Fractal dynamics of geomagnetic storms

We explore fluctuations of the horizontal component of the Earth’s magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29–31 October and 20–21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies.     

Counting statistics of f −β fluctuations: a new method for analysis of earthquake data

In a variety of biological and physical phenomena, temporal fluctuations are found, which are not explainable as consequences of statistically independent random events. If these fluctuations are characterized by a power spectrum density S(f) decaying as f ^– at low frequencies, this behaviour is called 1/f noise.Counting statistics applied to earthquake activity data leads to three time scales with different characteristics, represented by the exponent : at interval lengths less than 1 h, the shocks are randomly distributed as in a Poisson process. For medium time intervals (1 day to 3 months), the exponent 1 + is larger (1.4 for M ₀=3), but approaches unity for higher threshold magnitudes M ₀. In longer time ranges the exponent assumes values near 1.55, however, with increasing statistical variation at higher M ₀, due to lower counts.The temporal sequence is different from white noise; thus, it might be fruitful to apply neural network algorithms, because this method allows predictions in some other cases with similar characteristics.     

Undersampling power-law size distributions: effect on the assessment of extreme natural hazards

The effect of undersampling on estimating the size of extreme natural hazards from historical data is examined. Tests using synthetic catalogs indicate that the tail of an empirical size distribution sampled from a pure Pareto probability distribution can range from having one-to-several unusually large events to appearing depleted, relative to the parent distribution. Both of these effects are artifacts caused by limited catalog length. It is more difficult to diagnose the artificially depleted empirical distributions, since one expects that a pure Pareto distribution is physically limited in some way. Using maximum-likelihood methods and the method of moments, we estimate the power-law exponent and the corner size parameter of tapered Pareto distributions for several natural hazard examples: tsunamis, floods, and earthquakes. Each of these examples has varying catalog lengths and measurement thresholds, relative to the largest event sizes. In many cases where there are only several orders of magnitude between the measurement threshold and the largest events, joint two-parameter estimation techniques are necessary to account for estimation dependence between the power-law scaling exponent and the corner size parameter. Results indicate that whereas the corner size parameter of a tapered Pareto distribution can be estimated, its upper confidence bound cannot be determined and the estimate itself is often unstable with time. Correspondingly, one cannot statistically reject a pure Pareto null hypothesis using natural hazard catalog data. Although physical limits to the hazard source size and attenuation mechanisms from source to site constrain the maximum hazard size, historical data alone often cannot reliably determine the corner size parameter. Probabilistic assessments incorporating theoretical constraints on source size and propagation effects are preferred over deterministic assessments of extreme natural hazards based on historical data.     

Geometric analysis and scaling relations of deformation bands in porous sandstone

Displacement, length and linkage of deformation bands have been studied in Jurassic sandstones in southeastern Utah. Isolated deformation bands with lengths (L) that span more than three orders of magnitude show similar displacement (D) profiles with more or less centrally located maxima and gently increasing gradient toward the tips. Soft- and hard-linked examples exhibit steeper displacement gradients near overlap zones and immature hard links, similar to previously described fault populations. The deformation band population shows power-law length and displacement distributions, but with lower exponents than commonly observed for populations of larger faults or small faults with distinct slip surfaces. Similarly, the D_max-L relationship of the deformation bands shows a well-defined exponent of ca 0.5, whereas the general disagreement for other fault populations is whether the exponent is 1 or 1.5. We suggest that this important difference in scaling law between deformation bands and other faults has to do with the lack of well-developed slip surfaces in deformation bands. During growth, deformation bands link to form zones of densely spaced bands, and a slip surface is eventually formed (when 100 m < L < 1 km). The growth and scaling relationship for the resulting populations of faults (slip surfaces) is expected to be similar to ‘ordinary’ fault populations. A change in the D_max-L scaling relationship at the point when zones of deformation bands develop slip surfaces is expected to be a general feature in porous sandstones where faults with slip surfaces develop from deformation bands. Down-scaling of ordinary fault populations into the size domain of deformation bands in porous sandstones is therefore potentially dangerous.     

