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1.
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. 相似文献
2.
Yuehua Zeng 《Pure and Applied Geophysics》2006,163(2-3):533-548
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. 相似文献
3.
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%. 相似文献
4.
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. 相似文献
5.
Seismic coda Q and turbidity coefficient at the Phlegraean Fields volcanic area: Preliminary results
Digital recordings of microearthquake codas from shallow seismic events in the Phlegraean Fields region (south-central Italy) were used to calculate the attenuation factor Qc.A quite unusual frequency dependence was found for the coda attenuation comparable to Hawaii pattern of Qc. This is interpreted as due to the presence of magma that increases the amount of anelasticity. Amount of scattering at Phlegraean Fields was estimated through the « turbidity » coefficient (Dainty model), that shows a high degree of scattering due to inhomogeneities as compared to Hawaii. Probably this is due to the greater crustal thickness of Phlegraean Fields with respect to Hawaii that produces more scattering. 相似文献
6.
本文试用数字地震记录求取尾波Q值及其与频率的关系.在微机上处理触发数字地震仪记录的资料,原始记录经数字滤波器作窄带通滤波得到一组分频记录,经过时间序列分析的方法,可得到能量密度随时间衰减的曲线,该曲线比从可见记录求得的较为可靠.以散射模型的理论表达式进行曲线拟合,求得Q值及其与频率的关系.值得注意的是,这个结果对某一台站并非常数,尾波Q值是时间窗(即研究所用尾波的整个延续时间)的函数,其原因可能是由于不同到时的尾波采样区域和深度不同,以及多次散射的影响等.因此,当把Q值作为地震预报的一个参数时,延续时间是一个重要的可选择的因子. 相似文献
7.
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. 相似文献
8.
9.
Synthesis of coda waves in layered medium 总被引：3，自引：0，他引：3
10.
Anton M. Dainty 《Pure and Applied Geophysics》1990,132(1-2):221-244
The application of standard array processing techniques to the study of coda presents difficulties due to the design criteria of these techniques. Typically the techniques are designed to analyze isolated, short arrivals with definite phase velocity and azimuth and have been useful in the frequency range around 1 Hz. Coda is long in time and may contain waves of different types, phase velocities and azimuths. Nonetheless, it has proved possible to use or adapt array methods to answer two questions: what types of waves are present in coda and where are they scattered? Most work has been carried out on teleseismicP coda; work on local coda has lagged due to lack of suitable data and the difficulties of dealing with high frequencies. The time domain methods of beamforming and Vespagram analysis have shown that there is coherent energy with a high phase velocity comparable toP orPP in teleseismicP coda. These methods can detect this “coherent” coda because it has a fairly definite phase velocity and the same, or close to, azimuth as firstP orPP. This component must consist ofP waves and is either scattered near the source, or reflected in the mantle path as apdpP or precursorPP reflection. The Fourier transform method of the frequency-wavenumber spectrum has been adapted by integrating around circles of constant phase velocity (constant total wavenumber) to produce the wavenumber spectrum, which shows power as a function of wavenumber, or phase velocity. For teleseismicP coda, wavenumber spectra demonstrate that there is a “diffuse” coda of shear,Lg or surface waves scattered from teleseismicP near the receiver. Wavenumber spectra also suggest that the coherent coda is produced by near-source scattering in the crust, not mantle reflection, since it is absent or weak for deep-focus events. Crustal earthquakes have a very strong coherent component of teleseismic coda, suggesting scattering from shear to teleseismicP near the source. Three-component analysis of single-station data has shown the presence of off-azimuth arrivals and may lead to the identification of waves scattered from a single scatterer. 相似文献
11.
A. V. Nikolaev 《Pure and Applied Geophysics》1989,131(4):687-702
The processes of seismic wave scattering and dissipation are examined in a medium that, in addition to being inhomogeneous and anelastic, is nonlinear and seismically active (seismic emission). In such a medium, there is a complex interrelation between the effects of nonlinearity, scattering and dissipation. Thus, nonlinear interactions between the various components (primary, scattered and induced) of a developing wavefield cause nonlinear (or wave-on-wave) scattering and, by transferring part of the wave energy to the high-frequency region, contribute to its scattering and dissipation. On the other hand, whereas dissipation opposes the accumulation of nonlinear effects by reducing the wave amplitudes, scattering assists it by increasing the propagation distance (and hence the interaction time).Estimates based on results of field experiments involving vibrators indicate that, as a rule, scattering on inhomogeneities is much stronger than nonlinear scattering, and that nonlinear effects may often dominate dissipative ones.The nonlinearity of the transmitting medium explains observedQ-value anomalies, and its seismic activity explains the existence ofP coda and the temporal changes in codaQ. 相似文献
12.
