地震矩张量及其反演

用地震矩张量描述一般类型的地震点源时,二阶矩张量是可以用来简明地表征震源特征的物理量。比如,可用它将震源表示为膨胀中心和双力偶的叠加。二阶地震矩张量可以分解成各向同性部分和纯偏量部分的相加,并且对偏量部分还可作多种形式的分解。本文通过对在主轴坐标系下的矩张量本征值的不同组合,给出了几种矩张量分解的形式及由它们所确定的等效点源模型,并根据本征值的大小,讨论了点矩张量所表示的震源机制解。本文还介绍了反演地震矩张量的方法。     

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.     

根据震源的两个节面的走向角和倾角求滑动角

文中推导了双力偶点源模型震源机制解得出的震源参数和用地震矩张量反演得出的震源参数之间的转换关系。并给出了实例的计算结果     

一种矩张量反演新方法及其对2008年汶川MS8.0地震序列的应用

本文利用全球地震台网（GSN）的宽频带与长周期地震波形资料,采用矩张量反演的新方法,反演得到了2008年5月12日四川省汶川县MS8.0地震及其7个较大余震（MS5.0-6.0）的矩张量解与震源时间函数等震源参数.文章首先简要叙述矩张量反演新方法的理论背景和技术途径,并以汶川大地震的一个余震为例阐述了具体的实现过程;然后给出包括主震在内的8次地震的矩张量解和震源时间函数;最后分析探讨这些结果的构造意义.本文提出的矩张量反演新方法,不但与全球矩心矩张量（GCMT）一样,可以给出点源矩张量解,而且还可以给出点源的震源时间函数. 反演得到的汶川大地震的7个较大余震的震源时间函数表明,即使是中等强度的地震也可能有复杂的震源过程;汶川大地震的多数余震发生在以逆冲为主、兼具小量走滑分量的龙门山断裂带的主断裂上,但很可能有些余震则发生在主断裂附近的次级走滑断裂上.      

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.     

2009年11月至2010年11月27次中强地震的快速矩张量解

经过半个世纪的发展,地震震源的矩张量表示及其反演已日臻成熟(Dziewonski,Woodhouse,1983).矩张量解不但能够较好地反映地震震源的特性,还能为其它研究提供有用的参考.一些科研机构和组织,如美国地质调查局(USGS)和全球矩心矩张量研究组(GCMT)已经能够在震后5小时内准实时地发布矩     

黏弹性VTI介质微地震正演模拟与震源机制全波形反演

微地震矩张量能够描述储层岩石破坏的细节,有助于了解水力压裂储层的地质力学特征,震源机制矩张量反演对于非常规油气开发具有重要的作用.水力压裂通常在页岩油气储层中进行,震源区介质表现出速度和衰减各向异性,需要研究衰减各向异性介质中微地震信号的传播规律.基于观测到的微地震记录,通过波形反演能够获得矩张量,忽视震源区介质的衰减...     

震源深度误差对矩张量反演的影响

在用矩张量反演方法确定地震的震源机制和震源的破裂过程时，由于测定震源深度的误差，很难保证计算格林函数时所采用的震源深度(理论震源深度)和实际震源深度完全相等．理论震源深度和实际震源深度的差异(震源深度误差)对矩张量的反演或多或少会造成影响．借助于合成地震图较系统地讨论了震源深度误差对3种基本类型(正断层、逆断层和走滑断层)的震源反演造成的影响．对于正断层和逆断层，震源深度误差主要影响各向同性成分和补偿线性向量偶极成分．在理论震源深度大于实际震源深度时:对于正断层，震源深度误差导致出现虚假的正的各向同性分量和负的补偿线性向量偶极分量；随着差异的增大其绝对值逐渐增大；对于逆断层，震源深度误差导致出现虚假的负的各向同性分量和正的补偿线性向量偶极分量，其绝对值随着震源深度误差的增加而增加．在理论震源深度小于实际震源深度时，结果恰好相反:对于正断层，震源深度误差产生了虚假的负的各向同性分量和正的补偿线性向量偶极分量；对于逆断层，震源深度误差产生了虚假的正的各向同性分量和负的补偿线性向量偶极分量．同样，随着深度误差的增大，它们的绝对值也逐渐增大．对于走滑断层，震源深度误差对矩张量反演的影响则不同于正断层和逆断层两种情况，受影响最大的是震源时间函数的形状．无论理论震源深度小于还是大于实际震源深度，震源时间函数的形状都发生不同程度的拖尾现象．数字试验表明，当震源深度误差小于20 km时对于地震的总体机制的反演没有明显影响．另外，当理论震源深度大于实际震源深度时，震源深度误差对矩张量反演的影响相对较小．      

用远场资料反演西藏玛尼地震的高阶地震矩张量

采用扩展震源模型测定出更多的震源参数 .我们把震源用高阶地震矩张量表示 .为了减少在高阶地震矩张量表达式中出现的大量项 ,采用了 Haskell断层模型 .利用 GSN台网 32个台站的宽频带体波资料 ,反演了西藏玛尼地震的震源参数 .通过实际计算表明 ,该震源是一个走滑断层 ,破裂方向 75°,断层面为=77°、δ=88°,λ=0°,辅助面为=347°、δ=90°、λ=1 78°,破裂持续时间为 1 9s,断层尺度为 47km× 2 8km.这些结果将为地球动力学研究提供新的定量资料 ,对于震源层析成像研究等有实际意义 .     

