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.     

Attenuation of coda waves in northern Greece

The single scattering model has been applied for the estimation of codaQ values for local earthquakes that occurred in northern Greece during the period 1983–1989 and recorded by the telemetered network of the Geophysical Laboratory of the University of Thessaloniki. CodaQ estimations were made for four frequency bands centered at 1.5 Hz, 3.0 Hz, 6.0 Hz and 12.0 Hz and for the lapse time windows 10–20 sec, 15–30 sec, 20–45 sec, 30–60 sec and 50–100 sec. The codaQ values obtained show a clear frequency dependence of the formQ _c =Q ₀ f ⁿ , whileQ ₀ andn depend on the lapse time window.Q ₀ was found equal to 33 andn equal to 1.01 for the time window of 10 to 20 sec, while for the other windowsQ ₀ increased from 60 to 129, withn being stable, close to 0.75. This lapse time dependence is interpreted as due to a depth dependent attenuation. The high attenuation and the strong frequency dependence found are characteristic of an area with high seismicity, in agreement with studies in other seismic regions.     

Boundary-reflected waves and ultrasonic coda waves in rock physics experiments

Ultrasonic coda waves are widely used to study high-frequency scattering. However, ultrasonic coda waves are strongly affected by interference from by boundary-reflected waves. To understand the effect of boundary-reflected waves, we performed ultrasonic experiments using aluminum and shale samples, and the rotating staggered-mesh finite-difference method to simulate the wavefield. We analyzed the wavefield characteristics at the different receiving points and the interference characteristics of the boundary-reflected waves with the ultrasonic coda wave, and the effect of sample geometry on the ultrasonic coda waves. The increase in the aspect ratio of the samples delays the interference effect of the laterally reflected waves and reduces the effect on the ultrasonic coda waves. The main waves interfering with the ultrasonic coda waves are laterally reflected PP-, PS-, PPP-, and PPS-waves. The scattering and attenuation of the high-frequency energy in actual rocks can weaken the interference of laterally reflected waves with the ultrasonic coda waves.     

Probing mid-mantle heterogeneity using PKP coda waves

We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%.     

西昌地区地方震尾波衰减Q值

基于单次散射模型的尾波动功率谱分析法,利用西昌遥测台网地震波实时处理系统记录的２４个地震数字化波形资料,计算了西昌地区地球介质对应于１３个不同的ＱＣ值,在１．０－２０．０Ｈｚ频率范围内,以幂函数ＱＣ＝ＱＣｆ＾ｎ拟合ＱＣ值随的变化关系,其中Ｑ０值在４３．０－８２．４之间,ｎ值在０．２４－０．９４之间,平均值分别为６６．２和０．５３。     

Attenuation of coda waves in the Northeastern Region of India

Coda wave attenuation quality factor Qc is estimated in the northeastern region of India using 45 local earthquakes recorded by regional seismic network. The quality factor Qc was estimated using the single backscattering model modified by Sato (J Phys Earth 25:27–41, 1977), in the frequency range 1–18 Hz. The attenuation and frequency dependence for different paths and the correlation of the results with geotectonics of the region are described in this paper. A total of 3,890 Qc measurements covering 187 varying paths are made for different lapse time window of 20, 30, 40, 50, 60, 70, 80, and 90 s in coda wave. The magnitudes of the analyzed events range from 1.2 to 3.9 and focal depths range between 7 and 38 km. The source–receiver distances of the selected events range between 16 and 270 km. For 30-s duration, the mean values of the estimated Qc vary from 50 ± 12 (at 1 Hz) to 2,078 ± 211(at 18 Hz) for the Arunachal Himalaya, 49 ± 14 (at 1 Hz) to 2,466 ± 197 (at 18 Hz) for the Indo-Burman, and 45 ± 13 (at 1 Hz) to 2,069 ± 198 (at 18 Hz) for Shillong group of earthquakes. It is observed that Qc increases with frequency portraying an average attenuation relation for the region. Moreover, the pattern of Qc^− 1 with frequency is analogous to the estimates obtained in other tectonic areas in the world, except with the observation that the Qc^− 1 is much higher at 1 Hz for the northeastern region. The Qc^− 1 is about 10^− 1.8 at 1 Hz and decreases to about 10^− 3.6 at 18 Hz indicating clear frequency dependence. Pertaining to the spatial distribution of Qc values, Mikir Hills and western part of Shillong Plateau are characterized by lower attenuation.     

Effects of multiple scattering on coda waves in three-dimensional medium

The contribution of multiple scattering to the coda waves for three-dimensional elastic medium is investigated by extending the computational procedures developed earlier for the two-dimensional medium. It is shown that the effects of multiple scattering start to become important at a shorter lapse time,t _c = 0.65(n ₀σu)^?1, than in the two-dimensional case (t _c = 0.8(n ₀σu)^?1).     

