Statistical properties of Olami-Feder-Christensen model on Barabasi-Albert scale-free network

The Olami-Feder-Christensen model on the Barabasi-Albert type scale-free network is investigated in the context of statistical seismology. This simple model may be regarded as the interacting faults obeying power-law size distribution under two assumptions: (i) each node represents a distinct fault; (ii) the degree of a node is proportional to the fault size and the energy accumulated around it. Depending on the strength of an interaction, the toppling events exhibit temporal clustering as is ubiquitously observed for natural earthquakes. Defining a geometrical parameter that characterizes the heterogeneity of the energy stored in the nodes, we show that aftershocks are characterized as a process of regaining the heterogeneity that is lost by the main shock. The heterogeneity is not significantly altered during the loading process and foreshocks.     

Modeling of super-extreme events: An application to the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk

We analytically demonstrate and numerically simulate two utmost cases of dragon-kings’ impact on the (unnormalized) velocity autocorrelation function (VACF) of a complex time series generated by stochastic random walker. The first type of dragon-kings corresponds to a sustained drift whose duration time is much longer than that of any other event. The second type of dragon-kings takes the form of an abrupt shock whose amplitude velocity is much larger than those corresponding to any other event. The stochastic process in which the dragon-kings occur corresponds to an enhanced diffusion generated within the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk (WM-CTRW) formalism. Our analytical formulae enable a detailed study of the impact of the two super-extreme events on the VACF calculated for a given random walk realization on the form of upward deviations from the background power law decay present in the absence of dragon-kings. This allows us to provide a unambiguous distinction between the super-extreme dragon-kings and ‘normal’ extreme “black swans”. The results illustrate diagnostic that could be useful for the analysis of extreme and super-extreme events in real empirical time series.     

Black swans,power laws,and dragon-kings: Earthquakes,volcanic eruptions,landslides, wildfires,floods, and SOC models

Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.     

Advance in earthquake prediction by physical simulation on the baikal ice cover

The main challenge in the prediction of tectonic earthquakes and their control is still insufficient awareness of seismotectonic processes in the lithosphere and upper mantle during the preparation of strong earthquakes. This is associated in many respects with not quite appropriate equipment for researchers. Among relevant problems is also a lack of adequate models of preparation of earthquake sources at different stages, and this retards the development of earthquake prediction methods. The paper discusses long-term research on deformation and destruction of the Baikal ice cover in the context of physical mesomechanics. With certain combinations of meteorological factors (wind, temperature, precipitation, undercurrents, etc.) responsible for deformation, major cracks of many kilometers arise in the Baikal ice cover. Their spontaneous growth often involves seismic phenomena as ice quakes whose energy reaches E _max = 10⁴–10⁷ J. The nucleation of major cracks is similar to that of rock bursts of moderate strength or weak earthquakes. It is found that ice quakes and earthquakes are both preceded by foreshocks, seismic calm for tens of minutes, aftershocks and other events against the background of accelerated creep in fractures and increased seismoacoustic activity. Research data make it possible to put forward two genetically interrelated criteria among basic factors for ice quake prediction: variations in deformation modes at convergent boundaries of ice sheets and a specific intensification mode-generation of strong foreshocks in a segment in which ice sheets are prepared for dynamic motion. We substantiate the conclusion that simpler and clearer scenarios of preparation of strong seismic events in the Baikal ice cover allow successful physical simulation of preparation of tectonic earthquakes and rock bursts and advances in their prediction. We also consider and substantiate the feasibility of techniques for more efficient seismic risk reduction.     

Foreshocks and aftershocks in the Olami-Feder-Christensen model

With the help of numerical simulations we show that the established Olami-Feder-Christensen earthquake model exhibits sequences of foreshocks and aftershocks; this behavior has not been recognized in previous studies. Our results are consistent with Omori's empirical law, but the exponents predicted by the model are lower than observed in nature. The occurrence of foreshocks and aftershocks can be attributed to the nonconservative character of the Olami-Feder-Christensen model.     

