用全局反演方法确定地震震源的最佳和极端模型

本文发展了一种利用波形资料反演地震矩张量的全局方法．这种方法不依赖于初始解的选择，也不受目标函数和约束条件的具体形式限制．当以记录图与理论地震图的误差函数作为目标函数时，用该方法得到的是震源最佳模型；当分别以矩张量分量某种组合的最小或最大为目标，约束误差函数在允许的界限内，能够得到震源的极端模型．由于许多震源性质可以用矩张量分量的组合表示，因此极端模型能够估计出最佳模型的不确定性范围．我们利用一真实地震的波形资料反演结果，证明了这个方法的有效性．      

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．      

利用单台波形资料计算大柴旦6．3级地震余震震源机制

以2008年11月10日大柴旦Ms6．3级地震余震数字地震波观测资料为基础,运用矩张量反演方法,利用单台三分量波形资料计算余震的震源机制。收集整理大柴旦Ms6．3级地震公认的震源参数结果和青海区域地震台网数字地震波资料,以大柴旦Ms6．3级地震的震源参数作为约束,计算理论地震波来确定该区域的地壳速度模型。以此模型计算ML≥2．0级余震震源机制解。共收集160个余震资料,最后确定了85个余震震源机制解,其中最大震级为朋。4．7,最小震级为ML2.0。进行单台与多台联合矩张量反演结果对比,两种方法所确定的结果相差不大。实际计算表明,在观测资料信噪比较高的情况下,运用单台数字地震波观测资料可以较好地确定中小地震的震源机制。     

CAP方法反演震源机制的误差分析:以胶东半岛两次显著中等地震为例

利用区域波形数据使用CAP方法反演中强地震的震源机制正逐渐得到广泛应用.本文以胶东半岛近期发生的两次显著中等地震为例,讨论了使用CAP方法反演震源机制时的误差估计,展示了反演结果的不确定性分析过程.2013年11月23日和2014年1月7日在山东莱州和乳山分别发生了M4.6和M4.3级中等地震,两次事件均造成了较大影响.我们基于CAP方法,使用自助抽样(bootstrap)技术多次重复反演过程,得到大样本量的震源机制解数据;基于这些数据,使用粒子群算法和聚类分析技术给出了优化解,估计了震源机制解的误差范围,并利用震源机制解的P、T轴给出了震源球上的概率密度分布.     

利用地球自由振荡观测约束芦山地震的震源机制解

地球自由振荡的振幅和地震的震源机制有密切的关系．利用长周期自由振荡的观测可对地震的震源机制解进行分析和约束．芦山地震虽然是中等强度的地震,但也激发了可观测的自由振荡信号．根据芦山地震的4种不同震源机制解计算了芦山地震的自由振荡,然后与超导重力仪和宽频带地震仪观测的结果进行比对分析,结果表明可利用2．3～5mHz的球型简正模分析和约束芦山地震的震源机制解．研究发现地震的标量地震矩Mo对自由振荡振幅的影响较大,而断层走向、倾角、滑动方向角和震源深度对自由振荡的振幅影响较小．分析了不同震源机制解理论计算的地球自由振荡参数,发现由GCMT反演的地震矩与实际观测符合较好,其相应的震级能较好反映芦山地震释放的总能量,而利用远场体波反演的地震矩偏小,联合远场和近场观测数据反演可显著改善体波的震源机制解．     

2000年姚安MS6.5地震3.0≤ML ＜5.0余震的地震矩张量反演

建立合于云南地区的速度结构模型,对云南数字地震台网记录的2000年姚安Ms6．5地震3．0≤ML〈5．0余震的垂直分量进行频率域内的地震矩张量反演。结果表明：矩张量分解得到纯膨胀（各向同性）分量P、纯剪切（双力偶）分量M0和补偿线性矢量偶极C三部分,其中纯剪切（双力偶）分量帆占主要部分,表明地震的震源破裂过程以剪切破裂为主。从余震震源机制解可知,NW-NWW方位的节面占主导,结合余震分布尺度可以判断发震断裂是北西向的断裂。     

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.      