A single scattering model was used to analyse the temporary changes in the mean density of scattered waves in a discrete random medium. The model of the mean energy density, originally proposed bySato (1977) for spherical radiation and isotropic scattering, has been modified and applied to a medium in which the scatterers are confined to a specified volume. The time variation of the early part of the mean energy density function for the different source durations was investigated. The dominant effect on the theoretical mean energy density is caused by the specified volume containing scatterers. The duration of the source pulse influences the early part of the coda fort/t
0<1.2, wheret is the lapse time measured from the source origin time, andt
0is arrival time of the body wave.The analysis of the coda signal of micro-events occurring immediately in front of the face enables us to estimate the size of the fracture zone induced by the stope. The model of the mean energy density of coda for a medium containing scatterers close to the seismic source was used to analyse a large number of events recorded close to an advancing mine face in a deep level gold mine in South Africa. The coda decay rate has two trends: the first, with a steep decay of coda, is produced by a larger deviation of rock parameters and/or larger size of the scatterers; the second trend, which decays more slowly, has the corresponding mean-free path ranging from 20 m to 200 m. The analysis indicates that the rock mass about 15–20 m from the stope contains a large proportion of fractured and blocked rock, which is the source of scattering. The scattering of theS-wave was much stronger and more stable, with the mean-free path varying from 11 m to 45 m. This is due to the shorter wavelength of theS wave in comparison with theP wave. The quality factor for theP coda wave varies from 30 to 100 in the fracture zone of stope and outside this zone it has a value of 300. The quality factor of theS wave varies from 20 to 78 in the equivalent volume. For rock surrounding the stope the ratioQ
sp
–1
/Q
ss
–1
varied from 0.31 to 0.69. This suggests that the radii of scatterers are smaller than 3.5 m. 相似文献
13.
Antonio Rovelli 《Physics of the Earth and Planetary Interiors》1983,32(3):209-217
The frequency dependence of Qβ for seismic waves in a distance range with a maximum of 150 km from the epicentre of the Irpinia earthquake of November 23, 1980 has been sought using displacement spectral ratios computed from strong-motion accelerograms recorded in the region. The method has been applied to calculate the behaviour of Qβ as a function of frequency in the band 0.1–25 Hz, and to investigate whether azimuthal variations appear in seismic Qβ for the lithosphere in central southern Italy. The same result is obtained using data from stations in western south Italy as using data from eastern south Italy, namely, The linear relationship suggest that apparent Qβ depends more on the scale of heterogeneity of the lithosphere, affecting reflection and scattering mechanisms, than on intrinsic energy losses related to the anelasticity of the materials through which the seismic waves propagate.The existence of a peak in Qβ?1 has been investigated in the low-frequency band (0.1–2.5 Hz) using a higher resolution power. A stable result in this low-Qβ zone is not possible on the basis of the available data: only in six Qβ(f) profiles does an evident minimum exist, between 0.2 and 1 Hz, while in nine cases the curves are monotonically increasing from the lowest observable frequencies; a further nine cases appear of uncertain interpretation. 相似文献
14.
Ari Ben-Menahem 《Physics of the Earth and Planetary Interiors》1977,15(1):P10-P18
Source parameters of 27 major shallow earthquakes in the magnitude range 7.0–8.6, which occurred during 1906–1969, are used to establish dimensionless invariants involving the fault dimensions, average slip, and the rise time. It is found that these entities are expressible as simple functions of the subsonic shear Mach number (M) and the cube root of the seismic potency, . Moreover, a new principle is suggested according to which all dimensionless numbers which can be constructed from the basic fault elements are simple powers of the contraction factor with coefficients of the order unity. The laws of dynamical similarity thus found are those appropriate for subsonic rupture in which the Mach number is very close to unity and the radiation efficiency is between and . The empirical similarity laws are shown to be compatible with a source model in which the fault plane is simulated by a flexible membrane with additional restoring stiffness forces provided by an elastic medium attached to it on one side. Results suggest the possibility that earthquake rupture, together with the radiation of seismic waves, terminates at the moment that Mach 1 is reached. 相似文献
15.
