Multifractal and Chaotic Analysis of Vrancea (Romania) Intermediate-depth Earthquakes: Investigation of the Temporal Distribution of Events

The Vrancea seismic region contains an isolated cluster of events beneath the Carpathian Arc Bend in Romania, dipping to about 200 km depth. Seismic activity mainly occurs at intermediate depths (h > 60 km). The main goal of the paper is to perform an in-depth, complex analysis of the occurrence times of these intermediate-depth events. We also try to show the versatility of the methods used to characterize different aspects of the seismicity evolution and to offer a user-friendly software toolbox to do most of the related computations. The earthquake catalog used in this study spans from 1974 to 2002 and includes only the intermediate-depth events. In the first part of the paper, we analyze the multifractal characteristics of the temporal distribution of earthquakes. The study reveals two distinct scaling regimes. At small scales we found a clear nonhomogeneous, multifractal pattern, while at large scales the temporal distribution of events shows a monofractal, and close to Poissonian (random), behavior. The multifractal behavior at small scales (minutes-hours) is shown to be clearly an effect of the short aftershock sequences that occurred after some major Vrancea earthquakes. In the second part of the paper we analyze whether our temporal series shows a persistent (or anti-persistent) long-term behavior, by using the Detrended Fluctuation Analysis (DFA) method. The results suggest that the analyzed temporal series of Vrancea earthquakes is a non-correlated process. In part three of the paper we seek to determine whether the dynamics of our earthquake system (described by the occurrence time of Vrancea earthquakes) is deterministically chaotic, deriving from a rather simple evolution law, or whether it is stochastic and is generated by a system that possesses many degrees of freedom. The results suggest that our signal is stochastic (probably does not possess an attractor). The limited time-span of the catalog and the analysis performed in this paper cannot rule out the emergence of an interesting, quasi-deterministic and low-dimensional structure in the case of major Vrancea earthquakes.Acknowledgement One of the authors (BE) is grateful to the Japanese Ministry of Education for providing him a Monbusho scholarship for studying in DPRI, Kyoto University. We thank Z.R. Struzik, M Holschneider, J. Mori and D. Kaplan for their useful comments, and acknowledge the support of the staff of DPRI, Kyoto University and the National Inst. for Earth Physics, Bucharest. We thank the two reviewers, M.B. Geilikman and M. Anghel, for their useful suggestions which improved the quality of this work.     

Aftershock Statistics

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Båths law for the magnitude of the largest aftershock, and (3) the modified Omoris law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Båths law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omoris law.     

Demarcation and Scaling of Long-term Seismogenesis

A space-time envelope of minor seismicity related to major shallow earthquakes is identified from observations of the long-term Precursory Scale Increase () phenomenon, which quantifies the three-stage faulting model of seismogenesis. The envelope, which includes the source area of the major earthquake, is here demarcated for 47 earthquakes from four regions, with tectonic regimes ranging from subduction to continental collision and continental transform. The earthquakes range in magnitude from 5.8 to 8.2, and include the 24 most recent mainshocks of magnitude 6.4 and larger in the San Andreas system of California, the Hellenic Arc region of Greece, and the New Zealand region, together with the six most recent mainshocks of magnitude 7.4 and larger in the Pacific Arc region of Japan. Also included are the destructive earthquakes that occurred at Kobe, Japan (1995, magnitude 7.2), Izmit, Turkey (1999, magnitude 7.4), and W.Tottori, Japan (2000, magnitude 7.3). The space (A _P ) in the space-time envelope is optimised with respect to the scale increase, while the time (T _P ) is the interval between the onset of the scale increase and the occurrence of the earthquake. A strong correlation is found between the envelope A _P T _P and the magnitude of the earthquake; hence the conclusion that the set of precursory earthquakes contained in the envelope is intrinsic to the seismogenic process. Yet A _P and T _P are correlated only weakly with each other, suggesting that A _P is affected by differences in statical conditions, such as geological structure and lithology, and T _P by differences in dynamical conditions, such as plate velocity. Among other scaling relations, predictive regressions are found between, on the one hand, the magnitude level of the precursory seismicity, and on the other hand, both T _P and the major earthquake magnitude. Hence the method, as here applied to retrospective analysis, is potentially adaptable to long-range forecasting of the place, time and magnitude of major earthquakes.     

