Source parameters determination for earthquakes in Kushiro,Japan considering source time function

This paper applies a new formulation to do moment tensor inversion for earthquakes in the Kushiro area of Japan. Comparing with conventional moment tensor inversion method, the new one takes the effect of source time function into consideration. For the inversion, best solution is obtained by minimizing the difference between the observed seismograms and the synthetic ones. And the best-fitting focal depth is determined from the variance reduction. The results indicate that half duration of source time function is proportional to the magnitude of earthquakes. Large earthquakes have long half duration, whereas that of moderate-small earthquakes is comparatively shorter. The focal mechanisms of all three earthquakes are of thrust fault type, which is mainly ascribed to the collision of the North American plate with the Eurasia plate in the late Cretaceous or Paleogene.     

A new technique for moment tensor inversion with applications to the 2008 Wenchuan M S8.0 earthquake sequence

A MS8.0 earthquake occurred in Wenchuan County, Sichuan Province, China, on May 12, 2008, and subsequently, numerous aftershocks followed. We obtained the moment tensor solutions and source time functions (STFs) for the Wenchuan earthquake and its seven larger aftershocks (MS5.0~6.0) by a new technique of moment tensor inversion using the broadband and long-period seismic waveform data from the Global Seismic Network (GSN). Firstly, the theoretical background and technical flow of the new technique was briefly introduced, and an aftershock of the Wenchuan earthquake sequence was employed to illustrate the real procedure for inverting the moment tensor; secondly, the moment tensor solutions and STFs of the eight events, including the main shock, were presented, and finally, the interpretation of the results was made. The agreement of our results with the GCMT results indicates the new approach is efficient and feasible. By using this approach, not only the moment tensor solution can be obtained but also the STF can be retrieved; the inverted STFs indicate that the source rupture process may be com-plicated even for the moderate earthquakes. The inverted focal mechanisms of the Wenchuan earthquake sequence show that the most of the aftershocks occurred in the main faults of the Longmenshan fault zone with predomi-nantly thrustingwith minor right-lateral strike-slip component, but some of them may have occurred in the sub-faults with strike-slip faulting in the vicinity of the main faults.     

用接收函数建立区域模型的震源机制反演及其在芦山地震序列研究中的应用

本文提出并试验了一种基于接收函数建立区域模型进行震源机制反演的方法.选取四川地震台网记录的M≥3且信噪比高的近震波形资料,反演得到了芦山地震序列中74个地震的震源机制.通过对震源深度和震源机制的综合分析,探讨了芦山地震的发震构造和区域应力场状态.采用接收函数方法反演获取了26个台站下方的S波速度结构,对不同区域的台站反演结果进行叠加平均,以此区域平均S波速度作为本文震源机制反演使用的区域模型的S波速度;区域模型的P波速度由经验公式给出.反演稳定性测试表明,使用不同模型或对原始波形记录加入随机噪声的反演结果与原始反演相比,震源深度最大误差为1km,断层面各参数误差水平也很低,且显示的发震类型是一致的,其中随机噪声带来的误差小于模型带来的误差.主震反演得到的震源机制解为:震源深度17km,矩震级6.47;节面Ⅰ走向213°,倾角51°,滑动角98°;节面Ⅱ走向20°,倾角40°,滑动角80°;显示芦山主震可视为纯逆冲型地震,发震构造可能是某个具有较大倾角的逆冲断层,而不是低缓的推覆构造的基底滑脱面.同时本文反演获取的73个M≥3余震的震源机制绝大多数也显示了类似的发震类型,逆冲型地震为67个,占92%,具有绝对优势;走滑型地震为5个,正断型地震为1个.其中5个走滑型地震中的4个均分布在震源区的东北端.整个芦山地震序列深度集中在12~20km,且沿震源区短轴的余震深度剖面有自西向东呈逐步变浅的趋势,呈现清晰的铲形断面结构,结合本地地质构造,可以推断芦山地震序列主要发生在龙门山前山断裂以东的逆冲推覆体内的一个隐伏断裂上.P轴方位角优势方位与区域应力场及汶川震源区南段的相一致,表明芦山序列地震活动主要受区域应力场控制,且汶川震后该区应该不存在应力场变化.P轴仰角随深度分布则显示了孕震层在浅部为脆性上地壳,而深部已经进入了中地壳低速层.断层面的几何形态简单,倾角均值在不同深度保持稳定在55°左右,与主震倾角接近,这与汶川震源区南段的研究结果明显不同,揭示了龙门山断裂带南段与此次芦山发震断裂在断层面几何形态上的明显差异.     

