Self-Organized Criticality Applied to Natural Hazards

The concept of self-organizedcriticality evolved from studies of three simplecellular-automata models: the sand-pile, slider-block,and forest-fire models. In each case, there is asteady input and the loss is associated with afractal (power-law) distribution of avalanches. Each of the three models can be associated with animportant natural hazard: the sand-pile model withlandslides, the slider-block model with earthquakes,and the forest-fire model with forest fires. We showthat each of the three natural hazards havefrequency-size statistics that are well approximatedby power-law distributions. The model behaviorsuggests that the recurrence interval for a severeevent can be estimated by extrapolating the observedfrequency-size distribution of small and mediumevents. For example, the recurrence interval for amagnitude seven earthquake can be obtained directlyfrom the observed frequency of occurrence of magnitudefour earthquakes. This concept leads to thedefinition of a seismic intensity factor. Both globaland regional maps of this seismic intensity factor aregiven. In addition, the behavior of the modelssuggests that the risk of occurrence of large eventscan be substantially reduced if small events areencouraged. For example, if small forest fires areallowed to burn, the risk of a large forest fire issubstantially reduced.     

Symmetropy of Fault Patterns: Quantitative Measurement of Anisotropy and Entropic Heterogeneity

The purpose of the effort in this paper is to show symmetropy of fault patterns. This quantity can be considered as a measure of entropic heterogeneity and anisotropy. We describe this measure based on the discrete Walsh transform. The specific results of its applications are obtained as follows. When a rock specimen undergoes creep in a laboratory experiment, the fault propagation can be monitored by the decrease of symmetropy. Moreover, in a fault model with self-organized criticality, fault patterns of critical states and subcritical states are distinguished by the behavior of the symmetropy: subcritical fault patterns show almost constant value of symmetropy but it takes various values during critical states. These results demonstrate that symmetropy idea can be used for the quantification of fault patterns.     

松散体边坡灾害自组织临界性及工程应用研究

我国的松散体边坡灾害频繁。为了解松散体边坡灾害的共性，从整体上认识其规律性信息，文章采用多种形式的非均匀沙堆作为松散体边坡灾害的概化模型，通过多组实验研究其演化行为规律。自组织临界性是解释具有无序的、非线性复杂系统行为特征的理论之一，分形和闪烁噪声是其空间与时间结构的特征。实验发现几种概化模型表现出自组织临界性。分析滑坡、崩塌及泥石流等松散体边坡灾害实例，也发现其呈现自组织临界性特征。研究表明幂律特征及自组织临界性是许多松散体边坡灾害的共性。进一步模拟真实的松散体边坡的组成特征和某些防治工程措施，进行对比实验，表明不同工程措施的防治作用。最后结合挡、锚、喷、排等工程防治措施，探讨了自组织临界理论对松散体边坡灾害防治的指导作用。     

Constraints on the frequency–magnitude relation and maximum magnitudes in the UK from observed seismicity and glacio-isostatic recovery rates

Earthquake populations have recently been shown to have many similarities with critical-point phenomena, with fractal scaling of source sizes (energy or seismic moment) corresponding to the observed Gutenberg–Richter (G–R) frequency–magnitude law holding at low magnitudes. At high magnitudes, the form of the distribution depends on the seismic moment release rate M˙ and the maximum magnitude m _max . The G–R law requires a sharp truncation at an absolute maximum magnitude for finite M˙ . In contrast, the gamma distribution has an exponential tail which allows a soft or 'credible' maximum to be determined by negligible contribution to the total seismic moment release. Here we apply both distributions to seismic hazard in the mainland UK and its immediate continental shelf, constrained by a mixture of instrumental, historical and neotectonic data. Tectonic moment release rates for the seismogenic part of the lithosphere are calculated from a flexural-plate model for glacio-isostatic recovery, constrained by vertical deformation rates from tide-gauge and geomorphological data. Earthquake focal mechanisms in the UK show near-vertical strike-slip faulting, with implied directions of maximum compressive stress approximately in the NNW–SSE direction, consistent with the tectonic model. Maximum magnitudes are found to be in the range 6.3–7.5 for the G–R law, or 7.0–8.2 m _L for the gamma distribution, which compare with a maximum observed in the time period of interest of 6.1 m _L . The upper bounds are conservative estimates, based on 100 per cent seismic release of the observed vertical neotectonic deformation. Glacio-isostatic recovery is predominantly an elastic rather than a seismic process, so the true value of m _max is likely to be nearer the lower end of the quoted range.     