Montecarlo DLA-type simulations of wetting effects in fluid displacement in porous media

In this work, we report diffusion-limited aggregation (DLA)-type Montecarlo computations of a stochastic model of displacement of a viscous fluid by another that preferentially wets a porous medium, for the case when both fluids are immiscible in the absence of buoyancy forces. The model has the aim to simulate cooperative invasion processes found in experiments of immiscible wetting displacement. The model considers the nonlocal effects of the Laplacian pressure field and the capillary forces via hydrodynamic equations in the Darcy regime with a boundary condition for the pressure at the interface. The boundary condition contains two different types of disorder: the capillary term, which constitutes an additive random disorder, and a term containing an effective random surface tension, which couples to a curvature (it constitutes a multiplicative random term that carries nonlocal information of the whole pressure). We generate different displacement patterns for different setting of the parameters of the model. We analyze these patterns by studying the scaling properties of the interface that separate the two fluids and calculating the fractal dimension of the interface. The results show the existence of three distinct regimes of scaling. One regime at the smallest-length scales is due to the multiplicative random disorder together with the nonlocal coupling; it reveals itself in a roughness exponent α ≈ 0.80. Additionally, we find a DLA-type scaling regime with a roughness exponent α ≈ 0.60 at the largest scales and intermediate scaling regime with α ≈ 0.70 corresponding to invasion percolation with trapping. Each regime has definite scaling ranges that depend on the capillary number and the relative wetting tendency of the fluids. The behavior of the fractal dimensions of the interfaces of the aggregates constitutes a further confirmation of the existence of three scaling regimes and the multi-self-affinity of the perimeter of the interface boundaries.     

煤岩破坏声发射强度长程相关性和多重分形分布研究

通过单轴加载煤岩破坏全过程声发射试验,运用多重分形消除趋势波动分析法（MF-DFA）,分析了声发射强度序列的长程相关性及多重分形特征,在此基础上研究了不同应力水平下声发射强度序列长程相关指数H的变化趋势。结果表明：声发射强度时间序列内部波动不是完全随机的现象,而是由内在自相似机制决定的长程相关过程,其波动是一个有序的多重分形分布;H的变化与煤岩体的变形破坏过程能够较好的对应,声发射强度H值的“最大-减小”模式可以作为煤岩体失稳事件的前兆,这为利用声发射进行煤岩体稳定性现场监测预报提供了新的理论依据及方法     

Earthquake activity related to seismic cycles in a model for a heterogeneous strike-slip fault

We investigate the evolution of seismicity within large earthquake cycles in a model of a discrete strike-slip fault in elastic solid. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction and dislocation creep along the fault, and 3D elastic stress transfer. The fault consists of brittle parts which fail during earthquakes and undergo small creep deformation between events, and aseismic creep cells which are characterized by high ongoing creep motion. This mixture of brittle and creep cells is found to generate realistic aftershock sequences which follow the modified Omori law and scale with the mainshock size. Furthermore, we find that the distribution of interevent times of the simulated earthquakes is in good agreement with observations. The temporal occurrence, however, is magnitude-dependent; in particular, the small events are clustered in time, whereas the largest earthquakes occur quasiperiodically. Averaging the seismicity before several large earthquakes, we observe an increase of activity and a broadening scaling range of magnitudes when the time of the next mainshock is approached. These results are characteristics of a critical point behavior. The presence of critical point dynamics is further supported by the evolution of the stress field in the model, which is compatible with the observation of accelerating moment release in natural fault systems.     

Scale-invariance of soil moisture variability and its implications for the frequency-size distribution of landslides

