Estimation of Source Parameters for the Aftershocks of the 2001 Mw 7.7 Bhuj Earthquake, India

The source parameters for 213 Bhuj aftershocks of moment magnitude varying from 2.16 to 5.74 have been estimated using the spectral analysis of the SH- waveform on the transverse component of the three-componnet digital seismograms as well as accelerograms. The estimated stress drop values for Bhuj aftershocks show more scatter (Mo^{0.5 to 1} ∞ Δσ) toward the larger seismic moment values (log Mo ≥ 10^14.5 N-m, larger aftershocks), whereas, they show a more systematic nature (Mo³ ∞ Δσ) for smaller seismic moment (log Mo < 10^14.5 N-m, smaller aftershocks) values. This size dependency of stress drop has also been seen from the relation between our estimated seismic moment and source radius, however, this size-dependent stress drop is not observed for the source parameter estimates for the other stable continental region earthquakes in India and around the world. The estimated seismic moment (Mo), source radius (r) and stress drop (Δσ) for aftershocks of moment magnitude 2.16 to 5.74 range from 1.95 × 10¹² to 4.5 × 10¹⁷ N-m, 239 to 2835 m and 0.63 to 20.7 MPa, respectively. The near-surface attenuation factor (k) is found to be large of the order of 0.03 for the Kachchh region, suggesting thick low velocity sediments beneath the region. The estimated stress drop values show an increasing trend with the depth indicating the base of seismogenic layer (as characterized by larger stress drop values (>15 MPa)) lying in 22–26km depth range beneath the region. We suggest that the concentration of large stress drop values at 10–36km depth may be related to the large stress/strain associvated with a brittle, competent intrusive body of mafic nature.     

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.     

汶川MS8.0级地震发生背景与过程的研究

本文首先阐明汶川M_S8.0级地震发生在由区域布格重力异常和地震震中分布所确定的武都—松潘—茂汶—汶川—泸定地震带上.汶川地震所在地段是地震前兆和中小地震（M≤7.0）的空白区,震前出现明显的孕震空区,M_S8.0级地震发生在空区周围区域中小地震活动峰值之后的减少段里.地震的破裂超出孕震空区范围,空区内、外余震活动呈现出不同的衰减特征,依此将余震活动分为WS和NE两个区段.地震破裂过程、4级以上余震矩张量及震区应力场反演和余震应力降的测定结果表明,两个区域的位错、余震机制解和应力降及最大主应力的方〖JP2〗向等明显有别.根据这些特征和地震应力触发的研究,推测NE段地震的发生可能是〖JP〗由WS段主破裂的发生所触发.     

利用经验格林函数谱比法估计2013年芦山地震序列的应力降

本文以芦山地震余震为例,分析了基于强震动观测记录的经验格林函数（EGF）谱比法估计地震的拐角频率和应力降的可行性。首先给出能够可靠估计地震拐角频率和应力降的经验格林函数谱比曲线的质量标准;然后利用其估算出17次M_L3.8—5.4芦山强余震的拐角频率;最后,参考其它研究给出的地震矩震级,计算出地震应力降。结果显示,芦山强余震的拐角频率主要介于1.0—2.0 Hz之间,应力降平均值为9.98 MPa,且地震应力降表现出明显的震级相关性。      

Spectral analysis and earthquake scaling of the Petatlan earthquake (M s =7.6) aftershocks,recorded at stations along the pacific coast and between the coast and Mexico City

Spectral parameters have been estimated for 214 Petatlan aftershocks recorded at stations between Petatlan and Mexico City and between Petatlan and Acapulco. The spectral parameters were used to obtain empirical relations for the estimation of seismic moment from coda length and fromM _L . Stress drops, using Brune's model, were calculated for these aftershocks. Six events with large stress drop are located within a previously suggested asperity, and seven more suggest a boundary zone at the intersection of the Petatlan and Zihuatanejo aftershock rupture volumes. Stress drops increase with increasing seismic moment up to 10²⁰ dyne-cm but appear to be constant at greater moment values. The peak horizontal velocity times distance of aftershocks recorded near the coast and between the coast and Mexico City (30 to 270 km away), scales linearly with seismic moment, and predicts well the peak horizontal values of large (M _s 7.0) coastal thrust events recorded on rock sites at Mexico City. Peak horizontal velocity is a straightforward measurement, thus this relation allows us to evaluate expected ground motion between the Pacific coast and Mexico City from the seismic moment of subduction related earthquakes along the coast.     

2000年姚安地震的震源参数

根据近场小孔径观测台网记录的余震序列资料，研究了2000年1月15日云南姚安MS6.4地震序列的地震物理过程. 用地震标定律关系估算主震的地震矩M0=1.58×1018N·m，矩震级MW=6.0，平均位错=0.63m，断层长度L=16.6km，断层宽度W=5.6km. 余震序列的高精度定位结果和能量分布走向，很好地证实了主震的断层破裂走向为N50°W，震区马尾菁断裂为主震发震构造，断层错动性质以右旋走滑为主. 用横波记录资料及波谱分析方法估算出余震的震源参数: 地震矩范围为1010～1016N·m，震源破裂半径a为80～500m，地震应力降范围为0.01～9.5MPa. 较大应力降(Δσ>1.0MPa)沿主断层线性排列，大应力降(Δσ>2.0MPa)与ML≥3.0级地震相关. 余震能量释放和高应力降的地震多发生在6.0～11km的深度范围，说明在这一深度范围内最大程度地集中了地壳中的应力.     

