Earthquake Recurrence in Simulated Fault Systems

We employ a computationally efficient fault system earthquake simulator, RSQSim, to explore effects of earthquake nucleation and fault system geometry on earthquake occurrence. The simulations incorporate rate- and state-dependent friction, high-resolution representations of fault systems, and quasi-dynamic rupture propagation. Faults are represented as continuous planar surfaces, surfaces with a random fractal roughness, and discontinuous fractally segmented faults. Simulated earthquake catalogs have up to 10⁶ earthquakes that span a magnitude range from ～M4.5 to M8. The seismicity has strong temporal and spatial clustering in the form of foreshocks and aftershocks and occasional large-earthquake pairs. Fault system geometry plays the primary role in establishing the characteristics of stress evolution that control earthquake recurrence statistics. Empirical density distributions of earthquake recurrence times at a specific point on a fault depend strongly on magnitude and take a variety of complex forms that change with position within the fault system. Because fault system geometry is an observable that greatly impacts recurrence statistics, we propose using fault system earthquake simulators to define the empirical probability density distributions for use in regional assessments of earthquake probabilities.     

Upper-truncated Power Laws in Natural Systems

—?When a cumulative number-size distribution of data follows a power law, the data set is often considered fractal since both power laws and fractals are scale invariant. Cumulative number-size distributions for data sets of many natural phenomena exhibit a “fall-off?” from a power law as the measured object size increases. We demonstrate that this fall-off is expected when a cumulative data set is truncated at large object size. We provide a generalized equation, herein called the General Fitting Function (GFF), that describes an upper-truncated cumulative number-size distribution based on a power law. Fitting the GFF to a cumulative number-size distribution yields the coefficient and exponent of the underlying power law and a parameter that characterizes the upper truncation. Possible causes of upper truncation include data sampling limitations (spatial or temporal) and changes in the physics controlling the object sizes. We use the GFF method to analyze four natural systems that have been studied by other approaches: forest fire area in the Australian Capital Territory; fault offsets in the Vernejoul coal field; hydrocarbon volumes in the Frio Strand Plain exploration play; and fault lengths on Venus. We demonstrate that a traditional approach of fitting a power law directly to the cumulative number-size distribution estimates too negative an exponent for the power law and overestimates the fractal dimension of the data set. The four systems we consider are well fit by the GFF method, suggesting they have properties characterized by upper-truncated power laws.     

Parallel Fault Systems with Evolving Self-similar Sliding Zones

Catastrophic fault sliding is preceded by the development of sliding zones which grow further driven by the excess of the shear stress over friction at the loci of initiation. This growth is strongly affected by the interaction between the sliding zones. We propose a model of development of such zones based on two major simplifications. Firstly, each sliding zone is modelled as a disc-like shear crack driven by a pair of concentrated forces representing the excess of the shear stress over friction at the loci of initiation. Secondly, the interaction between these cracks is modelled based on the assumption that the distribution of their sizes is self-similar and the self-similarity is maintained in the process of their growth. We show that for parallel cracks the latter is only possible if the sliding zones are localised in a narrow layer. In this case the exponent and the prefactor of the distribution function are uniquely determined. The addition of new sliding zones does not change the distribution but rather increases the upper cut-off. This happens either by instantaneous growth of each added sliding zone to the maximum size producing the strongest microseismic event or by initiating a cascade of intermediate growth producing a series of smaller events. We determine the energy distribution associated with the cascade and the probability of hazardous events. We show that measuring the statistical properties of seismic energy alone is not sufficient for determining the parameters of the model; monitoring of fault deformation is also needed.     

黄土高原复杂地形条件下湍流观测的各态历经性检验

为了揭示黄土高原复杂地形条件下湍流涡旋的分布特征,提高湍流观测的精度,湍流的各态历经性研究随即成为实验研究的首要问题.文章利用甘肃省平凉市白庙塬地形条件下单点湍流观测的结果,对比分析并揭示了从稳定层结到不稳定层结,除小于10min尺度的湍流易于满足各态历经性外,地形易造成周期性存在的大尺度湍流相干结构.与平坦下垫面湍流...     

Ergodicity of turbulence measurements upon complex terrain in Loess Plateau

To display the distribution characteristics of turbulence eddy under condition of complex terrain in Loess Plateau,and to enhance the precision of turbulence measurements,the research of turbulence ergodicity is considered to be the prior section of the experiment.With the statistics of single-site turbulence measurements obtained in Baimiao Tableland,Ping Liang,Gan Su,analysis result shows that not only the turbulence with scale less than 10 min,which can easily satisfy the ergodicity,the tableland terrain can also be a major cause of the coherent structure of periodic,large-scale turbulence;compared to which for the turbulence above the flat underlying surface,the distribution of 10–40 min,large-scale turbulence in the tableland region tends to be more steady and,thus,can also satisfy the ergodicity easily.Under the condition of extremely unstable stratification,the wind is comparatively low in speed and features distinctly large-scale,periodical fluctuation,and with the trend of smooth increase in temperature,large-scale wind turbulence and temperature turbulence both tend to satisfy ergodicity.In comparison,under the condition of extremely stable stratification,the aperiodicity of large-scale wind turbulence and temperature turbulence caused by intermittency is comparatively strong,and the turbulence cannot satisfy ergodicity easily.     