Power spectral analyses of soil moisture variability are carried out from scales of 100 m to 10 km on the microwave remotely-sensed data from the Washita experimental watershed during 1992. The power spectrum S(k) has an approximate power-law dependence on wave number k with the exponent −1.8. This behavior is consistent with the behavior of a stochastic differential equation for soil moisture at a point, and it has important consequences for the frequency-size distribution of landslides. We present the cumulative frequency-size distributions of landslides induced by precipitation in Japan and Bolivia as well as landslides triggered by the 1994 Northridge, California earthquake. Large landslides in these regions, despite being triggered by different mechanisms, have a cumulative frequency-size distribution with a power-law dependence on area with an exponent ranging from −1.5 to −2. We use a soil moisture field with the above statistics in conjunction with a slope stability analysis to model the frequency-size distribution of landslides. In our model, landslides occur when a threshold shear stress dependent on cohesion, pore pressure, internal friction and slope angle is exceeded. This implies a threshold dependence on soil moisture and slope angle since cohesion, pore pressure and internal friction are primarily dependent on soil moisture. The cumulative frequency-size distribution of domains of shear stress greater than a threshold value with soil moisture modeled as above and topography modeled as a Brownian walk is a power-law function of area with an exponent of −1.8 for large landslide areas. This distribution is similar to that observed for landslides. The effect of strong ground motion from earthquakes lowers the shear stress necessary for failure, but does not change the frequency-size distribution of failed areas. This is consistent with observations. This work suggests that remote sensing of soil moisture can be of great importance in monitoring landslide hazards and proposes a specific quantitative model for landslide hazard assessment.     

额尔齐斯河流域上游地区近50 a来气温和降水变化的DFA分析

为查明新疆境内额尔齐斯河流域年及季节性气温和降水变化规律,并对未来的可能变化趋势做出预测,基于去趋势波动分析法（DFA）对流域近50 a来的气温、降水序列的平均值和极端值进行分析. 研究表明,年降水及春、夏的降水序列有较好的长程相关性,在较长时间尺度内均有继续保持原有趋势的可能,即年降水继续增加,春、夏降水维持稳定;秋、冬季降水则呈现弱持续性和强随机性,在短时间尺度上保持现状,长时间尺度上则存在改变的可能. 年均温及夏、秋、冬温也将继续保持升温的趋势,春季长时间尺度上存在改变的可能. 流域内温度和降水都将保持增长的趋势,而且温度的持续上升相对降水具有更高的可能性. 由DFA方法确定的极端阈值及相应极值序列显示：20世纪80年代以来,极端高温和极端降水事件开始增多,且量值增大,准周期变短,但极端高值并没有显著提高;极端低温事件的发生次数减少显著,平均值增大,同时低温极值增高明显,冬季气温对全球变化的响应更为敏感.     

过去530年中国东部旱涝事件模拟研究初探

利用CCSM2.0.1模式完成的千年模拟试验结果对近530年中国东部区域旱涝事件进行了初步的研究。结果表明模式一定程度能够反映过去530年中国东部降水变化规律,在年代际变化上与旱涝等级资料较为一致。模式能模拟出旱涝事件世纪尺度变化特征以及旱涝事件的群发现象。从模拟结果中发现,过去530年中国东部共发生了3次持续时间5年或5年以上的严重干旱事件,分别发生在1483～1488年、1635～1645年和1964～1968年; 4次持续时间5年或5年以上的严重洪涝事件,分别发生在1529～1533年、1749～1753年、1926～1932年和1978～1984年。其中,1483～1488年、1635～1645年和1964～1968年干旱事件以及1749～1753年洪涝事件与旱涝等级序列有较好的对应,说明模式对严重干旱事件具有一定的再现能力,而对严重洪涝事件的模拟能力还有待加强。对个例分析发现,对应较好的3次严重干旱事件发生时期降水空间型态的演化与1749～1753年严重洪涝事件不同,前者前期呈南涝北旱格局,旱区逐年向东、南扩大,后者前期同样也呈南涝北旱格局,但为涝区逐年向东、北扩大。模拟还发现中国东部夏季降水的异常变化主要受夏季风影响,发生严重干旱事件期间夏季风偏弱,发生严重洪涝事件期间夏季风偏强,模拟显示严重旱涝事件期间副热带高压无明显变化。     

扰动强度递增斜坡动力学演变规律的振动台试验

“5.12”汶川大地震和“4.20”芦山地震均触发了大量的崩塌、滑坡。实震资料显示,不同地震烈度区地震触发崩塌滑坡规模的整体分布规律会发生变化。这一统计层面的认知亟待得到物理试验的验证。在自组织临界状态理论的概念框架下,开展了振动台砂堆模型试验。试验表明：输入地震波峰值加速度（PGA）为0.075g～0.125g时,落砂量与发生频率的关系可用幂律描述;PGA增加到0.15g～0.25g时,该关系服从对数正态分布;PGA增加到0.35g～0.45g时,该关系具有正态分布特征。元胞自动机模拟试验结果表明,随扰动强度增加,砂堆模型的动力学特性也经历了幂律-幂律弱化-正态分布的演变过程。按照物理学中的普适性原理,汶川、芦山地震Ⅸ度区崩塌滑坡规模与出现频率之间所呈现负幂律分布的现象,以及汶川地震Ⅺ度区所呈现的对数正态分布,可能是具有普适性意义的规律。这些认识可望为不同烈度区地震触发崩塌滑坡灾势预测提供科学依据。     