新疆北天山中东段呼图壁地区震源深度的重新测定

联合Hyposat法、PTD法和gCAP矩张量反演法,重新测定新疆北天山中东段呼图壁地区2010—2017年502个地震的震源深度,并对震源深度剖面进行初步分析。结果表明,重新测定的震源深度优势分布为15—20km,平均震源深度为16km,呼图壁M_S 6.2地震的震源深度为20km;研究区南部和中部的震源深度集中分布在20km左右,与北天山壳内低速体的层位相当,可能是上地壳和下地壳之间的韧性剪切带存在的部位,起到滑脱层的作用,研究区北部的震源深度则向浅部扩展;呼图壁M_S 6.2地震的发震断裂可能在清水河子断裂下方的1条隐伏反冲断层上,可能是霍尔果斯断裂向前沿断坡冲断受阻而在相反方向上发育分支反冲断层的结果。     

基于Langston分解和Hilbert变换约束的区域偏量矩张量反演方法及其应用

本文基于Langston的震源机制分解方法以及Minson和Dreger修正后的近场位移的解析解表达式,给出了一种区域纯偏量矩张量的求解方法,方法使用基于Hilbert变换的波形包络作为增强约束．对该方法进行了数值试验. 试验结果表明,定位准确且速度结构已知的情况下,背景高斯噪声水平达30%时,该方法仍可以得到较稳定的解;使用0.01——0.1 Hz的中长周期频段进行反演,在随机震相到时误差最大plusmn;3 s的情况下,近90%的情况可以得到相对准确的解. 速度结构模型的干扰试验表明,平均模型接近真实地壳结构时,可以得到接近真实的解;模型与真实的地壳结构的误差在10%以内时,得到的解与真实解比较接近;误差接近20%时,矩张量解会出现很大的偏差;地震的定位误差主要影响震源深度的判定,从而导致最终解中出现虚假的非双力偶成分,但在约束为偏量矩张量的情况下,反演得到的断层面参数与真实解偏差不大;在台站方位角覆盖较差(＜60deg;)的情况下,使用平均模型仍可以得到较为准确的解．使用该方法研究了2010年10月24日河南周口太康MW4.7地震的震源机制,结果显示矩张量解与初动符号解较为一致．      

A new technique for moment tensor inversion with applications to the 2008 Wenchuan <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>8.0 earthquake sequence

A M_S8.0 earthquake occurred in Wenchuan County, Sichuan Province, China, on May 12, 2008, and subsequently, numerous aftershocks followed. We obtained the moment tensor solutions and source time functions (STFs) for the Wenchuan earthquake and its seven larger aftershocks (M_S5.0～6.0) by a new technique of moment tensor inversion using the broadband and long-period seismic waveform data from the Global Seismic Network (GSN). Firstly, the theoretical background and technical flow of the new technique was briefly introduced, and an aftershock of the Wenchuan earthquake sequence was employed to illustrate the real procedure for inverting the moment tensor; secondly, the moment tensor solutions and STFs of the eight events, including the main shock, were presented, and finally, the interpretation of the results was made. The agreement of our results with the GCMT results indicates the new approach is efficient and feasible. By using this approach, not only the moment tensor solution can be obtained but also the STF can be retrieved; the inverted STFs indicate that the source rupture process may be complicated even for the moderate earthquakes. The inverted focal mechanisms of the Wenchuan earthquake sequence show that the most of the aftershocks occurred in the main faults of the Longmenshan fault zone with predominantly thrustingwith minor right-lateral strike-slip component, but some of them may have occurred in the subfaults with strike-slip faulting in the vicinity of the main faults.     

2013年芦山MS7.0地震序列断层结构及震源区应力场特征

使用芦山地震序列2013年4月20日至5月20日一个月的地震震相数据和M_S4.0以上地震的波形数据, 通过双差定位方法得到了3398个地震的精定位结果, 利用时间域全波形反演方法得到17个地震的矩张量解。 综合分析地震双差定位结果和芦山地震序列中强地震震源机制解, 发现芦山地震发震构造由主震断层和次级反冲断层组成, 主震断层为一走向北东、 倾向北西、 倾角约为45°的高角度逆冲断层, 次级反冲断层与主震断层走向相同, 倾向相反, 两条断层均未出露地表。 主震和余震震源机制解均为逆冲型, 几乎没有走滑分量。 震源区主压应力方位为北西向, 与发震断层走向近乎垂直。     

