三维尾波散射问题的理论研究

在以前有关散射理论研究的基础上，研究了三维无限介质空间中震源距不为零时的单次与多次散射模型．基于各向同性散射体在统计意义上均匀分布于三维介质空间的假设，得到了单次散射尾波功率谱的解析表达式及多次散射尾波功率谱的积分表达式．      

不同散射模式下S波包络合成

为揭示地震波在地壳小尺度非均匀介质中的散射过程,更准确地描述地震波的包络展宽现象,本文基于多次各向异性散射理论,采用离散波数法求解能量密度积分方程,选取高斯型自相关函数表征的散射模式,得到S波能量密度包络。基于此,本文首先分析了单次散射和多次散射在形成S波能量密度包络中的贡献规律;然后探讨了吸收系数和总散射系数对合成S波能量密度包络的影响;最后对比了在不同散射模式下合成的S波能量密度包络的差异。结果显示:① 不同的散射模式下单次散射和多次散射对地震波散射过程的贡献规律是一致的,对于近震（震源距小于100 km）,单次散射模型可以近似合成S波能量密度包络;随着震源距增大,多次前散射模型可以更快地接近总能量密度包络;② 吸收系数增大会降低直达S波和尾波幅值,总散射系数增大会降低直达S波幅值,但使得S波尾波幅值升高;③ 前散射模式下S波能量密度包络随震源距的增大会导致峰值延迟,包络展宽,尾波衰减一致性更快等现象产生。      

多次各向异性散射模式对S波能量密度包络曲线的影响

在多次各向异性散射理论的基础上,本文重新推导了方向性散射系数的球函数展开式.引入特征时间的概念,来定义震源处初始地震波脉冲宽度,并在地震波能量密度积分方程中引入任意给定频率的初始脉冲能量谱密度的解析表达.通过离散波数方法求解了修正的地震波能量密度积分方程.基于积分方程的数值解,研究了不同散射模式对S波能量密度包络曲线的影响.计算结果表明:随着震源距的增加,在S波到时之后,多次各向异性散射模式与多次各向同性散射模式合成的能量密度包络差异逐渐增大.其中通过多次前散射模式,我们可以得到不同震源距的尾波能量密度包络的同一衰减趋势,以及S波能量密度包络随着震源距的增加而出现的展宽现象.最后,利用美国内华达州Wells地震余震的台站记录验证了多次前散射模式的实用性与有效性.     

北京地区尾波衰减的研究

Aki(1969)提出了单次反向散射模式,该模式认为,尾波是由许多随机分布的不均匀体产生的单次反向散射波叠加而成的,是随机过程的结果。因此,尾波的某些性质反映了不均匀介质的平均效应,而与震源到台站的具体路径无关。这个模式成功地解释了这样的观测事实,即不同的微震记录中尾波振幅随时间衰减的形式基本是一致的,与震中距的大小和波传播的具体路径无关。Aki和Chouet(1975)认为,由于散射波所经过的路径比震源距大得多,所以可把台站和震源近似地看作同一个点。在这种情况下,近震图上延迟时间为t的尾波是由半径为β·t/2的球体表面的不均匀体产生的单次反向散射波叠加而成(延迟时间t是从发震时刻算起的,β是S波波速)。如果散射体随空间分布是     

用尾波的强度和衰减估算北京地区 S 波的平均自由程h

Aki 提出的单次散射模型由于它的简单而显得很实用.作为单次散射模型的改进,本文表明应用多次散射模型也可给出一个简单可行的办法来估算一定地区地下介质的不均匀性.本文分别用尾波的强度和衰减求出与散射有关的 Q 因子.可以看到,尽管单次散射模型和多次散射模型两者给出了十分接近的结果,但后者显得更加合理并有其自相一致性.本文认为,无论运用哪个简化了的模型,方程(InA=1——Int——b1t 或 InA=2——0.5lnt——b2t)中的对数项是不可忽略的.本文应用北京地区地震台网资料,求出了频率在1Hz 左右北京地区 S 波的平均自由程,结果见表2.      

