Simultaneous measurement and inversion of surface wave dispersion and attenuation curves

Surface wave tests are non-invasive seismic techniques that have traditionally been used to determine the shear wave velocity (i.e. shear modulus) profile of soil deposits and pavement systems. Recently, Rix et al. [J. Geotech. Geoenviron. Engng 126 (2000) 472] developed a procedure to obtain near-surface values of material damping ratio from measurements of the spatial attenuation of Rayleigh waves. To date, however, the shear wave velocity and shear damping ratio profiles have been determined separately. This practice neglects the coupling between surface wave phase velocity and attenuation that arises from material dispersion in dissipative media. This paper presents a procedure to measure and invert surface wave dispersion and attenuation data simultaneously and, thus, account for the close coupling between the two quantities. The methodology also introduces consistency between phase velocity and attenuation measurements by using the same experimental configuration for both. The new approach has been applied at a site in Memphis, TN and the results obtained are compared with independent measurements.     

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.

     

Determining Q of near-surface materials from Rayleigh waves

High-frequency (≥2 Hz) Rayleigh wave phase velocities can be inverted to shear (S)-wave velocities for a layered earth model up to 30 m below the ground surface in many settings. Given S-wave velocity (V_S), compressional (P)-wave velocity (V_P), and Rayleigh wave phase velocities, it is feasible to solve for P-wave quality factor Q_P and S-wave quality factor Q_S in a layered earth model by inverting Rayleigh wave attenuation coefficients. Model results demonstrate the plausibility of inverting Q_S from Rayleigh wave attenuation coefficients. Contributions to the Rayleigh wave attenuation coefficients from Q_P cannot be ignored when Vs/V_P reaches 0.45, which is not uncommon in near-surface settings. It is possible to invert Q_P from Rayleigh wave attenuation coefficients in some geological setting, a concept that differs from the common perception that Rayleigh wave attenuation coefficients are always far less sensitive to Q_P than to Q_S. Sixty-channel surface wave data were acquired in an Arizona desert. For a 10-layer model with a thickness of over 20 m, the data were first inverted to obtain S-wave velocities by the multichannel analysis of surface waves (MASW) method and then quality factors were determined by inverting attenuation coefficients.     

Techniques for mode separation in Rayleigh wave testing

The spectral analysis of surface wave (SASW) developed in the early eighties has opened the way to the use of surface waves for the definition of shear wave velocity profiles in soil deposits or pavement structures without the need of any borings or intrusion. The SASW testing procedure was designed to minimize the contribution of higher modes and thus assumes that the Rayleigh waves which propagate at the surface belong only to the fundamental mode. Several studies have however demonstrated that, in some conditions, higher Rayleigh modes can contribute significantly to the dispersion curve. Different tests configurations exist today to deal with Rayleigh mode problem by the use of an array of receivers. In spite of that, the SASW configuration remains attractive due to the limited number of receivers, as well as, the Rayleigh modes contributing in SASW records configuration can be identified by multiple-filter technique and isolated using time-variable filters. The proposed techniques are first validated by simulated records and then applied to SASW records obtained in the field. The study confirms that higher modes can participate and even dominate in SASW records. An important contribution of higher Rayleigh modes can also exist, even if the shear wave velocity increases regularly with depth. The higher Rayleigh modes can significantly affect the accuracy of the shear wave velocity profile if they are not properly identified and separated. A multi-mode inversion process is shown to be important to have an accurate soil characterization.     

欧亚大陆及西太平洋边缘海地区瑞雷波群速度结构与各向异性分布

根据欧亚大陆及西太平洋地区102个数字化台站记录的近万次地震事件的长周期垂直向瑞雷波资料,利用时频分析方法测量并筛选后共得到11213条质量较高的基阶瑞雷波群速度频散资料.纯路径频散的反演中同时计算方位各向异性,反演获得了欧亚大陆及西太平洋边缘海地区(10°E—150°E,10°S—80°N)8—200s共28个周期的瑞雷波群速度及各向异性空间分布图象.瑞雷波高分辨率层析成像表明,30—60s周期,以青藏高原为中心呈极低速分布;100—120s周期,速度差异幅度较大,在东亚东部及西太平洋边缘海,自北向南显示出一条宽2500—4000km,长约8000km的巨型低速异常带.相对海洋来说,欧亚大陆各向异性强度较弱且快波方向较复杂.由于受到印度板块与欧亚板块的碰撞,中国大陆西部的各向异性强度明显大于东部.     

