Source parameters and scaling relations for small earthquakes in Kumaon Himalaya, India

We investigate the scaling relationships among earthquake source parameters using more than 300 good quality broad band seismograms from 30 small earthquakes in the Kumaon Himalaya from the spectral analysis of P and S waves. The average ratio of P/S wave corner frequency is found to be 1.13, which is suggestive of shift in the corner frequency. The estimated seismic moment range from 1.6?×?10¹³–5.8?×?10¹⁵ N?m, while the stress drop varies from 0.6 to 16 bars with 80 % of the events below 10 bars. An analysis of stress drop and apparent stress drop indicates the partial stress drop mechanism in the region. The source radii are between 0.17 and 0.88 km. The total seismic energy varies from 1.79?×?10⁸ to 7.30?×?10¹¹ J. We also observe the variation in seismic energy for a given seismic moment. The scaling relation between the seismic moment and stress drop suggests the breakdown of constant stress drop scaling for the range of seismic moments obtained here for the region. This shows the anomalous behavior of small earthquakes in the region. The study indicates that the stress drop is the dominant scaling factor for the moments studied here.     

山西地区震源新参数间关系初探

利用“十五”数字化后山西地震台网记录的612次 ML ≥2．0地震,使用中国地震局地震预测研究所推广的中小地震新参数计算软件,计算其中148次事件的震源新参数,对地震矩、矩震级、震源破裂尺度、应力降、拐角频率等参数间的定标关系做初步研究,得出 ML 震级与地震矩、矩震级间存在较好的线性正相关;震级与震源尺度间存在多项式关系;与应力降的对数呈显著正相关,当大于 ML 4．0后,随着震级的增大,释放的应力降略有变缓;与拐角频率的对数呈负相关。     

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。     

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.     

Low-frequency scaling applied to stochastic finite-fault modeling

Stochastic finite-fault modeling is an important tool for simulating moderate to large earthquakes. It has proven to be useful in applications that require a reliable estimation of ground motions, mostly in the spectral frequency range of 1 to 10 Hz, which is the range of most interest to engineers. However, since there can be little resemblance between the low-frequency spectra of large and small earthquakes, this portion can be difficult to simulate using stochastic finite-fault techniques. This paper introduces two different methods to scale low-frequency spectra for stochastic finite-fault modeling. One method multiplies the subfault source spectrum by an empirical function. This function has three parameters to scale the low-frequency spectra: the level of scaling and the start and end frequencies of the taper. This empirical function adjusts the earthquake spectra only between the desired frequencies, conserving seismic moment in the simulated spectra. The other method is an empirical low-frequency coefficient that is added to the subfault corner frequency. This new parameter changes the ratio between high and low frequencies. For each simulation, the entire earthquake spectra is adjusted, which may result in the seismic moment not being conserved for a simulated earthquake. These low-frequency scaling methods were used to reproduce recorded earthquake spectra from several earthquakes recorded in the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation Models (NGA) database. There were two methods of determining the stochastic parameters of best fit for each earthquake: a general residual analysis and an earthquake-specific residual analysis. Both methods resulted in comparable values for stress drop and the low-frequency scaling parameters; however, the earthquake-specific residual analysis obtained a more accurate distribution of the averaged residuals.     

柯坪块体震源介质参数测定

应用2011年1月-2015年4月柯坪块体及周边数字地震台站（38°-42.5°N,75°-80.5°E）记录的3.0 ≤ M ≤ 5.0地震事件,结合柯坪块体介质品质因子和各台站场地响应,计算各地震应力降、地震矩、震源破裂半径、拐角频率等新震源参数,并研究各背景值变化特征及彼此间对应关系。结果表明：柯坪块体地区地震震级与地震矩、矩震级、震源尺度之间表现为较好的正相关性,与地震拐角频率之间呈负相关。地震矩与震源破裂尺度整体呈正相关,但当震源破裂尺度较小时,地震矩变化不大,当震源破裂尺度大于250 m时,地震矩随震源破裂尺度的增大变化较快。由柯坪块体应力降时间分布特征分析可知,研究区具有地震前应力降呈现高值异常、震后缓慢恢复低值的演化过程。     

Implications of stress-drop models of earthquakes for the inversion of stress drop from seismic observations

