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.     

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。     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

Heterogeneities in the field of short period seismic wave attenuation in the lithosphere of central Tien Shan

Records of deep-focus Hindu Kush earthquakes in the depth ranges 70–110 and 190–230 km made by 45 digital and analogue seismic stations were analyzed to study the attenuation field of short period seismic waves in the lithosphere of central Tien Shan. The dynamic characteristics studied include the ratio of peak amplitudes in S and P waves (S/P) and the ratio of the S-wave maximum to the coda level in the range t = 400 ± 5 s, where t is the lapse time (S/c400) for 1.25 Hz. Comparatively high values of S/P are shown to prevail in most of the area, corresponding to lower S-wave attenuation. Upon this background is a band of high and intermediate attenuation in the west of the area extending along the Talas-Fergana fault in the south and afterwards turning north-northeast. The rupture areas of the two largest (M ≥ 7.0) earthquakes which have occurred in Tien Shan during the last 25 years are confined to this band. Abnormally high values of S/c400 were obtained for stations situated in the rupture zone of the August 19, 1992, magnitude 7.3 Suusamyr earthquake and around it. For two of the stations we found considerable time variations in the coda envelope before the earthquake. The effective Q was derived from compressional and shear wave data for the entire area, as well as for the band of high attenuation. Comparison with previous data shows that the attenuation field in the area has changed appreciably during 20–25 years, which can only be due to a rearrangement of the fluid field in the crust and uppermost mantle. It is hypothesized that a large earthquake is very likely to occur in the northern part of the attenuating band.     

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。     

Scattering coefficients in the mantle revealed from the seismogram envelope analysis based on the multiple isotropic scattering model

At longer periods, scattered ScS waves sometimes dominate over coda waves at large lapse times. Examining recordings of seismic envelopes at 9 IRIS seismic stations of regional earthquakes with focal depths deeper than 150 km in periods from 1 to 20 s for a wide lapse time range up to 2000 s, we found significant frequency dependence. The coda decay gradient at short periods is steeper than that at longer periods; however, the change of coda gradient associated with the ScS arrival becomes distinct as the period becomes longer. In particular, a clear offset of coda amplitude appears in central Asia for 10 and 15 s period bands. The multiple isotropic scattering process of S-waves in the heterogeneous mantle can be simply simulated by using the Monte Carlo simulation method based on the radiative transfer theory in scattering media. Assuming a two-plane-layer attenuation structure and smoothed velocity model of the PREM, we estimated the average total scattering coefficients of S-waves such as 7.52 × 10^− 4∼1.32 × 10^− 3 km^− 1 and 2.08 × 10^− 4∼6.23 × 10^− 4 km^− 1 at 4 s, and 4.51 × 10^− 4∼7.37 × 10^− 4 km^− 1 and 2.80 × 10^− 5∼2.71 × 10^− 4 km^− 1 at 10 s, for the lithosphere and the upper mantle and for the lower mantle, respectively. Our results indicate that scattering occurs mostly in the lithosphere and the upper mantle and support that medium heterogeneity spreads over the whole mantle though its scattering power is small. Strong scattering occurs beneath central Asia and Papua New Guinea, whereas the scattering beneath Italy and regions of east Russia is much weaker. The numerical calculation enables us to confirm that much stronger scattering than intrinsic attenuation causes the offset behavior with coda decay gradient change after the ScS arrival for 4 and 10 s period bands in some regions.     

单次与多次散射对地方震尾波的作用

在Aki(1969)的单次反向散射理论和高龙生(1983)的多次散射理论基础上,提出了震源距不为零的单次与多次散射模型。在此模型下,研究了二维无限介质空间中,由统计上均匀分布的各向同性散射体引起的单次与多次散射对地方震尾波功率谱的作用。推导出了二维情况下单次散射和多次散射尾波功率谱的解析表达式,并在二维情况下对不同震源距的单次散射与多次散射对尾波功率谱的作用进行了比较。      

