The Density Distributions and the Correlations of an Earthquake's Source Parameters

The data analysis of the source parameters of five sets of earthquake sequences, aftershocks and earthquakes scattered in a region shows that the scalar seismic moment is correlated with the linear size of the fault and the static stress drop. We tentatively imply that a correlation also exists between the radius of the faults and the static stress drops and it is suggested that the static stress drop may be decreasing with increasing radius of the source. It is shown that the density distribution of the source radius, calculated through the source rupture duration obtained from the body wave pulse (Boatwright, 1980) using the time T between the P-wave onset and the first zero crossing on the seismogram, may be represented by a power law as the density distribution of the stress drops and of the moment which are also computed. It is also suggested, and tentatively verified, that the density distribution of the areas of the broken barriers on the faults is similar to that of the density distribution of the static stress drops. It is finally suggested that the seismicity of a region may be studied two-dimensionally as a function of the stress drop and the radius of the source instead of the classic b and b₀ values. Concerning the discussion on the range of the values of the static stress drop, whether it is almost constant in a seismic region and varies only from one region to another, it is seen that in the aftershocks of the 1994 Northridge earthquake it covers a range of almost 5 orders of magnitudes. Finally it is ascertained that the density distribution of the source parameters does not give equipartition of seismic moment release.     

Characterization of Stress Drops on Asperities Estimated from the Heterogeneous Kinematic Slip Model for Strong Motion Prediction for Inland Crustal Earthquakes in Japan

Dense strong motion observation networks provided us with valuable data for studying strong motion generation from large earthquakes. From kinematic waveform inversion of seismic data, the slip distribution on the fault surface of large earthquakes is known to be spatially heterogeneous. Because heterogeneities in the slip and stress drop distributions control the generation of near-source ground motion, it is important to characterize these heterogeneities for past earthquakes in constructing a source model for reliable prediction of strong ground motion. The stress changes during large earthquakes on the faults recently occurring in Japan are estimated from the detailed slip models obtained by the kinematic waveform inversion. The stress drops on and off asperities are summarized on the basis of the stress change distributions obtained here. In this paper, we define the asperity to be a rectangular area whose slip is 1.5 or more times larger than the average slip over the fault according to the previous study for inland crustal earthquakes. The average static stress drops on the asperities of the earthquakes studied here are in the range 6?C23?MPa, whereas those off the asperities are below 3?MPa. We compiled the stress drop on the asperities together with a data set from previous studies of other inland earthquakes in Japan and elsewhere. The static stress drop on the asperity depends on its depth, and we obtained an empirical relationship between the static stress drop and the asperity??s depth. Moreover, surface-breaking asperities seemed to have smaller stress drops than buried asperities. Simple ground motion simulations using the characterized asperity source models reveal that deep asperities generate larger ground motion than shallow asperities, because of the different stress drops of the asperities. These characteristics can be used for advanced source modeling in strong ground motion prediction for inland crustal earthquakes.     

地震应力降与岩石破裂应力降

从应力降的静态理论,讨论了地震应力降的精度,并利用野外观测的最大位移和由地震波得到的地震矩,分别计算了十个研究较充分的地震应力降.对不同作者的结果作了比较,可以看出,应力降有因子为2的变化范围.但从统计观点看,地震应力降是分布在几巴到几百巴的数量级,大多数位于20-60巴;总结了地壳中代表性岩石在地壳温度、压力条件下,粘滑及脆性剪切破裂时的应力降,它们与温度、压力、岩性、含水矿物的存在有关.取值范围是从零到几千巴数量级;讨论了地震断层的物理状态,指出地震应力降是一种平均结果,并由于静态理论忽略了断层面破裂所消耗的能量,所以地震应力降比实际的应力降要低.      

