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．      

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.     

Fracture characteristics of the 1997 Jiashi, Xinjiang, China, earthquake swarm inferred from source spectra

Broadband P and S waves source spectra of 12 MS5.0 earthquakes of the 1997 Jiashi, Xinjiang, China, earthquake swarm recorded at 13 GDSN stations have been analyzed. Rupture size and static stress drop of these earthquakes have been estimated through measuring the corner frequency of the source spectra. Direction of rupture propagation of the earthquake faulting has also been inferred from the azimuthal variation of the corner frequency. The main results are as follows: ①The rupture size of MS6.0 strong earthquakes is in the range of 10～20 km, while that of MS=5.0～5.5 earthquakes is 6～10 km.② The static stress drop of the swarm earthquakes is rather low, being of the order of 0.1 MPa. This implies that the deformation release rate in the source region may be low. ③ Stress drop of the earthquakes appears to be proportional to their seismic moment, and also to be dependent on their focal mechanism. The stress drop of normal faulting earthquakes is usually lower than that of strike-slip type earthquakes. ④ For each MS6.0 earthquake there exists an apparent azimuthal variation of the corner frequencies. Azimuthally variation pattern of corner frequencies of different earthquakes shows that the source rupture pattern of the Jiashi earthquake swarm is complex and no uniform rupture expanding direction exists.     

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.     

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.     

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.     

利用CDSN资料研究中强地震的差异：—CDSN应用系列论文三

本文利用中国数字地震台网(CDSN)短周期垂直向的直达 P 波数字资料,通过频谱分析的方法,测定了3个5级左右的中强地震及其随后小地震的应力降和介质 Q 值。初步研究了不同类型的中强地震在这方面的差异。并指出,中强地震的应力降低,与随后发生的小地震的平均应力降比值也小时,有可能在震中附近还会发生更大的地震。相反,中强地震的应力降高,与小地震的平均应力降的比值大时,随后发生更大地震的可能性就小。同时还指出,中强地震发生前,往往介质 Q 值部较低。这在中强地震发生后,对及时估计地震趋势有一定的实用价值.     

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.     

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…     

长岛震群震源谱参数反演和震源参数特征

采用高频截止(High-Cut)震源模型,以均方根误差最小原则稳健地求解震源谱参数,并由此推算震源尺度和静态应力降。实际应用显示,该模型的理论谱对观测谱有很好的拟合,可明显改善拐角频率识别准确度。计算了长岛震群内71次M_L≥2.5地震事件的震源参数,结果表明：(1)拐角频率处于2～10 Hz范围,与震级大小存在一定的相关性,截止频率范围处于10～30 Hz之间,与地震大小的相关性不明显;(2)地震矩M₀分布在10¹²～10¹⁴ N·m,与震级M_L存在正相关关系：logM₀=0.977M_L+10.186;M_L与矩震级M_W之间的关系为：M_W=0.651M_L+0.766;(3)根据相对应力降时域演化发现,自2017年3月3日M_L4.5地震之后应力快速释放,应力降水平在均值附近波动,而且多数M_L≥3.5地震发生于...     

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.     

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.     

峰值速度和加速度对环境剪应力的依赖性

从导出的地震定标律和地震破裂过程的断裂力学模式出发,得到了震源平均位移、速度和加速度谱的表达式,进而又推导出震源的峰值位移d_m,速度v_m和加速度a_m的表达式:d_m=k_dM_0~2/~3τ_0~(2/3),v=k_vM_0~(1/3)τ_0~(4/3),a_m=k_aτ_0~2式中M_0是地震矩,τ_0是环境剪应力值,k_d,k_v,k_a为适当的常数.我们选用了66个地震的观测资料,这些地震的矩震级范围包括了从1级左右的极微震,3-5级的小震,直到6-7级的大震;地震矩从10~9-10~(20)Nm,跨越了10个数量级,并用这些地震检验了上述公式. 令所有地震的平均应力为5MPa,定出常数k_d,k_v,k_a,进而由速度和加速度观测资料求得66个地震的环境剪应力τ_0值,这些数值相当稳定.多数极微震的τ_0值在2-4MPa之间;小震的τ_0值多数在4-8MPa左右;大震的τ_0值为10MPa左右。τ_0值对震源深度和断层类型有明显的依赖性.一般深度很浅的小震和极微震,τ_0值很低;正断层地震的τ_0值相对较低;逆断层地震的τ_0值较高;走滑断层地震的τ_0值则居中.     

