Seismic anisotropy of the Pacific Ocean inferred from long-period surface waves dispersion

The dispersion of surface (Rayleigh and Love) waves in the period range 40–300 s along a large number of paths, allows the estimation of both the azimuthal anisotropy and the shear-wave polarization anisotropy. The regional dispersion is determined, taking into account simultaneously its dependence with age and an azimuthal factor. The Pacific Ocean has been divided into 5 regions for Rayleigh waves and into 3 regions for Love waves. This partition discriminates the regions of extreme age which show a fast variation of dispersion with age, from the regions of intermediate age where the variation is weak. A variation of ～ 2% of Rayleigh-wave group velocity with the azimuth of the path, measured with respect to the direction of spreading is displayed, up to very long-period. On the contrary, the azimuthal anisotropy for Love waves is difficult to resolve. For Rayleigh waves, the present-day direction of plate motion seems to agree best with the direction of maximum velocity. On the other hand, the isotropic inversion of the regional dispersion curves indicates, except for young regions, a discrepancy between Rayleigh-wave and Love-wave models. With this hypothesis, SH-velocities are higher than SV-velocities for the regions older than 23 Ma, down to a depth of 300 km, which is indicative of the presence of polarization anisotropy. The latter, very weak for the young part of the ocean, increases with age and reaches 7%, for the oldest region.     

微动中多模式面波频散曲线的映射式提取方法

为了避免微动勘探技术中因忽略高阶模式瑞雷波而影响反演精度的不足,提出从微动面波中提取多模式瑞雷波频散曲线的映射式方法.该方法从微动信号入手,首先通过相关法提取多半径台阵的相关系数曲线,然后建立从多条相关系数曲线到多模式瑞雷波频散曲线的映射模型,最后采用分区拟合准则优化实现模型结构,达到提取微动面波中多模式瑞雷波频散曲线的目的.为验证方法的有效性,通过有限差分方法数值计算实际近表面应用中三种常见典型地质结构中的微动信号,采用映射式方法提取微动面波中多模式瑞雷波频散曲线,将提取结果和理论值进行对比分析.结果表明,映射式方法提取微动面波中多模式瑞雷波频散曲线可以满足反演地质结构的要求.     

Crust and upper mantle structure in east China and sea areas

Introduction Rayleigh wave is a kind of seismic wave propagating along the surface of the Earth, its propagation speed depends chiefly on the S-wave velocity structure of the Earth. Rayleigh wave energy of different periods concentrated in different depth ranges. The layered structure of the Earth causes the phenomenon of dispersion of surface waves, that is, surface waves of different periods are propagated with different speeds. By measuring the dispersion curves of surface waves the S-wav…     

Dispersion of Rayleigh waves along the Prague-Warsaw profile

Summary Phase velocities of Rayleigh waves propagating along the Prague-Warsaw profile have been determined. A layered model of the Earth's crust and upper mantle, satisfying the observed dispersion of Rayleigh waves, has been derived. In constructing this model, the results of deep seismic soundings along international profile VII were also taken into account.     

Dispersion of surface waves recorded in Athens

Summary The records at Athens of 85 earthquakes with epicenters in several regions on the earth were used to determine group velocities along thirty five paths. The mean crustal thickness along each path has been estimated by comparing the observations withPress's standard curves. A linear relation has been found between the mean crustal thickness and mean elevation along each path. This relation is in agreement with Airy's isostatic hypothesis. Determination of Love wave dispersion along five paths and Rayleigh wave dispersion along two paths in southeastern Europe and northern Asia Minor gave values from 35 to 45 km for the crustal thickness in this region.     

黏弹性与弹性介质中Rayleigh面波特性对比研究

Rayleigh面波的频散特性可以用来研究地表浅层结构. 本文使用时域有限差分法来模拟复杂黏弹性介质中的Rayleigh面波,研究了Q值对面波频散特性的影响.文中采用旋转交错网格有限差分,以非分裂卷积形式的完全匹配层为吸收边界,推出了求解二阶位移-应力各向同性黏弹性波动方程的数值方法.为了检验数值解的精度,首先将简单模型的正演结果与解析解对比,验证了方法的正确性;然后模拟了横向缓变层状介质和含有洞穴的介质中的面波,对弹性和黏弹性介质中的面波的频散特性进行对比分析.模拟结果表明浅层Q值对面波的频散特性有显著的影响;强吸收情况下,高阶面波的能量相对低阶面波能量显著增强.     