秦岭及周边地区瑞雷波方位各向异性

除了使用前人提取的面波频散曲线外, 还从秦岭及周边地区布设的59个宽频流动地震台的数据和中国地震局及各省局台网的数据中筛选出的地震事件波形和台站间噪声互相关格林函数中提取瑞雷波群速度频散曲线. 利用二维面波层析成像反演获得了瑞雷波周期为10—50 s的各向同性群速度及方位各向异性分布. 结果显示： 周期为10 s的各向同性群速度和方位各向异性分布与各构造单元存在明显的对应关系; 周期为10—50 s的面波在四川盆地和鄂尔多斯盆地内的快波方向多为近NS向. 与前人研究结果不同的是, 本文得到的秦岭、 大巴山构造带周期为10—50 s的面波快波方向均与山脉走向近似平行, 且与SKS波分析得到的快波方向一致. 这表明秦岭和大巴山之下整个岩石圈的快波方向都与山脉走向平行, 预示着秦岭和大巴山整个地壳, 甚至岩石圈发生了类似的变形. 由于四川盆地和鄂尔多斯盆地面波快波方向与SKS波结果差别较大, 推测青藏高原隆升扩展对这两个盆地的地壳基本无影响, 但对其岩石圈上地幔却产生了重大影响.     

Tsunami and its Hazard in the Indian and Pacific Oceans: Introduction

The 2004 Indian Ocean tsunami caused an estimated 230,000 casualties, the worst tsunami disaster in history. A similar-sized tsunami in the Pacific Ocean, generated by the 1960 Chilean earthquake, commenced international collaborations on tsunami warning systems, and in the tsunami research community through the Tsunami Commission of International Union of Geodesy and Geophysics. The IUGG Tsunami Commission, established in 1960, has been holding the biannual International Tsunami Symposium (ITS). This volume contains selected papers mostly presented at the 22nd ITS, held in the summer of 2005. This introduction briefly summarizes the progress of tsunami and earthquake research as well as international cooperation on tsunami warning systems and the impact of the 2004 tsunami. Brief summaries of each paper are also presented.     

用Rayleigh面波方位各向异性研究中国大陆岩石圈形变特征

中国大陆地质构造历史非常复杂,岩石圈长期积累的形变较大,而利用地震面波传播的各向异性是研究岩石圈形变特征的强有力手段. 本文利用双台窄带通滤波-互相关方法与基于图像分析的相速度频散曲线提取技术,提取Rayleigh面波相速度频散资料,进而反演中国大陆及邻区20～120 s周期Rayleigh面波相速度方位各向异性空间分布图像. 检测板测试结果显示：中国大陆大部分区域的方位各向异性横向分辨率在5°左右. 各向异性研究结果表明：中国大陆地壳上地幔方位各向异性特征存在显著的空间差异,反映出形变特征的空间差异;104°E以东地区地壳上地幔各向异性弱于西部地区,表明其构造变形总体弱于西部地区. 青藏地块及其东缘地区地壳与上地幔顶部变形最为强烈. 但东部的局部地区如华南地块与珠江口地区、鄂尔多斯盆地西南缘以及秦岭-大别造山带,较强的各向异性显示这些区域在不同时期也经历了强变形. 青藏地块内中短周期快波方向自西向东顺时针旋转变化可能指示板块碰撞与挤压过程中软弱物质的流变方向. 青藏地块西部中下地壳和上地幔形变模式相似,可能处于壳幔耦合状态;而中东部及东缘地区地壳上地幔形变模式存在明显差异,壳幔似乎不具备垂直连贯的形变特征. 位于青藏地块北部的塔里木盆地、柴达木盆地以及祁连褶皱带同样经历了强变形. 包括四川盆地在内的上扬子地块快波方向的变化显示中地壳与下地壳上地幔形变模式不同,而形变特征一致的下地壳与上地幔应为强耦合. 大约以103°E为界,龙门山断裂带可分为南西段和北东段,南西段处于低速区,而北东段位于高速区,且方位各向异性强度明显大于南西段;2008年5月12日汶川M_S8.0级地震沿断裂带的单侧破裂模式除与北东段的高应力积累有关外,还可能与北东段地下介质物性存在密切关系,高速坚硬岩体的发育有利于应变能的积累与集中释放.     