空间尺度上推方法的精度评价——以内蒙古锡林郭勒盟土地利用数据为例

不同的空间尺度上推方法会导致不同程度的信息丢失、信息歪曲等后果;但目前少有研究在较长的尺度序列上、对不同尺度上推方法所得成果开展精度分析。本研究首先提出尺度上推方法精度评价的三个准则,即:保持土地类型构成特征、保持土地面积精度、保持土地空间分布格局和斑块形态;继而使用格点中心值、最大面积斑块、最大聚合面积斑块等3种尺度上推方法,配合100 m～50 km土地利用数据开展尺度转化实验;最后基于上述评价准则和尺度上推实验所得的系列输出结果,分析了不同尺度上推方法的精度。研究表明:(1)格点中心值上推方法能更好地保留区域土地类型构成、土地面积精度等特征;(2)锡林郭勒盟地区土地研究的适宜尺度应小于10 km,最大不应超过30 km;(3)在尺度上推过程中,土地斑块的平均面积、形态以及空间分布格局对尺度上推成果精度有着重要影响。     

岩石破裂过程中电磁辐射信号特征研究

为了探索震前电磁异常现象的物理机制,许多研究注重于分析岩石破裂过程中产生的电磁辐射信号。对花岗岩样品进行单轴加载,变形直至破裂,记录整个过程中产生的电磁辐射(EME)和声发射(AE)信号,对比分析。这里主要从两个方面分析岩石破裂过程中EME信号的特征:①利用非广延分析方法分析EME的能量分布情况,并与b值分析方法对比,推断岩石破裂类型以及裂纹发育过程;②利用统一等待时间定标律分析EME的时间特征,期望获得岩石破裂过程中EME信号等待时间的分布规律。结果表明,在拟合AE和EME信号的能量分布曲线时,发现b值只能拟合AE部分数据,完全不能拟合EME数据,而非广延参数q可以很好地拟合这两类信号。通过对比分析AE和EME信号的等待时间概率密度的分布情况,发现EME信号的集成效果相对较差,可能不满足统一等待时间定标律。     

标度律视角的城市效能测度及中国城市多维要素效能分析

“城市标度律”（urban scaling laws）揭示了城市系统中城市人口和城市要素间普遍存在的非线性规模缩放关系,但目前大多数城市评价忽视了这种关系,常使用人均指标比较不同规模的城市,这会导致评价结果偏差。为此,考虑城市人口和城市要素间的非线性规模缩放关系构建了要素效能指数,用以修正城市规模的影响,度量城市要素实际发挥出预期能力的程度。以城市发展不同维度上的9个城市要素为例,分别测度了2017年中国292个地级以上城市各要素的效能,识别了各要素效能的空间差异和集聚特征,分析了要素效能指数的优势并讨论了结果的政策启示。结果表明：① 9个城市要素都符合“城市标度律”,其中8个要素与城市人口呈非线性规模缩放关系;从标度律的视角测度城市效能是必要而且可行的。② 城市综合经济、商业消费和公共财政效能普遍以东部沿海地区较高;东北地区的基础教育和中西部地区的公共交通效能较低;土地和水资源禀赋较高的地区对应的效能值并不高;大部分城市的生态绿地效能较低。600万人以上的城市中,杭州、深圳、天津的各维度效能表现较均衡。③ 与人均指标评价结果的对比证明要素效能指数能够修正人口规模对城市评价的影响,对常用的总量和人均指标是有益的补充。标度律视角下的城市效能测度能够给城市人口管理和城市要素发展的决策提供明确的指导方向,同时为不同规模大小的城市提供更客观的比较标准,对国家城镇体系规划和落实中国新型城市化战略具有积极意义。     