Simulating Gravity Changes in Topologically Realistic Driven Earthquake Fault Systems: First Results

Currently, GPS and InSAR measurements are used to monitor deformation produced by slip on earthquake faults. It has been suggested that another method to accomplish many of the same objectives would be through satellite-based gravity measurements. The Gravity Recovery and Climate Experiment (GRACE) mission has shown that it is possible to make detailed gravity measurements from space for climate dynamics and other purposes. To build the groundwork for a more advanced satellite-based gravity survey, we must estimate the level of accuracy needed for precise estimation of fault slip in earthquakes. We turn to numerical simulations of earthquake fault systems and use these to estimate gravity changes. The current generation of Virtual California (VC) simulates faults of any orientation, dip, and rake. In this work, we discuss these computations and the implications they have for accuracies needed for a dedicated gravity monitoring mission. Preliminary results are in agreement with previous results calculated from an older and simpler version of VC. Computed gravity changes are in the range of tens of μGal over distances up to a few hundred kilometers, near the detection threshold for GRACE.     

Ergodicity examined by the Thirumalai-Mountain metric for Taiwanese seismicity

Ergodicity is a behavior generally limited to equilibrium states and is here defined as the equivalence of ensemble and temporal averages. In recent years, effective ergodicity is identified in simulated earthquakes generated by numerical fault models and in real seismicity of natural fault networks by using the Thirumalai-Mountain metric. Although the effective ergodicity is already reported for Taiwanese seismicity, an immediate doubt is the unrealistic gridded sizes for discretizing the seismic data. In this study, we re-examined the effective ergodicity in Taiwanese seismicity by using reasonable gridded sizes which corresponded with the location errors in the real earthquake catalogue. Initial time and magnitude cut-off were examined for the validity of ergodic behavior. We found that several subsets extracted from Taiwanese seismicity possessed effectively ergodic intervals and all terminations of these ergodic intervals temporally coincided with the occurrences of large earthquakes (M _L < 6.5). We thus confirm the ergodicity in the crustal seismicity by using the Thirumalai-Mountain metric.     

Ergodicity and the ‘scale effect’

Solute plume spreading in an aquifer exhibits a ‘scale effect’ if the second spatial concentration moment of a plume has a non-constant time-derivative. Stochastic approaches to modeling this scale effect often rely on the critical assumption that ensemble averages can be equated to spatial averages measured in a single field experiment. This ergodicity assumption should properly be evaluated in a strictly dynamical context, and this is done in the present paper. For the important case of trace plume convection by steady groundwater flow in an isotropic, heterogeneous aquifer, ergodicity does not obtain because of the existence of an invariant function on stream surfaces that is not uniform throughout the aquifer. The implications of this result for stochastic models of solute transport are discussed. © 1997 Elsevier Science Ltd. All rights reserved     

香港的新构造断裂活动与天然山体滑坡关系的初步研究

香港沙田河沥背地区西北向断裂的左旋错断构造运动,在断裂两分支之间造成转变挤压型地块抬升,形成一菱形地垒。表土层大致均匀分布在地垒及其两侧地区,并且没有被埘北向断裂错动。而表土层所覆盖的古台地亦没有经过明显剥蚀。待得到河沥背表土层及邻近黄竹洋村天然山体滑坡定年结果资料,即可以给出河沥背断裂最新错动年龄范围及断裂活动与区内天然山体滑坡事件的相互关系。     

Ergodicity and Earthquake Catalogs: Forecast Testing and Resulting Implications

Recently the equilibrium property of ergodicity was identified in an earthquake fault system (Tiampo et al., Phys. Rev. Lett. 91, 238501, 2003; Phys. Rev. E 75, 066107, 2007). Ergodicity in this context not only requires that the system is stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages when studying their behavior in space and time. In this work we show that this property can be used to identify those regions of parameter space which are stationary when applied to the seismicity of two naturally-occurring earthquake fault networks. We apply this measure to one particular seismicity-based forecasting tool, the Pattern Informatics index (Tiampo et al., Europhys. Lett. 60, 481–487, 2002; Rundle et al., Proc. National Acad. Sci., U.S.A., Suppl. 1, 99, 2463, 2002), in order to test the hypothesis that the identification of ergodic regions can be used to improve and optimize forecasts that rely on historic seismicity catalogs. We also apply the same measure to synthetic catalogs in order to better understand the physical process that affects this accuracy. We show that, in particular, ergodic regions defined by magnitude and time period provide more reliable forecasts of future events in both natural and synthetic catalogs, and that these improvements can be directly related to specific features or properties of the catalogs that impact the behavior of their spatial and temporal statistics.     