Effect of soil stiffness in the attenuation of Rayleigh-wave motions from field measurements

The amplitude of vertical ground surface vibrations generated by impact tests on the ground surface was measured at various radial distances from the point of impact at locations of Greece. The results of measurements were analyzed in the frequency domain (in the range from 0–100 Hz) and the attenuation characteristics of soil materials were studied in terms of a frequency-independent attenuation coefficient, a₀, of the empirical Bornitz equation. The aim of the study was to investigate the effect of soil stiffness (expressed by the value of low-amplitude shear wave velocity of soil, V_SO) on the value of attenuation coefficient, a₀. Values of V_SO for the tested soils were estimated by applying the methodology of Spectral Analysis of Surface Waves (SASW) technique and utilizing the surface vibration data. An empirical relationship between a₀ and V_SO1 (V_SO1 is the representative value of V_SO for the soil profile up to a depth of one wavelength) was established for values of V_SO1 ranging from 140 to 1000 m/s. A similar relationship in terms of the low-amplitude shear modulus of soil, G_O1, was also established by converting the V_SO1 values to G_O1 values. The experimental results were compared to values reported in the literature for comparable soil types and frequencies of vibration and a reasonable agreement was found to exist. The proposed empirical relationship can be utilized in many practical applications of soil dynamics requiring the knowledge of the attenuation rate of Rayleigh waves with distance in various types of soils.     

An evaluation of the classical and extended Rossby wave theories in explaining spectral estimates of the first few baroclinic modes in the South Pacific Ocean

Previous literature has suggested that multiple peaks in sea level anomalies (SLA) detected by two-dimensional Fourier Transform (2D-FT) analysis are spectral components of multiple propagating signals, which may correspond to different baroclinic Rossby wave modes. We test this hypothesis in the South Pacific Ocean by applying a 2D-FT analysis to the long Rossby wave signal determined from filtered TOPEX/Poseidon and European Remote Sensing-1/2 satellite altimeter derived SLA. The first four baroclinic mode dispersion curves for the classical linear wave theory and the Killworth and Blundell extended theory are used to determine the spectral signature and energy contributions of each mode. South of 17°S, the first two extended theory modes explain up to 60% more of the variance in the observed power spectral energy than their classical linear theory counterparts. We find that Rossby wave modes 2–3 contribute to the total Rossby wave energy in the SLA data. The second mode contributes significantly over most of the basin. The third mode is also evident in some localized regions of the South Pacific but may be ignored at the large scale. Examination of a selection of case study sites suggests that bathymetric effects may dominate at longer wavelengths or permit higher order mode solutions, but mean flow tends to be the more influential factor in the extended theory. We discuss the regional variations in frequency and wave number characteristics of the extended theory modes across the South Pacific basin.     

瑞利面波在地质勘察中的应用

在地质勘察中运用瑞利面波进行探测,对瑞利面波进行频谱分析和相关计算处理,根据速度结合钻孔资料进行地质分层,为钻探成果的内插和外推提供依据,使地质勘察资料更加翔实可靠.     

欧亚大陆及西太平洋边缘海瑞利面波频散反演

从亚洲、欧洲及西太平洋地区台网113个数字地震台所记录的分布在40°W~180°E,40°S~80°N范围内近万个地震事件中,挑选出发生在1982-2005年间,震级绝大部分在5.0~7.0之间,震源深度小于100 km的1 700余个事件。共得到周期在8~400 s之间9 980余条质量较高的瑞利面波频散曲线进行面波频散反演,得到欧亚大陆及西太平洋边缘海28个周期的群速度分布图。反映了欧亚大陆及西太平洋边缘海横向和纵向存在着明显的非均匀性。     

Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell

We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters , r ^p and compressional and shear-wave velocities , r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=–2. We obtain numerical results which agree with results obtained by other methods.     

Seismic wave attenuation in the upper Mantle beneath the Aegean region

A detailed study of P and S waves from earthquakes located along the Hellenic arc and recorded by the Greek seismological network, shows an abnormal distribution of the seismic waves in the central Aegean Sea. The data indicate a zone of anomalously high seismic wave attenuation in the Upper Mantle beneath the Cyclades plateau and the inner part of the volcanic arc. Several independent observations suggest the presence of magma beneath the Cyclades massif.In addition, geophysical data indicate the presence of low-density and rigidity material. Theoretical consideration of the propagation of elastic waves corroborate the observed absence of shear waves.     

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.     

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.     