姚安地震序列与大姚地震序列震源参数的对比研究

2000年1月15日在云南省姚安县发生了M_S6.5地震, 2003年7月21日和10月16日在云南省大姚县发生了M_S6.2、 M_S6.1地震。 这两个地震序列均发生在滇中块体, 震中位置相距42.5 km, 构造、 应力背景相似, 但序列类型不同, 时间间隔短。 为深入研究姚安地震和大姚地震序列的特征, 根据昆明区域数字台网记录的数字地震波资料, 利用遗传算法计算了2000年姚安地震和2003年大姚地震序列的震源参数。 研究结果表明, 姚安地震序列和大姚地震序列的地震矩和近震震级有很好的线性关系, 它们的地震矩M₀均在10¹²~10¹⁴ N·m, 地震矩与震源半径之间呈线性关系。 应力降随震级变化不明显。 拐角频率和地震矩之间有明显的依赖关系, 用最小二乘法拟合拐角频率和地震矩的关系式, 利用此关系式可计算出给定地震矩的拐角频率估计值f_a, 进而可分析实际计算的拐角频率与估计值之差(f_c-f_a)的时间变化曲线。 姚安地震序列和大姚地震序列实际计算的拐角频率与估计值之差(f_c-f_a)及应力降随时间的变化表现出了不同的特征: 姚安地震序列的应力降和拐角频率差值在4.3级和4.6级强余震前均有一个上升-下降过程, 反映余震区应力场有一个增高-下降过程; 大姚地震序列应力降和拐角频率差值在M_S≥4.6强余震发生之前均会出现高值异常, 但在M_S4.6～4.7地震之前出现的高值异常持续时间短, 在M_S6.1地震前出现的高值异常持续较长。 文中结合两个地震的发震构造, 序列类型等特征进行了分析讨论。     

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.     

The Patras earthquake (14 July 1993): relative roles of source, path and site effects

A damaging earthquake occurred on 14 July 1993 in Patras, Western Greece. The mainshock (local magnitude 5.1) was followed on the same day by two aftershocks of magnitudes 4.4 ML and 3.6 ML, respectively. The strong motion record of the mainshock is studied, based on the teleseismically determined seismic moment and focal mechanism. The Discrete Wavenumber (DW) and Empirical Green's Function (EGF) methods are used. The main conclusion is that the 1993 Patras mainshock had a complex S-wave group mainly due to structural (path and site) effect. However, some effects of the rupture stopping on the peak ground acceleration (0.2 g in the so-called S3 phase) cannot be ruled out. Two values of the source radius are suggested: R = 1.9 and 3.0 km. The strong motion record better agrees with R = 1.9 km. If the latter is true, the stress drop was of the order of 20 MPa, i.e., higher than often reported for comparable events in Western Greece. Regardless of the true source radius, the ratio of stress drops between the mainshock and aftershocks was about 1–2. The aftershock waveforms indicate significant lateral heterogeneities around Patras. Therefore, the ground-motion predictions of strong events in the area will remain highly non-unique until weak events from an immediate neighbourhood of the particular fault are recorded.     

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.     

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。     

四川长宁地区地震震源参数的时空分布特征

使用谱比法计算得到四川长宁地区2018年12月至2019年7月期间442个地震的震源参数,并进一步分析了震源参数之间的相互关系及应力降的时空分布特征。研究区的地震活动主要集中在长宁背斜核部和南部建武向斜页岩气开采区。研究结果显示,该地区M_L1.3~4.7地震的应力降位于0.02~7.26MPa范围内,超过90%的地震应力降小于2MPa,应力降总体呈现随震级增大而增大的趋势,但与震源深度的关系并不明显。长宁M_S6.0地震发生之前,震源区地震的应力降总体处于较低水平,主震发生之后,短期内余震的应力降较高,随后快速衰减。这些高应力降地震空间上主要集中在长宁余震区的西北段,也是余震强度较大、发生了几次M_S>5.0强余震的位置。建武向斜页岩气开采区地震的应力降总体略低于长宁背斜地区,但差异并不显著。     