Analysis of strong earthquake ground motion for prediction of response spectra

Prediction of response spectra for earthquake engineering purposes is considered from a new point of view based on the dislocation theory of earthquakes. It is shown that the traditional scaling of response spectra by the predicted peak acceleration should be limited to the high-frequency end of the spectrum, and that the peak acceleration in the near field is not strongly correlated with earthquake magnitude. The amplitude of the long-period end of response spectrum at source to station distances greater than about 10 source dimensions should be scaled with seismic moment, while for distances less than about one source dimension this amplitude should be proportional to the permanent ground displacement. To reconcile the existing extensive data on seismicity of active regions based on magnitude scale, it is shown that magnitude can be used to determine approximately the seismic moment.     

巧家、石棉的小震震源参数的测定及其地震危险性的估计

根据巧家、石棉的小地震的观测资料,指出P波初动半周期在震级比较小时几乎是恒定的,在震级比较大时随震级的增大而增大;并指出P波初动振幅的对数也随震级的增大而增大。以圆盘形均匀位错面作为中、小地震震源的理论模式,计算了它所辐射的地震波远场位移,从而导出了体波初动半周期及振幅与震源尺度及波速等物理量的定量关系,解释了P波初动半周期及振幅与震级之间的经验关系。考虑到波在介质中的衰减和频散、地表面的影响以及地震仪器的频率特性,通过褶积方法合成了上述位错源产生的理论地震图,提出了直接由实际地震图上的初动半周期及振幅测定震源尺度、地震矩、应力降和错距等震源参数以及介质的晶质因数Q的方法.运用上述方法,测定了巧家、石棉两地区介质的品质因数Q和小震的震源参数.这两个地区介质的品质因数Q分别为620和560.石棉地区小地震的应力降大约在2-30巴之间,巧家地区小地震的应力降比较接近,平均约1.4巴.将这个结果和1962年3月19日新丰江地震与1975年2月4日海城地震的前、主震的应力降作对比,我们看到,巧家地区小震的应力降的特征与上述两次大地震的前震的应力降的特征是类似的,因此不能排斥巧家地区的小震是一个较大地震的前震的可能性.以测得的小震应力降的平均值（约1.4巴）作为这个可能发生的较大地震应力降的下限估计值,从主震震级和主震应力降的经验关系可以推知,其震级的下限是5.2级.     

地震空间分布非空网格数的统计分布及地震活动增强-平静的定量检测l

以华北地区1980——2010年资料为例,以单位边长的网格覆盖研究区,考察中小地震空间分布非空网格数的变化．网格尺度足够小则非空网格数趋于该时段的地震数,网格尺度足够大则非空网格数为1．实际资料显示,当空间网格尺寸大于0.5deg;之后,对结果稳定性的影响逐渐减弱．中小地震空间分布非空网格数的变化与ldquo;背景rdquo;地震活动的空间扩展（增强）或收缩（平静）有关．不同网格尺寸条件下的非空网格数有基本一致的变化趋势,可能间接反映了区域应力的短时扰动或起伏．小地震有更高的丛集特性,随着震级下限的提高,不同网格尺寸非空网格数之间差异逐渐变小．华北地区小震活动非空网格数的频次分布符合统计正态分布,因而给定置信概率、依据正态分布密度函数可计算非空网格数的ldquo;正常rdquo;分布范围,超出此范围的数据可视为异常．统计显示,就华北地区而言,中小地震非空网格数ldquo;平静rdquo;型异常的预测效率最低,ldquo;增强rdquo;型异常具有最高的报警对应率,而同时考虑ldquo;增强rdquo;及ldquo;平静rdquo;的异常判据则具有最高的预报评分．这也意味着,华北中强地震前以ldquo;增强rdquo;型的中小地震活动异常为主．研究结果还显示,小地震时空活动格局的改变与后续中强地震似乎具有更强的统计关联特性．      

Dynamic Stress Drop of Recent Earthquakes: Variations within Subduction Zones

—Stress drop is a fundamental parameter of earthquakes, but it is difficult to obtain reliable stress drop estimates for most earthquakes. Static stress drop estimates require knowledge of the seismic moment and fault area. Dynamic stress drop estimates are based entirely upon the observed source time functions. Based on analytical formulas that I derive for the crack and slip-pulse rupture models, the amplitude and time of the initial peak in source time functions can be inverted for dynamic stress drop. For multiple event earthquakes, this method only gives the dynamic stress drop of the first event. The Michigan STF catalog provides a uniform data base for all large earthquakes that have occurred in the past four years. Dynamic stress drops are calculated for the nearly 200 events in this catalog, and the resultant estimates scatter between 0.1 and 100 MPa. There is some coherent tectonic signal within this scatter. In the Sanriku (Japan) and Mexico subduction zones, underthrusting earthquakes that occur at the up-dip and down-dip edges of the seismogenic zone have correspondingly low and high values of stress drop. A speculative picture of the stress state of subduction zones emerges from these results. A previous study found that the absolute value of shear stress linearly increases down the seismogenic interface to a value of about 50 MPa at the down-dip edge. In this study, the dynamic stress drop of earthquakes at the up-dip edge is about 0.2 MPa, while large earthquakes at the down-dip edge of the seismogenic plate interface have dynamic stress drops of up to 5 MPa. These results imply that (1) large earthquakes only reduce the shear stress on the plate interface by a small fraction of the absolute level; and thus (2) most of the earthquake energy is partitioned into friction at the plate interface.     