D.D. Singh B.K. Rastogi Harsh K. Gupta 《Physics of the Earth and Planetary Interiors》1979,18(2):143-152
The source characteristics of 33 earthquakes with magnitude mb between 4.4 and 6.0, which occurred in the Himalayan and nearby regions, are investigated using the records of the Hyderabad seismograph station. The P- and S-wave spectra of these events are interpreted in terms of Brune's seismic source model for estimating the source parameters, i.e., seismic moment, source dimension, stress drop, average dislocation, apparent stress and the radiated energy. Seismic moments, M0, vary between 0.3 × 1024 and 9.0 × 1026 dyne cm; source dimensions, r, between 4.3 and 18.6 km; stress-drops, Δσ between 0.3 and 151.6 bar; average dislocations, between 0.6 and 381 cm; apparent stresses, between 0.1 and 73.2 bar. The radiated energy, ER is estimated by the spectrum integration method and is found to vary between 0.2 × 1018 and 9.3 × 1022 erg. In general, the stress drop and apparent stress are found to be high, indicating high stresses in these regions. 相似文献
16.
Orson L. Anderson 《Physics of the Earth and Planetary Interiors》1982,29(1):91-104
It is shown that there is linearity between the thermal pressure PTH and T between the Debye temperature θ and some high temperature . has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of increases greatly as the pressure increases. It is therefore concluded that PTH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles. 相似文献
17.
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. 相似文献
18.
J.Peter Watt 《Physics of the Earth and Planetary Interiors》1981,25(1):57-63
Mean atomic weight profiles for the lunar mantle have been calculated from velocity-density systematic relations using lunar density and seismic velocity models. Despite large variability among the models, the calculation including Poisson's ratio yields a range of mean atomic weight values between 22 and 23 g mol?1 below 150 km. A similar calculation for the Earth's mantle produces a mean atomic weight of 21.1 ±0.4 g mol?1. This suggests that the Moon cannot be derived directly from the Earth's mantle, or that it has had a differentiation history different from the Earth's. The lunar require an Fe mole fraction between 0.25 and 0.33 for a pure olivine mantle, or between 0.33 and 0.45 for pure pyroxene.The present profiles are 0.5–3.0 g mol?1 higher than those calculated from lunar compositional models based on lunar rock compositions and petrology and assumed lunar histories, indicating inadequacies in either the seismic or compositional models, or in both. The mean atomic weight approach provides a method of comparing the consistency of seismic and compositional models of planetary interiors. 相似文献
19.
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. 相似文献
20.
George Purcaru 《Physics of the Earth and Planetary Interiors》1979,18(4):274-287
The available data on the destructive intermediate earthquakes () in the Vrancea, Romania, region have been examined with the aim of revealing some time-magnitude regularities. The basic idea is that the total sequence (? 1100–1973 yr.), which appears as random, could be decomposed in some regular source-components which, by extrapolation, are superimposed to predict the future total sequence.The common nature of faulting (reverse dip-slip) and inferred regularities in the time-magnitude pattern of destructive Romanian earthquakes — (a) three active (seismic) time-bands alternating with quiet periods, the existence of (b) “quasicycles” and of (c) “supercycles” — led to the following predictions: (1) the occurrence of a shock with in 1980 ± 13 years; and (2) later earthquakes are predicted in 2005, in 2030–2040 (), and one with nearly maximum magnitude () in 2070–2090.In every century, about 40 years represent a time interval of high seismic danger for Romania and, according to the proposed long-term time-magnitude model, three destructive earthquakes arc to occur in (and/or near) the evidenced seismic periods P1, P2 and P3.It is shown that, taking into account the actual difficulties involved in the earthquake prediction, the Vrancea destructive earthquake of March 4, 1977 (M = 7.1) was quite successfully predicted. 相似文献