经验格林函数方法理论上的改进

以往的经验格林函数方法存在着两个问题:一是要求大小地震需满足"相似"或"准相似"条件,这就限制了经验格林函数方法的适用范围。二是对大地震断层面的位错不均匀性考虑得不充分,而实际上大地震断层的位错一般是不均匀的。本文在假定大小地震不满足"相似"和"准相似"以及大地震断层面位错不均匀的前提下,对经验格林函数方法进行了改进,并应用于卢龙地震的模拟,模拟的结果与记录符合得比较好,说明改进的经验格林函数方法可以用来估计场地地震动过程。     

经验格林函数方法模拟地震动研究现状

经过30多年的发展,格林已经成为被地震工作者普遍接受的模拟地震动的方法.回顾发展历史,该方法可以分为3个阶段:第1阶段是经验格林函数理论建立阶段;第二阶段是经验格林函数方法逐步得到完善阶段;第三个阶段是经验格林函数方法的广泛应用阶段,该阶段提出了用该方法预测未来地震动的一般步骤,标志着用经验格林函数方法预测未来地震动,为建筑物的抗震设防提供依据已经到了比较成熟阶段.最后,对用经验格林函数方法和随机方法模拟地震动的优势和不足进行了比较.     

用改进的经验格林函数方法模拟唐山地震动

建筑物的抗震设防需要尽可能地掌握未来大地震强震动记录信息,但大地震强震动记录的匮乏阻碍了抗震设防实践的发展。经验格林函数方法作为模拟地震动的主要方法,可以提供可靠的大地震强震动记录,但也存在着许多问题,如缺乏对大地震断层滑动分布不均匀的描述、用经验确定小震数目、模拟方法受到大小地震相似条件的限制等。文中对上述经验格林函数方法存在的问题进行了研究,改进的经验格林函数方法,有效地解决了上述问题。并用其对唐山大地震进行了模拟,并把模拟的地震动时程和反应谱与实际记录相比较,发现用改进方法模拟的地震动加速度反应谱比用未改进方法模拟结果更接近实际的地震动记录加速度反应谱。由此说明改进的经验格林函数可更准确的模拟地震动。     

用经验格林函数法和随机方法模拟卢龙地震的比较

在介绍用经验格林函数方法和随机方法模拟地震动的基础上,分别用这两种方法模拟了卢龙5．7级地震。模拟结果表明,用经验格林函数方法模拟地震动的结果与地震记录符合得很好。用随机方法模拟地震动在高频部分与地震动记录符合得比较好,而在中、低频部分符合得不太好。两种方法比较,经验格林函数方法模拟的结果更符合实际记录。但随机方法具有计算简单、无需小震记录的优点,因此发展随机的方法是有意义的。随机方法中中、低频部分不太符合的原因是随机方法中的很多经验关系是在美国大陆得到的。因此建议加强对中国大陆经验关系的研究,并把中国大陆的经验关系加入到随机方法中,使随机的方法成为中国大陆普适的模拟地震动的方法。     

基于改进的经验格林函数方法的地震动模拟

改进的经验格林函数方法弃掉以往完全用经验方法确定用于合成大震的小震数目的方法,考虑了大地震断层各个子断层位错的不均匀性,使得经验格林函数方法的物理意义更加清楚。用改进的经验格林函数方法,以汶川MS6.4余震记录作为经验格林函数模拟了九寨白河台、松潘安宏台、皋兰台和成都中和4个台站的加速度时程,与以往的经验格林函数方法比较,模拟结果的反应谱与记录符合得更好,证明了改进的经验格林函数方法可以反映震源位错的复杂分布,可以在工程地震中用来估计场地地震动过程。     

经验格林函数方法模拟地震动研究

地震动模拟研究的目的是为建筑物的抗震设计提供未来地震动的时程或反应谱。本研究在总结了经验格林函数方法和随机方法模拟地震动的基础上,对所存在的问题进行了系统研究,得到如下成果:1改进了经验格林函数方法,提高了经验格林函数方法的严密性用经验格林函数方法模拟地震动的结果在高频部分偏低的部分原因是由于假设大小地震的滑动分布都是相     

考虑凹凸体理论的经验格林函数方法

以15次地震资料为基础,回归得到断层上所有凹凸体地震矩与凹凸体面积的关系;研究经验格林函数方法中凹凸体子源的应力降,提出基于断层凹凸体理论的经验格林函数方法;以唐山地震余震（Ms=6.9）作为经验格林函数,合成1976年唐山地震（Ms=7.8）的地震动,比较合成结果与观测记录表明,该方法符合断层破裂过程,计算结果可靠．      

