复杂介质地震定位中震源轨迹的计算

在地震定位中常常需要求解震源轨迹,但由于复杂介质中的震源轨迹较为复杂,难以给出其解析解,因此震源轨迹的计算通常仅限于简单介质模型.本文基于最小走时树射线追踪技术,提出了一种计算复杂介质中震源轨迹的方法.为回避发震时间问题,以观测到时差作为震源轨迹的约束条件.首先从模型节点中选出少量理论到时差与观测到时差之绝对差,即双重时差较小的点作为震源轨迹的代表点,然后以其中双重时差最小的点为初始点,在双重时差场中利用最小走时树射线追踪方法计算出初始点到其他震源轨迹代表点的射线路径作为震源轨迹.当选的震源轨迹代表点较多时,得到的震源轨迹较为粗略,此时可去掉射线经过次数较少的代表点的射线路径使震源轨迹更为精细.为减少计算量,对最小走时树射线追踪方法的终止条件做了修正.以一个复杂介质模型中的地震为例,计算了包括速度扰动、到时扰动等不同情况下的震源轨迹,结果表明所提出的震源轨迹计算方法切实可行.     

三维复杂速度模型中地震事件震源轨迹的计算

地球内部三维速度图像的广泛建立为进行高精度的地震定位提供了良好条件.使用震源轨迹确定震源位置不仅稳健而且直观,但三维复杂速度模型中的震源轨迹难以给出解析解.为此,本文提出了一种较准确地计算三维复杂速度模型中震源轨迹的数值方法.根据震源轨迹在残差场中的特点：（1）震源轨迹位于残差正负极性彼此不同的邻点之间;（2）绝对梯度在震源轨迹的法线方向最大;（3）在法线方向上越靠近震源轨迹残差绝对值越小,对于每个模型节点分别和残差正负极性与其不同的邻点组成的点对,将其中绝对梯度最大的点对作为震源轨迹法线点对,选取法线点对中残差绝对值较小的点（即震源轨迹所在模型单元的节点）作为震源轨迹代表点;在绝对残差场中数值较小的连通区域（可能有多个）内,利用最小走时树算法依次计算出每个连通区域中地震波从绝对残差最小点至同一连通区域内震源轨迹代表点的射线路径作为震源轨迹.算例表明：本文方法适用于三维复杂速度模型,对震源轨迹的稳定性及构成段数没有限制,计算的震源轨迹精细且较完整、可用于高精度的地震定位.     

一种基于插值技术高精度计算稀疏网格地震定位中震源轨迹的方法

区域和全球地震定位越来越多地基于更接近实际的横向非均匀速度模型.速度模型主要来自于地震体波层析成像结果,分辨率不是很高.这样,模型宜于以稀疏网格剖分以减少计算时间和计算机内存需求.当剖分的模型单元较大时,基于射线追踪技术计算复杂介质地震定位中震源轨迹的方法——选取震源轨迹所经过单元节点(位于单元中心,称为震源轨迹节点)为轨迹参考点,利用最小走时树射线追踪方法计算绝对残差场中连接轨迹参考点的射线路径作为震源轨迹——计算结果误差较大,难以满足精定位需要.针对该问题,本文对其进行了改进:不将震源轨迹节点作为轨迹参考点,而是基于插值技术计算每个轨迹节点其法线点对(即该节点与其周围残差正负极性不同的相邻节点组成的点对中梯度绝对值最大的那对)间残差为零的点作为震源轨迹参考点.算例表明:和原方法相比,改进方法计算的震源轨迹更为精细,计算精度提高数十(线性插值)至数百倍(非线性插值),而计算效率基本保持在同一数量级,使利用震源轨迹进行直观、快速和高精度的区域或全球地震事件定位成为可能;壳幔界面反射纵波(PmP)对震源的约束和直达纵波(Pg)相似;同一台站PmP-Pg波到时差约束的震源轨迹对震源深度有很好的约束.     