Dispersion splitting of Rayleigh waves in layered azimuthally anisotropic media

Rayleigh wave dispersion can be induced in an anisotropic medium or a layered isotropic medium. For a layered azimuthally anisotropic structure, traditional wave equation of layered structure can be modified to describe the dispersion behavior of Rayleigh waves. Numerical stimulation results show that for layered azimuthal anisotropy both the dispersion velocities and anisotropic parameters depend principally on anisotropic S-wave velocities. The splitting S-wave velocities may produce dispersion splitting of Rayleigh waves. Such dispersion splitting appears noticeable at azimuthal angle 45°. This feature was confirmed by the measured results of a field test. The fundamental mode splits into two branches at azimuthal angle 45° to the symmetry axis for some frequencies, and along the same direction the difference of splitting-phase velocities of the fundamental model reaches the maximum. Dispersion splitting of Rayleigh waves was firstly displayed for anisotropy study in dispersion image by means of multichannel analysis of surface waves, the image of which provides a new window for studying the anisotropic property of media.     

Propagation and attenuation of Rayleigh waves in generalized thermoelastic media

This study considers the propagation of Rayleigh waves in a generalized thermoelastic half-space with stress-free plane boundary. The boundary has the option of being either isothermal or thermally insulated. In either case, the dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. This dispersion equation is rationalized into a polynomial equation, which is solvable, numerically, for exact complex roots. The roots of the dispersion equation are obtained after removing the extraneous zeros of this polynomial equation. Then, these roots are filtered out for the inhomogeneous propagation of waves decaying with depth. Numerical examples are solved to analyze the effects of thermal properties of elastic materials on the dispersion of existing surface waves. For these thermoelastic Rayleigh waves, the behavior of elliptical particle motion is studied inside and at the surface of the medium. Insulation of boundary does play a significant role in changing the speed, amplitude, and polarization of Rayleigh waves in thermoelastic media.     

Anisotropy in the Earth's crust and uppermost mantle in southeastern Europe obtained from Rayleigh and Love surface waves

Digital seismograms from 25 earthquakes located in the southeastern part of Europe, recorded by three-component very broadband seismometers at the stations Vitosha (Bulgaria) and Muntele Rosu (Romania), were processed to obtain the dispersion properties of Rayleigh and Love surface waves. Rayleigh and Love group-velocity dispersion curves were obtained by frequency–time analysis (FTAN). The path-averaged shear-wave velocity models were computed from the obtained dispersion curves. The inversion of the dispersion curves was performed using an approach based on the Backus–Gilbert inversion method. Finally, 70 path-averaged velocity models (35 R-models computed from Rayleigh dispersion curves and 35 L-models computed from Love dispersion curves) were obtained for southeastern Europe. For most of the paths, the comparison between each pair of models (R-model and L-models for the same path) shows that for almost all layers the shear-wave velocities in the L-models are higher than in the R-models. The upper sedimentary layers are the only exception. The analysis of both models shows that the depth of the Moho boundary in the L-models is shallower than its depth in the R-models. The existence of an anisotropic layer associated with the Moho boundary at depths of 30–45 km may explain this phenomenon. The anisotropy coefficient was calculated as the relative velocity difference between both R- and L-models at the same depths. The value of this coefficient varies between 0% and 20%. Generally, the anisotropy of the medium caused by the polarization anisotropy is up to 10–12%, so the maximum observed discrepancies between both types of models are also due to the lateral heterogeneity of the shear-wave velocity structure of the crust and the upper mantle in the region.     