Site amplification effect of coda waves in West Tunnan Experimental Site

The site effect of coda waves for four types of basement under 6 stations was studied by using the local earthquakes from digital seismograph network of West Yunnan Experimental Site. Results from the band 0.75 to 24 Hz showed that the site effect was abviously interrelated with not only the frequency but also the site condition of the station. For those stations which sited on the hard-rock, such as Jianchuan (limestone), Shuanglang (limestone), Qiaohou (sandstone) and Eryuan (metamorghic rock), the site amplification as a function of frequency was similar in shape and the changes in amplification were flat. A typical behavior of sediment was measured at Qina station. The site amplification remained high at low frequency, but turned to a low level as frequency increased. However, in contrast to Qina, the variations of site amplification at Yangbi station were quite different. Such different behavior between the two sites could be caused by the difference in sediment thickness under valley basins. It could be seen that the site amplification pattern of horizontal motion approached approximately to the vertical despite of some differences. The Fourier spectra of small earthquakes also showed the character of site. It can be expected that the site response has an important effect on the shape of the spectra and that the size of the magnitude is not likely responsible for the spectra recorded at the same site. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, Supp., 1993.     

龙滩水库地区P波、S波和尾波衰减

利用发生在龙滩水库地区的144次ML≥1.0地震资料,研究了该地区地壳介质的衰减特征,并采用尾波归一化方法分别估算了P波、S波的品质因子QP和QS,用单次反散射模型计算了尾波品质因子QC．结果表明,该地区上述3个值与频率的依赖关系分别为QP（f）=（7.43±0.78）f(1.05±0.06),QS（f）=（13.08±3.20）f(1.76±0.15),QC（f）=（50.52±2.71）f(1.13±0.03),总体呈现低QO和高η值的特点．在所研究的频带范围1—16Hz内,QS／QP比值均大于1,表明该地区体波衰减中散射可能起着较大作用．QC与QS的比较结果表明,在小于8Hz时,QS＜QC;而大于8Hz时,则QS＞QC．这可能是由于介质的多次散射作用的结果．     

Temporal variations in coda duration of local earthquakes in the Wellington region,New Zealand

Temporal variations of coda duration, relative to event magnitude, for local earthquakes near Wellington have been investigated. The region is one of plate convergence and subduction. The data consist of routinely made observations for events from 1978 through 1985 (1552 events), magnitude 1.6 to 5.2, depth 0.5 to 90.0 km. The observed average (over time) correspondence between duration (as measured from the origin time) and magnitude is reasonably well predicted by the single backscattering theory of coda formation for events of magnitude 4 or less; for larger events the observed durations are longer than predicted. This theory predicts that a temporal increase in scattering attenuation will reduce the coda duration relative to magnitude. Thus, any temporal changes in the duration-magnitude relation can be interpreted in terms of changes inQ. However, it is necessary to consider spatial biases since the observed durations are relatively long for shallow events and, for events of all depths, at stations situated in the south-eastern half of the region, usually believed part of the accretionary border. For both these situations other evidence would suggest that the scattering coefficient would be relatively high (lowQ). These observations may be due to a relatively high component of surface wave scattering and the importance of multiple scattering in the later part of the coda in regions of lowQ as suggested by finite element studies of coda formation. Despite the lack of any significant earthquakes during the 1978–1985 period there is nevertheless a significant temporal change in duration observed in the Wellington region: a change from relatively long to relatively short codas occurred in mid-1981. This change correlates well with changes in the rate of activity,b-value, radon emission, and ground tilt as derived from lake levels. It is not yet clear how all these parameters are related physically, but an episode of aseismic slip, or creep, along the plate interface below the region may have been the cause.     

On the possibility of using the tidal modulation of seismic waves for forecasting earthquakes

The earthquake forecasting technique based on the effect of the modulation of high frequency seismic noise (HFSN) by the Earth’s tides is discussed and the experience of its practical application in Kamchatka is described based on the extensive measurement data for 1996–2013. The empirical development of the lower magnitude threshold on the epicentral distance is refined. The reliability and validity of the precursor are assessed. The efficiency of the precursor is estimated in two ways. It is shown that the results of applying the prognostic procedure statistically significantly differ from a random guess. The presented estimates are based on the catalog containing 68 earthquakes of 1996–2013 in the predicted magnitude interval M ≥ 5.0 at the epicentral distances that are linked to the magnitude by functional dependence.     

Attenuation characteristics of coda waves and estimation ofQc 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.     

Moment magnitudes of two large Turkish earthquakes on February 6, 2023 from long-period coda

Two large earthquakes (an earthquake doublet) occurred in south-central Turkey on February 6, 2023, causing massive damages and casualties. The magnitudes and the relative sizes of the two mainshocks are essential information for scientific research and public awareness. There are obvious discrepancies among the results that have been reported so far, which may be revised and updated later. Here we applied a novel and reliable long-period coda moment magnitude method to the two large earthquakes. The moment magnitudes (with one standard error) are 7.95±0.013 and 7.86±0.012, respectively, which are larger than all the previous reports. The first mainshock, which matches the largest recorded earthquakes in the Turkish history, is slightly larger than the second one by 0.11±0.035 in magnitude or by 0.04 to 0.18 at 95% confidence level.     

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.     