Elastic-anelastic Regional Structures for the Iberian Peninsula Obtained from a Rayleigh Wave Tomography and a Causal Uncoupled Inversion

The elastic and anelastic structure of the lithosphere and asthenosphere of the Iberian Peninsula is derived by means of tomographic techniques applied to local phase and group velocities and local attenuation coefficients of Rayleigh wave fundamental mode. The database consists of surface wavetrains recorded at the broadband stations located in the Iberian Peninsula on the occasion of the ILIHA project. Path-averaged phase and group velocities and attenuation coefficients were previously obtained by standard filtering techniques of surface wavetrains and, subsequently, local dispersion curves were computed according to the Yanovskaya-Ditmar formulation. First, a principal component analysis (PCA) and the average linkage (AL) clustering algorithm are applied to these local values in order to classify the Iberian Peninsula in several rather homogeneous domains from the viewpoint of the similarity of the corresponding local dispersion curves, without previous seismotectonic constraints. Second, averaged phase and group velocities and attenuation coefficients representing each homogeneous region are used to derive the respective elastic and anelastic models of the lithosphere and asthenosphere. This purpose is achieved by using the uncoupled causal inversion of phase and group velocities and attenuation coefficients. The main features of the homogeneous regions are discussed by taking as reference the Hercynic, Alpine and Neogene domains of the Iberian Peninsula, and two questions affecting the reliability of the elastic-anelastic models are revised. First, the coherence of the shear-velocity and Q_β⁻¹ models obtained by causal uncoupled inversion for each region is analysed. Second, the influence of the causal phase and group velocities on the shear-velocity models is evaluated by comparing elastic and anelastic models derived from causal uncoupled inversion with those deduced from non-causal inversion.     

利用瑞利激光雷达观测北京地区上平流层地形重力波活动

本文利用中国科学院空间科学与应用研究中心的瑞利激光雷达首次观测到了平流层地形重力波活动的现象,并结合美国国家环境预报中心(NCEP)的全球预报系统(GFS)的风场数据分析了该地形重力波的基本参数.与惯性重力波相比较,地形重力波的密度扰动没有下传的相位,在同一高度上,其扰动相位保持不变.北京空间科学与应用研究中心瑞利激光雷达自2012年开始观测实验以来,已经观测到多起地形重力波活动事件.本文以2013年11月11日的观测数据为例,研究北京上空的地形重力波活动,并结合GFS风场数据分析了北京上平流层地形重力波的波长、传播方向、传播速度等参量.通过分析得到在2013年11月11日北京上空存在一列传播方向为北偏西52.4°,水平波长为5.5 km,平均垂直波长约为6.0 km的地形重力波.     

含孔隙介质的分层半空间表面瑞利波的衰减特性

以分层半空间内部含有一层孔隙介质为物理模型进行数值计算,研究半空间表面瑞利波的传播和衰减特性.为更加接近实际,结合瑞利波的激发特性,确定了瑞利波的主衰减曲线,并主要以此进行规律分析.针对速度递增和含低速层这两种典型的地质模型,讨论了瑞利波的传播衰减在不同地质模型下的特性,并分析了各自的规律.结果表明,在这两种模型下瑞利波的主衰减曲线都受孔隙介质所处空间位置影响产生比较明显的变化,但衰减系数极大值对应的波长与模型的表层厚度存在较明显的线性对应关系,利用这一关系,可以在实际勘探中快速得到表层介质厚度.另外,通过对比分析还可以看到,瑞利波主衰减曲线随孔隙介质的孔隙度和渗透率的变化都强于主频散曲线的变化,表明衰减曲线对孔隙度和渗透率的变化更加敏感,理论上更加适合进行介质参数反演工作.综合对比结果,我们认为瑞利波主衰减曲线中包含了更丰富的介质参数信息,如果能够有效利用,将可以提高瑞利波勘探的准确性和应用范围.

     

Apparent phase velocities and fundamental-mode phase velocities of Rayleigh waves

Rayleigh wave dispersion data usually appear in the form of multimodal spectra for a layered model structure. The number of dispersion modal curves depends on the number of layers in the model. The measured dispersion velocities from the frequency–wavenumber (F–K) space, however, may not represent the true phase velocities of the fundamental-mode dispersion curve, but apparent phase velocities. The present study discusses how multimode curves are generated in the multichannel analysis of surface waves (MASW) method and the cause of the apparent velocity produced by the F–K method. Results from a field trial demonstrate that apparent phase velocities fail to reveal thin layers with low velocities. A better agreement of the inverted model with the geotechnical record is obtained by using the data points extracted from the fundamental-mode curve of the MASW spectral image.