We discuss the inversion of stress drops from seismic observations on the basis of crack or stress-drop models of earthquake mechanism. Since a formal inverse problem cannot be posed at present we discuss implications of solutions to direct problems. We first discuss the static approximations used to obtain stress drop from seismic moment and source dimensions. We show that the geometrical effects are quite significant if only one source dimension has been retrieved from seismic observations. The effect of variable stress drop is discussed and we show that the inverted stress drop is not a simple average of the actual stress drops on the fault. We discuss the energy release during faulting and show that the apparent stress has a complicated relation to the stress drop on the fault. We also show that the static stress drops obtained by seismologists are a lower bound to the actual dynamic stress drops on the fault. This may in part explain disagreements with laboratory results. Finally, we discuss the inversion of source dimensions from the far-field radiation. We analyse two extreme, simple dynamical source models, a circular fault and a rectangular fault and show that geometry has a much more pronounced effect on radiation than is usually acknowledged.     

Stress Release and Source Scaling of the 2010–2011 Canterbury,New Zealand Earthquake Sequence from Spectral Inversion of Ground Motion Data

The Canterbury earthquake sequence beginning with the 2010 M _W 7.2 Darfield earthquake is one of the most notable and well-recorded crustal earthquake sequences in a low-strain-rate region worldwide and as such provides a unique opportunity to better understand earthquake source physics and ground motion generation in such a tectonic setting. Ground motions during this sequence ranged up to extreme values of 2.2 g, recorded during the February 2011 M _W 6.2 event beneath the city of Christchurch. A better understanding of the seismic source signature of this sequence, in particular the stress release and its scaling with earthquake size, is crucial for future ground motion prediction and hazard assessment in Canterbury, but also of high interest for other low-to-moderate seismicity regions where high-quality records of large earthquakes are lacking. Here we present a source parameter study of more than 200 events of the Canterbury sequence, covering the magnitude range M _W 3–7.2. Source spectra were derived using a generalized spectral inversion technique and found to be well characterized by the ω ^?2 source model. We find that stress drops range between 1 and 20 MPa with a median value of 5 MPa, which is a factor of 5 larger than the median stress drop previously estimated with the same method for crustal earthquakes in much more seismically active Japan. Stress drop scaling with earthquake size is nearly self-similar, and we identify lateral variations throughout Canterbury, in particular high stress drops at the fault edges of the two major events, the M _W 7.2 Darfield and M _W 6.2 Christchurch earthquakes.     

Physics of Seismic Source Ⅱ. Mechanics of Seismic Source

An earthquake is regarded as a fracture from the viewpoint of continuum mechanics, in which stress and strain play key roles in understanding the nature of a seismic source. This review briefly outlines the mechanics of a seismic source in terms of the dislocation model and crack model. The introduction includes the Coulomb failure criterion, static stress drop, dynamic stress drop, the Griffith criterion, and the scaling of source parameters. The selection of topics in the introduction emphasizes the application of seismic data, i.e., in practice, the mechanical parameters introduced here are measurable in the interpretation and analysis of seismic waveform data.     

工业开采诱发地震的应力降研究现状和主要科学议题

诱发地震及其灾害风险已成为非常规油气资源开发和废水回注等新型工业活动顺利实施的重要威胁。应力降是反映地震破裂前后断层上平均应力差的物理量,对诱发地震中应力降的系统研究有助于揭示诱发地震的震源特征、高频地震动特征、构造背景和地震危险性。本文系统地总结了近20年来工业开采诱发地震中应力降的相关研究进展,分别从计算所用理论方法、获得的平均应力降数值、影响应力降数值的主客观因素、围绕应力降的重要科学讨论等方面做了归纳分析。介绍了直接进行谱拟合、经验格林函数(EGF)、谱叠加和广义反演3种适用性的计算方法,通过案例考察了工业开采诱发地震的应力降平均值,分析影响应力降测定数值的主客观因素,并总结应力降空间分布依赖性、与震源机制类型相依性、自相似性、深度依赖性等4个主要科学问题。同时,阐述了诱发地震应力降的测定可靠性仍未突破、主要科学问题存在广泛争议、在新型工业开采活动中具有重要应用潜力等现状。本文的总结分析可为从事新型能源开发、地震安全监管和科学研究领域的企业、管理人员和科学研究人员提供参考。     