闽北地区(土富)头-下柳源一带伟晶岩型铌钽矿产远景预测

通过特征分析模型分析和变量选取及关联度分级,对闽北地区头—下柳源一带伟晶岩型铌钽矿产进行远景预测研究。运用特征分析模型(Ⅰ-Ⅳ)计算统计矿床的关联度,对已知矿床模型单元进行检验及对未知统计矿床进行预测,并进行远景预测分级。     

高阶煤煤岩毛管压力曲线新数学模型及关键参数

毛管压力是影响煤层气赋存和开发的重要参数,为建立能够有效表征高阶煤煤岩毛管压力曲线的数学模型,以高阶煤为研究对象,开展了高压压汞实验,系统评价了目前常用的典型毛管压力曲线数学模型的适应性,建立拟合程度更高的数学模型。结果表明,6块高阶煤煤样毛管压力曲线基本没有中间平缓段,整体表现为向左上方凸出的形态,与常规砂岩、低阶煤差异明显;BC模型、贺承祖模型和Li模型均不能很好地拟合高阶煤的毛管压力曲线;建立的新毛管压力曲线数学模型,能够很好地拟合高煤阶煤样毛管压力实验数据,拟合程度达到97%以上;在双对数坐标中,毛管压力和最小毛管压力的对数差与进汞饱和度与最小毛管压力的对数差呈线性关系,可利用该线性关系直接求取毛管压力模型的斜率a和幂指数b,求解步骤较为简单;在其他条件相同时,毛管压力与斜率a和幂指数b均成反比。     

Numerical modeling of debris avalanche propagation from collapse of volcanic edifices

Debris avalanches produced from the collapse of volcanic edifices are destructive events that involve volumes up to two orders of magnitude larger (cubic kilometer) than most non-volcanic rock and debris avalanches. We replicate the motion and spreading of several volcanic collapses by means of a depth-averaged quasi-3D numerical code. The model assumes a frictional internal rheology and a variable basal rheology (i.e frictional, Voellmy and plastic). We back analyzed seven case-studies against observations reported in the literature to provide a set of calibrated cases. The ASTER and SRTM satellite-derived digital elevation models were used as topographic data. The numerical model captures the main features of the propagation process, including travel distance, lateral spreading and run up. At varying triggering factors and material characteristics the best fitting parameters span in a narrow interval and differ from those typical of non-volcanic rock and debris avalanches. The bulk basal friction angles (the sole parameter required in the frictional rheology) range within 3° and 7.5° whereas typical values for non-volcanic debris avalanches vary from 11° to 31°. The consistency of the back analyzed parameters is encouraging for a possible use of the model in the perspective of hazard mapping. The reconstruction of the pre-event topography is critical, and it is associated to large uncertainty. The quality of the terrain data, more than the resolution of the DEMs used, is relevant for the modeling. Resampling the original square grid to larger cell sizes determines a low increase in the back analyzed rheological parameters, as a result of the lower roughness of the terrain.     

The dynamic characteristics of GPS time series and their relation to the seismotectonic specific features of a region

The noise component in the time series of Earth surface displacements that were obtained with the Global Positioning System (GPS) is analyzed for 19 points. The methods of dynamic system and fractal set theory are applied. The analyzed parameters include the correlation dimension, spectral scaling parameter, fractal dimension, and the Hurst exponent. We detect that GPS time series demonstrate fractal properties in a range of over one order of magnitude of frequency (flicker noise). The fractal characteristics of the studied series and seismotectonic features of the studied regions are characterized by a relationship that can be explained by the dynamic characteristics of the block models and seismicity.     