利用CAP方法和瑞利面波振幅谱联合反演宁强5.3级地震震源深度

2018年9月12日19时6分,陕西省汉中市宁强县发生5.3级地震,不同机构给出的震源深度结果相差较大。为进一步确定宁强5.3级地震的震源深度,基于区域速度模型,首先利用CAP方法反演得到该地震的震源机制解,然后采用瑞利面波振幅谱和CAP深度误差函数联合反演,进一步测定了此次地震的矩心深度。结果显示:CAP方法得到的陕西宁强5.3级地震矩心深度约为12km,瑞利面波振幅谱测定的矩心深度为13km,结合引入的误差函数联合反演,最终确定陕西宁强5.3级地震的矩心深度为13km左右,表明此次地震仍属于发生于上地壳的地震。     

用地震波形资料反演中国大陆六个中强地震的矩张量和震源机制

利用 Helmberger(1968)的广义地震射线理论,研究了利用地震波形资料快速、大量地线性反演国内地震的地震矩张量和震源机制解的新方法,并对近年来先后发生在中国大陆的六个中强地震进行了反演,得到了这些地震的地震矩张量、标量地震矩、断层而解和震源时间函数等参数.     

CAP方法反演2014年山东乳山M4.2、M4.0地震震源机制解

选用山东数字地震台网波形资料,利用CAP方法反演乳山2014年1月7日M4.2及4月4日M4.0地震震源机制解。反演结果显示,两次地震均在矩心深度为6 km处获得最佳震源机制解,其节面参数基本一致,属于近走滑型地震。震中附近流动台站的震源距计算表明地震序列震源深度应略小于7 km,与CAP方法反演结果具有一致性,表明地震的主体破裂发生在上地壳。     

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.     

Fast and accurate earthquake location within complex medium using a hybrid globallocal inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares (RMS) error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Fréchet derivatives to simultaneously update all possible initial source parameters around most local minima (including the global minimum) in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to find the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.     

EM MODELLING USING SURFACE INTEGRAL EQUATIONS1

The theory by which the Surface Integral Equation method may be applied to the solution of electromagnetic transmission boundary value problems is presented. For a 3D target of arbitrary electrical property contrast with its host medium excited by an arbitrary time-harmonic source, two integral equations are derived which need to be simultaneously solved for tangential electric and magnetic source density on the target's surface. If the target is 2D, though still excited by an arbitrary source (the 2½ D case), the problem is best solved in the transform domain for a number of different wavenumbers in the target's strike direction. Then a set of four simultaneous scalar integral equations needs to be solved for the components of the surface source density transforms in the target's strike direction and in the direction of the tangent vector to the target's cross-sectional contour. Examples are presented in which the 2½D problem is solved numerically using the method of moments with piecewise linear basis functions. Although the results generally compare well with analytical solutions, or solutions obtained numerically by other means, errors appear in the calculation of the real response of these targets to excitation by a magnetic dipole source at low frequencies. This is attributed to ill-conditioning of the system resulting from a non-unique solution at zero frequency.     

2010年高雄地震震源参数的近远震波形联合反演

本文改进了传统基于近震波形数据的点源震源参数反演的Cut And Paste(CAP)方法,实现了近震Pnl波、面波和远震P波、SH波的联合反演的CAPjoint算法.对2010年3月高雄地震,分别进行单独反演以及联合反演,获得各自的震源机制解及深度,其中联合反演所得的最佳双力偶机制解参数为,节面1:走向317°,倾角36°,滑移角52°,节面2:走向181°,倾角62°,滑移角114°,深度为21 km.并对不同震中距波形对本次地震以及几种典型机制解断层几何参数的敏感性进行测试.为验证联合反演方法的可靠性,本文采用重抽样思想发展而来的Bootstrap方法,对近震数据的子集及其与远震数据的联合反演所得的参数进行统计,验证了在稀疏近台条件下联合反演中添加远震数据对地震震源参数约束的作用.     

A review of methods of parameter estimation for the extreme value type-1 distribution

Four important methods of estimating the parameters of the extreme value type-1 (Gumbel) distribution, namely: (1) moments (MMM); (2) maximum likelihood (MML); (3) maximum entropy (MME); and (4) probability weighted moments (PWM), are considered, suitable solution procedures are recommended and related problems discussed. Approximate formulae for computing the variances-covariances of the estimators by each method are given in terms of the population value of the scale parameter, and these are shown to indicate very well the performance of the related method.

A simulation study to evaluate the performance of these methods in terms of commonly used criteria, i.e. the bias, root mean square error and goodness-of-fit statistic is described. It was found that the MMM is not as good as the remaining three methods, of which the PWM is best in terms of the bias, and the MML is best in terms of the root mean square error and efficiency. The MME, by all the criteria, ranks second best and follows the MML more closely than the PWM.     

