Symmetropy of earthquake patterns: asymmetry and rotation in a disordered seismic source

We demonstrate that the idea of symmetropy can be used for quantification of earthquake patterns. The symmetropy can be considered as a measure of asymmetry. A pattern is richer in asymmetry when the symmetropy is smaller. The specific results of its applications are obtained as follows. In a discrete model of a seismic source with self-organized criticality, the spatial patterns of earthquakes during critical states and sub-critical states are distinguished by the behaviour of the symmetropy: sub-critical patterns show that the symmetropy is approximately a constant but this has various values during critical states. The critical patterns show asymmetric property without any asymmetric force from the outside and without asymmetric intracellular rule. We show that the emergence of asymmetric patterns is a generic feature of dynamic ruptures in our model. Such a generic asymmetry results from the model which is an inherently discrete system consisting of finite-sized cells. These cells may represent geometrical disordered fault zones. We further discuss rotational motions that generate seismic rotational waves. In micromorphic continuum theory, such rotations are attributed to dynamic ruptures in disordered systems. We note that the concept of disorder in this theory is expressed by a set of finite-sized microstructures and is consistent with the concept of disorder modelled in the present study. Thus, we suggest that the spatially asymmetric patterns of earthquakes might be related to the rotational motions, because both come from dynamic ruptures in a discrete fault zone without a well-defined continuum limit.     

固体地球系统的复杂性与自组织临界性

本世纪自然科学的发展趋是由极小（粒子物理学）→极大（宇宙学）→极复杂（复杂性科学）。“复杂性”研究具有科学发展的时代特点,是具有前瞻性和探索创新性的基础研究。笔者根据复杂性科学研究复杂性的涌现机制是２１世纪的科学的认识,结合固体地球系统的复杂性与自组织临界性的内禀基本属性,提高“固体地球系统的复杂性与自组织临界性”这一命题,从新的视角对古老而又常新的固体地球系统进行再认识,从广义地质学系统和过程的本质归纳出固体地球系统的基本问题,提出了它的三大基础理论问题,井拟定了以整体论为主导、还原论作辅助,宏观与微观处理相结合与互补的方法论。固体地球系统的复杂性和自组织临界性,是我国经济增长、社会进步和地学发展的重大科学问题之一。对于这一同题进行研究将成为21世纪地学发展中居于战略地位的生长点之一,使地学取得突破性进展,并带动许多相关学科的同步发展。     

溜砂坡动力学特性实验及防治

溜砂坡是川藏公路中段较为严重的一种山地灾害。本文在自组织临界性理论的概念框架下，通过干燥沙石散粒体临界态单面坡沙堆实验，对溜砂坡的坍滑动力学特性进行了探索。实验发现，颗粒均匀的沙坡出现正态分布的、准周期的大规模“雪崩”，而颗粒非均匀的沙坡的坍滑重量表现为难以界分的、多样化的负幂率分布，大规模坍滑的绝对规模较小，呈现自组织临界行为。基于自组织临界性系统具有的普适性，提出了溜砂坡“频率一规模”关系等灾害演化的初步规律。溜砂坡坡顶来沙和坡脚制约作用削弱，是造成坍滑发展的主要原因。针对坍滑的“牵引式”形式和实际工程条件，设计了一种能稳定溜砂坡坡脚、对基础条件要求低的新型支挡防护结构。     

降雨作用下砾石土斜坡坡面形态及临界特性

砾石土因其级配宽、不均匀系数大、透水性强等特点在工程防渗中得到广泛的应用,其强度和力学性质受粗细粒含量和粒间咬合程度、黏接状态等影响。通过人工降雨原型试验、模型试验、室内试验及理论分析,研究松散砾石土斜坡在降雨作用下坡面土体的形态特征和土体性状的变化以及斜坡稳定性和该过程中可能出现的临界状态,探索坡面松散砾石土触变液化的过程和机理。试验结果表明,砾石土斜坡在降雨过程中,坡面土体形态、坡面径流泥沙含量具有阶段性特性;各典型现象土体含水量分布具有区段性;土体强度和斜坡稳定性随着土体含水量的增加均存在明显的临界特征。     

Analysis of regional labour market dynamics: In search of indications for self-organised criticality

Self-Organised Criticality (SOC) is a concept developed over the last decade from dynamic systems analysis that aims to investigate the transition trajectories of evolutionary systems. The main emphasis in SOC is on the analysis of the impact of slow exogenous forces in combination with strong localised interactions between single elements or components of the systems concerned, with particular regard to the attainment of a critical state at the macro-level. Against this background, SOC serves to identify the critical conditions from the internal dynamics of the systems that lead to major and significant transformations of their behaviour. The present paper aims to offer insights and reflections originating from the SOC concept, as well as to explore its potential contribution to understanding the evolution of regional economic patterns, in particular the functioning of regional labour markets. In our study, the evolutionary dynamics of employment at a district level in West Germany as well as in the combined West and East German setting will be investigated, in order to detect the possible existence of a power law distribution of growth rates, which may be seen as an indication for SOC at the macro-economic level. In this context, SOC may help to explain the presence of large socio-economic regional fluctuations in a country, and, in general, the dynamics inherent to regional development.     

Self-organized Fractal Seismicity of Reservoir Triggered Earthquakes in the Koyna-Warna Seismic Zone,Western India

— Analysis of the Koyna-Warna earthquake catalog (1968–1996) shows that on an average there is a positive correlation between the b value (decrease) and fractal dimensions (decrease in both D₂^s and D₂^t) of earthquake epicenters 0.5 and 2.5 years prior to 1973 (M5.2) and 1980 (M5.5) events, respectively, except a negative correlation for about five years (1988–1993) prior to the 1993/1994 sequence (M5.4). This positive correlation indicates a weaker clustering, or that the epicenters tend to fill the two-dimensional plane. While the origin of the negative correlation seems to be that during periods of large events (low b value), there is strong clustering around the main shock epicenter (high fractal dimension). Interestingly, during the last year (1995–1996) of the studied period both the b value and correlation dimensions rose significantly, suggesting that stress release occurs through increased levels of low magnitude and increasingly scattered seismicity, suggesting an increased risk of larger magnitude events. Incidentally, during 2000 three earthquakes of magnitude M 5.0, one earthquake of M 4.0, 45 earthquakes of magnitude M 3.0–3.9, and several thousand earthquakes of M < 3 have occurred in the region. Thus it can be inferred that at local scales the relationship yields both positive and negative correlation that appears to be controlled by different modes of failure within the active fault complex.Acknowledgement. The authors are grateful to Dr. B.K. Rastogi of NGRI for providing the catalog of Koyna earthquakes and for useful scientific discussions. The comments of Dr. I. G. Main have improved the quality of paper for which we extend to him our sincere thanks. One of the authors (AOM) thanks the Third World Academy of Science and the Council of Scientific and Industrial Research, India for the Postdoctoral Fellowship award under which this work was carried out.