample sizes.Soil total phosphorus was the largest contributor to the variation in the numerical value of the scaling exponent.Conclusion:These results provide useful parameters for stoichiometric growth models,and advance our understanding of the mechanisms underlying plant nutrient dynamics.This study has potential implications in predicting responses of nutrient cycling in terrestrial ecosystem responses to changes in the environment.

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.

Experimental researches for scaling laws of low-order structure function in boundary layer

Scaling laws are addressed by analysing moments of velocity increments which obtained by Particle-image Velocimetry(PIV)system in the boundary layer of a flat plate.In the paper,we measure the moments of increments of upstream velocity(u'),longitudinal velocity(v')and ponderance of vorticity(dv'/dx)at Reθ=2167 in different wall distance and verify the anomaly of the scaling exponents of high-order structure functions with the increasing order of the moments,discuss the scaling of non-integer moments of order between+2 and-1.The difference of scaling exponents of low-order structure functions between the experimental data and Kolmogorov's,SL's(She & Leveque)prediction increases as the moment order decreases toward-1,which shows that the anomaly is manifested in low-oeder moments as well.However,for same order structure functions,the scaling exponents of v' and dv'/dx are not changeable in different wall distance.

On the Construction of the Kernel Matrix by Primitive BCH Codes for Polar Codes

The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2n-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2n-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.

EXPERIMENTAL ESTIMATION OF A SCALING EXPONENT FOR TIP VORTEX CAVITATION VIA ITS INCEPTION TEST IN FULL-AND MODEL-SHIP

Tip vortex cavitation noise of marine propeller became primary concems to reduce hazardous environmental impacts from commercial ship or to keep the underwater surveillance of naval ships. The investigations of the tip vortex and its induced noise are normally conducted through the model test in a water cavitation tunnel. However the Reynolds number of model-test is much smaller than that of the full-scale, which subsequently results in the difference of tip vortex cavitation inception. Hence, the scaling law between model- and full-scales needs to be identified prior to the prediction and assessment of propeller noise in full scale. From previous researches, it is generally known that the incipient caivtation number of tip vortex can be represented as a power of the Reynolds number. However, the power exponent for scaling, which is the main focus of this research, has not been clearly studied yet. This paper deals with the estimation of scaling exponent based on tip vortex cavitation inception test in both full- and model-scale ships. Acoustical measurements as well as several kind of signal processing technique for an inception criterion suggest the scaling exponent as 0.30. The scaling value proposed in this study shows slight difference to the one of most recent research. Besides, extrapolation of model-ship noise measurement using the proposed one predicts the full-scale noise measurement with an acceptable discrepancy.

RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS

There are a lot of continuous evolving networks in real world, such as Internet, WWW network, etc. The evolving operation of these networks are not an equating interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has proved that this system self-organizes into scale-free structures with scaling exponent γ=3＋a/m.

HIGH ORDER LAGRANGIAN VELOCITY STATISTICS IN A TURBULENT CHANNEL FLOW WITH Re_τ=80

The scaling properties of high-order Lagrangian velocity structure functions are investigated numerically for a turbulent flow with a friction-velocity based Reynolds number Re_τ=80.The Lagrangian particles are released from locations of different distances to the wall.The relative scaling exponents of the longitudinal velocity component are found to increase with the released distance to the wall and to approach asymptotically to theoretical predictions.However,the scaling exponents of the transverse velocity component are smaller than ,indicating a more intermittent nature.Specifically for the release locations in the center region,the relative scaling exponents agree very well with theoretical predictions.