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.     

Propagation and attenuation characteristics of the crustal phaseLg

TheLg wave consists of the superposition ofS waves supercritically reflected, and thus trapped, in the crust. This mode of propagation explains the strong amplitude of this phase and the large distance range in which it is observed. The numerical simulation leads to successful comparison between observed seismograms in stable continental areas and synthetics computed for simple standard crustal models. In regions with strong lateral variations, the influence of large-scale heterogeneities on theLg amplitude is not yet clearly established in terms of the geometrical characteristics of the crustal structure.The analysis of the decay of amplitude ofLg with epicentral distance allows the evaluation of the quality factor ofS waves in the crust. The results obtained show the same trends as codaQ: a clear correlation with the tectonic activity of the region considered, both for the value ofQ at 1 Hz and for its frequency dependence, suggesting that scattering plays a prominent part among the processes that cause the attenuation.The coda ofLg is made up of scatteredS waves. The study of the spatial attenuation of the coda indicated that a large part of the arrivals that compose the coda propagate asLg. The relative amplitude of the coda is larger at sites located on sediments because, in these conditions, a part ofLg energy can be converted locally into lower order surface modes.     

On the generation and decay of the long-period coda energy of large earthquakes

Seismic coda wave is the tail portion of the earthquake record after main arrivals. Studies on the coda usually focus on high-frequency data within several hours after regional events and attribute them to the scattering effect of the heterogeneities inside the earth. Here, we use records of seven large earthquakes at globally distributed seismic stations to examine the decay of long-period (100 s to 300 s) coda in the time window of 10,000 s to 140,000 s after the origin time and fit it with a statistical model. The geometric spreading effect in the estimated initial energy and a location-independent equivalent attenuation coefficient indicate that the long-period coda energy is less affected by the heterogeneity-induced scattering effect than that of shorter-period coda. The coda energy can reach the earth's inner core and can be explained by a 1D earth model, making it more effective for constraining the global attenuation model. It also has the potential to determine the magnitudes of large earthquakes and to explore the interior of planetary bodies.     

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.     

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.     

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.     

Characteristics of the seismic attenuation in two tectonically active zones of Southern Europe

The seismic energy attenuation in the frequency range of 1–18 Hz was studied in the two tectonically active zones of Irno Valley (Southern Italy) and Granada Basin (South-East Spain). Data were recorded by short period vertical components seismographs for low-magnitude local earthquakes. The method of coda waves, assuming singleS toS scattering approximation, was used to calculate the quality factorQ from the two data set. Results show a quality factor increasing with frequency, following the empirical lawQ=Q _o f ⁿ .Q _o andn are lower for the Irno Valley than for Granada. This result is interpreted in terms of different scattering environments present in the two investigated areas.     

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.     

澜沧江流域水电工程地区的尾波衰减

利用围绕澜沧江水利水电枢纽工程地区的8个地震台记录到的数字化波形资料,根据尾波散射理论,以不同的中心频率研究了该地区的尾波衰减。结果显示：研究区尾波的Q0值在46～80之间,平均值为63;田值在0．66～0．94之间,平均值为0．79。与云南其它地区相比,研究区的Q0值比构造活动强烈地区的要高,属于中等构造活动地区;与世界上其它地区相比,研究区的尾波衰减不同于构造地震活动相对较弱的地区,而与构造地震活动频繁、强烈的地区较为接近,因此判断澜沧江流域及周边地区未来有发生中强地震的可能。另外,地震波衰减与断层的破碎程度有明显的依赖关系,地震波经过断层破碎带时,被强烈散射和吸收,Q0值明显降低,而且,不但近场的地震波衰减具有这种性质,远场的地震波衰减也同样具有这种特性。     

A review of numerical experiments on seismic wave scattering

This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers.     

利用天然地震研究地壳Q值的方法和进展

从地震波衰减品质因子(Q值)的含义及其研究意义出发,介绍了国内外利用天然地震的体波、尾波、Lg波开展地壳介质品质因子Q值研究的方法和动态,阐述了各种方法的方法原理及应用范围等,并展望了利用天然地震研究介质Q值的趋势。     

上月壳中的散射引起月震尾波的数值模拟研究

在阿波罗月震记录中普遍存在着强烈持久的尾波信号,这样的波形特征无法用均匀分层月球模型解释.一个普遍被接受的解释是月震尾波由月球浅层结构对月震波的散射引起.我们采用基于交错网格的伪谱和有限差分混合方法模拟研究非均匀上月壳对月震波的散射效应,在此基础上解释月震尾波的形成机制,并估计出上月壳速度扰动的强度.我们发现,在均匀分层模型基础上,进一步考虑上月壳中的非均匀结构对月震波的散射效应,能有效地解释月震信号中强烈持久的尾波.我们认为月震尾波可能是由上月壳中的低波速、低衰减和散射这三个因素的共同作用所引起.采用不同的扰动标准差模拟上月壳的非均匀性,并比较模拟波形与真实月震图的相似程度,我们发现上月壳中速度扰动的标准差应该在3%到5%之间,很可能接近于3%.     

