The Theory of Coda Wave Interferometry

Coda waves are sensitive to changes in the subsurface because the strong scattering that generates these waves causes them to repeatedly sample a limited region of space. Coda wave interferometry is a technique that exploits this sensitivity to estimate slight changes in the medium from a comparison of the coda waves before and after the perturbation. For spatially localized changes in the velocity, or for changes in the source location, the travel-time perturbation may be different for different scattering paths. The coda waves that arrive within a certain time window are therefore subject to a distribution of travel-time perturbations. Here I present the general theory of coda wave interferometry, and show how the time-shifted correlation coefficient can be used to estimate the mean and variance of the distribution of travel-time perturbations. I show how this general theory can be used to estimate changes in the wave velocity, in the location of scatterer positions, and in the source location.     

山西太原东山地震台附近地区地震尾波Qc值变化特征研究

采用Aki单次散射模型,用太原东山地震台记录到的ML2.0~5.0地震,计算得到Qc值随频率的变化结果。得出,随着尾波窗长增大,平均采样体深度增加,Q0值增大,η值减小。当尾波窗长取20 s时,Q0值为70.1,η值为1.03,是东山台附近地区最佳的研究结果。     

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.     

Constituents of Vertical-component Coda Waves at Long Periods

Aki (1969) first modeled coda waves of a local earthquake as a superposition of scattered surface waves. This paper attempts to clarify the constituents of surface-wave coda at long periods at very long lapse times. For a large earthquake of magnitude 7 or larger, vertical component oscillation in periods from 90 to 180 s persists for more than 20 hours from the earthquake origin time. Although the early portion of the coda envelope is successfully modeled by assuming incoherent scattered Rayleigh waves by heterogeneities distributed all over the Earth, the later potion of the observed coda envelope (roughly later than 35,000 s) has systematically larger amplitude than theoretical prediction. To clarify the cause of this discrepancy, we studied the constituents of vertical-component seismograms of three large earthquakes recorded by the F-net in Japan using the f-k power spectral analysis. We found that the direct and scattered fundamental-mode Rayleigh waves of velocity about 3.7 km/s are dominant in the earlier part of each envelope. It justifies the use of a scattering model of the fundamental Rayleigh waves for synthesizing the envelope. At lapse times later than 20,000 s–35,000 s, higher modes with phase velocities around 20 km/s become dominant. The transition time to the dominance of higher modes is found to become earlier for a deeper focus earthquake. The small coda attenuation factor from (1.90±0.23) × 10⁻³ to (2.38±0.32) × 10⁻³ estimated from later coda envelopes recorded at IRIS stations distributed worldwide also agrees with the attenuation factor of spheroidal modes according to PREM. We may interpret that higher mode waves are uniformly distributed at large lapse time due to large velocity dispersion and/or scattering and they dominate over the fundamental mode waves because of smaller attenuation in the lower mantle. The coda attenuation measurement proposed by Aki is found to be useful even for long periods and at very large lapse times.     

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。     

Temporal Changes of Shallow Seismic Velocity Around the Karadere-Düzce Branch of the North Anatolian Fault and Strong Ground Motion

We analyze temporal variations of seismic velocity along the Karadere-Düzce branch of the north Anatolian fault using seismograms generated by repeating earthquake clusters in the aftershock zones of the 1999 M_w7.4 İzmit and M_w7.1 Düzce earthquakes. The analysis employs 36 sets of highly repeating earthquakes, each containing 4–18 events. The events in each cluster are relocated by detailed multi-step analysis and are likely to rupture approximately the same fault patch at different times. The decay rates of the repeating events in individual clusters are compatible with the Omori's law for the decay rate of regional aftershocks. A sliding window waveform cross-correlation technique is used to measure travel time differences and evolving decorrelation in waveforms generated by each set of the repeating events. We find clear step-like delays in the direct S and early S-coda waves (sharp seismic velocity reduction) immediately after the Düzce main shock, followed by gradual logarithmic-type recoveries. A gradual increase of seismic velocities is also observed before the Düzce main shock, probably reflecting post-seismic recovery from the earlier İzmit main shock. The temporal behavior is similar at each station for clusters at various source locations, indicating that the temporal changes of material properties occur in the top most portion of the crust. The effects are most prominent at stations situated in the immediate vicinity of the recently ruptured fault zones, and generally decrease with normal distance from the fault. A strong correlation between the co-seismic delays and intensities of the strong ground motion generated by the Düzce main shock implies that the radiated seismic waves produced the velocity reductions in the shallow material.     