A slow earthquake

Anomalous earthquakes such as creep events, tsunami earthquakes and silent earthquakes have been reported in the recent literature. In this paper we discuss an anomalous “slow earthquake” that occurred on June 6, 1960 in southern Chile. Although the surface-wave magnitude of this event is only 6.9, it excited anomalously large long-period multiple surface waves with a seismic moment of 5.6 · 10²⁷ dyn cm. The Benioff long-period seismogram of this earthquake recorded at Pasadena shows an extremely long, about 1.5–2 h coda of Rayleigh waves, with a period of 10–25 s. The coda length for other events with a comparable magnitude which occurred in the same region is about 10 min. This observation suggests that the long coda length is due to a long source rupture process which lasted at least 1 h. Although at least 15 distinct events can be identified in the coda, no short-period body waves were recorded corresponding to these, except for the first one. These results suggest that a relatively small (M_s ? 6.9) earthquake triggered a series of slow events; the duration of the whole sequence being longer than 1 h. This event probably occurred on a transform fault on the extension of the Chile Rise and provides important information regarding the nature of the transform fault.     

Frequency-Dependent Attenuation of Coda Waves in the Crust in Southwest Anatolia (Turkey)

The attenuation of coda waves in the earth’s crust in southwest (SW) Anatolia is estimated by using the coda wave method, which is based on the decrease of coda wave amplitude in time and distance. A total of 159 earthquakes were recorded between 1997 and 2010 by 11 stations belonging to the KOERI array. The coda quality factor Q _c is determined from the properties of scattered coda waves in a heterogeneous medium. Firstly, the quality factor Q ₀ (the value of Q _c at 1 Hz.) and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves for frequencies of 1.5, 3.0, 6.0, 8.0, 12 and 20 Hz. Secondly, the attenuation coefficients (δ) are estimated. The shape of the curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The average Q _c values vary from 110 ± 15 to 1,436 ± 202 for the frequencies above. The Q ₀ and η values vary from 63 ± 7 to 95 ± 10 and from 0.87 ± 0.03 to 1.04 ± 0.09, respectively, for SW Anatolia. In this region, the average coda Q–f relation is described by Q _c = (78 ± 9)f ^0.98±0.07 and δ = 0.012 km^?1. The low Q ₀ and high η are consistent with a region characterized by high tectonic activity. The Q _c values were correlated with the tectonic pattern in SW Anatolia.     

利用尾波测定四川部分地区的介质品质因子

按照安艺敬一(Aki)提出的地震尾波理论,利用同一地震的多台记录,以同一地震有一确定的地震矩为基础建立方程,并以文献[8]所得出的品质因子数为基准,测定了四川部份地区地壳浅部的介质品质因子.结果表明,地震尾波的衰减存在着明显的方位依赖.根据1971年至1975年间几次地震所给出 Q 值来看,四川部份地区大致可以分为三个不同的 Q 值区,值得注意的是:低 Q 区内曾发生过7.1级强震.     

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.     

Lateral variations of coda Q and attenuation of seismic waves in Southwest Anatolia

The seismic quality factor (Q _c) and the attenuation coefficient (δ) in the earth’s crust in southwest (SW) Anatolia are estimated by using the coda wave method based on the decrease of coda wave amplitude by time on the seismogram. The quality factor Q _o, the value of Q _c at 1 Hz, and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves. δ is determined from the observations of amplitude variations of seismic waves. In applying the coda wave method, firstly, a type curve representing the average pattern of the individual coda decay curves for 0.75, 1.5, 3.0, 6.0, 12.0, and 24.0 Hz values was estimated. Secondly, lateral variation of coda Q and the attenuation coefficients for three main tectonic patterns are estimated. The shape of the type curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The Q _o and η values vary from 30 to 180 and from 0.55 to 1.25, respectively for SW Anatolia. In SW Anatolia, coda Q–f relation is described by and δ = 0.008 km⁻¹. These results are expected to help in understanding the degree of tectonic complexity of the crust in SW Anatolia.     

Comparison of amplitude decay rates in reflection,refraction, and local earthquake records

Three types of seismic data recorded near Coalinga, California were analyzed to study the behavior of scattered waves: 1) aftershocks of the May 2, 1983 earthquake, recorded on verticalcomponent seismometers deployed by the USGS; 2) regional refraction profiles using large explosive sources recorded on essentially the same arrays above; 3) three common-midpoint (CMP) reflection surveys recorded with vibrator sources over the same area. Records from each data set were bandpassed filtered into 5 Hz wide passbands (over the range of 1–25 Hz), corrected for geometric spreading, and fit with an exponential model of amplitude decay. Decay rates were expressed in terms of inverse codaQ (Q _c ^–1 ).Q _c ^–1 values for earthquake and refraction data are generally comparable and show a slight decrease with increasing frequency. Decay rates for different source types recorded on proximate receivers show similar results, with one notable exception. One set of aftershocks shows an increase ofQ _c ^–1 with frequency.Where the amplitude decay rates of surface and buried sources are similar, the coda decay results are consistent with other studies suggesting the importance of upper crustal scattering in the formation of coda. Differences in the variation ofQ _c ^–1 with frequency can be correlated with differences in geologic structure near the source region, as revealed by CMP-stacked reflection data. A more detailed assessment of effects such as the depth dependence of scattered contributions to the coda and the role of intrinsic attenuation requires precise control of source-receiver field geometry and the study of synthetic seismic data calculated for velocity models developed from CMP reflection data.     

