Inversion of free oscillation data for an elliptical rotating earth in source moment tensor studies

It is shown, through numerical experiments, that the effect of ignoring ellipticity and rotation of the earth when inverting free oscillation data in moment tensor studies, is to introduce spurious spectral components in the solution. For numerical simulation of the data conditions of the 1970 deep Colombian event the spurious part has isotropic and deviatoric components, besides a distortion in the phase spectra which may lead to artificial precursive source in the solution. The magnitude of the artificial isotropic component is of the order of 10% of the real source moment tensor, depending on the data set used in the inversion. Measuring the excitation of each mode at each station using the technique of integrating over the spectral peaks does not cancel completely the effect of multiplet splitting, in particular that splitting due to rotation of the earth. The effect of lateral heterogeneities was simulated by introducing arbitrary splitting parameters which produced scattering in the eigenperiods compatible with those observed. For that splitting the inversion rendered additional isotropic components.We conclude that the observed implosive precursor the the 1970 Colombian event could have been artificially introduced by ignoring rotation, ellipticity and lateral heterogeneities of the earth.A procedure to invert free oscillation data for an elliptical rotating earth is proposed. It could be applied to a laterally inhomogeneous earth if the excitation for that model could be computed. Its application to real data for the deep Colombian event indicates that we will need to improve our knowledge on the effect of rotation, ellipticity, lateral heterogeneities and anelasticity on free oscillation and their excitation in order to solve accurately for the six components of the moment tensor independently.     

On the observability of isotropic seismic sources: The July 31, 1970 Colombian earthquake

Theoretical calculations are made to study the observability of isotropic components of seismic sources. In particular we consider the 1970 deep Colombian earthquake, for which a precursory isotropic component was previously reported by Gilbert and Dziewonski.We compare an ultra-long period vertical record at Pasadena of the 1970 event to synthetic seismograms calculated both for Gilbert and Dziewonski's source model and for the pure double-couple source of Furumoto and Fukao, and obtain better overall agreement for the latter. The amplitude of the long-period synthetic for the isotropic source is about 5–15 times smaller than the synthetic for the deviatoric source, suggesting that the data may be relatively insensitive to the presence of a small isotropic source. When this possibility was tested, the overall agreement was found to be almost completely insensitive to the presence of even a reasonably large isotropic component.However, the isotropic source was derived from multi-station moment tensor inversion, rather than from single-station studies. A numerical experiment on the effect of lateral heterogeneity of eigenfrequencies and of Q on the inversion for the moment tensor shows that even relatively small amounts of heterogeneity can produce spurious isotropic sources from moment tensor inversion.     

非对称地震矩张量时间域反演:理论与方法

本文在对称地震矩张量反演的基础上,进一步研究了非对称地震矩张量时间域反演的理论与方法,结果表明:非对称地震矩张量反演与对称地震矩张量反演类似,只需将对称地震矩张量反演方法略加改动,即增加3个待解参数,便可实现非对称地震矩张量反演.为了判断非对称地震矩张量反演相对于对称地震矩张量反演是否存在过度拟合,运用了AIC准则 (赤池信息准则).为了定量地描述地震矩张量之间的差异,引入了地震矩张量的矢量表示法.通过分析格林函数与地震矩张量各分量之间的关系,得出:在非对称地震矩张量反演时,若仅用垂直向地动位移数据,将无法区分M_xy与M_yx这两个分量, 需要同时运用垂直向与水平向地动位移数据进行联合反演才能区分M_xy与M_yx; 若采用不同的速度结构模型或不同的格林函数计算方法,则需重新评估地震矩张量各分量的分辨度问题.为检验非对称地震矩张量反演方法的可行性, 利用合成地震图进行了一系列数值试验.数值试验结果表明,在非对称地震矩张量反演中,有必要引入S波进行P波与S波联合反演以提高反演的准确性和判定断层面的能力.      

Full moment tensor inversion constrained by double-couple focal mechanism for induced seismicity*

In this study, we propose a new method to determine full moment tensor solution for induced seismicity. This method generalizes the full waveform matching algorithm we have developed to determine the double-couple (DC) focal mechanism based on the neighbourhood algorithm. One major difference between the new method and the former one is that we adopt a new misfit function to constrain the candidate moment tensor solutions with respect to a reference DC solution in addition to other misfit terms characterizing the waveform matching. Through synthetic tests using a real passive seismic survey geometry, the results show the new constraint can help better recover the DC components of inverted moment tensors. We further investigate how errors in the velocity model and source location affect the moment tensor solution. The synthetic test results indicate that the constrained inversion is robust in recovering both the DC and non-DC components. We also test the proposed method on several real induced events in an oil/gas field in Oman using the same observation system as synthetic tests. While it is found that the full moment tensor solutions without using the DC constraints have much larger non-DC components than solutions with the DC constraints, both solutions are able to fit the observed waveforms at similar levels. The synthetic and real test results suggest the proposed DC constrained inversion method can reliably retrieve full moment tensor solutions for the induced seismicity.     