Lapse time and frequency-dependent attenuation characteristics of coda waves in the Northwestern Himalayas

We analyzed the local earthquakes waveform recorded on a broadband seismic network in the northwestern Himalayan Region to compute lapse time and frequency dependence of coda Q (Q _c). The observed Q _c values increase with increasing lapse time at all frequency bands. The increase in Q _c values with lapse time is attributed to an increase in Q _c with depth. This implies that attenuation decreases with increasing depth. The approximate radius of medium contributing to coda generation varies from 55 to 130 km. By comparing the Q _c values with those from other regions of the world, we find that they are similar to those obtained from tectonically active regions. The estimated Q _c values show a frequency-dependent relationship, Q _c = Q ₀ f ⁿ , where Q ₀ is Q _c at 1 Hz and n represents degree of frequency dependence. They represent the level of heterogeneity and tectonic activity in an area. Our results show that northwest Himalayas are highly heterogeneous and tectonically very active. Q ₀ increases from 113 ± 7 to 243 ± 10 and n decreases from 1.01 ± 0.05 to 0.85 ± 0.03 when lapse time increases from 30 to 70 s. As larger time window sees the effect of deeper part of the Earth, it is concluded that Q ₀ increases and n decreases with increasing depth; i.e., heterogeneity decreases with depth in the study area.     

Attenuation characteristics of coda waves and estimation of Qc values in eastern China

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利用超声尾波观测1.5 m长岩石断层黏滑实验的波速变化

在实验室内利用超声尾波观测大尺度（1.5 m）岩石断层的黏滑过程.利用基于尾波干涉的观测方法,我们获得了高达10^-6的相对波速变化的观测精度,这相当于~10 kPa的应力变化.利用高精度的测量,我们获取两种不同加载速率下（1 μm·s^-1,10 μm·s^-1）黏滑过程三个阶段（恢复、加载和滑动）基于波速变化的特征量.我们更进一步获取了断层失稳阶段波速变化的时空演化过程.最后讨论了该观测方法需要改进的地方.以上研究结果表明作为一种对现有实验观测手段的有益补充,利用超声尾波观测实验室大尺度岩石断层的动力学过程是可行的.

     

Surface waves from earthquakes in Northern Atlantic-Arctic Ocean

Summary Earthquakes in the region of Jan Mayen exhibit two different appearances on records of near-by stations: classa with extremely well developed Love waves and less well developed Rayleigh waves, classb with poorly developed or missing Love waves but with clear Rayleigh waves. The difference between the two classes is ascribed to different focal depths. The Love waves of classa start simultaneously with theS wave and have initial periods over 40 sec; they have a small vertical component increasing along the wave train. They are unable to propagate beyond the continental margin for any considerable distance, probably due to a breakdown of the condition for constructive interference valid for their oceanic propagation.The oceanic dispersion curves both of Love and Rayleigh waves have been deduced using records at Kiruna, Uppsala, Bergen, Copenhagen, Scoresby Sund, Reykjavik, and Akureyri. The average thickness of the oceanic crust is around 15 km in the Norwegian Sea. For the Mid-Atlantic Ridge southwest of Reykjavik a crustal thickness of 10 km is obtained. The average thickness of unconsolidated sediments is around 2.4 km for the Norwegian Sea, and around 1.0 km in shallower regions of the ocean toward Iceland and Greenland.

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Zusammenfassung Erdbeben in der Gegend von Jan Mayen zeigen zwei verschiedene Erscheinungen in den Aufzeichnungen naheliegender Stationen: Klassea mit ausserordentlich gut entwickelten Love-Wellen und weniger gut ausgebildeten Rayleigh-Wellen, Klasseb mit schwach entwickelten oder fehlenden Love-Wellen aber mit deutlichen Rayleigh-Wellen. Der Unterschied zwischen den beiden Klassen wird verschiedener Herdtiefe zugeschrieben. Die Love-Wellen der Klassea beginnen unmittelbar mit derS-Welle und haben Anfangsperioden über 40 sek; sie haben eine geringe vertikale Komponente, die im Laufe des Wellenzuges zunimmt. Sie können sich nicht über den Kontinentalrand beträchtlich weit fortpflanzen, was möglicherweise einem Aufhören der Voraussetzung für konstruktive Interferenz, die bei ihrer ozeanischen Ausbreitung vorhanden ist, zugeschrieben werden muss.Unter der Benutzung der Aufzeichnungen von Kiruna, Uppsala, Bergen, Kopenhagen, Scoresby Sund, Reykjavik und Akureyri wurden ozeanische Dispersionskurven sowohl für Love- als auch für Rayleigh-Wellen bestimmt. Die mittlere Mächtigkeit der ozeanischen Kruste beträgt ungefähr 15 km unter dem Europäischen Nordmeer. Für die Mittelatlantische Schwelle südwestlich von Reykjavik wurde eine Krustenmächtigkeit von 10 km erhalten. Die mittlere Mächtigkeit von unbefestigten Sedimenten ist ungefähr 2.4 km für das Europäische Nordmeer und ungefähr 1.0 km in Gegenden flacheren Meeres nach Island und Grönland hin.