Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

Attenuation of seismic waves of very low frequency

The quality factor of the free oscillations of the earth is calculated from the observed time rate of decay of the energy. Records of the I.P.G.P. long-period data acquisition system are used, after a process enhancing a chosen mode, so that the scatter in the Q results is reduced. Determination of attenuation is made for the spheroidal and torsional fundamental modes and two torsional higher modes.The attenuation of seismic waves is determined from the decay of energy of standing-wave patterns with time, and from the damping of travelling waves with distance, using the surface mantle waves recorded at a single I.P.G.P. long-period seismic station after each great circle path (Gaulon, 1971).     

Multiple scattering ofSH waves in 2-D media with many cavities

The full waveform synthetic seismogram of multiple scatteredSH waves by many cylindrical cavities in two-dimensional homogeneous elastic media is computed. We used the so-called single-layer potential integral representation of the scattered field and a discretization scheme with line source distribution for each cavity. The total field is the sum of the incident wave plus the field radiated from all sources, each multiplied by an unknown complex constant representing its strength. These constants are determined by imposing the appropriate boundary conditions in the least-squares sense. Here we solve scattering problems involving one, two, four, twelve and fifty cavities regularly distributed in a half-space. The seismograms computed along the free-surface show regions where the incident wave is strongly attenuated, as well as the arrivals of all multiple scattered phases. The accuray of the method is estimated from the degree of agreement of our solution for one cavity with the corresponding analytical solution, and also from the magnitude of the residual tractions along the boundaries of two cavities separated at various distances. Finally we apply the method to compute the case of fifty cylindrical cavities, each of radiusa, randomly distributed in a region 80a wide by 30a deep in a half-space. The value of scattering loss is obtained from the amplitude decay of the primary wave with distance for wavelengths in the range from 1.7a to 13.3a, using the synthetic seismogram calculated for the same distribution of 50 cavities as above, but in full-space.     

Dispersion ofSH body waves in a continuously stratified elastic half space

Summary The dispersion ofSH body waves in a continously stratified isotropic medium is studied theoretically. Limiting forms of the displacement are given for zero, small and large values of the horizontal component of the wave number. It has been shown that below a certain characteristic frequency the dependence of the displacement on the distance from the free surface is monotonic instead of periodic.     

Propagation ofSH waves in an infinite elastic plate with Cauchy's initial transverse stress

Summary Cauchy theory of initial stress has been applied to investigate the problem of SH waves in an initialy stressed elastic plate. The initial stress is assumed to be a uniform tension or compression along the thickness of the plate. It is found that the initial stress influences the velocities of the dispersive modes only but, it has no influence on the velocity of the non-dispersive wave.     

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.     

Attenuation of high-frequency earthquake waves in South America

Earlier attenuation studies for the South American continent indicate that for Sn and Lg waves there is low attenuation in the shield region east of the Andes, whereas in the west of South America, with some exceptions, there is high attenuation. Those studies, however, were nonquantitative. In this study theQ ₀ (1-Hz values) for Lg waves for South America are presented, based on a scattering model ofAki (1969) as extended byHerrmann (1980) for the coda waves of shallow local and near-regional earthquakes. The results of the codaQ method are compared with those obtained byNuttli's method (1973). TheseQ ₀ values are in good agreement with the apparentQ ₀ of Lg waves obtained by the latter method. The data were obtained from over 100 local and regional earthquakes recorded by 12 WWSSN stations throughout continental South America. They provided a range of frequencies from 0.4 to 1.4 Hz, for which the frequency dependence ofQ was investigated by assumingQ=Q ₀(f/f ₀). The observed data indicate that the tectonic region of western South America is characterized by lowQ ₀ and a large frequency-dependent factor , the values ranging from 150 to 350 and 0.4 to 0.7, respectively. TheQ ₀ values increase in the shield region east of the Andes, but frequency dependence decreases. The average crustalQ ₀ for north and central Argentina ranges from 420 to 580, and ranges from 0.2 to 0.3. TheQ ₀ is larger in the Brazil region, ranging from 580 to 980, and varies from 0.0 to 0.2. In the lower-attenuation region of eastern South America higher values of attenuation correlate with greater thickness of the sedimentary layers.     

Attenuation of multiple ScS waves beneath the Japanese Arc

36 pairs of multiply-reflected ScS waves from deep earthquakes around Japan are analyzed to investigate the anelastic properties of the mantle on the continental and oceanic sides of the dipping slab. The average Q-value for shear waves passing through the mantle on the oceanic side is found to be 226 in the frequency range 10–40 mHz. This Q-value is in good agreement with the Q models SL8 (Anderson and Hart, 1978) and QBS (Sailor and Dziewonski, 1978) which have been derived from free oscillation data. Assuming that the Q-value for the mantle deeper than 400 km on the continental side of the Japanese Arc is the same as that for the model SL8, we obtain a value of Q = 53 in the upper mantle above the dipping slab beneath the Sea of Japan. Higher Q-values are obtained for the mantle behind the northern Izu-Bonin arc.     