Discrimination of induced seismicity by full moment tensor inversion and decomposition

Human activities, including operations related to mining and reservoir exploitation, may induce seismicity and pose a risk for population and infrastructures. While different observations are commonly used to assess the origin of earthquakes, there is a lack of rules and methods for the discrimination between natural and induced seismicity. The inversion and decomposition of the full moment tensor and the observation of relevant deviation from a pure double couple (DC) model may be an indicator for induced seismicity. We establish here a common procedure to analyse a set of natural and induced events of similar magnitude, which occurred in Germany and neighbouring regions. The procedure is based on an inversion method and on a consistent velocity model and recording network. Induced seismicity is recorded during different mining and/or reservoir exploitations. Moment tensors are inverted using a multi-step inversion approach. This method, which was successfully applied in previous studies at regional and teleseismic distances, is further developed here to account for full moment tensor analysis. We first find a best DC solution and then perform a full moment tensor inversion, fitting full waveforms amplitude spectra at regional distances. The moment tensor solution is decomposed into DC, compensated linear vector dipole and isotropic terms. The discrimination problem is then investigated through the evaluation of distributions of non-DC source components for natural and induced data sets. Results illustrate the potential of the inversion and discrimination approach. Additional detailed analyses are carried out for the two most significant induced earthquakes, and rupture models are compared with the full moment tensor solutions.     

用应变地震观测求解震源矩张量的基本原理

震源机制解,即对地震矩张量的推断,对于地震研究具有至关重要的意义.应变地震观测是张量观测,与摆式地震仪的位移矢量观测不同,可以为地震研究提供新的数据源.本文讨论用应变地震观测求解震源矩张量的基本原理.在距离震源足够远的地方,地震波可以看成平面波,其性质决定于震源矩张量.假设平面地震波的应变张量可以由震源矩张量通过坐标变换计算得到,就可以通过观测应变地震波求解震源机制.这个假设至少对于双力偶震源机制是成立的.由此可以证明,在理想的无限介质中,只要有两个以上不同地点的应变地震波观测,就可以解出震源矩张量.这为解决震源机制问题提供了新的方法.目前的地震矩张量求解方法需要两方面的条件:或者需要很多观测点(例如体波反演),或者需要长周期地震波资料(例如面波反演).这些方法只适用于分析比较大的地震.对于小震,因为通常其震中周围不会有足够多的摆式地震仪观测点观测到其地震波,而地震波周期又短,难以利用传统方法给出可靠的震源机制解,所以只需少数观测点就能求解震源矩张量的新方法特别有意义.用应变地震观测求解震源机制,可以给出更为精确的结果.     

Shear-tensile crack as a tool for reliable estimates of the non-double-couple mechanism: West Bohemia-Vogtland earthquake 1997 swarm

Shear-tensile crack is a model for an earthquake mechanism that is more constrained than the moment tensor but that can still describe a non-shear focus. As such, the shear-tensile crack model is more robust than the moment tensor model and yields more reliable estimates for the earthquake mechanism. Such an advantage verifies the credibility of the non-double-couple component found for some events of the 1997 West Bohemia-Vogtland earthquake swarm. As expected, in several cases, a significantly resolved non-double-couple component was obtained where the moment tensor approach failed. Additionally, for non-shear sources, the shear-tensile crack model offers optimization of the Poisson number within the focus, concurrently with retrieval of the mechanism. However, results obtained for the joint inversion of the 1997 swarm indicate that resolution is low. A series of synthetic experiments indicated that limited observations during 1997 were not the cause. Rather, hypothetical experiments of both very good and extremely poor network configurations similarly yielded a low resolution for the Poisson number. Applying this method to data for recent swarms is irrelevant because the small non-double-couple components detected within the inversion are spurious and, thus, the events are pure double-couple phenomena.     