Structure of the crust in the Black Sea and adjoining regions from surface wave data

Group velocities of Rayleigh and Love waves along the paths across the Black Sea and partly Asia Minor and the Balkan Peninsula are used to estimate lateral variations of the crustal structure in the region. As a first step, lateral variations of group velocities for periods in the range 10–20 s are determined using a 2D tomography method. Since the paths are oriented predominantly in NE–SW or N–S direction, the resolution is estimated as a function of azimuth. The local dispersion curves are actually averaged over the extended areas stretched in the predominant direction of the paths. The size of the averaging area in the direction of the best resolution is approximately 200 km. As a second step, the local averaged dispersion curves are inverted to vertical sections of S-wave velocities. Since the dispersion curves in the 10–20 s period range are mostly affected by the upper crustal structure, the velocities are estimated to a depth of approximately 25 km. Velocity sections along 43° N latitude are determined separately from Rayleigh and Love wave data. It is shown that the crust under the sea contains a low-velocity sedimentary layer of 2–3 km thickness, localized in the eastern and western deeps, as found earlier from DSS data. Beneath the sedimentary layer, two layers are present with velocity values lying between those of granite and consolidated sediments. Velocities in these layers are slightly lower in the deeps, and the boundaries of the layers are lowered. S-wave velocities obtained from Love wave data are found to be larger than those from Rayleigh wave data, the difference being most pronounced in the basaltic layer. If this difference is attributed to anisotropy, the anisotropy coefficient = (SH - SV)/Smean is reasonable (2–3%) in the upper layers, and exceeds 9% in the basaltic layer.     

Effect of lateral variation and model parameterization on surface wave dispersion inversion to estimate the average shallow structure in the Paraná Basin

The average layered structure of the intracratonic Paraná Basin, SE Brazil, is investigated with surface-wave group velocities from a small regional earthquake recorded by two broadband stations. Rayleigh and Love waves in the period range 1–4.2 s are used to infer average properties down to about 4 km. Genetic algorithm techniques are used to find the best fitting 1-D S-wave model. The inverted 1-D models show fair correlation with the average properties of the propagation paths as expected from geology and borehole information. However, different S-wave velocity models are obtained for the different inversion parameterizations. Since lateral heterogeneities are expected along the paths, several synthetic tests are performed with heterogeneous propagation paths. For approximately homogenous path (i.e., little lateral variation), the main features of the average synthetic model can be retrieved for different model parameterizations. For strong lateral variations, however, the average dispersion curve can produce very different 1-D inverted models depending on the parameterization. Also, the 1-D inverted models may differ significantly from the average properties of the inhomogeneous path, and wrong depths to interfaces may be inferred. For real data inversions, it is then suggested that various different parameterizations should be tested. If the resulting models show consistent features, this probably indicates homogeneity in the propagation path. But, if very different and unstable features are obtained in the 1-D inversions, then strong lateral variation may be present in the propagation path, and the average 1-D model may not represent average properties along the path.     

Verification of the Litho-spheric Structure along Profile Uppsala-Prague Using Surface Wave Dispersion

Experimental dispersion curves of Rayleigh and Love waves along the Uppsala-Prague profile have been determined using records of several Italian earthquakes. To interpret the dispersion data, results of previous geophysical investigations in this region were first analyzed. Seven blocks of the crust and upper mantle were distinguished along the profile on the basis of deep seismic sounding and other seismic data. Layered models were proposed for these blocks. Computation of Rayleigh and Love waves shows a large differentiation of theoretical dispersion curves for the northern (Precambrian) and southern (Palaeozoic) part of the profile. A laterally inhomogeneous model for theUppsala - Prague profile, composed of the seven blocks, satisfies the surface wave data for the profile. Moreover, a mean layered model for the whole profile has also been proposed.     