Extreme events and predictability of catastrophic failure in composite materials and in the Earth

Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a ‘black swan’. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify ‘characteristic’ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragon’s domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models.     

Thermal effect in metamorphic rock around an intrusion zone with ESR studies

Hornfels, and intrusion rocks were studied with electron spin resonance (ESR) as a function of the distance from an intrusion zone in Mino Natural Park, Osaka, Japan. The temperature distribution in metamorphic rocks around an intrusion zone was calculated based on a simplified model of one-dimensional thermal conduction. The age as well as the thermal effect due to an intrusion rock were assessed using ESR signal intensities of paramagnetic defect centers (E’, oxygen-hole, and Al) in quartz grains. Geothermal heating effects are observable more than ten million years later for stable detects such as the E’ center.     

Experimental studies on perturbed acoustic resonant spectroscopy by a small rock sample in a cylindrical cavity

A measurement system for acoustic resonant spectroscopy (ARS) is established, and the effects of resonant cavity geometry, inner perturbation samples and environmental temperature on the ARS are investigated. The ARSs of the small samples with various sizes and acoustic properties are measured. The results show that at the normal pressure, the resonant frequency decreases gradually with the increase of liquid temperature in the cylindrical cavity, while the resonant amplitude increases. At certain pressure and temperature, both the resonant frequency and the amplitude decrease greatly when there exist air bubbles inside the cavity fluid. The ARS is apparently affected by the sample porosity and the sample location in the resonant cavity. At the middle of the cavity, the resonant frequencies reach their maximum values for all of the measurement samples. The resonant frequencies of the porous rock samples are smaller than those of the compacted samples if other acoustic parameters are the same. As the sample is moved from the top to the middle of the cavity along its axis, the resonant amplitude increases gradually for the compacted rocks while decreases for the unconsolidated rocks. Furthermore, the resonant amplitude increases firstly and then decreases if the porosity of the rock sample is relatively small. In addition, through the comparisons between the experimental and theoretical results, it is found that the effects of the acoustic parameters and sizes of the samples and the size of the cylindrical cavity on the laboratory results agree well with the theoretical ones qualitatively. These results may provide basic reference for the experiment study of rock acoustic properties in a low frequency using ARS.     

论地震发生机制

地震发生的物理机理和过程是还没有认识清楚的问题. 此前人们将浅源地震归因于弹性回跳,根据这一观点和岩石实验结果计算得到的地震能量与实际观测结果有很大矛盾,被称之为“热流佯谬”. 中源和深源地震发生在地幔区域,其成因也没有合理的解释. 考虑到地壳和地幔是离散集合态物质体系及其慢动力学运动行为的基本特点,本文根据物理学原理,特别是近年凝聚态物理发展出来的相关新观念,并依据已有观测事实,从新的视角探究地震发生的物理机制. 1) 关于地壳岩石层中的应力分布:在不考虑构造力时,依据万物皆流的流变学原理,原始地壳岩石在自重压强长时间作用下,纵向和横向应力相同,没有差应力. 大地构造力推动岩块滞滑移动挤压断层泥,施加于其他岩块,逐渐传递和积累. 这种附加的横向构造力与原始岩石中应力叠加,形成地壳岩石层中的实时应力. 由于断层泥属于颗粒物质体系,具有与岩石不同的力学特征,其弹性模量比岩石小得多,且随压强而增大,导致构造作用力随深度非线性增大. 给出了地壳中构造应力分布及其变化规律. 2) 关于地壳岩石层强度:地壳岩石的自重会使岩石发生弹性–塑性转变. 通过对弹性–塑性转变深度的计算,并根据实际情况分析,给出了地壳岩石弹性、部分塑性和完全塑性三个区域的典型深度范围. 在部分塑性区,塑性体比例达到约10%以上时,发生塑性连通,这时岩石剪切强度由塑性特征决定. 塑性滑移的等效摩擦系数比脆性破裂小一个数量级以上,致使塑性滑移时岩石剪切强度比脆性破裂小得多. 同时,随深度增大,有多种因素使得岩石剪切屈服强度减小. 另一方面,地震是大范围岩石破坏,破坏必然沿薄弱路径发生. 因此,浅源地震岩石的实际破坏强度必定比通常观测到的岩石剪切强度值低. 给出了地壳岩石平均强度和实际破坏强度典型值随深度的分布规律. 3) 关于地震发生的条件和机制:地震发生必定产生体积膨胀,只有突破阻挡才可膨胀. 地震发生的条件是:大地构造力超过岩石破坏强度、断层边界摩擦力以及所受阻挡力之和. 因此,浅源地震是岩石突破阻挡发生的塑性滑移. 在此基础上提出了浅源地震发生的四种可能模式. 深源地震是冲破阻挡发生的大范围岩块流. 浅源地震和深源地震都是堵塞–解堵塞转变,是解堵塞后岩石层块滑移或流动造成的能量释放. 4) 关于地震能量和临震前兆信息:地震能量即为堵塞–解堵塞转变过程释放的动能. 以实例估算表明,地震岩石滑移动能与使岩块剪切破坏和克服周围摩擦阻力所需做的功相一致,不会出现热流佯谬. 同时指出,通过观测地震发生前构造力的积累过程、局域地区地质变迁以及岩石状态变化等所产生的效应,均可能获得有价值的地震前兆信息. 关键词： 地震发生机制 热流佯谬 地壳岩石应力和强度 堵塞–解堵塞转变     