2013年前郭MS5.8震群矩张量研究

2013年吉林前郭M_S5.8震群为爆发性震群,目前余震活动仍然在持续.基于吉林、辽宁、黑龙江、内蒙古四省地震台网记录的前郭震群波形资料,利用波形信噪比、震源类型、台站及速度模型组合的指标选择最佳的反演方案,应用矩张量的三种反演模式,对序列中5个M_S≥5.0地震进行矩张量反演研究,获得了全矩张量、偏矩张量和纯双力偶的矩张量.使用F-test对地震的三种模式的矩张量反演结果进行显著性检验来确定最佳反演模式.结果显示,5个地震的最优矩张量解均为全矩张量模式反演获得的结果,其双力偶分量仅有20%~65%,矩心深度位于地下3~4 km处,地震在Hudson震源类型图上的投影远离双力偶震源类型区域.这些结果表明,震源类型并非典型的构造地震,推断前郭地震可能是与人类活动有关的诱发地震.     

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．      

利用区域台网快速自动反演中等强度地震矩张量

震后快速得到地震矩张量, 可以更好地为烈度速报、 应急救援和震后趋势判定等服务。 本文基于中国区域地震台网现状, 对Dreger的矩张量反演方法进行改进。 结合区域地震速报系统, 将系统触发、 地震相关信息与地震波形记录获取、 矩张量反演计算和最佳解挑选等过程实现自动化, 建立了地震矩张量快速自动反演系统。 将该系统在线运行于福建地震台网, 实现了对闽台地区中等强度地震的矩张量在线快速自动反演。 将反演结果与其他研究机构的结果对比, 验证了本文方法的可靠性。     

Seismic Moment Tensor Resolution on a Local Scale: Simulated Rockburst and Mine-induced Seismic Events in the Kopanang Gold Mine, South Africa

Seismic records contain information about the effect of the source as well as the effect of wave propagation through the rock mass. The effect of wave propagation is usually not well known as only simplified models of geological structures are available. Therefore, the information about the source retrieved by inverting seismograms may include errors due to incomplete knowledge of the rock mass along the propagation path, which in turn cause a distortion in the calculated moment tensor (MT). The distortion of the MT on a local scale was observed by inverting records of a simulated rockburst conducted at the Kopanang gold mine in South Africa. A dominant isotropic component of the explosive characteristics was found from the inversion. The deviatoric components retrieved from the blast are spurious. A test of their stability indicated that they are not significant, assuming an uncertainty above 5% for velocities and 10% for attenuation within the homogeneous model available for the mine. Thus, the retrieval of the MT from records of local networks in mines using a homogeneous model of the rock mass seems to be feasible. However, the homogeneous model of the rock mass can only be applied to close stations, within a few kilometers of the source. The seismic records from distant stations were too complex to be modelled by a homogeneous rock mass. Records of six mine-induced seismic events recorded at the Kopanang gold mine were also inverted. A vertical linear dipole along the pressure (P) axis was found for three of the events, suggesting a pillar burst. The mechanism of two events contains an isotropic implosion together with a nearly vertical dip-slip, and seems to indicate a combination of a cavity collapse with a down dip-slip along a nearly vertical fault. One event corresponds to a dipole along the tensional (T) axis. However, it is vertical, thus its association with tensile faulting of the hangingwall is uncertain.     

Inversion of seismograms to determine simultaneously the moment tensor components and source time function for a point source buried in a horizontally layered medium

Summary A method of determining simultaneously the moment tensor and source time function in the point source approximation is presented. For trial values of the moment tensor components and of the source time function, parametrized by the sum of overlapping triangles delayed in time, theoretical seismograms can be synthetized and compared with the recorded ones. The iterative procedure determines the adjustment of source parameters until a good correlation of both synthetic and observed records is reached. The Green functions in a horizontally stratified medium are constructed with the use of a modal summation method.The limits of applicability of the algorithm are illustrated by the inversion of four synthetic seismograms constructed for two horizontally stratified models of the structure in Friuli area, Italy. The records constructed for the same structural model as for which the Green functions were computed can be inverted even in the high-frequency range. In the opposite case, when the records and Green functions used corresponded to different structural models, a good correlation of the input records with the final synthetics was obtained for low - pass filtered data only.Additional tests performed with input seismograms contaminated with random noise yielded good resolution of the moment tensor and the duration of the source time function even for a high noise to signal ratio.     