从背景噪声提取瑞利面波频散曲线——方法与应用实例

利用地震背景噪声提取台站间的面波频散信息,进而进行地下结构研究是目前地球物理学的研究热点之一.本文详细介绍了该方法的发展历程,并以流动台阵和固定地震台站数据为例给出了较为详细的噪声数据处理过程,重点阐述了如何利用地震背景噪声提取瑞利面波的频散曲线.此外,对基层科研人员如何更好地应用固定台站数据资料的技术细节问题给出了具体解决方案.     

利用Aki模型对山西地区尾波Q值的研究

选取2001年1月至2011年12月山西地震台网记录的ML≥2．0地震的数字地震波资料,运用单次散射Aki模型,计算得到山西地区尾波Q值,拟合Q值对频率的依赖关系。其中,右玉、代县、夏县、东山4个地震台站属于低Q值、高n值,为特质的构造运动活跃地区的尾波性质。     

论全球地震面波层析成像的参数化与样条插值模型

本文的参数化方法考虑不完全依赖数据分布的基函数的构造方法。借助函极小问题与样条插值问题的密切联系,得到了样条函数形式的参数化方法,即样条插值模型,样条插值模型是著名的Ｂａｃｋｕｓ－Ｇｉｌｂｅｒｔ模型在球面情形的推广。     

桩式地震表面波屏障减震试验与数值分析

在双层均质土地基条件下,以桩长和桩间距为参数,采用模型试验法和数值分析法研究屏障桩对地震表面波的减震效果。研究结果表明,设置屏障桩可有效减弱地震表面波在土体中的传播,使桩后方减震区域加速度响应明显减弱;屏障桩长度和间距均对地震表面波在土体中的传播影响显著;在桩长试验中,减震率变化同时受桩长和地基土层影响,实际工程中应根据地基中土层分布情况进行桩长设计;在桩间距试验中,减震区域减震率达46%～56%,桩间距宜取约1.5倍桩径。     

依舒断裂带北段尾波Q值特征研究

研究表明,地震波穿过构造活动相对稳定地区时,能量衰减不明显且具有高Q值;而穿过构造活动地区时,能量会发生强烈衰减且具有低Q值。本文利用Sato模型对依舒断裂带北段萝北-通河地区15个数字化地震台站记录到的266条M_L≥2.0地震尾波Q_c值进行了分析和研究,发现黑龙江萝北、通河附近地区Q_c值具有明显的复杂性和差异性,且萝北地区Q_c值远低于通河地区Q_c值,其原因一方面与区域构造活动有关,另一方面与区域地壳构造复杂、地下介质破碎、区域应力不断变化有关。本文还讨论了萝北、通河附近地区Q值随着频率变化的关系及Q_0值空间分布特征,有效地分析了该区域介质状态的变化过程,对萝北地区地震活动性的研究和预测有指导意义。     

地震波散射研究的新进展——第25届IASPEI大会S13专题报告会“地震波散射与衰减”简介

本文以IASPEI的“地震波的散射与衰减”专题报告会为主,评述了近几年在地震波散射方面的研究进展.述评所涉及的方面有:1.关于地震尾波的起源;2.大震前尾波包络的前兆性变化;3.地震尾波包络衰降的机理;4.区分散射和吸收的新方法;5.新领域的开拓和研究.     

利用Stao模型研究上海地区中小地震尾波

利用2011—2017年上海台网记录的上海及周边50km内的地震事件,使用Stao模型,计算了东滩台、大洋山台、佘山台、天平山台、秦皇山台所在地区的尾波值,结果显示:上海及邻近地区整体呈现西高东低的分布,在东部沿海地区较低,浦西地区较高;根据上海台网的地震事件记录,发现上海地区地震虽然基本呈现弥散性分布,并没有出现沿断裂分布趋势,而整体分布为东部沿海地区及海域多于浦西地区;结合上海地区尾波值分布规律分析表明,所得值数据能够较好地反映该区域地震活动性。     

基于sato模型的山西北部地区尾波Q值研究

依据sato单次散射模型,对山西北部（北纬380-41^0）2001年至2011年13个数字遥测子台记录的地震波形资料进行计算和分析。拟合尾波窗长40S时尾波Q值对频率的依赖关系,得到山西北部地区Q值随频率的变化关系式。其中,阳原台Q。值最高,大同台Q0值最低。研究区多数台站都表现为低Q0值,高q值,符合Q值与频率的依赖关系,表明该地区地下介质非均匀程度高,构造活动强烈;另外,研究区大同台、右玉台和偏关台相对于本次研究的其他台站为低Q0值区,这一区域正好位于我省西北部NNE走向的口泉活动断裂处,中间以盆地为分割,与恒山、六棱山断裂分开,表明研究结果与研究区活动断裂和沉积厚度有一定的关系。     