三维复杂速度模型的交切法地震定位

地震定位是地震监测与减灾研究重要基础.基于均匀或横向均匀介质模型,利用震源轨迹确定震源位置的交切法具有稳健和效率高的优点,但定位精度较低,特别是震源深度.为提高震源定位精度,我们提出适用于三维复杂速度模型的地震定位交切法.将地壳速度模型由均匀或横向均匀介质模型扩展为三维复杂速度模型;均匀或横向均匀介质模型对应的原假设为球面或双曲面的震源轨迹通过最小走时树射线追踪技术予以确定.确定震源位置的震源轨迹以到时差作为约束条件;将震源定位于震源轨迹交汇最密集的点处,即总的到时差残差(RDT)最小的点处.定位结果的不确定性可通过RDT值较小节点的空间分布予以定性表示.考察了准确速度模型、扰动速度模型、扰动观测到时及地震在台网外等4种情况下改进方法的地震定位效果,结果表明改进的交切法可用于三维复杂速度模型的地震定位;综合利用P波与S波的到时差信息,可明显改善震源位置约束;使用多条震源轨迹进行定位,有助于减少由随机因素导致的定位误差.     

运用改进的地震定位交切法重定位2001—2010年云南地震

传统地震定位方法利用震源轨迹确定震源位置,但基于均匀或横向均匀介质模型必然导致定位误差。为此对传统方法进行改进,发展适用于三维复杂地壳速度模型的地震定位交切法。利用最小走时树射线追踪技术,以离散方式准确计算三维复杂地壳速度模型中的震源轨迹,将震源定位于震源轨迹交汇的密集点。将该方法应用于云南地区地震重定位,得到较高定位精度。     

干涉走时微地震震源定位方法

本文基于地震波场干涉原理,建立了干涉走时微地震震源定位方法.该方法将两个接收点相对于一个微地震事件的走时差(称为干涉走时)的扰动作为残差函数,通过迭代求解最小残差函数,最终获得震源的空间位置.干涉走时震源定位方法利用两个接收点的到时差消除发震时刻未知和速度模型误差的影响,简化了震源定位算法.数值计算表明,本文提出的干涉走时定位方法在速度模型有误差的情况下仍然可以获得准确的微地震震源定位.     

宽角反射地震波走时模拟的双重网格法

在研究地壳结构的人工源宽角反射地震资料解释中,常规宽角反射波走时和射线路径计算大都假定地壳模型为层状块状均匀介质.为了逼近实际地壳结构模型,要求模型尺度较大,为了提高地震资料解释的可靠性,须减小模型离散单元的尺寸,但同时计算量大大增加,使资料解释的效率较低.为此,本文尝试同时提高宽角反射地震资料解释效率和可靠性的方法,即使用双重网格计算宽角反射地震波走时和射线路径的最小走时树方法.双重网格法在均匀介质内部仅计算大网格节点,在速度变化点、震源点和检波点区域,同时计算小网格节点;在界面边界点使用比介质内部节点更大的子波传播区域.模型计算结果表明,对于大尺度的层状块状均匀介质模型,在保证精度的条件下,本文所提出的双重网格射线追踪方法的计算效率比单网格方法显著提高.     

二维无限频率初至走时反演井间地震实际资料

使用Zelt和Barton的方法,通过一个计算效率高的有限差分求解eikonal方程,正演计算走时和射线路径.使用最小二乘QR分解法,求解稀疏线性系统方程组.使用正则化层析反演,结合用户给定的最小的、最平坦和最平滑的扰动限制,每一个加权因子随深度变化.结合数据残差和模型粗糙度的最小化,为数据残差提供一个最平滑的近似模型.该反演方法为非线性反演,需要一个初始模型,在每一次迭代时,需要计算新的射线路径.使用二维初至走时数据,对某油田二维井间地震实际资料进行无限频率初至走时层析反演.将反演所得到的速度与井的测井速度曲线相比较,二者吻合程度较高,表明该反演方法所得速度的分辨率比较高.证实了二维无限频率初至走时层析反演可以为全波形反演提供一个分辨率较高的长波长速度模型,从而为全波形反演井间地震实际资料提供了一个比较可靠的初始速度模型.     