2012年11月20日宁夏永宁MS4.6 地震震源机制解与发震构造

2012年11月20日在宁夏银川市永宁县与兴庆区交界处发生M_S4.6地震,为了更好地了解此次地震的发震构造,首先采用Hypo2000绝对定位方法得到该地震的震中位置及余震分布;然后采用CAP方法反演了此次地震的震源机制解和震源深度. 反演结果表明,永宁M_S4.6地震是一个带有少量逆冲分量的右旋走滑地震.该地震矩震级为M_W4.3,最佳双力偶解为:节面Ⅰ走向11°,倾角74°,滑动角171°;节面Ⅱ走向103°,倾角81°,滑动角16°.最佳震源深度为8km左右.从该地震震中和震源机制解以及震源深度剖面分布来看,这次地震很可能发生在银川隐伏主断层西侧的次级断层上.      

含衰减地层微地震震源机制反演及其反演分辨率

微地震震源机制的反演对于非常规油气开发具有至关重要的作用.微地震信号主频高、能量小,容易受地层吸收衰减作用的影响使其波形发生畸变,本文提出了一种考虑地层吸收衰减作用的微震源机制反演方法,并利用费雷谢偏导矩阵的SVD分解(特征值分解)方法,分析研究了地层的吸收衰减因子的变化对于微地震震源机制反演分辨率的影响,根据理论计算给出了不同地震数据对各种震源机制反演的适用条件.理论计算证明,采用直达P波和S波数据联合反演震源的T值,单独利用直达P波反演震源的k值,可以有效降低地层吸收衰减作用对反演结果的影响.     

由地震释放的地震矩叠加推导平均应力场

文中给出了根据地震释放的总地震矩求解平均应力场的方法,并使用加入随机误差的人工合成震源机制解数据和唐山余震区震源机制解数据对其进行检验。由检验结果可知,该方法可以应用于区域平均应力场的求解。使用的震源机制解资料越多,所得结果越稳定,且更接近真实的区域应力场。该方法的优点是: 用每个地震的震级作为权重,能够较好地反映出大小地震在应力场反演中的不同贡献; 并且在计算过程中不需要知道震源机制解2个节面中哪个节面为地震断层面。     

FOCAL MECHANISM OF THE AUGUST 8, M7.0 SICHUAN JIUZHAIGOU AND AUGUST 9, M6.6 XINJIANG JINGHE EARTHQUAKES OF 2017

The W-phase is a long period phase arriving between the P and S wave phases of a seismic source, theoretically representing the total near-and far-field long-period wave-field. Recent study suggests that the reliable source properties of earthquake with magnitude greater than ~M_W4.5 can be rapidly inverted by using the W-phase waveform data. With the advantage of W-phase, most of major earthquake research institutes in the world have adopted the W-phase based inversion method to routinely assess focal mechanism of earthquake, such as the USGS and GFZ. In this study, the focal mechanism of the August 8, 2017 M7.0 Sichuan Jiuzhaigou and August 9, 2017 M6.6 Xinjiang Jinghe earthquakes were investigated by W-phase moment tensor inversion technique using global seismic event waveform recordings provided by Incorporated Research Institutions for Seismology, Data Management Center. To get reliable focal mechanism, we strictly select raw waveform data and carry out inversion in stages. At first, we discard waveform without correct instrument information. Then we carry out an initial inversion using selected waveform data to get primary results. Using the preliminary results as input, we carry out grid-search based inversion to find the final optimal source parameters. The inverted results indicate that the August 8, M7.0 Sichuan Jiuzhaigou shock resulted from rupturing on a NW-trending normal fault with majority of strike-slip movement. The parameters of two nodal planes are strike 152.7°, dip 61.4°, rake -4.8° and strike 245.0°, dip 85.8°, rake -151.3° respectively, and focal depth is 14.0km. The August 9, Xinjiang Jinghe M6.6 shock resulted from rupturing on a south-dipping thrust fault with left-lateral strike-slip. The parameters of two nodal planes are strike 100.6°, dip 27.5°, rake 114.1° and strike 259.3°, dip 65.1°, rake 78.0°, and the focal depth is 16.0km. The direction of two nodal planes is consistent with regional seismotectonic background.     