云鹏水电站及其周围地震尾波Q_c值研究

利用云鹏水电站周边5个数字地震台站记录到的2000年1月至2008年12月间的108个地震的数字波形资料,采用Aki单次散射模型,计算了各台站周围423条地震记录的尾波Q0值。结果显示:云鹏水电站地区尾波的Qc值与频率的关系为Qc(f)=90.2f0.94。该地区的Q0值比云南其它构造活动强烈地区的要高,因此属于中等构造活动地区。云鹏水电站蓄水后弥勒台记录到的108个地震的尾波Q0值及分频Qc值有所下降,但下降幅度不大,表明水库蓄水对库区及其附近区域地下介质性质有所影响,但影响的程度有限。     

Effect of anelastic and scattering structures of the lithosphere on the shape of local earthquake coda

A simple model of single acoustic scattering is used to study the dependence of the shape of local earthquake coda on the anelastic and scattering structures of the lithosphere. The model is applied to the coda of earthquakes located near Stone Canyon, central California, and provides an explanation for the features observed in the data, which include an interesting temporal variation in the coda shape. A surficial layer with aQ of 50 and thickness of 10 or 25 km underlain by a zone with aQ of 1000 extending to the bottom of the lithosphere, together with a scattering scale length,a, that varies with depthz according to the relationa=0.3 exp[-(z/45)²] are found to constitute the simplest structure of the medium compatible with the coda data and with body and surface wave attenuation data. The profile of heterogeneity sizes implies that the scattering strength increases strongly with depth, a constraint required by the necessity to boost the energy of the later coda without forcing the intrinsicQ to be excessively high in the uppermost mantle. This constraint is viewed as an artifact of the single scattering model which overstimates the scattering coefficient due to the neglect of multiple scattering. The observed temporal variation of the signal is difficult to explain by a simple change of the intrinsicQ at some depth. Rather, it is suggested that the scattering properties at depth changed with time through a variation of the fractional rms velocity fluctuation on the order of one percent.     

关中、陕南及周边地区尾波衰减特性（Qc）研究

根据单次散射模型的尾波功率谱分析方法,利用陕西数字地震台网宽频带数字地震波形记录资料,计算了关中陕南及周边地区13个频段的Qc值。结果显示:在2ts~35 s的时间窗内,Q0值在37.54~72.59之间,全区平均值为58.44,在上升运动显著的秦岭山脉值较大,关中盆地和陕南值较小;在2ts~70 s的时间窗内,Q0值在194.74~283.50 之间,全区平均值为186.79,莫霍界面高波速区值较大,低速区和低速梯度带值较小。     

基于潜在破裂面源模型的南北地震带南段地震区划研究

南北地震带南段大震活动频繁。已有的研究结果表明,大震近场范围场点的地震危险性与地震破裂面产状及其尺度密切相关。因此,在南北地震带南段需要考虑潜在震源三维特征进行地震危险性分析和地震区划研究。本文在充分搜集大震发震构造资料的基础上,在南北地震带南段构建了考虑震源尺度和产状的潜在震源模型,改进了地震危险性概率分析方法,进而对该地区进行地震区划研究。结果表明,考虑潜在震源三维特征的地震危险性分析结果可以有效地反映南北地震带南段发震构造的产状和尺寸特征,提高地震区划结果的合理性。     

Verification of the Litho-spheric Structure along Profile Uppsala-Prague Using Surface Wave Dispersion

Experimental dispersion curves of Rayleigh and Love waves along the Uppsala-Prague profile have been determined using records of several Italian earthquakes. To interpret the dispersion data, results of previous geophysical investigations in this region were first analyzed. Seven blocks of the crust and upper mantle were distinguished along the profile on the basis of deep seismic sounding and other seismic data. Layered models were proposed for these blocks. Computation of Rayleigh and Love waves shows a large differentiation of theoretical dispersion curves for the northern (Precambrian) and southern (Palaeozoic) part of the profile. A laterally inhomogeneous model for theUppsala - Prague profile, composed of the seven blocks, satisfies the surface wave data for the profile. Moreover, a mean layered model for the whole profile has also been proposed.