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.     

Changes in source and site effects compared to codaQ −1 temporal variations using microearthquakes doublets in California

We analyse spectral ratio of the coda of doublets of microearthquakes. Our purpose is to find evidence for temporal changes of the attenuation in the crust before a large magnitude earthquake. A Moving Window Cross Spectral analysis of the coda of doublets gives a plot of the spectral ratio as a function of lapse time along the seismogram, for several frequency bands (SR(T, f) plot). From a certain pattern in theSR(T, f) plot, we should infer a temporal change in coda attenuation. Several doublets recorded in Central California by the USGS network are analysed.Using events very close in time from one another, we show that the radiation pattern can be different enough to induce important variations in the spectral ratio of the first arrivals and of the coda.Another doublet exhibits a strong variation of the low frequencies for stations in the region of Hollister (California), wherePhillips andAki (1986) have noted a strong amplification of low frequencies, that they attribute to site effects on unconsolidated sediments in the fault zone. These variations could be related to slight changes in local conditions (creep, or water table).On the other hand, some doublets, in the vicinity and close in time to the August 1979 Coyote Lake Earthquake (M=5.9), show no variation inSR(T, f) related to this earthquake: this proves that there was no major change in attenuation in the crust preceding this large shock. If a change occurred, it should have been confined to a very limited region, which was not sampled by the many paths we studied.The employed method probably provides today the most accurate estimation of spectral ratio in the coda of microearthquakes. It shows that there are numerous kinds of variations and that it is not straightforward to relate them to coda attenuation changes only. Also, we must be circumspect when dealing with the coda of microearthquakes in relation to forecasting earthquakes.     

2005年云南文山地震余震序列尾波Qc值研究

基于Aki等（1975）的地方震尾波单次散射模型,利用文山地震台记录到2005年8月13日在云南文山县发生的5.3级地震余震序列的数字化波形观测资料,测量了震源区尾波Q（f）值。测量结果表明,当中心频率为1．5Hz时,文山地区的尾波Q值在52～155之间,平均值为91,尾波的振幅衰减率β（f）在0.013～0．039之间,平均值为0．024;测量得到该区尾波Qc值与频率f的关系为Qc（f）=62f^“0.87;尾波波源因子A0与震级ML成正比关系,满足关系lgA0=1．02ML-0．73。此次地震的发震构造为文山断裂带,地震波受到破碎带强烈的非弹性吸收,尾波Qc值明显降低。     

Study of Sediment Nonlinearity Using Explosion Data in the Mississippi Embayment

Strong and weak motion data from the Mississippi Embayment Seismic Excitation Experiment (ESEE) were analyzed for signatures of nonlinear site responses. This experiment was performed jointly by the University of Memphis and U. S. Geological Survey in October 2002, by detonating two explosions of 2500 and 5000 lbs. Intrinsic and scattering Q estimates (Q_I and Q_S) from the coda of the strong motion data were found to be very low compared to previously determined Q values of P- and Rayleigh waves of weak motion data from the same explosions. The Q_I estimates from P-wave late coda of the strong motion data are less by more than 100 at 3 Hz and by more than 200 at 10 Hz, compared to the P-wave Q values determined from the weak motion data by Langston et al (2005). Also, Q_I determined from the late coda of strong motion Rayleigh-wave data is less by more than 200 at 0.5 Hz and by more than 50 at 3.0 Hz, compared to Q values determined from Rayleigh-wave weak motion data. A resonance peak spectral amplitude of the early part of a strong motion seismogram is shifted to lower frequencies compared to that from a later part of the same seismogram. Spectral amplitude ratios between transverse and vertical components of the strong motion data are degraded between frequencies 2 and 10 Hz for P waves, and less than 4 Hz for Rayleigh waves compared to the weak motion transverse to vertical spectral ratio. All these are signatures of nonlinear site responses during strong ground motion. This study proves the non-transportability of weak motion attenuation results to estimate ground motion from a future large earthquake that may take place in areas like the New Madrid Seismic zone.     