Moment tensor inversion of some aftershocks of the April 18, 1985 Luquan earthquake of Yunnan Province, China

Based on the three component accelerograms, recorded at near-field distance by a temporary seismic network consisting of digital cassette tape recording accelerographs, the focal mechanisms of three aftershocks of the April 18, 1985, Luquan, Yunnan Province, China, earthquake ofM _S=6.1, are calculated using seismic moment tensor inversion technique. The phases of direct P, S and converted SP waves in the displacement seismograms, produced by twice integrations of the observed accelerograms, are identified via forward calculation using Green’s functions for homogeneous semi-infinite elastic medium, and used in the inversion. The results of inversion show that a better fit of synthetic to the observed seismograms of direct as well as converted phases can be achieved if appropriate weighting functions are used in solving the over definite linear equations. While these aftershocks are of different magnitudes (M _L=4.8, 3.2 and 3.5, respectively) and hypocentral locations, their focal mechanisms are very similar and consistent with that of the main shock. This feature demonstrates the intrinsic correlation between the occurrence of aftershocks and the seismogenic fault of main shock. Our experimentations show that using the near field accelerogram obtained from the digital seismic network with appropriate azimuthal coverage on the focal sphere, with the aid of even simple medium model, not only the shear dislocation source, but also the isotropic part and CLVD (compensated linear vector dipole) can be retrieved by the technique of moment tensor inversion. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 412–419, 1991. This work is supported by the Chinese Joint Seismological Sciences Foundation and the Western Yunnan Earthquake Prediction Test Site (WYEPTS), State Seismological Bureau.     

The 2011 Lorca seismic series: Temporal evolution,faulting parameters and hypocentral relocation

The Lorca 2011 seismic series was recorded by an unprecedented set of high quality on scale broadband seismograms and strong motion accelerograms. The waveforms from permanent and temporary broadband seismic networks deployed in the region by different institutions allowed to invert regional moment tensor for the fore, main and largest aftershock of the complete seismic sequence. Using double-difference algorithm we have performed a precise relocation of the seismic series, where body wave travel times from strong ground motion accelerograms were included in the data set. Regional moment tensor inversion for the three main events show similar oblique-reverse faulting regime with a northeast-southwest fault orientation. The scalar seismic moment, moment magnitude and focal depth retrieved from the inversion yield the following values for each event: \(\hbox {Mo}=6.5\times 10^{16}\) Nm (Mw = 5.2) for the mainshock, \(\hbox {Mo}= 9.6 \times 10^{15}\) Nm (Mw = 4.6) for the foreshock and \(\hbox {Mo}=7.3\times 10^{14}\) Nm (Mw = 3.9) for the large aftershock. The centroid depths range between 4 and 6 km. The double-difference relocation of the seismic series shows significant epicentral differences with the preliminary routine location. The epicentral solutions given by this relocation show a seismic sequence distributed following a NE–SW strike, subparallel to the Alhama de Murcia fault and compatible with the faulting parameters inverted from the moment tensor analysis. The hypocenters of the series generate a subvertical trend in depth distribution, being concentrated between 2 and 6 km. The depth distribution of the main events, which range from 4.6 to 5.5 km, is in good relationship with the faulting and depth parameters deduced from the moment tensor inversion technique. The regional moment tensor solutions for the three largest earthquakes, the epicentral distribution and the focal depths show good relationship with the surface geometry and tectonic regime of the Alhama de Murcia fault. The stress drop deduced for the mainshock gives a value ranging between 58 and 85 bars, which does not support the idea of a high stress drop release as a main factor contributing to the high ground acceleration recorded at Lorca. The PGA values observed at Lorca, which contributed to the high damage independently of structural deficiencies, could be generated mainly by shallowness and proximity to the seismic source together with a directivity effect in the seismic radiation.     

陕西地区小微震震源机制研究

小微震事件的震源机制是区域应力场及诸多地球动力学研究的基础资料。陕西地区为多个地震带的交汇区,近些年积累了丰富的小微震波形资料。运用新近发展的适用于求解小微震震源机制的广义极性振幅技术(GPAT),结合陕西2015地壳速度模型,求解陕西测震台网2011年4月至2015年12月间记录的121次ML1.5~3.5事件的震源机制。反演结果表明:(1)以上事件的震源机制大部分为走滑及正断类型,其比例占64.5%;逆断型机制占22.3%。(2)反演震源机制得到的震源深度与定位深度具有良好的一致性;矩震级与近震震级间存在差别,且这种差别随事件的变小而增大。(3)对比渭河断陷带相关研究成果,验证了该区域震源机制以正断型为主,具有拉张应力状态。     