动态网络最短路径射线追踪

最短路径射线追踪算法,用预先设置的网络节点的连线表示地震波传播路径,当网络节点稀疏时,获得的射线路径呈之字形,计算的走时比实际走时系统偏大. 本文在波前扩展和反向确定射线路径的过程中,在每个矩形单元内,通过对某边界上的已知走时节点的走时进行线性插值,并利用Fermat原理即时求出从该边界到达其他边界节点的最小走时及其子震源位置和射线路径,发展了相应的动态网络算法. 从而克服了最短路径射线追踪算法的缺陷,大大提高了最小走时和射线路径的计算精度.     

复杂速度模型的地震交切定位方法

交切法是最基本的地震定位方法之一,该定位方法具有稳定性强、速度快的优点。由于速度模型假设为均匀或水平均匀介质,与实际介质有较大偏差,因此定位精度较低,特别是震源深度。为克服传统交切法的缺点,我们对其进行了改进。在改进的方法中,震源轨迹不再假设为圆形或双曲线形,而是利用最小走时树射线追踪方法进行精确计算。数值模型计算表明,本文提出的改进方法,可用于复杂速度模型的地震定位。     

Earthquake location in transversely isotropic media with a tilted symmetry axis

The conventional intersection method for earthquake location in isotropic media is developed in the case of transversely isotropic media with a tilted symmetry axis (TTI media). The hypocenter is determined using its loci, which are calculated through a minimum travel time tree algorithm for ray tracing in TTI media. There are no restrictions on the structural complexity of the model or on the anisotropy strength of the medium. The location method is validated by its application to determine the hypocenter and origin time of an event in a complex TTI structure, in accordance with four hypotheses or study cases: (a) accurate model and arrival times, (b) perturbed model with randomly variable elastic parameter, (c) noisy arrival time data, and (d) incomplete set of observations from the seismic stations. Furthermore, several numerical tests demonstrate that the orientation of the symmetry axis has a significant effect on the hypocenter location when the seismic anisotropy is not very weak. Moreover, if the hypocentral determination is based on an isotropic reference model while the real medium is anisotropic, the resultant location errors can be considerable even though the anisotropy strength does not exceed 6.10%.     

线性单事件地震定位方法的改进及应用尝试

根据大震速报和快速预警实际需要,首先对Inglada线性单事件定位方法进行了适当的改进, 使其在仅有P波到时数据的情况下也能快速定位,且求解过程仅需简单迭代而不用奇异值分解; 其次, 尝试将改进后的方法从单层均匀模型引入到分层均匀模型中的近源台网定位情形,并通过单层均匀和分层均匀两种不同模型的理论实验讨论了该方法的可行性和适用范围; 最后整合了质量高且分布较好的距离2008年汶川M_S8.0地震震中最近的强震、微震, 以及川西流动台阵等观测记录资料,对汶川M_S8.0主震初始破裂点的时空参数进行了多种模型的定位实验. 结果表明, 改进后的线性单事件定位方法简单、快捷、易用,可广泛应用于近源地震定位,尤其是用于无法得到S波到时的中强以上直至巨大地震的速报、地震现场流动台网的快速定位以及地震的快速预警等.      

Relocation of Swarm Events in the June 1987 Earthquake Sequence from the Lake Aswan Area in Egypt