Femtosecond laser-based fabrication of a new model material to study fracture

The ductile fracture process consists of the nucleation, growth and coalescence of voids in a material. Predictive models of ductility require a complete understanding of the coalescence event. However, coalescence occurs over very small strains and is therefore difficult to observe experimentally. We have addressed this by developing a new class of model material. It consists of femtosecond laser drilled holes and diffusion bonded metallic sheets, which can be mechanically tested in situ either by scanning electron microscopy (SEM) or by X-raycomputed tomography (XRCT). The fabrication steps are presented and the model material is characterized by optical and electron microscopy, nanoindentation and tomography. The heat affected zone around the laser holes is found to be harder than the unaffected material and consists of nano-scale grains. Finally we show that the coalescence event is well captured using both SEM and XRCT. The fabrication method is adaptable to a wide range of materials and enables one to produce 2D and 3D arrays of holes or cracks with controlled size, volume fraction and distribution. PACS  62.20.Mk; 62.25.+g; 79.20.Ds     

利用显微红外光谱技术表征非均质油气储层裂缝特征——以任丘潜山蓟县系雾迷山组碳酸盐岩储层为例

油气储层裂缝既是重要的储油空间,又是油气运移的主要通道,因此,裂缝表征非常重要。然而储层岩石具有强烈的非均质性,如何精确表征非均质储层裂缝是需要亟待解决的问题。利用显微红外光谱技术可以对矿物分子的光谱曲线进行分析,得到不同的峰值特征,精确获得岩石介质成分、裂缝的大小、裂缝充填物特性等。以任丘潜山型碳酸盐岩非均质储层为例,基于显微红外光谱技术,通过分析岩心光片显微红外成像光谱图和不同特征区域的光谱曲线,获得了目标样品岩石介质的物化特性和空间分布特征,预测了裂缝可能发育的区域, 并分析了裂缝的有效性。结果表明,岩心样品主要介质为白云岩;储层裂缝中含有烃类有机物和盐水包裹体,它们主要赋存于白云岩介质中;裂缝充填物中盐水包裹体所占比例为51.7%,烷烃有机物所占比例为26.0%,裂缝发育从岩心样品左上方区域延伸至右下方区域,表明该延伸区域可能是流体运移的通道;盐水包裹体会阻碍油气的运移,导致裂缝的渗透率降低;实验测得岩石裂缝宽度为1~1.5 mm,属于大裂缝,油气可以顺利通过,因此,裂缝的有效性好。研究表明利用显微红外光谱成像技术表征非均质储层裂缝特征是切实可行的,为非均质油气储层精确表征提供了一种新方法。     