Comparison of source parameters estimated in the frequency and time domains for seismic events at the Rudna copper mine,Poland

Source parameters estimated in the frequency domain for 100 selected seismic events from the Rudna copper mine, with moment magnitude ranging from 1.4 to 3.6, were collected to study their scaling relations and to compare them with the parameters estimated in the time domain. The apparent stress and static stress drop, corrected for the limited bandwidth recording, increase slightly in a similar manner with increasing seismic moment. The ratio of apparent stress to static stress drop, a measure of radiation efficiency, is practically constant and its mean value is close to 0.1. For 37 seismic events, with moment magnitude between 1.9 and 3.4, source parameters were estimated in the time domain from relative source time functions, that displayed unilateral rupture propagation, and their rupture velocity could be estimated. It ranges from 0.23 to 0.80 of shear wave velocity and is almost independent of seismic moment. The fault length, estimated from the average source pulse width and rupture velocity, is clearly dependent on seismic moment and is smaller than the source radius estimated from the corner frequency on the average by about 25 percent. There is no correlation between the values of static stress drop estimated in the frequency and time domains, but the time domain stress drop is in general similar to that estimated in the frequency domain. The apparent stress increases with increasing rupture velocity, and the ratio of apparent stress to static stress drop seems also to depend on rupture velocity.     

Bounding of near-fault ground motion based on radiated seismic energy with a consideration of fault frictional mechanisms

The energy radiated as seismic waves strongly depends on the fault rupture process associated with rupture speed and dynamic frictional mechanisms involved in the fault slip motion.Following McGarr and Fletcher approach,we derived a physics-based relationship of the weighted average fault slip velocity vs apparent stress,rupture speed and static stress drop based on a dynamic circular fault model.The resultant function can be approximately used to bound near-fault ground motion and seismic energy associated with near-fault coseismic deformation.Fault frictional overshoot and undershoot mechanisms governed by a simple slip-weakening constitutive relation are included in our consideration by using dynamic rupture models named as M-and D-models and proposed by Madariaga(1976) and Boatwright.We applied the above function to the 2008 great Wenchuan earthquake and the 1999 Jiji(Chi-Chi) earthquake to infer the near-fault ground motion called slip weighted average particle velocity and obtained that such model-dependent prediction of weighted average ground velocities is consistent to the results derived from the near-fault strong motion observations.Moreover,we compared our results with the results by McGarr and Fletcher approach,and we found that the values of the weighted average particle velocities we obtained for these two earthquakes are generally smaller and closer to the values by direct integration of strong motion recordings of the near-fault particle velocity waveform data.In other words,if this result comes to be true,it would be a straightforward way used to constrain the near-fault ground motion or to estimate source parameters such as rupture speed,static and dynamic stress drops.     

1995年陡河地震前后小震震源参数及其相互关系

在震源谱的多台多震尾波解法的基础上,应用Brune震源模型,求解1995年10月6日陡河ML5.9地震前后在其周围发生的48次小地震的震源因子和震源波谱,进而估算了地震矩、拐角频率和应力降,并讨论了它们之间的相互关系和在陡河地震前后随时间的变化．结果表明:小震震源因子表现出相当大的稳定性,震源因子的峰值频率和随频率的变化形态都很相似．发现震前一年左右曾多次出现应力降较高的事件．需要指出的是,考虑到应力降由地震矩和拐角频率计算得到以及地震矩和拐角频率的相关关系,实际上,这里的高应力降指的是拐角频率高于正常值的情形．      

The focus parameters and their correlation from small earthquakes before and after the 1995 Douhe earthquake

IntroductionTheseismoIogymethodofearthquakepredictionissometimessimplycalled"predictingearthquakebyearthquake",thatis,animpendinglargeearthquakeispredictedonbasisofsomefeaturesofsmaIlearthquakesoccurredbeforeit.Forthispurpose,thecharactersoftemporaryspatiaIandmagnitudedistributionofsmalIearthquakesareintensiveIyinvestigated,whichareusuallycalIedasseismicitymethod.ThesuccessfuIpredictionofHaichengearthquakeinl975wasitSremarkabIeappIication.Besides,thepossibIechangesincharactersofseismicsou…     

Stress drop assessment of the August 8, 2017, Jiuzhaigou earthquake sequence and its tectonic implications*