Source parameters of the earthquakes of the Baikal rift system

The dynamic parameters of the earthquake source—the seismic moment, the moment magnitude, the source radius, the stress drop, and the amplitude of displacement—are determined by the amplitude Fourier spectra of the body shear waves (S-waves) for 62 earthquakes of the Baikal rift system with the energy class of K _P = 9.1–15.7. In the calculations I used the classical Brune model. The seismic moment of the earthquakes being investigated changes from 3.65 × 10¹¹ N m to 1.35 × 10¹⁸ N m, and the radii of earthquake sources vary from 390 m to 1.84 km. The values of the drop in stress Δσ grow with an increase in the seismic moment up to 1.7 × 10⁸ Pa. For the group of weak earthquakes (M _w = 1.7–3.3), extremely low values of the drop in stress 10³–10⁴ Pa are observed. The maximum amplitude of displacement in the source amounts to 5.95 m. The empirical equations between the seismic moment and the other dynamic parameters of the source are determined. The regional dependence of the seismic moment and energy class is obtained: log M ₀ ± 0.60 = 1.03K _P + 3.17. The character of the relationship between the seismic moment and the corner frequency indicates that the classical scaling law of the seismic spectrum for the earthquakes in question is not fulfilled. The obtained estimates of the dynamic parameters are in satisfactory agreement with the published data concerning the analogous parameters of the other rift zones, which reflects the general regular patterns of the destruction of the lithosphere and the seismicity in the extension zones of the lithosphere.     

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.     

利用广义叠加反演方法估算长岛震群应力降

地震应力降是表征震源特性的一个重要参数,通常由震源谱计算得到.但如何从大量地震的观测谱中校正路径和台站效应,准确地分离出震源谱并计算应力降,仍是一个难题.本文采用广义叠加反演方法通过分阶段叠加从观测谱中迭代分离出震源项、台站项和路径项,并利用分震级的叠加震源项与理论谱的拟合得到经验格林函数,再利用由经验格林函数校正后的真实震源谱估算出应力降.该方法不需要知道仪器响应、场地响应和传播路径上的衰减系数,并且不用事先假设震源具有自相似的恒应力降特征,计算效率很高,适用于反演大量地震的震源参数.我们将广义叠加反演方法应用于长岛震群,利用S波谱估算了1431个ML≥1.0地震的应力降.结果表明,广义叠加反演方法获得的震源参数和用传统方法得到的结果一致;长岛震群地震的应力降较小(中值是0.3 MPa),变化范围很大(0.009～3.04MPa之间),属于低应力降事件集;同时应力降中值随地震矩增大而增大,偏离了自相似理论.应力降空间变化不均匀,高应力降事件主要集中在震群的端部(NW端),到最近断层距离的依赖性不强,在9、10km处的应力降中值略高于其他深度.根据应力降的变化特征和区域构造条件,我们推测地下流体在长岛震群的活动中起到一定的作用.     

紫坪铺水库地区蓄水前后视应力标度率变化研究

本文利用紫坪铺水库台网记录到的波形资料,计算了2004～2008年170个M_L≥1.0级地震的震源参数.紫坪铺水库震源参数计算结果与其他大陆地区有明显不同:(1)拐角频率远低于其他大陆地区结果,表明库区地震波传播经过了较强的衰减过程;(2)视应力计算结果比其他地区小3个数量级,可能是由于库区地震波的高频成分衰减强烈,低估了能量集中在高频的小地震的地震辐射能量.分析了蓄水前后拐角频率和地震矩以及视应力和地震矩关系(视应力标度率)变化,结果表明:相同地震矩的地震蓄水后拐角频率增加,地震高频成分相对丰富;蓄水前视应力与地震矩的关系不明显,蓄水后视应力随地震矩的增加而增加.视应力标度率的改变可能是蓄水后地震震源物理过程逐渐改变的直接反映.     

2013年岷漳地震和2014年景谷地震的能矩比对比研究

2013年岷漳地震和2014年景谷地震两个地震的矩震级均为M_W6.1,但相同等级烈度区域的面积差异显著,前者均明显大于后者.地面震动的强烈程度与震源破裂过程中辐射的地震波高频成分密切相关,作者系统地测定与研究了这两个地震的震源谱和反映其震源特征的能矩比等震源参量.结果表明,虽然岷漳地震和景谷地震释放的地震矩基本相同,分别为1.6×10¹⁸Nm和1.8×10¹⁸Nm,而且前者还比后者略小些,但其释放的地震波辐射能却差异显著,分别为1.3×10¹⁴J和0.6×10¹⁴J;因而前者的能矩比（8.1×10^-5）是后者能矩比（3.3×10^-5）的大约2.5倍.相应地,岷漳地震的视应力和应力降也都明显大于景谷地震的视应力和应力降.此外,这两个地震震源谱结果均显示出其高频趋势均按角频率ω的-2幂次衰减,符合"ω²模式";采用理论震源谱公式计算结果分别约占实际结果的54%和50%,两个地震的地震波辐射能解析解之间的差异依然约2.3倍.震源破裂特征的显著差异导致岷漳地震单位地震矩释放的地震波辐射能更多,即岷漳地震能矩比更大,是导致这两个矩震级均为M_W6.1地震的地震烈度差异显著的一个重要原因.     