2018年5月28日吉林松原MS5.7地震发震构造分析

利用黑龙江、吉林、内蒙古三省数字地震台网的三分量宽频带波形资料对2018年5月28日吉林省松原市宁江区发生的M_S5.7地震进行了全波形矩张量反演,获取了此次地震的震源机制解和矩心位置;并使用震源-矩心方法讨论了该地震的发震断层。研究结果显示:松原M_S5.7地震的矩震级为M_W5.2,矩心位置为（45.225°N,124.685°E）,矩心深度为7 km。震源机制解参数显示:该地震为走滑型;节面Ⅰ的走向、倾角和滑动角分别为217°,82°和164°;节面Ⅱ的走向、倾角和滑动角分别为309°,74°和8°;双力偶成分占96.4%,方差减少为93%。震源?矩心图显示震源更接近节面Ⅰ,与北东向的扶余—肇东断裂走向及倾角一致,因此,推测扶余—肇东断裂为发震断层。      

Inversion of near-field waveform data for earthquake source rupture process ( II ): Inversion of Chi Chi earthquake source, 20 September, 1999, Taiwan

The new inversion algorithm developed based on the recent progress in the nonlinear programming study by us is used to invert the earthquake source process of Chi Chi earthquake M _w7.6, 20 Semptember, 1999, Taiwan. A curve fault model is constructed in our inversion to make the fault model close to the real rupturing fault to reduce the influence from the discrepancy between the constructed fault model and the real rupturing fault. The results show that (1) the rupture process of the Chi Chi earthquake source lasted about 32 seconds and the main faulting occurred between 6th to 21st second after the start of the ruptures and the high slip area were mainly located at the northern segment of the fault. (2) The slip was dominated by thrust faulting. The average rake angle was 64.5°, which was very consistent with those inverted by USGS, Harvard and CWB (Central Weather Bureau of Taiwan). The amount of the moment inverted in this paper was 7.76×10²⁰ NM, which was a slightly bigger than those inverted by USGS and Harvard. (3) A clear nucleation step existed in the source faulting process and it lasted about 6 seconds. The moment release rate accelerated obviously at the end of the nucleation step. The faulting started from the southern segment and mainly occurred at the northern segment after 10 seconds. At the end of this paper, we analyzed the reliability of the inversion result via comparing with the GPS observations and discussed its scientific signification.     

Inversion of source process and related studies of the Taiwan Strait earthquake using genetic algorithm

Applying genetic algorithm to inversion of seismic moment tensor solution and using the data of P waveform from digital network and initial motion directions of P waves of Taiwan network stations, we studied the moment tensor solutions and focal parameters of the earthquake of M=7.3 on 16 September of 1994 in Taiwan Strait and other four quakes of M _L≥5.8 in the near region (21°–26°N, 115°–120°E). Among the five earthquakes, the quake of M=7.3 on September 16, 1994 in Taiwan Strait is the strongest one in the southeastern coast area since Nan’ao earthquake of M=7.3 in 1918. The results show that moment tensor solution of M=7.3 earthquake is mainly double-couple component, and is normal fault whose fault plane is near NW. The strike of the fault plane resembles that of the distributive bands of earthquakes before the main event and fracture pattern shown by aftershocks. The tension stress axis of focal mechanism is about horizontal, near in NE strike, the compressive stress axis is approximately vertical, near in NWW strike. It seems that this quake is controlled by the force of Philippine plate’s pressing Eurasian plate in NW direction. But from the viewpoint of P axis of near vertical and T axis of near horizontal, it is a normal fault of strong tensibility. There are relatively big difference between focal mechanism solution of this quake and those of the four other strong quakes. The complexity of source mechanism solution of these quakes represents the complexity of the process of the strait earthquake sequences. Contribution No. 98A01001, Institute of Geophysics, State Seismological Bureau, China. The subject is supported and helped by Academician Yun-Tai CHEN, Profs. Qing-Yao HONG, Zhen-Xing YAO, Tian-Yu ZHENG, Yao-Lin SHI, Ji-An XU, Bo-Shou HUANG and colleague Mei-Jian AN, Xue-Reng DING, Rui-Feng LIU. De-Chong ZHANG and Ming Li provided the digital data warm-heartedly. Lin-Ying WANG offered us the catalogue of earthquakes in southeastern coastal area in China. Xi-Li WANG and Tong-Xia BAI provided us the issued annual reports data. The authors would like to express their gratitude to all of these people. This paper is sponsored by the National Natural Science Foundation of China and Scientific and Technological Commission of Shantou, Guangdong Province.     