应用动力学拐角频率对经验格林函数法的改进

针对大小震拐角频率的差异,假设大震断层上每个子源的拐角频率与已破裂的子源个数平方根成反比,基于ω2震源谱模型,通过理论推导构建了一个函数,将动力学拐角频率引入经验格林函数法。以汶川地震余震记录为格林函数,分别用改进前和引入动力学拐角频率后的经验格林函数法合成5·12汶川大地震强地面运动。对比合成结果与观测记录,结果表明改进前经验格林函数法合成的地震动在低频部分相对实际记录偏低;引入动力学拐角频率之后的经验格林函数法合成的结果在高频基本保持不变,低频部分得到提高,并与实际记录符合。引入动力学拐角频率后,大部分合成结果很好地符合实际记录。说明动力学拐角频率可有效改善经验格林函数法的低频合成结果,同时验证了经验格林函数法对MW7.9特大地震地震动合成的有效性。     

Prediction of strong ground motion at EURO-SEISTEST site using the empirical Green's function method

This paper presents some tests on the empirical Green's function method, performed in order to check its effectiveness to predict strong ground motion during future large earthquakes. These investigations basically consist of blind or pseudo-blind tests using part of the data set obtained at the Volvi (Greece) test-site within the framework of the EURO-SEISTEST project. In a first step, a moderate event (M_L=4.1) is simulated by using a small event (M_L=2.5), and taking into account the a priori knowledge of the relevant source parameters (magnitude and stress-drop) for both the base and target events. This check emphasizes the sensitivity of the prediction to the stress-drop values. In a second step, a pseudo-blind prediction is carried out in which the information on the target event is only the magnitude (M_L=5.3) besides the geometrical parameters such as source location, strike and dip. The other important parameters (seismic moment, fault area, stress-drop) are determined on the basis of specific empirical scaling laws derived from several small and moderate events occurring in the area. The synthetic motions are computed for two nearby sites, which are located on the southern edge and in the center of the Mygdonian graben, respectively, and correspond to much different site conditions: weathered rock and thick sediments. They are found in good agreement with the observations, which were unveiled after the simulation. In particular, the amplitude and the phase of the late, local surface waves generated on the southern edge of the graben, are very well reproduced at valley center. Finally, the last step is an attempt to predict strong ground motion for a hypothetical large earthquake of magnitude M_L=6.5. The results are shown to depend very significantly on the scaling laws.     

用经验格林函数法模拟2008年日本岩手-宫城地震的强地面运动

运用经验格林函数方法,对2008年6月13日日本岩手—宫城(MW6.9)地震进行了近场强地面运动的模拟研究.首先,利用震源谱拟合方法和遗传优化算法计算了经验格林函数法所需的参数,进而估算求得了此次地震主断层面上强震生成区的面积和上升时间.基于所获得的震源模型,计算了近震源区域的强地面运动时程,并同实际观测记录在时域和频域作了分析比较.结果显示,多数台站合成谱与观测谱符合得很好,部分台站两者在低频上有一定的偏差.通过遗传算法搜寻,所得强震生成区的面积与经验关系预测的一致,而上升时间则比经验关系预测的要小.     

Ground motion prediction with the empirical Green's function technique: an assessment of uncertainties and confidence level

An assessment of uncertainties for ground motion predictions with the aid of the empirical Green's function (EGF) technique is presented. The main input parameters were identified, and their respective uncertainties were assessed by means of an international expert inquiry. The repercussion of these input uncertainties on the final ground motion estimates were investigated by means of the Latin Hypercube Sampling technique. The mean ground motion estimates (response spectra) and their standard deviations were compared with results obtained from empirical attenuation laws. The most sensitive input parameter turned out to be the seismic moment corresponding to the EGF. In general, if the source parameters are well determined, equivalent uncertainties, statistically speaking, can be expected from the EGF technique and from the application of attenuation laws. Therefore, if EGFs with well known source parameters are available, the EGF technique seems to be preferable: site effects are automatically taken into account, and physically realistic acceleration time histories can be obtained. However, further investigations on the reliability of the EGF technique should be performed, and finally, it is recalled that the EGF technique is based on the assumption of linearity. If conditions are such that this assumption cannot be maintained, the EGF technique should be combined with non-linear geotechnical methods.     