Moment Tensor Inversion of Regional Phases: Application to a Mine Collapse

—?The aim of our study consists of analyzing potentially non-double-couple seismic events recorded at regional distances. In order to define the nature of the seismic source, a moment tensor inversion is carried out as this method is general enough not to initially constrain the source mechanism. In this paper we present an application to a seismic event induced by a mine collapse which occurred near the town of Halle in Germany. Because of its induced nature, many parameters such as the location and geometry of this seismic source are known. This information allows us to test the influence of inadequate propagation modeling on the moment tensor obtained from the inversion. Green's functions have been computed with the reflectivity method in a flat layered medium, using the European model EurID (Du et? al., 1998; Dufumier et al., 1997). From the inversion of P-wave seismograms recorded by the German Regional Seismic Network will, we obtained a source time function which can be decomposed into two subevents. The first one has a large isotropic part and a deviatoric mechanism with near vertical nodal planes. No volume change is observed for the second subevent, but a deviatoric component opposite of the first one. The addition of S-waves does not change the results of the inversion which are stable. Surface waves were not used because of their poor dispersion curves. Based on the moment tensor obtained from these inversions, the physical process at the source is compatible with a large cavity collapse.     

2007年甘肃部分地震的震源参数反演

2007年甘肃测震台网记录到M_L>3.0的地震43次,本文选取了其中17例,利用垂直向PG波初动波形进行了地震矩张量反演,给出了最佳双力偶解,并对一些地震发震背景和发震机理进行了分析讨论.对地震机理研究及未来地震预报提供了参考依据.     

区域台网地震矩张量快速反演系统研究

基于美国内华达大学地震实验室的矩张量反演程序,采用JAVA和HTML语言,研发了一套近实时全波形矩张量快速反演系统,用于区域台网地震矩张量的快速产出.该系统由区域地震速报系统触发,能自动实现中等强度地震矩张量的快速反演,同时也包含人机交互模块,可进行人工校正,最终以网页形式对外服务.本文将系统运行以来成功反演的结果与USGS和中国地震局地球物理研究所的计算结果进行对比,验证了该系统的可靠性.      

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.     

2009年4月6日意大利拉奎拉(L＇Aquila)地震快速矩张量解.

2009年4月6日1点32分42秒协调世界时（UTC）,在意大利中部地区发生了MW6.4地震．作者利用矩张量快速反演技术,通过反演全球台网的宽频带P波波形得到了这次地震的矩张量解,并判断走向132deg;、倾角53deg;、滑动角——103deg;的节面是地震发生的断层面．      

2017年9月23日朝鲜ML3.4地震矩张量反演

利用区域地震台网数字波形资料,对2017年9月23日朝鲜M_L3.4地震进行地震矩张量反演计算与参数稳定性评估,获得了此次地震的震源机制解.结果表明,地震矩心深度为3 km,标量地震矩为1.34×10¹⁴ N·m,矩震级为M_W3.4.地震矩张量结果分解后,双力偶分量（DC）为96.4%,补偿线性矢量偶极分量（CLVD）为-0.8%,震源体体积变化的各向同性分量（ISO）为-2.8%.主压应力P轴方位角为144°,倾角为74°,主张应力T轴方位角为341°,倾角为15°.其中一个节面的参数为：走向248°,倾向60°,滑动角-94°.地震震源体积变化分量很小,震源机制类型属于典型的由断层剪切位错引起的正断层型地震事件,且主张应力T轴方向与区域近地表应变率场方向一致.由于朝鲜2017年9月3日核试验释放的能量对局部区域应力场进行了扰动,致使核试验场附近地壳岩体处于破裂的临界状态,2017年9月23日朝鲜M_L3.4地震事件可能是区域应力场作用下的一次山体滑动事件.     

2011年云南腾冲5.2级双震发震机理

本研究联合使用观测震相到时和波形互相关数据,采用双差法对2011年6月20日与8月9日发生在云南腾冲的5.2级双震及其余震序列进行重定位,并采用gCAP(generalized Cut and Paste)方法反演了该双震全矩张量解.结果显示,双震震中位于龙川江断裂的西侧,余震序列在深度上为一个倾斜的柱状体,且倾向腾冲火山区;6月20日和8月9日5.2级地震均表现为体积缩小的闭合型破裂,包含有显著的非双力偶成分,但后者包含的非双力偶成分相对明显减小.这些结果表明,云南腾冲5.2级双震及余震活动可能与火山下方的地壳岩浆作用密切相关,龙川江断裂为热物质向上运移提供了通道,而双震型地震的发生可能与首次地震的破裂体积缩小挤出的流体作用于断裂密切相关.