中国大陆部分大震前Hurst指数异常变化特征

对中国大陆1970年以来12组7级以上地震进行了前后10年左右地震时间间隔序列的R／S分析，滑动计算其Hurst指数H值。H值的时间进程显示，9组大震前2年左右H值在较为稳定的背景上开始出现异常变化，其异常特征为“下降－低值－回升”，地震大多发生在H值回升的过程中，具有中、短期前兆意义。H值的异常过程揭示了在大震孕震系统内地震活动从无序向有序的时间演化过程。     

A discussion on the application of b-value to the prediction of seismic tendency

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…     

A discussion on the application ofb-value to the prediction of seismic tendency

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.     

River flow mass exponents with fractal channel networks and rainfall

An important problem in hydrologic science is understanding how river flow is influenced by rainfall properties and drainage basin characteristics. In this paper we consider one approach, the use of mass exponents, in examining the relation of river flow to rainfall and the channel network, which provides the primary conduit for transport of water to the outlet in a large basin. Mass exponents, which characterize the power-law behavior of moments as a function of scale, are ideally suited for defining scaling behavior of processes that exhibit a high degree of variability or intermittency. The main result in this paper is an expression relating the mass exponent of flow resulting from an instantaneous burst of rainfall to the mass exponents of spatial rainfall and that of the network width function. Spatial rainfall is modeled as a random multiplicative cascade and the channel network as a recursive replacement tree; these fractal models reproduce certain types of self-similar behavior seen in actual rainfall and networks. It is shown that under these modeling assumptions the scaling behavior of flow mirrors that of rainfall if rainfall is highly variable in space, and on the other hand flow mirrors the structure of the network if rainfall is not so highly variable.     

A SPECTRUM OF LYAPUNOV EXPONENTS OBTAINED FROM A CHAOTIC TIME SERIES

A complete spectrum of Lyapunov exponents (LEs) is obtained from 1970— 1985 daily mean pressuremeasurements at Shanghai by means of a correlation matrix analysis technique and it is found that there exist LEs≥0,and <0. with their sum 0λ_i=K=0.110405 whereuponT=1 /K =9 is obtained as the predictable time scale, a result close to that acquired by the dynamic-statistical approachin early days and also in agreement with that present by the authors themselves(1991).     

山东大尹格庄金矿蚀变岩中矿体分布稳定性的动力学控制参量探讨

元素品位分布的相依性指标——赫斯特指数(Hurst指数)是矿体分布稳定性的动力学控制参量,重标极差(R/S)分析是相依性分析的有效方法。利用R/S分析对胶东大尹格庄金矿黄铁绢英岩内不同勘探线金元素品位系列的Hurst指数计算发现,Hurst指数主要介于0.59至0.89之间,均值为0.75,标准差为0.09,均大于随机行走经验Hurst指数的均值与标准差;计算结果说明元素品位分布存在正相关性,但由于受多种因素影响,其空间分布的相依性具有一定波动。元素品位分布的正相依性显示在特定的地质背景内,矿体连续分布或者间断出现,发育相对稳定,其与大尹格庄金矿的地质事实相吻合。     