APPARENT STRESS VARIATION CHARACTERISTICS BEFORE AND AFTER BADONG EARTHQUAKE IN THE THREE GORGES RESERVOIR AREA

The causes of earthquakes in the Three Gorges reservoir area are complex. In order to study the cause of earthquakes happening in the region, we calculated the source parameters of 394 M_L ≥ 2.0 earthquakes occurring in Three Gorges reservoir area based on waveform data observed by the regional seismic network of Hubei Province and Three Gorges, obtained the apparent stress spatial-temporal variation map of Three Gorges reservoir area, and analyzed apparent stress spatial-temporal variation characteristics before and after the main earthquakes in the Three Gorges reservoir area. The results show that:1)Before the Badong M_L5.5, Zigui M_L4.7 and Zigui M_L5.1 earthquake, high apparent stress of earthquakes with different magnitudes is concentrated in Xinhua-Shuitianba Fault and Gaoqiao Fault. The distribution of high value area shows the high degree of synergism before the earthquake and the scattering after the earthquake, which indicates that the area accumulated a high stress before the earthquake, and the fault was in a locked state; 2)In the study area, the apparent stress before and after the earthquake showed significant rise in the first and then decline, the earthquake occurred in the process of rising; 3)Apparent stress depth profiles show that apparent stress at different depths has a positive correlation with the size of magnitude of earthquake, and the phenomenon of "small magnitude and strong apparent stress" did not appear. The small earthquakes occurring after the major earthquakes in the study area belong to low strain release under the background of low stress release, and there are no new apparent stress anomaly concentration areas appearing, this indicates that the Badong-Gaoqiao Fault, Zhoujiashan-Niukou Fault and Zigui Xiannushan Fault have been effective in releasing after the Badong earthquake and Zigui earthquakes and the probability of destructive earthquake is small on these faults.     

Probability of earthquake recurrence with nonuniform stress rates and time-dependent failure

Current methods for calculation of long-term probabilities for the recurrence of large earthquakes on specific fault segments are based upon models of the faulting process that implicitly assume constant stress rates during the interval separating earthquakes and instantaneous failure at a critical stress threshold. However, observations indicate that the process of stress recovery following an earthquake involves rate variations at all time scales in addition to stress steps caused by nearby earthquakes. Additionally, the existence of foreshocks, aftershocks and possible precursory processes suggest that there may be significant time dependence of the earthquake nucleation process. A method for determining the conditional probabilities for earthquake occurrence under conditions of irregular stressing is developed that could be useful at all time scales including those pertinent to short-and intermediate-term prediction. Used with models for earthquake occurrence at a stress threshold, the addition of variable stressing introduces a simple scaling of the conditional probabilities by stress level and stress rate. A model for the time-dependent nucleation of earthquake slip has been proposed recently that is based upon laboratory observations of fault strength. This failure criterion results in large but relatively short duration changes in the probability of earthquake recurrence particularly following stress steps. Applied to populations of earthquakes the models predicts a 1/t decay of seismicity following stress steps as observed for aftershocks and for frequency of foreshock-mainshock pairs. The model suggests that variations of seismicity rates of small earthquakes in the nucleation zone of the expected earthquake directly indicate variations in probability of recurrence of the large earthquake.     

Multiasperity fault model and the nature of short-period subsources

We suggest to consider the breaking of an asperity,i.e., a small contact patch between fault walls, as a typical subsource producing an elementary short-period radiation pulse from a source of a large earthquake. Based on the results ofDas andKostrov we propose formulas to describe amplitudes and spectra of acceleration for a multiasperity fault/source model. The stress drop over an asperity is determined in several ways; the estimates agree to give the average value of several hundred bar. Theoretical acceleration spectral shapes for the case of similar asperities agree with the observed ones, they reproduce such features as lower-frequencyf ¹ slope, peak, and high-frequency cutoff. The statistical stress-drop distribution over the population of asperities, and also the related distribution of peak accelerations are discussed. There distributions are found to be the power-law ones with exponent near to 2. This means that acceleration peaks are formed normally by breaking of individual asperities. We consider small earthquakes as produced by breaking of single asperities, this idea explains the observed correlation between the upper cutoff frequency of acceleration spectrum and the typical characteristic frequency of small earthquakes.