By using a broadband Lg attenuation model developed for the Tibetan Plateau, we isolate source terms by removing attenuation and site effects from the observed Lg-wave displacement spectra of the M7.0 earthquake that occurred on August 8, 2017, in Jiuzhaigou, China, and its aftershock sequence. Thus, the source parameters, including the scalar seismic moment, corner frequency and stress drop, of these events can be further estimated. The estimated stress drops vary from 47.1 kPa to 7149.6 kPa, with a median value of 59.4 kPa and most values falling between 50 kPa and 75 kPa. The estimated stress drops show significant spatial variations. Lower stress drops were mainly found close to the mainshock and on the seismogenic fault plane with large coseismic slip. In contrast, the highest stress drop was 7.1 MPa for the mainshock, and relatively large stress drops were also found for aftershocks away from the major seismogenic fault and at depths deeper than the zone with large coseismic slip. By using a statistical method, we found self-similarity among some of the aftershocks with a nearly constant stress drop. In contrast, the stress drop increased with the seismic moment for other aftershocks. The amount of stress released during earthquakes is a fundamental characteristic of the earthquake rupture process. As such, the stress drop represents a key parameter for improving our understanding of earthquake source physics.     

Variation of seismic source parameters and stress drops within a descending slab and its implications in plate mechanics

A least-squares searching technique has been developed to estimate the source dimensions of intermediate and deep focus earthquakes using azimuthal variations of body wave pulse-widths. With this method and also amplitude data, modes of rupture propagation, seismic moments, and stress drops of 17 intermediate and deep focus earthquakes in the Tonga-Kermadec region have been determined in order to investigate variations in source properties and the state of stress within the descending slab there. Three different modes of rupture; unilateral, bilateral, and circular faults, are compared and tested against observations. Results indicate that the unilateral fault is the best model for most of the earthquakes studied. Stress drops of the 17 events vary within a very large range, from 20 bar to about 4.6 kbar, and change significantly with depth. The magnitude of stress drops for depths between 220 and 430 km is very much higher than at shallower depths. This change in stress drop magnitude at about 220 km-depth seems to reflect a change in material properties both in the mantle and within the slab. Two regions of high stress drop are observed at depths of about 360 and 640 km. A relative minimum of stress drop is found at about 450–560 km where the earthquake frequency is particularly high. Earthquakes at the northern end to the Tonga arc, where the Benioff zone is laterally bent, show systematically higher stress drops than other events at comparable depths, but away from the bend. Also, events in regions of low seismicity appear to have higher stress drops than those in regions of high seismicity. The upper bound of seismic efficiency is found to decrease with depth, implying an increase of frictional force with depth at the earthquake source.     

胶东半岛地区震源波谱参数研究

利用山东数字地震台网记录到的胶东半岛及附近地区2010年以来的地震波形资料,采用Brune模型,并结合遗传算法反演了本区134次2.0级以上地震的震源波谱参数.结果表明胶东半岛地区中小地震的地震矩在9.76×1011～5.9×1014N·M之间;应力降范围在0.017～25MPa之间,均值是0.97MPa;视应力范围在0.06～10.2MPa,平均应力水平在0.396MPa.地震矩、应力降和视应力都与震级呈正相关关系,拐角频率与震级的关系不是很明显;地震矩和拐角频率成负相关关系.根据本区震源参数和震级的定量统计关系,去除震级影响,通过应力降和视应力随时间的变化得到目前正处于应力的释放时期.     

An effective approach to determine the dynamic source parameters

In this study, we present a new and effective method to determine the dynamic source parameters (i.e., stress drop and strength distribution). We first assume that the kinematic source parameters, i.e., the slip and rupture time distributions on the fault plane, are known from the previous source inversion studies. Then, using the seismic source representation theorem we determine the dynamic stress field on a fault plane from known kinematic parameters. Finally, we determine the strength of the fault defined as the peak stress just before the rupture. We have tested the validity of this method by using an illustrative two-dimensional analytical example. To assess the applicability of this method, we have applied it to study the 1979 Imperial Valley earthquake, and obtained consistent results with those ofMiyatake's (1992) andQuin's (1990). Compared with previous methods, this new method is simple, straightforward and accurate, and needs much less calculation. Therefore, it is expected to be useful in exploring the seismic source process.     