Phase and Correlation in `Random' Seismic Fields and the Reconstruction of the Green Function

We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of P to S energy ratio indicating the modal equipartition of the wavefield. This property clearly shows that the coda waves are in the regime of multiple scattering. Numerical solutions of the elastic radiative transfer equation are used to illustrate the evolution of the wave-field towards P-to-S energy stabilization, and asymptotically to complete isotropy. The energy properties of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering enhancement, an expression of the so-called `weak localization', demonstrates that interference effects still persist for multiple diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green function between two stations by averaging the cross correlation of coda waves produced by distant earthquakes and recorded at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wavefield. Using broadband seismic coda waves, we show that the dominant phases of the Green function in the band 2 s–10 s, namely fundamental mode Rayleigh and Love waves, are reconstructed. We analyze the time symmetry of the cross correlation and show how the level of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering by randomly distributed scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the Earth. Surface waves can be extracted from long time series. The dispersion curves of Rayleigh waves are deduced from the correlations. On paths where measurements from earthquake data are also available, we show that they are in good agreement with those deduced from noise correlation. The measurement of velocities from correlation of noise along paths crossing different crustal structures opens the way for a `passive imaging' of the Earth's structure.     

Phase and group velocities and Q of mantle Love and Rayleigh waves of the first two modes and their azimuthal dependences for the 1963 Kurile Islands earthquake

Phase and group velocities and Q of mantle Love and Rayleigh waves from the 1963 Kurile Islands earthquake (M_w = 8.5) were determined over 37 great circle paths by a time variable filtering technique, in a period range 100–500 s for the fundamental modes and 100–275 s for the first higher modes. The preliminary reference Earth model (PREM) explains reasonably well the average dispersion results for the fundamental Love and Rayleigh waves. There exists a small, but significant inconsistency between the observation and the model for the first higher Love and Rayleigh waves. The Q structure of PREM is inconsistent with the observation for the fundamental Love waves, but explains other observations reasonably well. The dispersion of each mode shows a clear azimuthal dependence from which the four azimuthal windows were established. The phase and group velocity measurements for each window were, in general, shown to be mutually consistent. The azimuthal variations are largest for the first higher Rayleigh waves, indicating strong lateral heterogeneity in the structure of the low velocity zone. The first of the four windows is characterized by the largest fraction of Precambrian shields and the second window by the largest fraction of normal oceans. A comparison of these two windows may give some insight into deep lateral heterogeneity between continents and oceans. The observed phase and group velocities of the first window are systematically higher than those of the second window for the fundamental Love and Rayleigh waves at periods up to 400 s, and for the first higher Love and Rayleigh waves up to 175 s. Their differences are greatest for the first higher Rayleigh waves and least for the fundamental Rayleigh waves. Although the fundamental Rayleigh waves show the least velocity differences, their persistence up to a period of longer than 300 s is in striking contrast with some of the pure path phase velocities derived earlier for continents and oceans. A set of models for continents and oceans. PEM-C and PEM-O are not consistent with our observation. The third azimuthal window is characterized by trench-marginal seas and the fourth window by mountainous areas, typically the Asian high plateaus from northern China to the Middle East through Tibet. A comparison of these two windows gives some information about deep structural differences between subduction zones and continental collision zones, both belonging to plate convergence zones. For the fundamental and the first higher Love waves, the phase and group velocities for the third window are markedly low, whereas those for the fourth window are somewhat comparable to those for the second window. Slow Rayleigh waves are evident for two windows, with the fourth window apparently being the slowest for the fundamental Rayleigh above 200 s and for the first higher Rayleigh. For the fundamental Rayleigh waves, the third window is very slow below 200 s, but becomes progressively fast as the period increases and tends to be the fastest window around 400 s, suggesting a deep seated high velocity anomaly beneath trench-marginal seas. The dispersion characteristics of the fourth window indicate a thick high velocity lid with an extensive low velocity zone beneath it. The shield-like lithosphere, coupled with an extensive low velocity zone, may be a characteristic feature of continental collision zones. The particle motion of the fundamental Love waves was found not to be purely transverse to a great-circle connecting the epicenter to a station. The departure from the purely transverse motion is systematic among different periods, different G arrivals (G₂, G₃,…) and different stations, which may be interpreted as being due to lateral refraction.     