尾波持续时间比τH/τV 在强震短临预报中的应用

本文根据Aki等人提出的尾波理论,导出了地方震尾波水平分量与垂直分量的持续时间比的具体表达式: τ_H/τ_V=I_H/I_V(Q_H/Q_V)~(1/4)·B_H/B_V。该式表明,τ_H/τ_V的变化主要反映了震源体一定范围内,由于介质的各向异性而引起的尾波在不同方向上的激发及衰减能力的差异。本文还讨论了地震前τ_H/τ_V短临异常的物理机制,认为异常的产生与孕震期间介质内裂隙的出现和闭合有关。1986年门源6.4级地震和1975年海城7.3级地震前,τ_H/τ_V都有不同程度的短期低值异常及临震高值突跳。门源地震前后门源台记录的直达S波的最大振幅比A_(mH)/A_(mv)也有与尾波持续时间比类似的异常。最后通过对一些震例的分析,初步得到震级与异常时间的关系为M=0.657lnT+3.44。     

Attenuation of P- and S-waves in the Chamoli Region, Himalaya, India

The attenuation properties of the crust in the Chamoli region of Himalaya have been examined by estimating the frequency-dependent relationships of quality factors for P waves (Q_α) and for S waves (Q_β) in the frequency range 1.5–24 Hz. The extended coda normalization method has been applied on the waveforms of 25 aftershocks of the 1999 Chamoli earthquake (M 6.4) recorded at five stations. The average value of Q_α is found to be varied from 68 at 1.5 Hz to 588 at 24 Hz while it varies from 126 at 1.5 Hz to 868 at 24 Hz for Q_β. The estimated frequency-dependent relations for quality factors are Q_α = (44 ± 1)f^(0.82±.04) and Q_β = (87 ± 3)f^(0.71±.03). The rate of increase of Q(f) for P and S waves in the Chamoli region is comparable with the other regions of the world. The ratio Q_β/Q_α is greater than one in the region which along with the frequency dependence of quality factors indicates that scattering is an important factor contributing to the attenuation of body waves in the region. A comparison of attenuation relation for S wave estimated here (Q_β = 87f^0.71) with that of coda waves (Q_c = 30f^1.21) obtained by Mandal et al. (2001) for the same region shows that Q_c > Q_β for higher frequencies (>8 Hz) in the region. This indicates a possible high frequency coda enrichment which suggests that the scattering attenuation significantly influences the attenuation of S waves at frequencies >8 Hz. This observation may be further investigated using multiple scattering models. The attenuation relations for quality factors obtained here may be used for the estimation of source parameters and near-source simulation of earthquake ground motion of the earthquakes, which in turn are required for the assessment of seismic hazard in the region.     

Attenuation characteristics of Garwhal–Kumaun Himalayas from analysis of coda of local earthquakes

Coda of local earthquakes that occurred during 2006–2007 are used to study the attenuation characteristics of the Garhwal–Kumaun Himalayas. The coda attenuation characteristics are represented in terms of coda Q or Q _c . It is observed that Q _c increases with frequency. Q _c also varies with increase in lapse time of coda waves. Q _c increases up to an 85-s average lapse time. This is similar to observations around the world reported by many workers who have interpreted this as a manifestation of the fact that heterogeneity decreases with depth. However, around a 90-s average lapse time Q _c is lower than its values for lower and higher average lapse times. This is interpreted as an indication of possible presence of a fluid-filled medium or a medium having partial melts at around a 160-km depth. Q ₀, i.e., Q _c at 1 Hz, increases, and frequency parameter n decreases with increasing lapse time, barring around a 90-s lapse time. This again shows that in general, heterogeneity decreases with increasing depth. The Q ₀ and n values for smaller lapse times are similar to those for tectonically active areas. By comparing Q _c values obtained in this study with those obtained by us using the 1999 Chamoli earthquake aftershocks, it is concluded that the crust is turbid and the mantle is more transparent. However, whether the variation in Q _c values between 1999 and 2006–2007 is temporal or not cannot be definitely established from the available data set.