Chaotic dynamics of planet‐encountering bodies

The dynamics of two families of minor inner solar system bodies that suffer frequent close encounters with the planets is analyzed. These families are: Jupiter family comets (JF comets) and Near Earth Asteroids (NEAs). The motion of these objects has been considered to be chaotic in a short time scale,and the close encounters are supposed to be the cause of the fast chaos. For a better understanding of the chaotic behavior we have computed Lyapunov Characteristic Exponents (LCEs) for all the observed members of both populations. LCEs are a quantitative measure of the exponential divergence of initially close orbits. We have observed that most members of the two families show a concentration of Lyapunov times (inverse of LCE) around 50–100yr. The concentration is more pronounced for JF comets than for NEAs, among which a lesser spread is observed for those that actually cross the Earth's orbit (mean perihelion distance q < 1.05 AU). It is also observed that a general correspondence exists between Lyapunov times and the time between consecutive encounters. A simple model is introduced to describe the basic characteristics of the dynamical evolution. This model considers an impulsive approach, where the particles evolve unperturbedly between encounters and suffer ‘kicks’ in semimajor axis at the encounters. It also reproduces successfully the short Lyapunov times observed in the numerical integrations and is able to estimate the dynamical lifetimes of comets during a stay in the Jupiter family in correspondence with previous estimates. It has been demonstrated with the model that the encounters with the largest effect on the exponential growth of the distance between initially nearby orbits are neither the infrequent deep encounters, nor the frequent and far ones; instead, the intermediate approaches have the most relevant contribution to the error growth. Such encounters are at a distance a few times the radius of the Hill's sphere of the planet (e.g. 3). An even simpler model allows us to get analytical estimates of the Lyapunov times in good agreement with the values coming from the model above and the numerical integrations. The predictability of the medium‐term evolution and the hazard posed to the Earth by those objects are analysed in the Discussion section. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of seismic dynamical systems

A procedure is presented for the analysis of complex stationary time series for which the Fourier power spectra reveals broadband noise or broadened pulses. We first determine the Hurst exponent from which we may know whether the time series under study is mainly random or if the data points present correlations. If the data are correlated, a chaotic analysis will reveal whether they may be interpreted as a low dimensional nonlinear system (defined by a low correlation dimension and a finite and positive Kolmogorov entropy and largest positive Lyapunov exponent) or as a stochastic process. We have studied three kind of temporal series: inter-event time series of infrasonic pulses recorded at Stromboli volcano, and, S-coda waves and microseisms, that have been recorded at the eastern Pyrenees. Results show that microseisms and Coda waves can be modeled as a low dimensional deterministic system, Correlation dimensions 2.3, 3.2, respectively. At the contrary infrasonic has resulted stochastic. This chaotic character can be attributed to the medium properties. Coda waves with scattering through a fractal distribution of scatters or to multiple reflection inside resonators (for example sedimentary basins) and microseisms as a propagation of wave guide of variable cross section which have the same temporal characteristics as a nonlinear forced oscillator.     

Generalisation of a Nonlinear Dynamo Model

In order to gain a better understanding of the physical processes underlying fast dynamo action it is instructive to investigate the structure of both the magnetic field and the velocity field after the dynamo saturates. Previously, computational results have been presented (Cattaneo, Hughes and Kim, 1996) that indicate, in particular, that Lagrangian chaos is suppressed in the dynamical regime of the dynamo. Here we extend their model by removing the assumption of neglecting the inertial term. This allows for an investigation into the effect of this term on the evolution of the dynamo via a comparison of the two models. Our results indicate that this term plays a crucial role in the physics of the dynamo.     

月表虹湾Hurst指数分析

月球遥感是在登月技术还不完善的情况下,利用遥感数据,通过各种分析来研究月球演化、内部结果和表面特征的方法。粗糙度是地表隆升、沉降、侵蚀和火山喷射物覆盖在行星表面留下的记录,因此对行星表面粗糙度的定量分析可以精确反映其地质演化过程。而Hurst指数则是粗糙度的精确反映。文中利用LOLA制作的DEM,以月球正面虹湾为例,选取水平方向的12条剖面和垂直方向的15条剖面对其各粗糙度参数进行计算,并结合月表成熟度对Hurst指数与底层年龄的相关性进行了分析,得出如下结论:(1)在1km的剖面长度上,虹湾地区均方根高程的平均值在3m左右;在0.2～3km研究尺度范围内,虹湾地区的坡度不超过2°,说明该地表起伏度小。(2)虹湾地区的Hurst指数跨度比较大,尤其在垂直方向(南北)上,在0.4到0.9之间,表明其构造样式丰富。(3)在0.2～3km研究尺度范围内,Hurst指数自北往南增大、自西往东增大,表示在虹湾地区粗糙度自西北向东南方向增大。(4)虹湾地区地质年龄为自西北向东南方向变小,与Hurst指数增大方向一致。(5)在月表年轻撞击坑地区月表成熟度与Hurst指数大致呈负相关关系。