黏弹性介质瑞雷波有限差分模拟与特性分析

本文通过数值模拟研究了介质黏弹性对瑞雷波传播的影响.模拟采用结合了交错Adams-Bashforth时间积分法、应力镜像法和多轴完美匹配层的标准交错网格高阶有限差分方案.通过模拟结果和理论结果对比,测试了方法的精度,验证了结果的正确性.在均匀半空间模型中,分别从波场快照、波形曲线及频散能量图三个角度,对黏弹性介质瑞雷波衰减和频散特性进行了详细分析.两层速度递增模型被用于进一步分析瑞雷波在黏弹性层状介质中的特性.结果表明：由于介质的黏弹性,瑞雷波振幅发生衰减,高频成分比低频成分衰减更剧烈,衰减程度随偏移距增大而增强;瑞雷波相速度发生频散,且随频率增大而增大,频散能量的分辨率有所降低;黏弹性波动方程中的参考频率,不会影响瑞雷波振幅衰减和相速度频散的程度,但决定了黏弹性和弹性介质瑞雷波相速度相等的频率位置.本研究有助于人们更好地理解地球介质中瑞雷波的行为,并为瑞雷波勘探的应用和研究提供了科学和有价值的参考.     

The phase velocities of Rayleigh waves and the lateral variation of lithospheric structure in Tibetan Plateau

According to a Sino-U. S. joint project, eleven broadband digital PASSCAL seismometers had been deployed inside the Tibetan Plateau, of which 7 stations were on the profile from Lhasa to Golmud and other 4 stations situated at Maxin, Yushu, Xigatze and Linzhi. Dispersions and phase velocities of the Rayleigh surface waves (10s–120s) were obtained on five paths distributed in the different blocks of Tibetan Plateau. Inversions of the S-wave velocity structures in Songpan-Ganzi block, Qiang-Tang block, Lhasa block and the faulted rift zone were obtained from the dispersion data. The results show that significant lateral variation of the S-wave velocity structures among the different blocks exists. The path from Wenquan to Xigatze (abbreviated as Wndo-Xiga) passes through the rift-zone of Yadong-Anduo. The phase velocities of Rayleigh waves from 10s to 100s on this path are significantly higher than that on other paths. The calculated mean crustal velocity on this path is 3.8 km/s, much greater than that on other paths, where mean crustal velocities of 3.4–3.5 km/s are usually observed. Low velocity zones with different thicknesses and velocities are observed in the middle-lower crust for different paths. Songpan-Ganzi block, located in the northern part of Tibetan Plateau is characterized by a thinner crust of 65 km thick and a prominent low velocity zone in the upper mantle. The low velocity zone with a velocity of 4.2 km/s is located at a depth form 115 km to 175 km. While in other blocks, no low velocity zone in the upper mantle is observed. The value of Sn in Songpan-Ganzi is calculated to be 4.5 km/s, while those in Qiang-Tang and Lhasa blocks are about 4.6 km/s. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, Supp., 566–573, 1992.     

Time-domain Pure-state Polarization Analysis of Surface Waves Traversing California

-- A time-domain pure-state polarization analysis method is used to characterize surface waves traversing California parallel to the plate boundary. The method is applied to data recorded at four broadband stations in California from twenty-six large, shallow earthquakes which occurred since 1988, yielding polarization parameters such as the ellipticity, Euler angles, instantaneous periods, and wave incident azimuths. The earthquakes are located along the circum-Pacific margin and the ray paths cluster into two groups, with great-circle paths connecting stations MHC and PAS or CMB and GSC. The first path (MHC-PAS) is in the vicinity of the San Andreas Fault System (SAFS), and the second (CMB-GSC) traverses the Sierra Nevada Batholith parallel to and east of the SAFS. Both Rayleigh and Love wave data show refractions due to lateral velocity heterogeneities under the path, indicating that accurate phase velocity and attenuation analysis requires array measurements. T he Rayleigh waves are strongly affected by low velocity anomalies beneath Central California, with ray paths bending eastward as waves travel toward the south, while Love waves are less affected, providing observables to constrain the depth extent of anomalies. Strong lateral gradients in the lithospheric structure between the continent and the ocean are the likely cause of the path deflections.     