Source process of the 1990 Gonghe,China, earthquake and tectonic stress field in the northeastern Qinghai-Xizang (Tibetan) plateau

TheM _s =6.9 Gonghe, China, earthquake of April 26, 1990 is the largest earthquake to have been documented historically as well as recorded instrumentally in the northeastern Qinghai-Xizang (Tibetan) plateau. The source process of this earthquake and the tectonic stress field in the northeastern Qinghai-Xizang plateau are investigated using geodetic and seismic data. The leveling data are used to invert the focal mechanism, the shape of the slipped region and the slip distribution on the fault plane. It is obtained through inversion of the leveling data that this earthquake was caused by a mainly reverse dip-slipping buried fault with strike 102°, dip 46° to SSW, rake 86° and a seismic moment of 9,4×10¹⁸ Nm. The stress drop, strain and energy released for this earthquake are estimated to be 4.9 MPa, 7.4×10^–5 and 7.0×10¹⁴ J, respectively. The slip distributes in a region slightly deep from NWW to SEE, with two nuclei, i.e., knots with highly concentrated slip, located in a shallower depth in the NWW and a deeper depth in the SEE, respectively.Broadband body waves data recorded by the China Digital Seismograph Network (CDSN) for the Gonghe earthquake are used to retrieve the source process of the earthquakes. It is found through moment-tensor inversion that theM _s =6.9 main shock is a complex rupture process dominated by shear faulting with scalar seismic moment of the best double-couple of 9.4×10¹⁸ Nm, which is identical to the seismic moment determined from leveling data. The moment rate tensor functions reveal that this earthquake consists of three consecutive events. The first event, with a scalar seismic moment of 4.7×10¹⁸ Nm, occurred between 0–12 s, and has a focal mechanism similar to that inverted from leveling data. The second event, with a smaller seismic moment of 2.1×10¹⁸ Nm, occurred between 12–31 s, and has a variable focal mechanism. The third event, with a sealar seismic moment of 2.5×10¹⁸ Nm, occurred between 31–41 s, and has a focal mechanism similar to that inverted from leveling data. The strike of the 1990 Gonghe earthquake, and the significantly reverse dip-slip with minor left-lateral strike-slip motion suggest that the pressure axis of the tectonic stress field in the northeastern Qinghai-Xizang plateau is close to horizontal and oriented NNE to SSW, consistent with the relative collision motion between the Indian and Eurasian plates. The predominant thrust mechanism and the complexity in the tempo-spatial rupture process of the Gonghe earthquake, as revealed by the geodetic and seismic data, is generally consistent with the overall distribution of isoseismals, aftershock seismicity and the geometry of intersecting faults structure in the Gonghe basin of the northeastern Qinghai-Xizang plateau.Contribution No. 96 B0006 Institute of Geophysics, State Seismological Bureau, Beijing, China.     

Use of long-period surface waves for rapid determination of earthquake-source parameters

A method for rapid retrieval of earthquake-source parameters from long-period surface waves is developed. With this method, the fault geometry and seismic moment can be determined immediately after the surface wave records have been retrieved. Hence, it may be utilized for warning of tsunamis in real time. The surface wave spectra are inverted to produce either a seismic moment tensor (linear) or a fault model (nonlinear). The method has been tested by using the IDA (International Deployment of Accelerographs) records. With these records the method works well for the events larger than M_s = 6, and is useful for investigating the nature of slow earthquakes.For events deeper than 30 km, all of the five moment tensor elements can be determined. For very shallow events (d ? 30 km) the inversion becomes ill-conditioned and two of the five source moment tensor elements become unresolvable. This difficulty is circumvented by a two-step inversion. In the first step, the unresolvable elements are constrained to be zero to yield a first approximation. In the second step, additional geological and geophysical data are incorporated to improve the first approximation. The effect of the source finiteness is also included.     

On the limits of linear moment tensor inversion of surface wave spectra

Some theoretical and practical limits to linear moment tensor inversion of surface waves are analyzed in detail, in particular when one or few stations are used for rapid determination of source parameters. The theory is briefly outlined and steps of preprocessing, especially corrections for source history and propagation, are discussed in order to guarantee the validity of the moment tensor inversion. The inverse problem is first studied from a theoretical point of view. Then the feasibility of the moment tensor inversion is tested from synthetic computations and the formalism is improved in order to obtain a better system conditioning. Finally, some cases of practical nonuniqueness of the solution are shown and possible restrictions to the applicability of the method are discussed. All steps are illustrated with the example of theM _s =6.9 Erzincan (Turkey) earthquake of March, 13, 1992.