A single-station coda solution for source, attenuation and site factors

Based on the empirical formulation formed from coda observations, the digital waveforms from 33 local events with magnitude M _L ranging between 2.1 and 3.5, recorded at Changli station of Beijing Telemetered Seismographic Network from 1989 to 1991, are used to compute coda Q for the Changli region and the source factors of all earthquakes by single-station coda method. Furthermore, assuming a certain source model, we have obtained the station site frequency response and source spectra, as well as source parameters such as corner frequencies, seismic moments and stress drops and so on. Their variations with time are monitored before and after larger earthquakes. Because the coda method can more effectively reduce the influence of source radiation pattern and a particular propagation path than direct wave method, more data can be used and more accurate results can be obtained, which provided a possible approach to study the source properties and reveal the variation of source parameters before larger earthquakes. Contribution No. 97A0107, Institute of Geophysics, SSB, China.     

汶川地震余震震源参数及地震动衰减与场地影响参数反演分析

基于强震动观测台钻孔数据, 统计得到了四川、 甘肃地区20 m深的浅硬土层场地平均剪切波速模型． 通过与美国加州地区的波速模型对比, 结合四川、 甘肃地区地震预报的地壳模型, 延拓剪切波速模型至40 km． 应用四分之一波长法计算了浅硬土层场地的平均场地放大系数． 利用场地放大系数, 消除13次余震中浅硬场地的台站场地响应, 反演了龙门山断层上、 下盘的介质品质因子以及13次余震的有效应力降． 通过与普通土层场地的强震动记录对比, 对浅硬土层场地的放大系数进行调整, 得到了深厚土层场地的平均放大系数．      

Study on inelastic attenuation coefficient, site response and source parameters in Shanxi region

Introduction Seismic recording is the information recorded by seismograph when earthquake occurs, which is a kind of comprehensive information, including the characteristics of earthquake focus, propagation path of seismic wave and site response, etc. Therefore, we must try to distinguish source effect, propagation path and site response in the seismic recordings in order to obtain accu-rate parameters. The method of Atkinson has better solved the problem (Atkinson, Mereu, 1992), which is bas…     

The inversion of anelastic coefficient,source parameters and site respond using genetic algorithm

It gradually becomes a common work using large seismic wave data to obtain source parameters, such as seismic moment, break radius, stress drop, with completingof digital seismic network in China (Hough, et al, 1999; Bindi, et al, 2001). These parameters are useful on earthquake prediction and seismic hazard analysis.Although the computation methods of source parameters are simple in principle and the many research works have been done, it is not easy to obtain the parameters accurately. There are two factors affecting the stability of computation results. The first one is the effect of spread path and site respond on signal. According to the research results, there are different geometrical spreading coefficients on different epicenter distance. The better method is to introduce trilinear geometrical spreading model (Atkinson, Mereu, 1992; Atkinson, Boore, 1995; WONG, et al, 2002). In addition, traditional site respond is estimated by comparing with rock station, such as linear inversion method (Andrews, 1982), but the comparative estimation will introduce some errors when selecting different stations. Some recent research results show that site respond is not flat for rock station (Moya, et al, 2000; ZHANG,. et al, 2001; JIN, et al, 2000; Dutta, et al, 2001). The second factor is to obtain low-frequency level and corner frequency fromdisplacement spectrum. Because the source spectrum model is nonlinear function,these values are obtained by eye. The subjectivity is strong. The small change of corner frequency will affect significantly the result of stress drop.     

柯坪块体震源介质参数测定

应用2011年1月-2015年4月柯坪块体及周边数字地震台站（38°-42.5°N,75°-80.5°E）记录的3.0 ≤ M ≤ 5.0地震事件,结合柯坪块体介质品质因子和各台站场地响应,计算各地震应力降、地震矩、震源破裂半径、拐角频率等新震源参数,并研究各背景值变化特征及彼此间对应关系。结果表明：柯坪块体地区地震震级与地震矩、矩震级、震源尺度之间表现为较好的正相关性,与地震拐角频率之间呈负相关。地震矩与震源破裂尺度整体呈正相关,但当震源破裂尺度较小时,地震矩变化不大,当震源破裂尺度大于250 m时,地震矩随震源破裂尺度的增大变化较快。由柯坪块体应力降时间分布特征分析可知,研究区具有地震前应力降呈现高值异常、震后缓慢恢复低值的演化过程。     

Temporal change in scattering and attenuation associated with the earthquake occurrence—A review of recent studies on coda waves

The study of coda waves has recently attracted increasing attention from seismologists. This is due to the fact that it is viewed as a new means by which the stress accumulation stage preceding a large earthquake can be measured, since the scattering paths nearly uniformly cover a fairly large region around the focus and observation stations, compared with the direct ray paths. To date, we have had many reports on the temporal variation of the relation between coda duration and amplitude magnitude, and that of the coda attenuationQ _c ^–1 which is estimated from coda amplitude decay. Some of these have shown a precursor-like behavior; however, others seem to have shown a coseismic change. We have critically reviewed these reports, and discussed what these observational facts tell us about the change in the heterogeneous crust. We found significant temporal variations, not only in the mean but also in the scatter ofQ _c ^–1 , associated with the mainshock occurrence. The formation of new cracks, the reopening and growing of existing cracks, the interaction of these cracks, and the pore water movement through these cracks might correspond to such variations. In addition, we may expect an inhomogeneous distribution of crack clusters in a fairly large region, compared with the aftershock region. The gradual appearance of such crack clusters seems to be the most plausible mechanism by which coda decay gradients are caused to largely scatter in the stress accumulation stage.     