近震源宽频带记录的地震矩张量反演

以1985年4月18日云南禄劝地震(Ms=6.1)的15次余震为例, 使用简单介质模型进行近震源记录的地震矩张量反演, 并试图通过反演结果的讨论, 进一步明确有关方法的意义和限度。将DCS-302数字磁带加速度仪组成的小孔径流动台网获得的三分向近震源宽频带记录进行两次积分得到位移地震图, 对依据震相特征选出的信噪比较大的直达P波、直达S波和SP转换波波形在频率域进行矩张量反演。反演中采用均匀弹性半空间的格林函数。计算结果表明, 采用简单的介质模型, 选取信噪比较大的震相进行矩张量反演, 对MLL约为4-5的地震可以较好地给出震源机制解。在不十分了解详细结构的情况下, 用本文所发展的反演方法处理大量中小地震求震源机制和构造应力场是十分便利的。地震矩张量反演的结果给出禄劝地区的主压应力轴为近NNW向, 接近水平, 表明该地震与欧亚板块和印度板块边界的构造运动有关。      

Decomposition of seismic moment tensors for underground nuclear explosions

Generally the decomposition of a seismic moment tensor is not unique. However, to favorably view the characteristics of a certain seismic source, one must decompose a seismic moment tensor into parts according to assumptions about the properties of the seismic source. Different from natural earthquakes in which the shear dislocation component plays a predominant role in the source process, and the seismic moment tensor can be separated into an isotropic component, a double couple, and a compensated linear vector dipole (CLVD), underground nuclear explosions have three major components in their source process, i.e., the explosion, the tensional spalling, and the tectonic strain release associated with the explosion. In such a situation the conventional moment tensor decomposition for earthquakes is not convenient to estimate the yield of the explosion and to characterize the tectonic strain release. In this paper, an alternative decomposition scheme is proposed to deal with the moment tensor of underground nuclear explosions, which might benefit the approach to study the tectonic strain release induced by underground nuclear detonations.     

断层厚度的地震效应和非对称地震矩张量

本文导出了具有厚度和滑动弱化区域的断层的非对称地震矩张量表示式,指出要求地震矩张量具有对称性不是一个绝对必要的限制.在非对称地震矩张量中,位错项对应于对称地震矩张量,拉力项对应于非对称地震矩张量.由于拉力项等效于单力偶,所以在非对称地震矩张量解的两个节面上,沿滑动矢量方向的力偶强度不再相同,与较大力偶相联系的节面为断层面,与较小力偶相联系的节面为辅助面.这一性质可用以从两个正交的节面中判断哪一个节面是断层面.如果忽略拉力项,会高估与位错对应的标量地震矩.只有满足相应的约束条件的非对称地震矩张量才能表示具有厚度和滑动弱化区域的断层模型,并从中分离出与位错和拉力对应的地震矩张量.     

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.     

The determination of the best fitting and the extreme source models by a global inversion method

In this paper, a global inversion method is developed for seismic moment tensor inversion by using the body wave forms. The algorithm depends on neither the selection of starting model nor the forms of objective function and constraints. When the error function, measure of the difference between the observed and synthetic waveforms, is chosen as the objective function, the best fitting source model is found; when a certain combination in seismic moment tensor elements is selected as the objective function and the values of error function are constrained in a suitable bound, the extreme source models can be produced by minimizing or maximizing this combination. By changing the form of the combination of moment tensor elements, a variety of different source characteristics can be considered. Therefore the extreme solution provides an estimation of the uncertainty in the best fitting source model. The seismic waveform data was used to evaluate the effectiveness of this algorithm. This research was supported by the National Natural Science Foundation of China.     

Ambiguous Moment Tensors and Radiation Patterns in Anisotropic Media with Applications to the Modeling of Earthquake Mechanisms in W-Bohemia

Anisotropic material properties are usually neglected during inversions for source parameters of earthquakes. In general anisotropic media, however, moment tensors for pure-shear sources can exhibit significant non-double-couple components. Such effects may be erroneously interpreted as an indication for volumetric changes at the source. Here we investigate effects of anisotropy on seismic moment tensors and radiation patterns for pure-shear and tensile-type sources. Anisotropy can significantly influence the interpretation of the source mechanisms. For example, the orientation of the slip within the fault plane may affect the total seismic moment. Also, moment tensors due to pure-shear and tensile faulting can have similar characteristics depending on the orientation of the elastic tensor. Furthermore, the tensile nature of an earthquake can be obscured by near-source anisotropic properties. As an application, we consider effects of inhomogeneous anisotropic properties on the seismic moment tensor and the radiation patterns of a selected type of micro-earthquakes observed in W-Bohemia. The combined effects of near-source and along-path anisotropy cause characteristic amplitude distortions of the P, S1 and S2 waves. However, the modeling suggests that neither homogeneous nor inhomogeneous anisotropic properties alone can explain the observed large non-double-couple components.The results also indicate that a correct analysis of the source mechanism, in principle, is achievable by application of anisotropic moment tensor inversion.     

On the possibility of detecting complex sources of earthquakes from data of the centroid moment tensor catalog

In their analysis of the crustal stress-strain state and the study of strong earthquake sources, a number of authors use the parameter ? measuring the deviation of the focal mechanism from the double-couple model. Can one obtain reliable estimates of ? from regular determinations of the seismic moment tensor components made at world seismological centers and use these estimates to gain constraints on the rupture at the source? Comparing centroid moment tensor solutions of Harvard University with determinations made at the National Earthquake Information Center (United States) and analyzing some strong earthquakes, we arrive at a negative answer to this question. The values of ? and the consideration of determination uncertainties in seismic moment tensor components cannot provide a reliable idea of the source complexity, so that independent geological and geophysical information should be invoked.     

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.     

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.