利用主动震源检测汶川地震余震引起的浅层波速变化

为了监测汶川地震后断裂带附近的波速变化,2008年6月,我们利用快速响应探测系统,在龙门山断裂带北端进行了为期3周的连续观测实验.实验使用电动落锤作为主动震源,GPS连续同步授时的高精度数采作为接收系统.利用记录到的高时间精度观测数据,结合互相关时延检测技术,计算了P波和面波走时的相对变化,来表征地下波速的变化.我们观测到两次面波波速的异常变化,变化幅度最高达到2%,远远大于气压变化所能引起的波速变化.结合该时段内地震活动记录,我们认为面波的波速变化是由在附近发生的两次地震事件的同震效应引起的,该观测结果同理论计算结果相符.     

有限断层地震波辐射能估算及其在合成强地面运动中的应用

对有限断层地震波能量辐射的估算通常采用断层面上子源能量的逐点求和方法。基于Brune圆盘模型,Anderson推导出有限断层地震波能量辐射S波的求解公式,即 ,其中 为断层面上地震矩, 为剪切模量, 和 分别为动态应力降和静态应力降,并指出在复合震源模型强地面运动预测应用中 以满足能量守恒。Rivera和Kanamori则从能量辐射表象定理出发,给出了有限断层中辐射能量的积分表达式,明确地指出了逐点求和所存在的问题。依据该积分表达式,本文推导出了复合源模型中新的辐射能完整的求解方法,指出Anderson方法实为断层面上点源辐射能量的简单叠加求和,后者则充分考虑了断层面上任一点在任一时刻能量传播过程中受到的断层面上所有位移破裂路径的交互影响。以1976年唐山7.6地震为例,应用上述方法分别计算了有限断层模型的辐射能量及近场强地面运动,如质点运动加速度,速度。结果表明如果模型参数满足 时,由本文给出的求解方法计算所得到的地震波辐射能已远远超出实际的辐射能量值,直接导致了对近场强地面运动参数如质点速度、加速度等的过高估算。因此,Zeng等和Anderson工作的局限性是非常明显的:地震矩守恒以及非物理的 无法准确地预测近场地面运动。未来工作中,对于有限断层模型的建立,在地震矩守恒这一约束条件的基础上,远场和近场能量解（或视应力）将可作为另一个重要的约束条件,为强地面运动的模拟提供一个更为恰当的求解方案。      

甘肃地区震源参数的相关性研究

通过对甘肃数字地震台网2008年1月-2009年6月记录的ML 2.0-ML 6.0中小地震,S波观测谱中噪音、仪器、路径、场地等影响的逐一消除,利用遗传算法反演得到甘肃地区273条地震的震源谱,进而根据Brune的圆盘震源模型,计算地震矩、应力降、拐角频率、震源半径等震源参数,并研究甘肃地区震源参数的特征及相似关系....     

Slip-Weakening Models of the 2011 Tohoku-Oki Earthquake and Constraints on Stress Drop and Fracture Energy

We present 2D dynamic rupture models of the 2011 Tohoku-Oki earthquake based on linear slip-weakening friction. We use different types of available observations to constrain our model parameters. The distribution of stress drop is determined by the final slip distribution from slip inversions. As three groups of along-dip slip distribution are suggested by different slip inversions, we present three slip-weakening models. In each model, we assume uniform critical slip distance eastward from the hypocenter, but several asperities with smaller critical slip distance westward from the hypocenter. The values of critical slip distance are constrained by the ratio of deep to shallow high-frequency slip-rate power inferred from back projection source imaging. Our slip-weakening models are consistent with the final slip, slip rate, rupture velocity and high-frequency power ratio inferred for this earthquake. The average static stress drop calculated from the models is in the range of 4.5–7 MPa, though large spatial variations of static stress drop exist. To prevent high-frequency radiation in the region eastward from the hypocenter, the fracture energy needed there is in the order of 10 MJ/m², and the average up-dip rupture speed cannot exceed 2 km/s. The radiation efficiency calculated from our models is higher than that inferred from seismic data, suggesting the role of additional dissipation processes. We find that the structure of the subduction wedge contributes significantly to the up-dip rupture propagation and the resulting large slip at shallow depth.     