利用大地测量数据反演地震位错Love数和格林函数的理论与方法

本文提出一种利用大地测量观测技术反演地震位错Love数及格林函数的理论和方法.首先根据地震位错理论建立理论同震变化和大地测量观测值之间的关系式;其次,以2011年Tohoku-Oki地震（M_W9.0）为例,反演体现局部构造特征的地震位错Love数和格林函数.结果表明：反演得到的位错Love数与PREM模型下的位错Love数随深度和阶数变化不同,反映出局部三维地球模型的构造差异,由此计算的同震变化跟实际大地测量观测值的吻合度提高了~60%~~80%.通过大地测量观测数据反演的地震位错Love数能体现局部地球真实的构造信息,为该地区地震研究提供更加精确的地震位错格林函数.

     

Green's function interpolations for prestack imaging

A new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade-off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root-mean-square velocity, v _RMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates v _RMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated.
The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms.     

基于小震经验格林函数研究中等地震破裂方向性: 以2008年攀枝花MS6.1地震为例

中小地震破裂方向性研究在确定实际发震面以及地震灾害评估中具有非常重要的意义.本文以2008年8月30日攀枝花M_S6.1地震为研究实例, 以较小余震作为经验格林函数地震, 利用表观震源时间函数随台站方位角变化特性, 确定了主震的破裂方向、破裂尺度以及破裂速度, 验证了该方法的适用性和可行性.研究结果表明, 主震的破裂方向为几乎正南的184°, 破裂长度8.05 km, 破裂速度3.35 km·s^-1, 进一步确认了主震震源机制解其中沿南北向的节面是地震实际发震面, 主震在水平方向沿着南北向元谋断裂从北往南破裂.攀枝花地震震源破裂速度接近地壳剪切波速度, 这可能是造成此次地震虽然震级不大但破坏性严重的重要原因.本文综合分析主震的矩心深度、震源机制解、破裂方向性以及构造应力背景等信息, 探讨了地震发生的破裂过程以及灾害严重的原因.

     

震源因素对尾波干涉提取经验格林函数的影响

尾波干涉提取经验格林函数作为现今地震学一项重要的研究,其受震源因素的影响值得细致地探讨.本文通过模拟和实际数据的尾波干涉,系统性讨论了震源倾角、方位角和走向以及震中分布对于提取经验格林函数（主要是PKIKP²和PKIIKP²震相）的影响.我们发现PKIKP²震相的平均信噪比随倾角的增大呈现先增大后减小的变化趋势,并在倾角约为45°时达到最大.基于稳相点分析,本文认为这种变化趋势是因为提取的PKIKP²震相主要贡献来源于近乎径向方向,而倾角为45°的倾滑型断层事件辐射出的P波能量在径向上最大.此外,断层走向对尾波干涉提取Rayleigh面波并无明显影响,而方位角的影响非常显著.当事件近似在台站对的大圆弧上时,尾波干涉才能提取清晰的Rayleigh面波,这与面波稳相区的空间分布一致.对于PKIKP²和PKIIKP²震相,只有当事件分布与台站对大圆弧近垂直并且事件断层走向与线状台阵近平行时,才能提取清晰的波形.通过计算不同事件和台站分布的震源辐射能量,上述方位角和走向最有利于地核震相的提取.最后,震中分布对尾波干涉提取PKIKP²震相也有一定的影响：当震中与地心连线和PKIKP²震相射线路径之间的锐角夹角越小,并且震中距越小时,提取的地核震相的信噪比越高.

     

Equipartitioning is not sufficient for Green's function extraction

The extraction of the Earth's Green's function from field fluctuations is a rapidly growing area of research.The principle of Green's function extraction is often related to the requirement of equipartitioning,which stipulates that the energy of field fluctuations is distributed evenly in some sense.We show the meaning of equipartitioning for a variety of different formulations for Green's function retrieval.We show that equipartitioning is not a sufficient condition,and provide several examples that illustrate this point.We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green's function in seismology.The theory for Green's function extraction is usually based on a statistical theory that relies on ensemble averages.Since there is only one Earth,one usually replaces the ensemble average with a time average.We show that such a replacement only makes sense when attenuation is taken into account,and show how the theory for Green's function extraction for oscillating systems can be extended to incorporate attenuation.