山东长岛地区地震波非弹性衰减Q值、场地响应及震源参数研究

利用山东台网记录的长岛震群2017年2月14日—9月1日期间的波形与震相资料研究长岛地区非弹性衰减系数,得到该地区介质平均Q值与频率f的关系式为Q(f)=363.9f1.374 1。采用Moya等[1]提出的利用遗传算法联合反演得到长岛周边台站的场地响应,根据Brune模型震源参数计算公式求解长岛震群序列地震震源参数。结果显示,各个震源参数之间均存在一定的相关关系,地震矩随ML震级的增大而增加,地震矩与破裂半径R之间存在半对数关系,拐角频率fc随地震矩的增大而减少;长岛地震序列的应力降数值普遍偏小,最大不超过0.9MPa,这意味着长岛震源区整体构造应力较低,也可能指示长岛震群为低摩擦应力的断层作用;震源参数随时间的变化方面,整体而言,长岛震群地震应力降变化起伏很大,在M4.1地震发生前,拐角频率与应力降均发生快速下降后随即翻转上升的现象,证明在M4.1地震发生前震源区整体应力的挤压逐渐增强。     

云南地区中小地震静力学和动力学参数定标关系

Source spectra for moderate and small earthquakes are obtained after removing the path effect, site effect, and instrument response, etc. in the observed S-wave spectra. Based on the Brune source model...     

An Overview of the Study on Stress Magnitude

Crustal stress field holds an important position in geodynamics research, such as in plate motion simulations, uplift of the Qinghai-Xizang (Tibet) Plateau and earthquake preparation and occurrence. However, most of the crustal stress studies emphasize particularly on the determination of stress direction, with little study being done on stress magnitude at present. After reviewing ideas on a stress magnitude study from geological, geophysical and various other aspects, a method to estimate the stress magnitude in the source region according to the deflection of stress direction before and after large earthquakes and the stress drop tensor of earthquake rupture has been developed. The proposed method can also be supplemented by the average apparent stress before and after large earthquakes. The stress direction deflection before and after large earthquakes can be inverted by massive focal mechanisms of foreshocks and aftershocks and the stress drop field generated by the seismic source can be calculated by the detailed distribution of the earthquakes rupture. The mathematical relationship can then be constructed between the stress drop field, where its magnitude and direction are known and the stress tensor before and after large earthquakes, where its direction is known but magnitude is unknown, thereby obtaining the stress magnitude. The average apparent stress before and after large earthquakes can be obtained by using the catalog of broadband radiated energy and seismic moment tensor of foreshocks and aftershocks and the different responses to stress drops. This relationship leads to another estimation of stress magnitude before a large earthquake. The stress magnitude and its error are constrained by combining the two methods, which provide new constraints for the geodynamics study.     

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。     

新疆精河M_W6.3地震产生的静态应力变化研究

利用精河M_W6.3地震有限断层破裂模型,计算了精河地震产生的位移场、应力场、周围主要断层上的静态库仑应力变化以及主震对余震的触发作用。结果表明:(1)精河地震产生的地表隆升最大值约为6.6cm,沉降最大值约为1.8cm;水平位移方向呈现震中南北侧向震中汇聚、震中东西侧向外"流出"的特点。(2)精河地震产生的水平面应力场展布南北侧物质主要受到指向震中的拉张力作用,东西两侧物质主要受到因震中过剩物质东西向排出而导致的东西向挤压力作用。(3)震中西侧距震中约20km的库松木契克山前断裂中段和震中东北部距震中约50km的四棵树-古尔图南断裂西段的库仑应力加载均大于0.01MPa,即2处为地震危险区。(4)在震源深度为8~12km的余震事件中,约有85.5%处于库仑应力加载区,即受到主震的的触发作用;在深度为4~8km的余震事件中,约有87%受到主震的应力触发作用。     

Seismotectonic study of Kishtwar region of Jammu Province using local broadband seismic data

Two moderate earthquakes of Mw 5.7 on the first of May and Mw 5.2 on the second of August occurred in the Kishtwar region in the year 2013. Our broadband seismic observatories located in the region recorded these events and the aftershocks. We analyzed these data to understand the seismotectonics of this region. Most of the events were located between 33.03° to 33.29° N latitude and 75.40° to 76.07° E longitude. Focal depths of these shallow earthquakes range from 7 to 12 km and are confined between Panjal Thrust (PT) and Kishtwar Window (KW). Spectral analysis of these events reveals that stress drop, source radius, corner frequency, and moment magnitude varied between 3.3 and 70.1 bars, 0.121 and 3.55 km, 0.397 and 6.06 Hz, and Mw 2.2 and Mw 5.7, respectively. The low stress drop of small-magnitude earthquakes reveals the brittle nature of the upper crust which is coincident with the field observations. The variation of stress drop with magnitude shows positive correlation whereas no such relation was observed between stress drop and depth of focus. The b value calculated (0.83) for the area reveals high stress accumulation within the incompetent rock zones in the area.     

Source parameters of some significant earthquakes near Koyna dam,India

Seismic moment, stress drop, source radius, and fault dislocation have been determined for nineteen significant earthquakes in the Konya area, India using displacement spectra of shear waves computed from strong-motion accelerograph records. Though the stress-drop shows a definite increasing trend with the seismic moment, its correlations with source radius and corner frequency indicate that a constant stress drop of 170 bars represents a good mean value to describe the source mechanism of the Koyna dam earthquakes. An empirical relationship also has been established between magnitude and seismic moment.     

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.