--We have examined the digital waveform data and relocated a number of events within the June 1987 earthquake swarm, which occurred beneath the northern part of Lake Aswan, 70 km southwest of the Aswan High Dam in Egypt. This swarm occurred between June 17th and 19th with a maximum magnitude event of "M_L"=3.5.¶Cross correlation between a chosen master and the analyzed events has been carried out on seismograms from stations of the Aswan network. The cross correlation demonstrates the presence of a difference in both the P wave ((t_p) and the S wave ((t_s) arrival times at each station in the network relative to the arrival times of the master event at the same stations. (t_p ranges between т.15 and 0.11 second, while (t_s ranges between т.17 and 0.11 second.¶The primary interpretation is that the se time differences represent an error in the manually picking arrival times. Then, (t_p and (t_s values for each event result from a change in the hypocentral parameters from those of the master event, assuming the P- and S-wave velocity distribution remains constant during the swarm activity. This interpretation enables us to determine the relative distribution of hypocenters with respect to the hypocentral location of the master event. We present the results from a swarm of 9 events demonstrating they originate from a nearly unique location, rather than the zone identified from the preliminary locations which used manually picked onset times.     

One-dimensional velocity model of the Middle Kura Depresion from local earthquakes data of Azerbaijan

We present the method for determining the velocity model of the Earth’s crust and the parameters of earthquakes in the Middle Kura Depression from the data of network telemetry in Azerbaijan. Application of this method allowed us to recalculate the main parameters of the hypocenters of the earthquake, to compute the corrections to the arrival times of P and S waves at the observation station, and to significantly improve the accuracy in determining the coordinates of the earthquakes. The model was constructed using the VELEST program, which calculates one-dimensional minimal velocity models from the travel times of seismic waves.     

The influence of one-dimensional velocity sections on determining the key parameters of the earthquake sources in Azerbaijan

The paper addresses the construction of one-dimensional (1D) velocity models in the seismogenic regions of Azerbaijan taken individually and the analysis of implications of these models for estimating the key parameters of earthquake sources in Azerbaijan. We considered and analyzed the seismological data from the local earthquakes, the arrival times of the P-, P-g, Pn-, S-, Sg-, and Sn-waves recorded by the network of telemetry stations during the period from 2005 to 2014 with ml ≥ 2.5. For constructing the models, we used the VELEST program which calculates 1D velocity models from travel times of seismic waves. As a result, the 1D models were built for ten regions of Azerbaijan; the key parameters of the hypocenters of the earthquakes were recalculated; and the corrections to the body-wave arrival times at the observation stations were obtained, which increased the accuracy of locating the hypocenter of earthquakes.     

Accurate Location of Synthetic Acoustic Emissions and Location Sensitivity to Relocation Methods, Velocity Perturbations, and Seismic Anisotropy

Acoustic emission (AE) monitoring is a non-invasive method of monitoring fracturing both in situ, and in experimental rock deformation studies. Until recently, the major impediment for imaging brittle failure within a rock mass is the accuracy at which the hypocenters may be located. However, recent advances in the location of regional scale earthquakes have successfully reduced hypocentral uncertainties by an order of magnitude. The least-squares Geiger, master event relocation, and double difference methods have been considered in a series of synthetic experiments which investigate their ability to resolve AE hypocentral locations. The effect of AE hypocenter location accuracy due to seismic velocity perturbations, uncertainty in the first arrival pick, array geometry and the inversion of a seismically anisotropic structure with an isotropic velocity model were tested. Hypocenters determined using the Geiger procedure for a homogeneous, isotropic sample with a known velocity model gave a RMS error for the hypocenter locations of 2.6 mm; in contrast the double difference method is capable of reducing the location error of these hypocenters by an order of magnitude. We test uncertainties in velocity model of up to ±10% and show that the double difference method can attain the same RMS error as using the standard Geiger procedure with a known velocity model. The double difference method is also capable of precise locations even in a 40% anisotropic velocity structure using an isotropic model for location and attains a RMS mislocation error of 2.6 mm that is comparable to a RMS mislocation error produced with an isotropic known velocity model using the Geiger approach. We test the effect of sensor geometry on location accuracy and find that, even when sensors are missing, the double difference method is capable of a 1.43 mm total RMS mislocation compared to 4.58 mm for the Geiger method. The accuracy of automatic picking algorithms used for AE studies is ±0.5 μs (1 time sample when the sampling rate is 0.2 μs). We investigate how AE locations are effected by the accuracy of first arrival picking by randomly delaying the actual first arrival by up to 5 time samples. We find that even when noise levels are set to 5 time samples the double difference method successfully relocates the synthetic AE.     