The physical implication of coda amplitude ratio and its possible application

The physical implication of coda amplitude ratio is discussed in term of energy ratio. The digitized data recorded at the station of Beijing Telemetered Seismograph Network between 1989 and 1990 are used to calculate amplitude ratios of coda to direct S wave, and energy ratios. The spectral energy ratios are used to estimate the coda Q and mean free path l in the Beijing area, as well as the two quality factors Q _i and Q _S separately due to intrinsic absorption and scattering attenuation. The decay of seismic waves in their propagation seems mainly resulted from the intrinsic absorption in Beijing region. The temporal variations of amplitude ratio and energy ratio at Changli station during the above two years are inspected; some of them largely depart from their mean value. It may reflect the seismogenic process, but using the data lasting longer time with more case histories needs further study. This study is sponsored by the Key Project of State Science and Technology of China, No. 96-918.     

腾冲火山区剪切波和尾波衰减初步研究

用云南腾冲火山地区观测的地震数字化记录进行了尾波和剪切波的衰减测量。用AkiandChouet和Sato单次散射模型获得 5 2秒和 18秒流逝时间尾波的品质因子分别为Qc (f) =5 7×f- 0 94和Qc (f) =2 6×f- 0 95 ,表明地壳上部和地壳上地幔的地震波衰减频率变化率一致。两者均未显示出活火山地区尾波衰减的异常特征。尾波掠过空间椭球的平均半轴 ,前者约为 80km ,大大超出了腾冲火山分布的地理范围 ,后者约为 30km ,在腾冲火山分布的地理范围之内。用尾波规一双台S波振幅比法进一步缩小所用地震波掠过的空间 ,最后获得了S波随频率的衰减有类似于前人报导的活火山地区尾波频率衰减的特征 :相对于低频 (1 5～ 6Hz) ,高频 (6～2 0Hz)的Q- 1s 变化很小。从地表位置看 ,腾冲最年青的全新世的马鞍山和老龟坡火山就在S波掠过范围内 ,打鹰山火山也在近旁。这一结果表明在这三座火山体之下存在低速高衰减体。火山或处于休眠状态 ,或在消亡过程之中。     

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。     

Attenuation characteristics of coda waves and estimation of Q c values in eastern China

For short-period near-earthquake records in eastern China, from the empirical attenuation formula of coda ground motion amplitudeA with timeτ: lgA=G−2. 235 lgτ, using the single scattering theory modified with epicentral distance, we obtain the curve family of corrected coda amplitudeA _c(r,t), andω/2Q _c values for each time interval of coda. From this,Q _c(f,h) values, which correspond to each observational average frequency and sampling depth, are calculated. The results substantially agree with those observationalQ _c values in Yunnan, Beijing and central Asia.     

Estimation of frequency dependent coda wave attenuation structure at the vicinity of Cairo Metropolitan Area

Estimation of seismic wave attenuation in the shallow crust in terms of coda wave Q structure previously investigated in the vicinity of Cairo Metropolitan Area was improved using seismograms of local earthquakes recorded by the Egyptian National Seismic Network. The seismic wave attenuation was measured from the time decay of coda wave amplitudes on narrow bandpass filtered seismograms based on the single scattering theory. The frequency bands of interest are from 1.5 to 18 Hz. In general, the values obtained for various events recorded at El-Fayoum and Wadi Hagul stations are very similar for all frequency bands. A regional attenuation law Q _c = 85.66 f ^0.79 was obtained.     

Phase and Correlation in `Random' Seismic Fields and the Reconstruction of the Green Function

We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of P to S energy ratio indicating the modal equipartition of the wavefield. This property clearly shows that the coda waves are in the regime of multiple scattering. Numerical solutions of the elastic radiative transfer equation are used to illustrate the evolution of the wave-field towards P-to-S energy stabilization, and asymptotically to complete isotropy. The energy properties of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering enhancement, an expression of the so-called `weak localization', demonstrates that interference effects still persist for multiple diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green function between two stations by averaging the cross correlation of coda waves produced by distant earthquakes and recorded at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wavefield. Using broadband seismic coda waves, we show that the dominant phases of the Green function in the band 2 s–10 s, namely fundamental mode Rayleigh and Love waves, are reconstructed. We analyze the time symmetry of the cross correlation and show how the level of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering by randomly distributed scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the Earth. Surface waves can be extracted from long time series. The dispersion curves of Rayleigh waves are deduced from the correlations. On paths where measurements from earthquake data are also available, we show that they are in good agreement with those deduced from noise correlation. The measurement of velocities from correlation of noise along paths crossing different crustal structures opens the way for a `passive imaging' of the Earth's structure.