Estimation of Source Parameters of M w 6.9 Sikkim Earthquake and Modeling of Ground Motions to Determine Causative Fault

In this study, source parameters of the September 18, 2011 M _w 6.9, Sikkim earthquake were determined using acceleration records. These parameters were then used to generate strong motion at a number of sites using the stochastic finite fault modeling technique to constrain the causative fault plane for this earthquake. The average values of corner frequency, seismic moment, stress drop and source radius were 0.12 Hz, 3.07 × 10²⁶ dyne-cm, 115 bars and 9.68 km, respectively. The fault plane solution showed strike-slip movement with two nodal planes oriented along two prominent lineaments in the region, the NE-oriented Kanchendzonga and NW-oriented Tista lineaments. The ground motions were estimated considering both the nodal planes as causative faults and the results in terms of the peak ground accelerations (PGA) and Fourier spectra were then compared with the actual recordings. We found that the NW–SE striking nodal plane along the Tista lineament may have been the causative fault for the Sikkim earthquake, as PGA estimates are comparable with the observed recordings. We also observed that the Fourier spectrum is not a good parameter in deciding the causative fault plane.     

A preliminary empirical model for frequency-dependent attenuation of Fourier amplitude spectra In Serbia from the Vrancea earthquakes

We present the frequency-dependent attenuation model for Fourier amplitude spectra of strong earthquake ground motion in Serbia from intermediate depth earthquakes in the Vrancea source zone in Romania. The development of this type of scaling is the essential first step toward developing the corresponding attenuation and scaling equations for pseudo relative velocity spectra (PSV), which are necessary for seismic macro- and microzoning in the territory of Serbia. Such scaling is necessary because the Vrancea source zone produces large earthquakes with shaking that attenuates differently from the local earthquakes in Serbia. Development of such a scaling model is associated with several difficulties, the principal one being the lack of recorded strong motion accelerograms at epicentral distances exceeding 300 km. To reduce uncertainties with such scaling, we require our preliminary scaling equations to be consistent with independent estimates of seismic moment, stress drop, and radiated wave energy. In the future, when the recorded strong motion data from Vrancea earthquakes increases several-fold of what it is today, it will become possible to perform this analysis again, thus leading to more reliable and permanent scaling estimates.     

广西南丹大厂矿区震源参数研究

利用广西南丹县大厂矿区地震监测台网记录的地震波资料,采用Brune（1970）模型,将速度记录谱归算为震源位移谱,使用遗传算法计算拐角频率及零频极限,然后计算地震矩、应力降等小震震源参数,并系统分析各种参数之间的关系。大厂矿区38次较大地震的震源参数计算结果为：地震矩范围在2.18×1011~7.89×1012 N·m之间;震源破裂半径78~439m;地震应力降在0.01~1.79 MPa之间。表明：地震矩与震级、震源半径、拐角频率之间呈线性关系,而应力降不依赖于地震矩,分布较为离散。大厂矿区应力降值明显偏低,这可能与该区域背景应力低有关。     

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.     

安徽地区震源参数的相关性研究

基于安徽数字地震台网2010年1月至2017年12月记录到的ML2.5~5.0级地震,根据中小地震震源参数测定原理,利用多台多地震联合反演Atkinson方法和Moya方法分别计算了安徽地区地壳平均非弹性衰减因子Q值和安徽24个省属专业地震的台站场地。在此基础上,运用遗传算法求得安徽地区96个地震事件的震源谱参数,进而根据Brune中小地震圆盘模型计算其拐角频率、地震矩、应力降、矩震级、震源尺度等震源参数,并分析其特征及相互之间的关系。研究结果表明:安徽地区中小地震的ML震级与其他震源参数之间存在一定相关关系,而地震矩M0与应力降Δσ、震源尺度r和拐角频率fc之间并未表现出明显的相关关系。