地震前后电离层截止频率处电场频谱强度变化分析——以2006年汤加Mw8.o地震为例

以汤加Mw8.0地震为例,着重分析了DEMETER卫星记录中截止频率附近电磁场频谱在震前的异常演化特征.根据地震前后该区域3个月的数据对比,发现电场频谱增强与地震孕育的关系很不明显.而长时间、大范围的电场频谱减弱现象可能更值得关注,白天和夜间的电场频谱显示同一特征.2006年夏秋季节38次6级以上强震短期异常的统计平均...     

裂缝、裂隙介质衰减频散研究

为研究裂缝、裂隙介质中波致流引起的衰减,将裂缝看作背景孔隙岩石中非常薄且孔隙度非常高的层状介质,并等价成White周期层状模型.分别考虑不同类型的裂隙和孔隙之间的挤喷流影响,结合改进的Biot方程,推导得到裂缝裂隙介质的刚度与频率的关系.当缝隙中饱含流体时,介质的衰减和速度频散受裂缝、孔隙之间和裂隙、孔隙之间流体流动的显著影响.在低频极限下,裂缝裂隙介质的性质由各向异性Gassmann理论和挤喷流模型获得;而在非常高的频率时,由于缝隙中的压力来不及达到平衡,波致流的影响可忽略.分析表明,裂隙密度主要影响波的衰减,而裂隙纵横比主要控制优势衰减频率和速度显著变化的频率范围;由于不同裂隙的衰减机制不同,衰减和速度频散大小有所差异,但基本趋势相同.

     

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤M_L≤4.6) recorded at a three-component digital network.By applying the pulse broadening method to the first P-wave pulse, we found an average Q_p value of ca. 140. The application of the frequency decay method provided a Q_p value of ca. 120, in the low-frequency band (3-9 Hz). Conversely, in the high frequency range (16-27 Hz) the average Q_p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2-5 Hz) the estimated average Q_s is ca. 190. As for Q_p, also Q_s, in the high frequency range (16-27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q_p and Q_s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

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.     

Attenuation of seismic waves from moderate earthquakes of the Vrancea zone

The paper presents results of studying the attenuation of ground accelerations from earthquakes of the Vrancea with magnitudes less that 6.0 at distance greater than 300 km in a narrow sector located northeast of the focal region, within the limits of which are located acting and planned nuclear power plants (NNPs). Attenuation of peak ground accelerations in individual sections along the Vrancea–IRIS OBN station path is approximated by individual functions. It is shown that for a rough estimation of the seismic effect of earthquakes from the Vrancea zone it is acceptable to use the empirical relationship obtained by F.F. Aptikaev. For a more accurate estimate, it needs to be modified by adding a constant, whose value depends on the specific conditions of the NPP sites. It is shown that the results of data analysis on moderate earthquakes can be extrapolated to an earthquake with the maximum possible magnitude for the Vrancea zone and used to estimate the maximum seismic effects at the sites of operating and planned NPPs.     

含混合裂隙、孔隙介质的纵波衰减规律研究

地下多孔介质中的孔隙类型复杂多样,既有硬孔又有扁平的软孔.针对复杂孔隙介质,假设多孔介质中同时含有球型硬孔和两种不同产状的裂隙(硬币型、尖灭型裂隙),当孔隙介质承载载荷时,考虑两种不同类型的裂隙对于孔隙流体压力的影响,建立起Biot理论框架下饱和流体情况含混合裂隙、孔隙介质的弹性波动方程,并进一步求取了饱和流体情况下仅由裂隙引起流体流动时的含混合裂隙、孔隙介质的体积模量和剪切模量,随后,在此基础上讨论了含混合裂隙、孔隙介质在封闭条件下地震波衰减和频散的高低频极限表达式.最后计算了给定模型的地震波衰减和频散,发现地震波衰减曲线呈现"多峰"现象,速度曲线为"多频段"频散.针对该模型分析讨论了渗透率参数、裂隙纵横比参数以及流体黏滞性参数对于地震波衰减和频散的影响,表明三个参数均为频率控制参数.     

Attenuation of P and pP waves in Vrancea area – Romania

The seismic attenuation in the Vrancea region (Romania) is investigated from teleseismic recordings of P and pP waves during the four major, intermediate-depth Romanian events that occurred since the onset of digital instrumentation. Most stations are located in Canada and in the United States, being equipped with a variety of sensors, especially short-period ones. The amplitude spectral ratio method is used, assuming no frequency dependence of the Q _P factor in the range 0.2–2 Hz. No apparent correlation between the derived attenuation value and the type of recording sensor is observed. Lateral variations of the attenuation are obtained, with a very low Q _P area (values down to 33) located in the northwestern part of the Vrancea seismogenic volume. For the stations with different azimuth angles in relation to the epicentral area, Q _P values routinely exceed 200. Most likely, the low attenuation values are related to an upwelling mantle material located immediately beneath the crust, but limited in depth to at least 100 km.     

Exact solutions ofSH wave equation in transversely isotropic inhomogeneous elastic media

Summary TheSH wave equation in a transversely isotropic inhomogeneous elastic medium, where the elastic parameters and density are functions of vertical coordinate, is considered. A general procedure is given for finding the inhomogeneities for which the equation can be solved in terms of hypergeometric, Whittaker, Bessel and exponential functions. A few simple inhomogeneities and the corresponding solutions in terms of these transcendental functions are presented.     

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.