Multifractal process of runoff fluctuation of the Kaidu River in Xinjiang,China

Based on the hydrological data in the headwater region of the Kaidu River during 1972–2011, the multifractal process of runoff fluctuation was analyzed. Results indicated that, in the past 40 years, the overall runoff of the Kaidu River in Xinjiang has shown significant multifractal behavior. Its singular curve lnχ_q(ε)–ln(ε) verified a favorable scale invariance over the entire time scale. τ(q)–q proved that evolution of the runoff time series presented multifractal characteristics. Moreover,the multifractal spectrum f(α)–α curve was hooklike leftward which indicated that, compared to relatively large runoff events. And Δf0 indicated that these relatively small events took the leading role; B0 explained the Kaidu River's daily-runoff ascending tendency presented during 1972–2011. Besides that, the multifractal behavior of the Kaidu River's runoff variability over four decades was also analyzed. Generally speaking, by decades, their four corresponding spectrum variations were not noticeable. These Δα values showed larger runoff events occupied the leading position with some local values falling. During the 1970 s to the 1990 s, Δf0 illustrated the probability of the daily runoff at the lowest point is always larger than that of the highest during three continuous decades. At the beginning of the 21 st century, for Δf0 the trend presented was contrary from the 1970 s to the 1990 s. B values suggested an overall trend of increases during1972–2011. Until the 21 st century, the runoff with a slightly descending tendency on the whole explained these relatively large runoff events taking the leading role for the Kaidu River; but sometimes, some small events also played the dominant role.     

基于GIS和空间句法的城市形态实证研究

近年来,空间句法理论作为复杂理论众多分支中的一个,受到众多学者的关注,它被广泛应用于GIS领域,为城市形态研究提供了新视角。Axwoman,既是新兴的空间句法工具,同时又是集成于ArcGIS的用于城市形态分析的功能扩展,常被用来计算空间形态变量和评估空间形态。本文以斯德哥尔摩市街道网络为例构建轴线图,并对其连接值引入相关尺度分析方法,计算结果显示,轴线图连接值服从幂律分布规律。     

基于时空热点分析的城市交通违法行为特征识别方法

交通违法行为是引发交通事故的重要原因,然而现有研究主要关注交通违法行为的整体特征,缺少面向交通违法治理需求的分析框架。本文基于时空热点分析方法,提出从热点区域时间分布特征和典型时段热点区域空间分布特征两个角度识别交通违法行为特征的分析框架,分别用于支撑局部交通违法热点以及全局违法模式的原因分析和精准治理。基于该方法对福州市的机动车和非机动车（含行人）违法行为特征进行了识别分析,结果表明：机动车和非机动车违法行为在时间维度均呈现出9:00和16:00一日双峰特征,在空间维度呈现出“一片区、多热点”的聚集分布特征。二者也存在明显差异,具体表现为：① 在时间维度,非机动车违法行为呈现出更大的变化幅度,高峰时段与中午低谷时段、工作日与周末的违法行为数量差异均明显高于机动车;② 在空间维度,机动车违法行为在商业中心、医院等重要场所和交通枢纽呈现出聚集特征,分布范围更广,而非机动车违法行为则主要在人流量大且人车混行严重的城市中心路口区域呈现聚集特征;③ 不同违法热点地区产生的原因存在差异,需要有针对性制定治理措施。上述发现表明了本文方法能够全面快速识别交通违法行为特征,可以帮助指导城市交通违法行为动态监测分析系统建设,为持续优化城市交通现场执法警力动态分配以及交通违法行为精准治理提供决策支持。     

Investigating hydrogeomorphic floodplain mapping performance with varying DTM resolution and stream order

Hydrogeomorphic models allow parsimonious, fast and effective floodplain extent mapping using topographic data as the main input. Hydrogeomorphic approaches enforce the principle that floodplains are well-distinguished and unique landscape features within river corridors. We investigated the sensitivity of a hydrogeomorphic floodplain delineation algorithm, based on a hydrological power law, relating flow depth to contributing area, digital terrain model (DTM) resolution and river network hierarchy. In addition, we compared the results to other common floodplain mapping methods using standard flood-hazard maps as a reference. Taking the Arno River Basin, Italy, as a case study, our results show a dependency between the optimal power law parameters and DTM resolution, with larger parameter values required to reach optimal consistency with flood-hazard maps as DTM resolution increased. Floodplain mapping performance was also found to depend on stream order. We further tested the model consistency at a larger scale to evaluate its performance with respect to inundation maps in Hungary, Italy, Spain and the UK. Our study suggests that pre-defined power law parameters can be assumed, considering DTM resolution and stream order, supporting the use of the presented hydrogeomorphic model for large-scale floodplain mapping in ungauged basins where reference flood-hazard maps are not available.