我国境内瑞利波的相速度

本文利用新不列颠岛两个地震在十二个基本台站所记录到的瑞利波,计算了我国不同地区的相速度.着重讨论鉴别和对比不同台站记录中同一震相的方法.在大部分台站的记录中,见到有周期约为35秒的相位,和后面的位相比较,它的周期较大,振幅较小.波形的对比对初步鉴别震相有很大的帮助.详细的震相对比是根据周期随距离变化的规律和各震相到时的规律.两个地震所得的相速度很符合.计算的结果表明:利用三台计算相速度时,如果射线的路程差别较大,海洋路程的校正是不能忽略的.因为有关我国地壳构造的资料还很少,我们所得的瑞利波相速度只能与普瑞司修正后非洲大陆的相速度理论相比较,由此得到我国不同地区的地壳厚度.这样所得的厚度,虽然不能视为最后的结果,但是它们仍然表现与主要地质单元之间有密切的联系.     

Crustal structure beneath Liaoning province and the Bohai Sea and its adjacent region in China based on ambient noise tomography

The velocity structure of the crust beneath Liaoning province and the Bohai sea in China was imaged using ambient seismic noise recorded by 73 regional broadband stations. All available three-component time series from the 12-month span between January and December 2013 were cross-correlated to yield empirical Green's functions for Rayleigh and Love waves. Phasevelocity dispersion curves for the Rayleigh waves and the Love waves were measured by applying the frequencytime analysis method. Dispersion measurements of the Rayleigh wave and the Love wave were then utilized to construct 2D phase-velocity maps for the Rayleigh wave at8–35 s periods and the Love wave at 9–32 s periods,respectively. Both Rayleigh and Love phase-velocity maps show significant lateral variations that are correlated well with known geological features and tectonics units in the study region. Next, phase dispersion curves of the Rayleigh wave and the Love wave extracted from each cell of the 2D Rayleigh wave and Love wave phase-velocity maps,respectively, were inverted simultaneously to determine the3 D shear wave velocity structures. The horizontal shear wave velocity images clearly and intuitively exhibit that the earthquake swarms in the Haicheng region and theTangshan region are mainly clustered in the transition zone between the low-and high-velocity zones in the upper crust, coinciding with fault zones, and their distribution is very closely associated with these faults. The vertical shear wave velocity image reveals that the lower crust downward to the uppermost mantle is featured by distinctly high velocities, with even a high-velocity thinner layer existing at the bottom of the lower crust near Moho in central and northern the Bohai sea along the Tanlu fault, and these phenomena could be caused by the intrusion of mantle material, indicating the Tanlu fault could be just as the uprising channel of deep materials.     

Propagation and attenuation of Rayleigh waves in a semi-infinite unsaturated poroelastic medium

An analytical model for describing the propagation and attenuation of Rayleigh waves along the free surface of an elastic porous medium containing two immiscible, viscous, compressible fluids is developed in the present study based on the poroelastic equations formulated by Lo et al. [Lo WC, Sposito G, Majer E. Wave propagation through elastic porous media containing two immiscible fluids. Water Resour Res 2005;41:W02025]. The dispersion equation obtained is complex-valued due to viscous dissipation resulting from the relative motion of the solid to the pore fluids. As an excitation frequency is stipulated, the dispersion equation that is a cubic polynomial is numerically solved to determine the phase speed and attenuation coefficient of Rayleigh waves in Columbia fine sandy loam permeated by an air–water mixture. Our numerical results show that, corresponding to three dilatational waves, there is also the existence of three different modes of Rayleigh wave in an unsaturated porous medium, which are designated as the R1, R2, and R3 waves in descending order of phase speed, respectively. The phase speed of the R1 wave is non-dispersive (frequency-independent) in the frequency range we examined (10 Hz–10 kHz) and decreases as water saturation increases, whose magnitude ranges from 20% to 49% of that of the first dilatational wave with respect to water content. However, it is revealed numerically that the R2 and R3 waves are functions of excitation frequency. Given the same water saturation and excitation frequency, the phase speeds of the R2 and R3 waves are found to be approximately 90% of those of the second and third dilatational waves, respectively. The R1 wave has the lowest attenuation coefficient whereas the R3 wave attenuates highest.