Physical modeling of seismic source generation in failure of fault asperities

A series of full-scale experiments was performed to study the influence of impact loads on the parameters of seismic vibrations initiated in variable friction. The study was conducted on a test setup Tribo which is a movable concrete slab modeling an allochthon on a rough plane of the Angara fault segment in Baikal region. Contact interactions of asperities in the slip zone were recorded using strain and load measuring equipment and four seismic stations Baykal-7HR widely used for recording earthquakes. The proposed physical modeling method and obtained results can be of interest for the development of new physical models of differently scaled sources of seismic energy dissipation in tectonic faults and can be useful for seismological studies, related data interpretation, and improvement of extended forecast of rock bursts and earthquakes.     

Dynamics of a creep-slip model of earthquake faults

Starting off from the relationship between time-dependent friction and velocity softening we present a generalization of the continuous, one-dimensional homogeneous Burridge–Knopoff (BK) model by allowing for displacements by plastic creep and rigid sliding. The evolution equations describe the coupled dynamics of an order parameter-like field variable (the sliding rate) and a control parameter field (the driving force). In addition to the velocity-softening instability and deterministic chaos known from the BK model, the model exhibits a velocity-strengthening regime at low displacement rates which is characterized by anomalous diffusion and which may be interpreted as a continuum analogue of self-organized criticality (SOC). The governing evolution equations for both regimes (a generalized time-dependent Ginzburg–Landau equation and a non-linear diffusion equation, respectively) are derived and implications with regard to fault dynamics and power-law scaling of event-size distributions are discussed. Since the model accounts for memory friction and since it combines features of deterministic chaos and SOC it displays interesting implications as to (i) material aspects of fault friction, (ii) the origin of scaling, (iii) questions related to precursor events, aftershocks and afterslip, and (iv) the problem of earthquake predictability. Moreover, by appropriate re-interpretation of the dynamical variables the model applies to other SOC systems, e.g. sandpiles.     

Intermittent criticality in the long-range connective sandpile (LRCS) model

We here propose a long-range connective sandpile model with variable connection probability Pc which has an important impact on the slope of the power-law frequency-size distribution of avalanches. The long-range connection probability Pc is changed according to an explicit function of the size of the latest event, although the evolution rule of Pc may be different in various physical systems. Such version of the sandpile model demonstrates large fluctuations in the dynamical variable 〈Z〉(t) (the spatially averaged amount of grains retained within the grid at each time step), indicating the state of intermittent criticality in the system. Many researches have suggested that the earthquake fault system is an intermittent criticality system, which would imply some level of statistical predictability of great events. Our modified sandpile model thus provides a testing ground for many proposed precursory measures related to great earthquakes.     

Sliding size distribution in a simple spring-block system with asperities

We use a simple spring-block system as a qualitative analogous of a seismic fault. The role of the asperities present in a real seismic fault is played by sandpapers of several grades. With this experimental array Gutenberg-Richter type-laws are obtained. We also observed that the maximum characteristic event in each experimental run depends on both the mass of the sliding blocks and the age of the sandpapers used at the interface between the blocks and the rough track.     

Aftershocks in coherent-noise models

The decay pattern of aftershocks in the so-called ‘coherent-noise’ models [M.E.J. Newman, K. Sneppen, Phys. Rev. E 54 (1996) 6226] is studied in detail. Analytical and numerical results show that the probability to find a large event at time t after an initial major event decreases as t^−τ for small t, with the exponent τ ranging from 0 to values well above 1. This is in contrast to Sneppen and Newman, who stated that the exponent is about 1, independent of the microscopic details of the simulation. Numerical simulations of an extended model [C. Wilke, T. Martinetz, Phys. Rev. E 56 (1997) 7128] show that the power-law is only a generic feature of the original dynamics and does not necessarily appear in a more general context. Finally, the implications of the results to the modelling of earthquakes are discussed.     