2007年宁洱6.4级地震余震序列尾波QC值研究

基于Aki和Chouet的地方震尾波单次散射模型,利用思茅台记录到的2007年云南宁洱6.4地震余震的数字化波形观测资料,测量了震源区尾波Qc(f)值。当中心频率为1.5Hz时,宁洱地区的尾波Qc值在51～147之间,平均值为79,尾波的振幅衰减率βc(f)在0.014～0.039之间,平均值为0.028;测量得到该地区尾波Qc值与频率f的关系为Qc(f)=53f0.88;尾波波源因子与震级成正比关系,满足关系lgA0=1.51ML-0.94;测量结果显示宁洱地震余震序列的尾波值Qc较低,表明宁洱震源区属于构造运动较为活跃区。     

尾波干涉原理及其应用研究进展综述

本文首先简述了尾波干涉方法的基本原理, 随后介绍了尾波干涉方法在研究震源位置变化和监测散射体运移状态的相关应用与进展, 最后探讨了利用重复地震、 人工主动源和噪声互相关函数监测地下介质波速变化的尾波干涉方法的优缺点及发展方向. 尾波干涉方法基于尾波的多次散射特性, 能够提取震源位置与介质的细微变化, 其中介质的动态变化可为地震(火山)的孕育、 形成及发展提供研究思路与指导意义.      

2000年姚安MS65地震震源及近邻区的低QS

利用震源距23 km范围内观测的2000年姚安MS65地震余震记录，计算了震源及近邻区域的尾波规一直达S波在频率15～20 Hz之间的傅里叶谱振幅.结果显示谱振幅随震源距增大而增大， 在对谱振幅进行了震源辐射方向性校正之后, 才出现谱振幅随震源距衰减的现象.由此获得了震源及近邻区域S波的Q(f)值,可表示为QS(f)=89f098其值比由尾波得出的姚安地区的平均QC(f)值低得多，表明了震源破裂带的强烈非均匀性对QS(f)的重大影响.     

2000年姚安MS65地震震源及近邻区的低QS

利用震源距23 km范围内观测的2000年姚安MS65地震余震记录，计算了震源及近邻区域的尾波规一直达S波在频率15～20 Hz之间的傅里叶谱振幅.结果显示谱振幅随震源距增大而增大， 在对谱振幅进行了震源辐射方向性校正之后, 才出现谱振幅随震源距衰减的现象.由此获得了震源及近邻区域S波的Q(f)值,可表示为QS(f)=89f098其值比由尾波得出的姚安地区的平均QC(f)值低得多，表明了震源破裂带的强烈非均匀性对QS(f)的重大影响.     

1830年磁县7．5级地震震源区尾波衰减特征

利用磁县数字地震台记录到的近震波形资料,采用Aki尾波单次散射模型,计算1830年磁县7．5级大地震震源区50km范围内的尾波Qc值;经多地震拟合得出在尾波流逝时间为20s时,Qc=（70．2±29．3）f^（0.8054±0.1615）;40s,时Qc=（96．6±25．3）,f^（0.7772±0.1098）。结果表明,磁县震源区Q0值较低,震区地震波衰减比邢台、唐山震区快;η值表明Qc值对频率的依赖性弱于邢台和唐山震区。     

Theoretical researches on three-dimensional coda wave scattering problem

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Scattered Surface Wave Energy in the Seismic Coda

One of the many important contributions that Aki has made to seismology pertains to the origin of coda waves (Aki, 1969; Aki and Chouet, 1975). In this paper, I revisit Aki's original idea of the role of scattered surface waves in the seismic coda. Based on the radiative transfer theory, I developed a new set of scattered wave energy equations by including scattered surface waves and body wave to surface wave scattering conversions. The work is an extended study of Zeng et al. (1991), Zeng (1993) and Sato (1994a) on multiple isotropic-scattering, and may shed new insight into the seismic coda wave interpretation. The scattering equations are solved numerically by first discretizing the model at regular grids and then solving the linear integral equations iteratively. The results show that scattered wave energy can be well approximated by body-wave to body wave scattering at earlier arrival times and short distances. At long distances from the source, scattered surface waves dominate scattered body waves at surface stations. Since surface waves are 2-D propagating waves, their scattered energies should in theory follow a common decay curve. The observed common decay trends on seismic coda of local earthquake recordings particular at long lapse times suggest that perhaps later seismic codas are dominated by scattered surface waves. When efficient body wave to surface wave conversion mechanisms are present in the shallow crustal layers, such as soft sediment layers, the scattered surface waves dominate the seismic coda at even early arrival times for shallow sources and at later arrival times for deeper events.     

Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL _s and time in terms of the mean-free timesL _s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ _i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q _s>Q _i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ _i, then as the distance increases, effects of scatteringQ _s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ _i should not be smaller than one tenth ofQ _s.Project Sponsored by the Joint Earthquake Science Foundation of China.     

Discussion on the Measurement Method for the Coda Wave Quality Factor

The Quality factor is the parameter that can be used to describe the energy attenuation on seismic wave. In theory, we can obtain the relationship between the change of the coda wave quality factor with time and the strong earthquake preparation process on the basis of the quality factor of a coda wave in a same ray path. However, in reality the coda wave quality factor measured by different seismic coda waves corresponds to different seismic wave ray paths. The change of the quality factor with time is related to non-elastic characteristics of the medium and the volume of scattering ellipsoid constrained by scattered wave phase fronts, besides the change of regional stress field. This paper discusses the relationship between quality factor, epicenter distance and different lapse time, and then discusses the relationship between quality factor and frequency. Furthermore the determination method of the coda wave quality factor is put forward. The improved determination method of the quality factor, which removes the influence of different earthquakes or propagation depth of scattered waves, may increase measurement precision, thus information pertaining to abnormal changes in quality factor and the relationship between the quality factor and earthquake preparation process can be acquired.     

地方震尾波震级的初步研究

地方震尾波由地壳横向不均匀性而产生的反向散射波组成。从这一观点出发,根据尾波随掠过时间的衰减特性,结合地震矩对数和地方震里克特地震级的线性关系,导出利用任一掠过时间的震尾来计算的尾波震级Mc公式。它的简化形式可以和持续时间震级的表达式近似一致。尾波震级可作为持续时间震级的一种广义形式,它是直接从震源地震矩导出的震级标度,从而为解释持续时间震级物理基础提供了可能的途径。应用于丹江地震台的资料,得到丹江口及邻区的尾波品质因子和介质函数以及地震矩对数和震级的期望关系,同时得到实用于该台的持续时间震级和简化尾波震级公式。     

Seismic codas on the Earth and the Moon: a comparison

The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance $\text{x1}$, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if $\text{x1/L ? 1}$, diffusion scattering is an appropriate model, but if $\text{x1/L ? 1}$, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than $\text{x1}$. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of $\text{(x1L)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.     

Coda waves: A review

The analysis and interpretation of coda waves have received increasing attention since the early seventies. In the past few years interest in this subject has spread worldwide, and the study of high-frequency seismic coda waves has become a very important seismological topic. As a conclusion of the studies accomplished in this time, coda waves are considered the result of scattering processes caused by heterogeneities acting on seismic waves.P andS waves play a particularly important role in this interaction. The process introduces an attenuation which, added to the intrinsic absorption, gives the observed apparent attenuation. Therefore, coda waves constitute a thumbprint left by the heterogeneities on the seismograms. Coda waves offer decisive information about the mechanism of how scattering and attenuation take place. This review describes coda waves in detail, and summarizes the work done in this subject to 1986. The relation between coda waves and attenuation in the context of research on seismic scattering problems is stressed. Particular attention has been given to the application of coda waves to estimate source and medium parameters. The state-of-the-art of the temporal variations of coda wave shape, and the possible use of these variations as an earthquake precursor also are presented. Care has been taken to introduce the statistical models used to deal with the heterogeneities responsible for scattering.     

Coda wave analysis for distinguishing attenuation due to isotropic scattering from attenuation due to absorption

When the quality factorQ is taken into account in attenuation studies, it is necessary to know the relative losses of wave energy due to scattering and to anelastic absorption. The coda is the most important phenomenon now known which is related to elastic scattering of seismic waves. Utilizing coda, this study presents relationships which give theQ factors of the medium around the recording station and discriminate between attenuations arising from elastic scattering (under the assumption of isotropic scattering) and those arising from anelastic absorption. This work proposes a technique for separately determining the attenuation due to isotropic scattering and that due to absorption from the observed envelope of coda waves.