A New Model for Quantifying Anisotropic Scale Invariance and for Decomposition of Mixing Patterns

A new power–law function has been derived to represent the relationship between area of the set consisting of wave numbers with spectral energy density above S (A(>S)) on the two-dimensional frequency plane and S. The power–law relation holds if the field concerned possessing isotropic scale invariance or generalized scaling invariance involves rotational and ratio-scale changing transforms. The equation is valid for dealing with common exploration geophysical and geochemical fields encountered in mineral exploration and environmental assessment. This power–law function not only provides a new model for characterizing anisotropic scaling invariance for generalized scaling field, for example, estimating the power exponent of power spectrum of generalized scale invariance measure in frequency domain, but also forms a theoretical base for the S–A filtering technique developed for decomposing a mixing field into components on the basis of distinct scaling properties in the frequency domain. It is demonstrated that the method has potential to become a general technique for image processing and pattern recognition.     

模型试验的分离相似设计方法——以锚索格构加固边坡模型试验为例

提出了模型试验的分离相似设计方法,以锚索、格构梁加固边坡振动台试验为例进行介绍。将传统量纲分析法中描述振动台试验各个相关参数之间关系的函数关系式定义为1级特征方程。根据边坡、锚索、格构和地震波特性的不同,将1级特征方程进行分离处理,得到分别用于边坡、锚索、格构和地震波相似设计的2级特征方程。根据每个2级特征方程中参数的重要程度不同,将关键设计参数从2级特征方程中分离出来,组成3级特征方程。根据3级、2级和1级特征方程可以分别推导得到针对边坡、锚索、格构梁和地震波各自的关键参数、相关参数和无关参数相似比,选择关键参数相似比作为模型设计的主要依据,并对试验模型进行了相似设计。解决了按照传统量纲分析法要求,模型试验无法同时满足所有参数相似比要求的问题。     

Fractal analysis revisited by the continuous wavelet transform of AVO seismic data

The main goal of this paper is to establish reservoirs media heterogeneities by the wavelet transform modulus maxima lines. First, we gathered amplitude versus offsets (AVO) amplitudes at the top of the reservoirs, then we calculated the 2D wavelet transform after we calculated its maxima, and we estimated the Hölder exponent at each maxima. Variation of the Hölder exponent can give more information about lithology and fluid nature at any point. We applied the proposed idea at a 2D synthetic AVO intercept model, obtained results showed that the wavelet transform modulus maxima lines can be used as a seismic image processing tool. We suggest application of the proposed idea on real AVO seismic data and its attributes. It can give more ideas about reservoirs model.     

Metal in CR chondrites

In section many low-FeO CR chondrules are surrounded by rings of metal; this metal-cladding seems to have formed during chondrule melting events as films of metal that wetted the surface. Electron microprobe studies show that in each ring the metal is very uniform in composition, consistent with efficient mixing during formation of the metal film. In contrast the mean Ni contents of 13 different rings vary by up to a factor of 2. There is no FeS associated with ring metal. Ring metal Co is positively correlated with Ni but the Co/Ni ratio seems to decrease with increasing Ni. We observed a weak negative correlation between ring metal Ni and the fayalite content of the host olivine. Coarse interior metal has higher Ni contents than that in the surrounding rings. At any specific chondrule location, smaller grains tend to have lower Ni contents than larger grains. These trends in Ni seem to reflect two processes: (1) The mean Ni content of metal (and easily reduced sulfides or oxides) in chondrule precursor materials seems to have decreased with the passage of time; on average, the metal in earlier-formed chondrules had higher Ni contents than the metal in later-formed chondrules. (2) Some oxidized Fe was reduced during chondrule formation leading to lower Ni contents in small grains compared to large grains; prior to reduction the Fe was in FeS or in FeO in accessible (fine-grained) sites. We suggest that the compositional evolution of nebular solids was responsible for the interchondrule variations whereas reduction of minor amounts of FeS or FeO was responsible for the size-related small variations in Ni content. We suggest that, during chondrule formation events, CR chondrules experienced relatively long thermal pulses that were responsible for the thorough loss of FeS and the common granoblastic texture observed in low-FeO chondrules. The preservation of the structures of internal rings shows, however, that even though high temperatures occurred in the secondary chondrule, temperatures in the centers of large (>20 μm) metal and silicate grains in the primary chondrule did not get high enough to cause appreciable melting.