Space- and Time-Dependent Probabilities for Earthquake Fault Systems from Numerical Simulations: Feasibility Study and First Results

In weather forecasting, current and past observational data are routinely assimilated into numerical simulations to produce ensemble forecasts of future events in a process termed “model steering”. Here we describe a similar approach that is motivated by analyses of previous forecasts of the Working Group on California Earthquake Probabilities (WGCEP). Our approach is adapted to the problem of earthquake forecasting using topologically realistic numerical simulations for the strike-slip fault system in California. By systematically comparing simulation data to observed paleoseismic data, a series of spatial probability density functions (PDFs) can be computed that describe the probable locations of future large earthquakes. We develop this approach and show examples of PDFs associated with magnitude M > 6.5 and M > 7.0 earthquakes in California.     

Nucleation and Evolution of Sliding in Continental Fault Zones under the Action of Natural and Man-Made Factors: A State-of-the-Art Review

Izvestiya, Physics of the Solid Earth - Abstract—A review is presented of the state-of-the-art publications concerning the nucleation and evolution of fault slip in the Earth’s crust....     

地质雷达在乌拉山山前断裂探测中的应用

地质雷达是利用电磁波对地下不同电性介质进行探测的地球物理仪器，其探测速率快、分辨率高，可弥补探槽和其他地球物理方法存在探测盲区的缺陷，正在越来越多地应用于活动断层探测领域。本文以乌拉山山前断裂为例开展地质雷达探测工作，使用无人机正射影像技术对测线进行地形校正，获得断层浅部地质雷达图像。研究结果表明，本文研究方法能有效反映探槽揭露的地层单元和断层分布。本次探测中，雷达波形图像特征为:浅地表的土壤层反射波总体较弱；粗粒沉积为主的砾石层反射波总体较强，同相轴连续性好；细粒沉积为主的砂层反射波弱于砾石层，波形以中、高频为主，同相轴具有弱连续性；对于洪冲积地区，地质雷达能分辨具有一定特征的地层单元，这为剖面图像的断层识别提供了标志；通过无人机正射影像技术对地质雷达测线进行地形校正，有利于获得更为准确的探测结果。     

氡断层气测量在佛山西淋岗活断层探测中的应用研究

在佛山西淋岗活断层附近,垂直断层走向等距测量了断层附近载体中氡气相对含量值,得到了氡含量曲线图．分析了断层气上氡异常形态分布特征,探讨了断层气载体对氡异常形成的影响。     

断层泥中石英碎砾溶蚀形貌的测年研究

考虑到同一条断层的同一个位置所取的断层泥中,不同碎砾的溶蚀形貌并不相同,即使是同一个碎砾,其不同的表面,溶蚀形貌也可能不同,将统计学参数估计的方法引入结果处理中,并把在金川水电站坝区F1断层一次所取得断层泥样品碎砾的各个表面的总体当作一个整体进行处理,得出此断层的活动时间可能为早更新世的结果。与ESR法测得的结果基本一致。     

断层泥在基岩区断层新活动研究中的意义

断层泥在基岩区断层新活动研究中的意义在于：利用断层泥中粘土矿物的组合、成分、结晶程度可以判定断层活动时的物理环境；断层泥带的宽度与断层的位移量有一定的线性关系，从而可用于确定断层的位移量；断层泥的显微构造特征及其中石英碎砾的表面结构，可以提供有关断层活动方式、性质、期次、时代等重要信息。对断层泥进行包括野外详细观测、室内显微构造分析以及年龄测定在内的综合研究，是确定基岩区断层新活动特征的行之有效的方法。     

东秦岭内部铁炉子断裂带的最新走滑活动

通过对东秦岭内部铁炉子断裂错断晚更新世以来形成的水系位移测量和阶地砾石层的年代学研究，得到铁炉子断裂距今10万年以来的左旋位移约为125m，活动速率约为1．25mm／a。距今0．20～0．25Ma的中更新世中期以来的左旋滑动速率为3．0～3．75mm／a。估算出东秦岭地区活动断裂系左旋活动速率约为2．25～4．75mm／a，它大致反映了中晚第四纪华南与鄂尔多斯、华北平原活动地块向东滑动速率的差异。