Heterogeneous transition dynamic equations and the self-organized origin of the nesting rhythmic beddings in Panzhihua lithosomes

Dynamic equations were developed for heterogeneous phase-transition in a system of coupled nucleation, growth and ripening. Based on these equations, a self-organized origin of small-scale nesting rhythmic beddings in Pahzhihua lithosomes was investigated and the results showed that the beddings could be formed by the cross supersaturated nucleation-crystallization of augite and feldspar successively. This process could be implemented by coupling with supersaturated nucleation, Ostwald ripening, component diffusion and the primary grain diffusion under a proper temperature gradient. The slightly intensive supersaturated nucleation and Ostwald ripening occurring in Panzhihua lithosomes may relate closely to the mineral components such as V-Ti-Maanetite.     

Self-organized crystallization mechanism of non-equilibrium 2:1 type phyllosilicate systems

The crystallization mechanism of 2:1 type regular interstratified minerals is investigated in views of non-equilibrium thermodynamics. The structural chemistry of relative layers and their interstratified combinations is analyzed and six kinds of non-equilibrium chemical systems have been induced. The universal laws of chemical reactions which happened in the interface region of these non-equilibrium systems have been summarized. From these laws, two reaction systems crystallizing out Tosudite and Rectorite respectively have been recovered. The kinetic model of chemical reactions has been developed by means of the mass conservation law. The oscillatory solution showing regular interstratified features has also been obtained numerically. These results indicate that the difference in original chemical composition among systems can affect the chemical connotation of reactants, intermediate products and resultants, and the flow chart of chemical reaction, but cannot change their crystallization behavior of network-forming cations, bigger and smaller network-modifying cations during crystallization. Hence, their kinetic model reflecting the universal crystallization law of these cations is just the same. These systems will crystallize out regular interstratified minerals at suitable parameters, which always exist as domain with nanometer-sized in thickness and can be called the self-organized ordering structure.     

Earthquake mechanism and predictability shown by a laboratory fault

Slip events generated in a laboratory fault model consisting of a circulinear chain of eight spring-connected blocks of approximately equal weight elastically driven to slide on a frictional surface are studied. It is found that most of the input strain energy is released by a relatively few large events, which are approximately time predictable. A large event tends to roughen stress distribution along the fault, whereas the subsequent smaller events tend to smooth the stress distribution and prepare a condition of simultaneous criticality for the occurrence of the next large event. The frequency-size distribution resembles the Gutenberg-Richter relation for earthquakes, except for a falloff for the largest events due to the finite energy-storage capacity of the fault system. Slip distributions, in different events are commonly dissimilar. Stress drop, slip velocity, and rupture velocity all tend to increase with event size. Rupture-initiation locations are usually not close to the maximum-slip locations.     

地震及其前兆的观测研究与地震预测

通过对地震灾害及预测观察研究现状的分析,解析了地震预测研究中存在的问题和不足,指出了地震及其前兆观测在预测研究中的作用,同时认为,地震前兆观测既不能盲目,也不能随波逐流也进行,其进展以决于地震孕育机理的深入理解和有效观测途径或方法的选择,并简述了２０年来在震前准静电场观测研究中取得进展和体会。     

Frequency–size distribution of global seismicity seen frombroad-band radiated energy

The frequency–energy distribution of global seismicity is studied using broad-band radiated energy of shallow earthquakes from January 1987 to December 1994 estimated by NEIC. Rank-ordering statistics are applied to enhance the resolution in retrieving the power-law distribution with undersampled data, namely a few tens of events. Seen in the perspective of broad-band radiated energy with higher resolution, a single (Gutenberg–Richter-type) power-law distribution can fit the data. For earthquakes with energy larger than 10¹⁴ J, the number N of events with energy E depends on E via N∝E ^−B , with the scaling constant B = 0.64 ± 0.04, corresponding to b = 0.95 ± 0.06. This relation is different from that of scalar seismic moment, which shows a transition of power-law distributions between small and large earthquakes. To demonstrate such a difference we use the same set of earthquakes with both broad-band energy estimation and CMT estimation. It is found that for the same data set, the energy distribution and the moment distribution show different patterns. The moment distribution has a clear kink between small and large earthquakes, while the energy distribution shows a single power law with no convincing kink between small and large earthquakes. To investigate the effect of different focal mechanisms and different seismic regions, events with strike-slip mechanisms and events within the Japan–Kuril region are considered. For these subsets of events, a similar pattern exists, in which the moment distribution shows a kink between small and large earthquakes, while the energy distribution shows a single power law.     

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。