浙江珊溪水库地震：震源参数测定及断层结构和应力状态描述

利用遗传算法,搜索符合Brune ω^2模型的拐角频率（fc）及零频幅值（Ωc）的最佳值,测定浙江珊溪水库震区88条小震（1．5≤ML≤4．6）的地震矩（M0）、震源尺度（r）及静态应力降（△σ）。地震矩M0在10^10～10^14N·m范围内,与拐角频率fc遵循Mo∝fc^-3的规律;震源尺度和地震矩、应力降之间呈现多重标度特征,地震矩大于临界值2．3×10^12N·m（相应的震源尺度特征值约160m）时,震源尺度与地震矩的关系较强;而应力降（△σ）在震源尺度大于160m后基本趋向恒定,不随震源尺度的增大而增大。浙江珊溪水库震区自2002年7月以来,经历2次大规模的震群活动。震群释放的应力降大小与该震群的规模成正比关系,大的应力降集中在发震断层中段5～6km深度的区域,其发生时间既可以在主震之前,也可以在主震之后。     

静态应力触发在应用中存在问题的讨论以玉树地震为例

大地震应力触发概念自提出至今被广泛应用。 库仑应力与后续地震活动对应效果受到多种因素影响。 其中, 不同深度断层滑动量不同导致不同深度静态库仑应力图像差异, 选取哪一个深度的应力图像来讨论后续地震趋势是一个重要问题。 本文提出一个计算方法, 首先计算不同深度静态库仑应力, 然后在同一个位置取不同深度库仑应力最高值, 绘制静态应力分布图像, 并以2010年玉树地震为例, 结合地震活动及静态库仑应力分布对这种计算方法的效果进行对比。 结果显示, 按照本文提出的计算方法, 利用不同学者给出的玉树地震破裂模型计算均显示, 玉树地震后2年内3级以上余震几乎全部发生在库仑应力增加区。     

宁夏及邻区地震震源衰减模型及震源参数研究

选取2003年1月至2011年12月宁夏及邻区发生的201个M_L2.0以上地震事件进行反演, 用经验格林函数计算得到本区地震震源谱衰减模型。 在已知非弹性衰减系数和场地响应的条件下, 计算得到震源谱并研究了近震震级与拐角频率、 地震矩、 震源破裂半径及应力降之间的关系。 详细分析了震源参数误差大小及各种误差影响因素。 对剩余应力降时空演化特征分析研究结果表明: 高剩余应力降集中分布在宁夏北部宁蒙交界地区、 低剩余应力降分布在宁夏中部同心、 中卫一带, 银川盆地中南部的吴灵地区和宁夏南部海原断裂带中东段剩余应力降变化较为明显, 在时间分布上这两个区域剩余应力降在中强地震前均有降低—增强的趋势。     

Earthquake dynamics on circular faults: a review 1970–2015

We review the development of earthquake dynamics taken from the point of view of the origin of seismic radiation instead of the detailed study of rupture propagation on complex surfaces. Many features of seismic radiation can be explained by simple models that serve as elementary canonical problems. Some of these properties are very well known like the fact that at low frequencies, the seismic spectrum is proportional to the seismic moment. At high frequencies, on the other hand, radiation is generated by the motion of the rupture front, in particular stopping phases and geometrical obstacles (barriers). A rupture front moving at constant speed does not produce far-field radiation. For many practical applications, for determining source size and stress drop, for example, it is not necessary to determine geometrical details of the rupture. For such cases, a simple circular crack model is quite sufficient. An improvement on this method is to do dynamic inversion on simple, elliptical-shaped sources and letting the rupture start arbitrarily from a point on the fault. This problem can be solved nowadays with finite differences and a variety of inversion techniques.