安徽地区地震波衰减、场地响应及震源新参数的测定

根据安徽数字地震台网7个地震台的143条波形资料,研究了安徽地区的衰减模型和各台站的场地响应。采用三段几何衰减模型拟合,得到了安徽及邻近地区的几何衰减函数,得到安徽地区非弹性衰减Q值随频率f的关系为Q(f)=235.3×f0.616;7个台站的场地响应均无明显的放大效应,这与它们均处于岩石地基相符;并在本地区地震预测研究中尝试使用新参数,进行了初步的应用。     

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.     

四川地区震源参数和台站场地响应初步研究

利用成都遥测数字地震台网数字地震波形数据资料,采用Atkinson方法得到四川地区的品质因子Q值与频率,的关系为：Q（f）=203．1f0.834。采用Moya方法反演得到了地震的场地响应,采用Moya方法与Atldnson方法分别得到了相应地震的震源谱参数,两种方法的结果保持了很好的一致性。得到的震源参数结果表明：地震矩与震级的关系为：logM0=17．27＋1．18Mt,地震矩与拐角频率关系,即随着地震矩的增大,拐角频率减小,这些地震的应力降在10-400巴之间,应力降与地震矩之间没有明显的依赖关系。     

Scaling of stress drop and high-frequency fall-off of source spectra

It has been observed for a long time that the high-frequency fall-off constant of source spectra is about 2 for "large" earthquakes and about 3 for "small" earthquakes. For earthquakes between "large" and "small", the highfrequency fall-off constant is not an integer and varies with the size of the earthquake. In this article such a variation is explained in the perspective of the scaling of stress drop, which proposes a new approach to the study of the scaling of stress drop using seismic data with lower quality of completeness and high-frequency characteristics. The study on the source spectra of the aftershocks of the 1988 Lancang-Gengma, Yunnan, China earthquake shows that the high-frequency fall-off of source spectra and its variation with the size of earthquake can be well explained by the model that for "large" earthquakes the stress drop is a constant while for "small" earthquakes the stress drop increases with the size of the earthquake.     

场地响应、震源参数与介质衰减的同时反演

采用Ω平方模型来约束中小地震的震源位移振幅谱，从而实现对震源参数、介质的几何扩散特征、介质的非弹性衰减以及场地响应等参数的同时反演，数值模拟结果表明该方法是可靠的。江苏省苏南地区的几何扩散较好地符合三段衰减统计模型，该地区的品质因子与频率的依赖关系以频率3．0Hz为界分为低频、高频二部分．且均符合指数衰减关系，而全部频率点的品质因子频率依赖关系似乎与四元素流变模型的Q值理论频率特征曲线比较一致。该地区中小地震地震矩对数值与震级ML具有较好的线性关系；地震矩与拐角频率呈现出良好的双对数关系，且该地区的地震应力降与震源半径之间的关系在震源半径小于300m时与圆盘静态破裂模式理论关系较吻合。     

A model for attenuation and scattering in the Earth's crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB ₀=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q _o f ⁿ , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500Q _o2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (QQ _o f ^0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.     

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.     

京西北延庆—怀来盆地的QSH值和小震震源参数的测定

用在一个地震台接上到的同一震源区内的较小地震的振幅谱去除大地震的振幅谱，求得较大地震震源同频趋势的斜率。利用Ｑ值在０．０００１－１００Ｈｚ之间几乎是常数是特性，用网格搜寻法对较大地震的振幅谱因衰减造成的损耗进行补偿，同时确定自震源对地震吧途径上的介持的品质因数、拐角频率和补偿后的频谱的零频极限。用这种方法，利用中－欧合作北京西北怀来数字地震台网的记录，确定了延庆－怀来盆地的品质因数ＱＳＨ值并测定了     

新疆伽师地区非弹性衰减、场地响应与震源参数研究

本文用伽师地区11个数字地震台记录的地震波形资料,用Atkinson方法反演该地区地震波的非弹性衰减;用Moya方法反演11个台的场地响应。扣除地震记录中的传播路径、场地响应与仪器响应后,用遗传算法测定参与计算的76次地震震源参数。分析结果表明:伽师地区Q0值小于天山中东段地区Q0值,这表明该地区构造运动要比天山中东段剧烈,地震活动反映的情况也是如此;11个台的台基都有不同程度的放大效应。在单对数坐标下,76次地震震级与地震矩、震源尺度成正相关关系,与拐角频率成反相关关系。地震震级与应力降之间没有明显依赖关系,表明该地区地震应力降值可作为一个参数为地震预测服务。     