On the Problem of Deep Earthquakes in Crimea–Black Sea Region

It is a common opinion that only crustal earthquakes can occur in the Crimea–Black Sea region. Since the existence of deep earthquakes in the Crimea–Black Sea region is extremely important for the construction of a geodynamic model for this region, an attempt is made to verify the validity of this widespread view. To do this, the coordinates of all earthquakes recorded by the stations of the Crimean seismological network are reinterpreted with an algorithm developed by one of the authors. The data published in the seismological catalogs and bulletins of the Crimea–Black Sea region for 1970–2012 are used for the analysis. To refine the coordinates of hypocenters of earthquakes in the Crimea–Black Sea region, in addition to the data from stations of the Crimean seismological network, information from seismic stations located around the Black Sea coast are used. In total, the data from 61 seismic stations were used to determine the hypocenter coordinates. The used earthquake catalogs for 1970–2012 contain information on ~2140 events with magnitudes from–1.5 to 5.5. The bulletins provide information on the arrival times of P- and S-waves at seismic stations for 1988 events recorded by three or more stations. The principal innovation of this study is the use of the original author’s hypocenter determination algorithm, which minimizes the functional of distances between the points (X, Y, H) and (x, y, h) corresponding to the theoretical and observed seismic wave travel times from the earthquake source to the recording stations. The determination of the coordinates of earthquake hypocenters is much more stable in this case than the usual minimization of the residual functional for the arrival time of an earthquake wave at a station (the difference between the theoretical and observed values). Since determination of the hypocenter coordinates can be influenced by the chosen velocity column beneath each station, special attention is focused on collecting information on velocity profiles. To evaluate the influence of the upper mantle on the results of calculating the velocity model, two different low-velocity and high-velocity models are used; the results are compared with each other. Both velocity models are set to a depth of 640 km, which is fundamentally important in determining hypocenters for deep earthquakes. Studies of the Crimea–Black Sea region have revealed more than 70 earthquakes with a source depth of more than 60 km. The adequacy of the obtained depth values is confirmed by the results of comparing the initial experimental data from the bulletins with the theoretical travel-time curves for earthquake sources with depths of 50 and 200 km. The sources of deep earthquakes found in the Crimea–Black Sea region significantly change our understanding of the structure and geotectonics of this region.     

Determining hypocentral parameters for local earthquakes under ill conditions using genetic algorithm

We demonstrate that GA-MHYPO determines accurate hypocentral parameters for local earthquakes under ill conditions, such as limited number of stations (phase data), large azimuthal gap, and noisy data. The genetic algorithm (GA) in GA-MHYPO searches for the optimal 1-D velocity structure which provides the minimum traveltime differences between observed (true) and calculated P and S arrivals within prescribed ranges. GA-MHYPO is able to determine hypocentral parameters more accurately in many circumstances than conventional methods which rely on an a priori (and possibly incorrect) 1-D velocity model. In our synthetic tests, the accuracy of hypocentral parameters obtained by GA-MHYPO given ill conditions is improved by more than a factor of 20 for error-free data, and by a factor of five for data with errors, compared to that obtained by conventional methods such as HYPOINVERSE. In the case of error-free data, GA-MHYPO yields less than 0.1 km errors in focal depths and hypocenters without strong dependence on azimuthal coverage up to 45°. Errors are less than 1 km for data with errors of a 0.1-s standard deviation. To test the performance using real data, a well-recorded earthquake in the New Madrid seismic zone and earthquakes recorded under ill conditions in the High Himalaya are relocated by GA-MHYPO. The hypocentral parameters determined by GA-MHYPO under both good and ill conditions show similar computational results, which suggest that GA-MHYPO is robust and yields more reliable hypocentral parameters than standard methods under ill conditions for natural earthquakes.