Powdered rock versus solid rock comparisons in particle-induced X-ray emission measurements for planetary geochemical exploration

Grain size is an important consideration in the determination of the bulk chemistry of Martian rocks and unconsolidated materials in situ by the alpha particle X-ray spectrometer (APXS), deployed on the NASA-led Mars Science Laboratory mission. We used 2.5 MeV protons to emulate the particle-induced X-ray emission (PIXE) branch (5 MeV alphas) of the APXS. Seven polished rock slabs (igneous and sedimentary), ranging from fine- to coarse-grained, were analyzed by PIXE in their original form, then milled to powders and pressed into pellets for further analysis. The summed area (160 mm²) over 10 interrogated regions on each slab is comparable to the area interrogated on the APXS; analysis of two pellets per rock, each using a 16 mm² region, was found to be appropriate. The mean pellet/slab concentration ratio for Na, Mg, Al, Si, K, Ca, and Fe was close to 1.0 for fine-grained samples, but changed by ±10% for the coarser cases. The variability among PIXE concentration values across the 10 rock regions increased monotonically with coarseness in the rock slabs. Comparison of overall PIXE concentrations with values measured by borate-fusion WDXRF provides further quantitative support to the direct comparison of pellet and slab PIXE concentrations. This work affirms the use of the APXS on fine-grained Martian materials but recommends larger interrogation areas (including rastering) when analyzing coarser-grained materials. It also demonstrates that the presence of relatively large mineral grains (phenocrysts) or rock/mineral fragments within fine-grained materials can contribute to greater error for specific elements associated with those phenocrysts/fragments.     

Violation of the scaling relation and non-Markovian nature of earthquake aftershocks

The statistical properties of earthquake aftershocks are studied. The scaling relation for exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks.     

Critical features in electromagnetic anomalies detected prior to the L’Aquila earthquake

Earthquakes (EQs) are large-scale fracture phenomena in the Earth’s heterogeneous crust. Fracture-induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. Electromagnetic (EM) emissions in a wide frequency spectrum ranging from kHz to MHz are produced by opening cracks, this can be considered as the so-called precursors of general fracture. We emphasize that the MHz radiation appears earlier than the kHz on both laboratory and geophysical scales. An important challenge in this field of research is to distinguish characteristic epochs in the evolution of precursory EM activity and identify them with the equivalent last stages in the EQ preparation process. Recently, we proposed the following two-stage model. (i) The first epoch, which includes the initial emergent MHz EM emission, is thought to be due to the fracture of a highly heterogeneous system that surrounds a family of large high-strength asperities distributed along the activated fault sustaining the system. (ii) The second epoch, which includes the emergent strong impulsive kHz EM radiation, is due to the fracture of the asperities themselves. A catastrophic EQ of magnitude Mw=6.3 occurred on 6 April, 2009 (06/04/09) in central Italy. The majority of the damage occurred in the city of L’Aquila. Clear kHz–MHz EM anomalies had been detected prior to the L’Aquila EQ. Here, we investigate the seismogenic origin of the MHz part of the anomalies. The analysis, which is in terms of intermittent dynamics of critical fluctuations, reveals that the candidate EM precursor (i) can be described as analogous to a thermal continuous phase transition and (ii) has anti-persistent behavior. These features suggest that this candidate precursor was triggered by microfractures in the highly disordered system that surrounded the backbone of asperities of the activated fault. A criterion for underlying strong critical behavior is introduced. In this field of research, reproducibility of results is desirable; and is best done by analyzing a number of precursory MHz EM emissions. We refer to previous studies of precursory MHz EM activities associated with nine significant EQs that have occurred in Greece in recent years. We conclude that all the MHz EM precursors studied, including the present one, can be described as analogous to a continuous second-order phase transition having strong criticality and anti-persistent behavior.     

Relaxation dynamics of aftershocks after large volatility shocks in the SSEC index

The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility (constructed using 1-minute data) and minutely volatility (using intra-minute data) decays as a power law. The power-law relaxation exponent increases with the volatility threshold and is significantly greater than 1. Taking financial volatility as the counterpart of seismic activity, the power-law relaxation in financial volatility deviates remarkably from the Omori law in Geophysics.