Estimation of site amplification,attenuation and source spectra of S-waves in the East-Central Iran

Generalized inversion of the S-wave amplitude spectra from the strong-motion network data in the East-Central Iran has been used to estimate simultaneously source parameters, site response and the S-wave attenuation (Q_s). In this regard, 190 three-component records were used corresponded to 40 earthquakes with the magnitudes M3.5–M7.3. These earthquakes were recorded at 42 stations in the hypocentral distance range from 9 to 200 km. The inverse problem was solved in 20 logarithmically equally spaced points in the frequency band from 0.4 to 15 Hz. The frequency-dependent site amplification was imposed, as a constraint, on two reference site responses in order to remove the undetermined degree of freedom in the inversion and obtain a unique inverse solution. Also, a geometrical spreading factor was assumed for removing the trade-off between geometrical spreading and anelastic attenuation. Different source parameters, such as seismic moment (M₀), seismic energy (E_s), corner frequency (f_c) and Brune stress drop (Δσ), were estimated for each event by fitting an ω² model to the spectra obtained from the inversion. The stress drop values of earthquakes, obtained in this research, are in good agreement with those of other studies. Also average site response values were correlated to the average shear wave velocities in the uppermost 30 m, in high and low frequency bands. The peak frequencies of site amplifications, estimated by the generalized inversion method, where in good agreement with those of horizontal to vertical (H/V) spectral ratios for the S-wave portion of records. However, no perfect matching in amplitude was obtained due to the deficiencies of the H/V ratio technique. By supposing a free shape for Q factor, a frequency dependent function was found, the logarithm of which could be approximated by a linear function, Q(f)=151f^0.75. The uncertainties of model parameters have been evaluated by covariance matrix of least-square fit. The residuals were also analyzed in order to assess the validity of the model. The analysis of residuals with respect to magnitude and distance indicates that they are distributed normally with approximately zero mean. The robustness of the results has been studied concerning their sensitivities to the omission of different datasets, selected randomly from original database. The results obtained here can be used in predicting ground-motion parameters applying stochastic methods.     

中小地震震源参数的求解及其相似关系

根据广东数字地震台网记录的区域性地震记录,利用遗传算法采用由"三段几何衰减模型"拟合得到的广东地区的衰减模型,得到广东地区Q值与频率的关系(Q(f)=454 8f0 37),由此衰减模型反演得到各台站的场地响应,最终得到72个中小地震的震源参数;并研究了广东地区震源参数的特征及其相似关系。这些地震的地震矩在1012N·m与1014N·m之间,求出与地方震震级之间的相似关系;该地区中小地震的应力降在0 02到3 2MPa之间,未显示与地震的规模(地震矩)有明显的依赖关系。     

Spectral analysis and earthquake scaling of the Petatlan earthquake (M s =7.6) aftershocks,recorded at stations along the pacific coast and between the coast and Mexico City

Spectral parameters have been estimated for 214 Petatlan aftershocks recorded at stations between Petatlan and Mexico City and between Petatlan and Acapulco. The spectral parameters were used to obtain empirical relations for the estimation of seismic moment from coda length and fromM _L . Stress drops, using Brune's model, were calculated for these aftershocks. Six events with large stress drop are located within a previously suggested asperity, and seven more suggest a boundary zone at the intersection of the Petatlan and Zihuatanejo aftershock rupture volumes. Stress drops increase with increasing seismic moment up to 10²⁰ dyne-cm but appear to be constant at greater moment values. The peak horizontal velocity times distance of aftershocks recorded near the coast and between the coast and Mexico City (30 to 270 km away), scales linearly with seismic moment, and predicts well the peak horizontal values of large (M _s 7.0) coastal thrust events recorded on rock sites at Mexico City. Peak horizontal velocity is a straightforward measurement, thus this relation allows us to evaluate expected ground motion between the Pacific coast and Mexico City from the seismic moment of subduction related earthquakes along the coast.     

Spectral characteristics of natural and artificial seismic events in the Lop Nor test site, China

Seismic discriminants based on the spectral seismogram and spectral magnitude techniques have been tested to discriminate between three events; a nuclear explosion which took place in Lop Nor, China with m _b 6.1 and two earthquakes from the closest area with m _b 5.5 and 5.3, respectively. The spectral seismogram of the three events shows that the frequency content of the nuclear explosion differs from that of the earthquakes where the P wave is richier in high frequency content in the nuclear explosion than the corresponding earthquakes. It is also observed that the energy decays more rapidly for the nuclear explosion than for the earthquakes. Furthermore, the spectral magnitudes reveal significant differences in the spectra between the nuclear explosion and the two earthquakes. The observed differences appear to be quite enough to provide a reliable discriminant. The estimated stress drop from the magnitude spectra indicates a higher stress drop of the nuclear explosion relative to the earthquakes of the same tectonic region.