Non-linear three-dimensional inversion of cross-well electrical measurements

Cross-well electrical measurement as known in the oil industry is a method for determining the electrical conductivity distribution between boreholes from the electrostatic field measurements in the boreholes. We discuss the reconstruction of the conductivity distribution of a three-dimensional domain. The measured secondary electric potential field is represented in terms of an integral equation for the vector electric field. This integral equation is taken as the starting point to develop a non-linear inversion method, the so-called contrast source inversion (CSI) method. The CSI method considers the inverse scattering problem as an inverse source problem in which the unknown contrast source (the product of the total electric field and the conductivity contrast) in the object domain is reconstructed by minimizing the object and data error using a conjugate-gradient step, after which the conductivity contrast is updated by minimizing only the error in the object. This method has been tested on a number of numerical examples using the synthetic 'measured' data with and without noise. Numerical tests indicate that the inversion method yields a reasonably good reconstruction result, and is fairly insensitive to added random noise.     

致密气藏烃源岩地化参数测井综合评价方法研究

针对塔里木盆地库车坳陷北部侏罗系烃源岩受泥浆污染、分析数据少、样品分布不连续及类型多样等问题突出,利用测井资料来对有机地球化学参数进行评价难度大,无法满足勘探需求.本文阐述了不同类型烃源岩的有机质级别、测井响应特征、有机地球化学参数定量计算及品质评价等多种方法,来研究富集区烃源岩对致密气储层的持续供气能力.文中介绍了煤层、碳质泥岩、暗色泥岩等3种类型烃源岩的有机质级别和测井响应特征.首先,提出分不同岩性烃源岩的ΔlogR法,其计算结果与铀曲线相关法、多元回归法对比,效果最好;再次建立了生烃潜率、氯仿沥青“A”及镜质体发射率等多个有机质地球化学参数的测井评价模型;最终,考虑能够反映烃源岩性质的参数来综合定义烃源岩品质指数,形成了完善的烃源岩测井综合评价方法研究技术.研究表明,利用这套地球物理技术提供了烃源岩定量评价和品质分类研究方法及实际应用案例.     

煤矿井下微震震源高精度定位研究

煤矿井下微震震源准确定位,对于动力灾害监测预警具有重要意义.由于微震震源需要通过井下传感器接收信息反演确定,传感器的安装位置限制于煤矿井下巷道周围,传感器沿巷道近平面的不合理布置将大大降低震源定位精度.针对由传感器信息反演震源位置引起的病态问题,本文提出了基于微震监测测点优化布置的震源高精度定位算法.首先通过计算系数矩阵条件数,判定病态问题;然后利用中心化法和行平衡法联合进行病态矩阵预处理.对预处理后的矩阵A、b利用L曲线法计算正则参数,结合Tikhonov正则化算法计算得到震源坐标正则解.研究结果表明,中心化法有效降低了矩阵数量级,行平衡预处理降低了病态条件数,预处理后Tikhonov正则解的震源坐标误差最小可以达到3.09m,与预处理前的高斯消去解相比误差大大降低.通过上述优化处理,实现了井下受限空间微震监测震源高精度定位.     

Estimation of Degradation Rates by Satisfying Mass Balance at the Inlet

Using a steady-state mass conservative solute transport analytical solution that is based on the third-type (or flux-type or Cauchy) source condition, a method is developed to estimate the degradation parameters of solutes in groundwater. Then, the inadequacy of the methods based on the first-type source-based analytical solute transport solution is presented both theoretically and through an example. It is shown that the third-type source analytical solution exactly satisfies the mass balance constraint at the inlet location. It is also shown that the first-type source (or constant source concentration or Dirichlet) solution fails to satisfy the mass balance constraint at the inlet location and the degree of the failure depends on the value of the degradation as well as the flow and solute transport parameters. The error in the first-type source solution is determined with dimensionless parameters by comparing its results with the third-type source solution. Methods for estimating the degradation parameter values that are based on the first-type steady-state solute transport solution may significantly overestimate the degradation parameter values depending on the values of flow and solute transport parameters. It is recommended that the third-type source solution be used in estimating degradation parameters using measured concentrations instead of the first-type source solution.     

基于粒子群优化的双力偶模型振幅谱反演方法及应用

发展了一种基于全波形振幅谱的频率域双力偶震源机制反演方法. 通过理论振幅谱与观测振幅谱的拟合搜寻断层面参数, 基于粒子群优化算法可以在较短的时间内得到稳定可靠的解． 数值试验表明, 在定位误差较大, 以及台站布局较差的情况下, 振幅谱反演仍可较为准确地得到震源机制, 并且由此计算得到的最优震源深度仍比较接近真实的震源位置． 使用该方法用2010年5月17日渤海ML4.0地震的震源机制进行了检验, 结果与加权P波初动解非常一致． 应用该方法对山东半岛及近海地区2003——2010年14次MLge;4.0地震震源机制进行了估计．