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1.
High-frequency (≥ 2 Hz) Rayleigh-wave phase velocities have been utilized to determine shear-wave velocities in near-surface geophysics since the early 1980s. One of the key steps is to calculate theoretical dispersion curves of an earth model. When the earth model contains a low-velocity half-space, however, some roots of the dispersion equation turn out to be complex numbers, which makes phase velocities disappear at some frequencies. When encountering this situation, the common practice is to append an additional high velocity layer as the half-space to the model to make the roots real or use the real parts of complex roots as Rayleigh-wave phase velocities. The correctness of the first method has been verified. The correctness of the second method, however, remains to be unproved. We use synthetic data generated by numerical modeling of the wave equation to verify the correctness of the second method. In this paper, we firstly discuss the reasons that only complex numbers of the dispersion equation exist at some frequencies when an earth model contains a low velocity half-space. Then we discuss how the nearest offset affects a synthetic model and recommend an optimal nearest offset in generating synthetic data that are close to real-world situations. Several synthetic models are used to verify correctness of using real parts of complex roots as Rayleigh-wave phase velocities when an earth model contains a low velocity layer as the half-space. 相似文献
2.
Rayleigh-wave phase velocities have been utilized to determine shear (S)-wave velocities in near-surface geophysics since early 1980s. One of the key steps is to calculate theoretical dispersion curves of an earth model. When the S-wave velocity of the surface layer is higher than some of the layers below, however, the Rayleigh-wave phase velocity in a high-frequency range calculated by existing algorithms approaches the lowest S-wave velocity among the layers above the half-space, rather than a value related to the S-wave velocity of the surface layer. According to our numerical modeling results based on wave equation, trends of the Rayleigh-wave dispersive energy approach about a 91% of the S-wave velocity of the surface layer at a high-frequency range when its wavelength is much shorter than the thickness of the surface layer, which cannot be fitted by a dispersion curve calculated by existing algorithms. We propose a method to calculate Rayleigh-wave phase velocities of models with a high-velocity surface layer by considering its penetration depth. We build a substituted model that only contains the layer with the lowest S-wave velocity among the layers above the half-space and the layers above it. We use the substituted model to replace the original model to calculate phase velocities when the Rayleigh-wave wavelength is not long enough to penetrate the lowest S-wave velocity layer. Several synthetic models are used to verify fitness between the dispersion curve calculated by our proposed method and the trend of the highest dispersive energy. Examples of inversion also demonstrate high accuracy of using our method as the forward calculation method during the inversions. 相似文献
3.
Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity 总被引：2，自引：1，他引：1
Jianghai Xia Yixian Xu Yinhe Luo Richard D. Miller Recep Cakir Chong Zeng 《Surveys in Geophysics》2012,33(5):841-860
As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves. 相似文献
4.
A detailed dispersion analysis of Rayleigh waves generated by local earthquakes and occasionally by blasts that occurred in
southern Spain, was undertaken to obtain the shear-wave velocity structure of the region at shallow depth. Our database includes
seismograms generated by 35 seismic events that were recorded by 15 single-component short-period stations from 1990 to 1995.
All these events have focal depths less than 10 km and body-wave magnitudes between 3.0 and 4.0, and they were all recorded
at distances between 40 and 300 km from the epicentre. We analysed a total of 90 source-station Rayleigh-wave paths. The collected
data were processed by standard digital filtering techniques to obtain Rayleigh-wave group-velocity dispersion measurements.
The path-averaged group velocities vary from 1.12 to 2.25 km/s within the 1.0-6.0 s period interval. Then, using a stochastic
inversion approach we obtained 1-D shear-wave velocity–depth models across the study area, which were resolved to a depth
of circa 5 km. The inverted shear-wave velocities range approximately between 1.0 and 3.8 km/s with a standard deviation range
of 0.05–0.16 km/s, and show significant variations from region to region. These results were combined to produce 3-D images
via volumetric modelling and data visualization. We present images that show different shear velocity patterns for the Betic
Cordillera. Looking at the velocity distribution at various depths and at vertical sections, we discuss of the study area
in terms of subsurface structure and S-wave velocity distribution (low velocity channels, basement depth, etc.) at very shallow
depths (0–5 km). Our results characterize the region sufficiently and lead to a correlation of shear-wave velocity with the
different geological units features. 相似文献
5.
面波多道分析方法(MASW)是获取垂向剪切波速度剖面的一种有效方法。频散曲线反演是MASW中关键的一步。由于瑞雷波频散曲线反演具有非线性、多参数和多极值的特征,这对于常规的局部线性化反演方法是极大的挑战。为此,本文采取确定性的全局优化算法,广义模式识别算法(GPS)对瑞雷波频散曲线进行反演。其原理可以简述为:算法首先通过模式以确定性的方式对目标函数进行采样来搜索一个点序列;然后使序列中每一个点到下一个点的目标函数值逐渐减少,从而使点序列逐渐逼近全局最优解,最后的解便为待求的最优模型参数。为验证GPS的有效性,首先利用设计的3种典型的6层地质模型通过快速矢量传递算法正演模拟产生基模式频散曲线(频率范围为5~101Hz,频率间隔为2Hz,频点数为49),并对理论频散曲线进行反演。反演结果表明,模型的真实值已经被高度精确地重建。说明GPS可以用于实际勘探中的基模式频散曲线反演。为进一步验证GPS的有效性,在吉林大学校园采集瑞雷波实测数据,并提取基模式频散曲线,应用GPS进行反演。反演重建的横波速度剖面与先验的地质信息吻合得很好。理论模型和真实数据的反演结果表明,GPS可以应用在瑞雷波频散曲线非线性反演中。 相似文献
6.
Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method 总被引：1，自引：0，他引：1
Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface
geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might
match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and
a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (≥2 Hz) Rayleigh-wave phase
velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated
and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there
are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides
insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure.
Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities
within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because
of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that
selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution
matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices
in these examples to show the potential of increasing model resolution with selected surface-wave data. 相似文献
7.
针对横向各向同性地层随钻声波测井模型,通过模式分析的方法,考察了快速地层和慢速地层井孔内随钻单极子、偶极子和四极子声源激发的斯通利波、弯曲波和螺旋波的相速度频散和激发强度特征,计算了这些模式波对于地层弹性常数的灵敏度,并与电缆测井中的情况进行了比较.结果表明:随钻斯通利波在低频时对地层弹性常数中c66的灵敏度较电缆测井中有了很大提高,可用于反演地层水平向横波速度;随钻偶极子最低阶弯曲波在低频时不能用于直接获取地层横波信息,但在慢速地层中频率较高(例如6 kHz)时却可以间接得到地层垂直向横波速度;随钻四极子螺旋波的特征与电缆测井中的类似,可用于获取地层垂直向横波速度. 相似文献
8.
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media 总被引：1，自引：0，他引：1
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity–stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10–16% when the frequency is above 10 Hz due to the velocity dispersion of P and S waves. 相似文献
9.
面波多道分析方法(MASW)通过分析高频瑞雷波确定浅地表剪切波速度.在过去的20年中,由于该方法具有非侵入性、无损、高效及价格低的特点,越来越受到浅地表地球物理和地质工程学界的重视,视为未来最有希望的技术之一.这篇综述论文将介绍中国地质大学(武汉)浅地表地球物理团队近年来在研究高频面波的传播理论和应用中取得的部分成果.非几何波是一种仅存在于浅地表介质,尤其是未固结的沉积物中的独特的地震波.它的存在对快速而准确地获得表层S波速度有一定价值.我们的研究表明非几何波是一种具有频散特性的泄漏波.泄漏波的存在可能导致将其误认为瑞雷波的基阶或高阶能量,从而造成模式误判.这种模式误判会导致错误的反演结果.我们通过求取高基阶分离后的瑞雷波格林函数证明虚震源法瑞雷波勘探的可行性.这个结果将极大地降低野外瑞雷波勘探成本.勒夫波多道分析方法(MALW)中未知参数比瑞雷波的少,这使得勒夫波的频散曲线比瑞雷波的简单.因此,勒夫波反演更稳定,非唯一性更低.勒夫波数据生成的能量图像通常比瑞雷波的清晰,并具有更高的分辨率,从而可以更容易地拾取精确的勒夫波的相速度.利用雅克比矩阵分析波长与探测深度的关系表明对相同波长的基阶模式而言,瑞雷波的探测深度是勒夫波的1.3~1.4倍;而两种波的相同波长的高阶模式波的探测深度相同.我们也尝试了时间域勒夫波反演.按照勒夫波分辨率将地球模型剖分成了不同尺寸的块体,利用反卷积消除了地震子波对勒夫波波形的影响,通过更新每个块体的S波速度来拟合勒夫波波形,从而获得地下S波速度模型.该方法不基于水平层状模型假设,适用于任意二维介质模型. 相似文献
10.
竖向非均匀介质中的Love面波 总被引：2，自引：0，他引：2
本利用ＫＷＢＪ２（即几何近似）理论研究介质参数随深度作连续变化的竖向非均匀弹性半空间上覆盖一层厚度为Ｈ的元首中向同性的弹性介质时Ｌｏｖｅ面波的频散问题。给出了频散方程。中以剪切弹性模量和质量密度随深度呈抛物线变化的非均匀介质为例,给出其最低阶振型的频散曲线 相似文献
11.
S波速度结构能够反映地球介质的物性差异,是地壳内低速区结构特征判别的重要依据.本文尝试利用空间自相关法(SPAC法)从地震台站微动信号的垂直分量中提取瑞利波相速度频散曲线,通过对频散曲线的反演获得地下介质的S波速度结构.以国家数字测震台网8个宽频带地震台站的实测微动数据为例,采用SPAC方法获得了首都圈地区北京附近约30 km 深度范围内的一维S波速度结构.结果表明,该区结晶基底埋深较浅约2 km;分别在5~8 km 和12~16 km 深处发育S波低速层;8 km 和 20 km 处是S波速度差异较大的速度分界面.这一结果与以往地震学及人工地震探测结果较为吻合,表明SPAC法估算地壳S波速度结构是可行、有效的. 相似文献
12.
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. 相似文献
13.
多极子阵列声波测井仪器采集的单极和偶极数据受到地层、井孔、仪器测量系统的影响.在处理实际声波测井数据时,必须考虑多极子模式波的频散效应,以及测井仪器在其中的影响.根据仪器等效理论和相位匹配方法,本文提出了一种从多极子阵列声波测井数据中同时获得纵、横波慢度的联合反演方法.这种方法的关键在于利用相同仪器-地层模型计算多极子模式波频散曲线,以此来匹配频域内纵波与横波数据的相位.相对于将泄漏纵波和弯曲波频散效应分开处理的其他方法,该方法不仅可以减少纵横波速度反演的不确定性,而且还避免了从声波数据中提取频散数据的繁琐过程.通过理论分析和现场数据处理证明了本文联合反演方法的准确性和有效性. 相似文献
14.
Rayleigh波勘探方法在探测近地表横波速度、动力学特征等环境与工程地球物理领域获得了广泛应用.这种方法以弹性层状介质理论为基础,然而实际介质具有黏弹性,研究面波在层状黏弹性介质中的传播特征,将为近地表面波勘探提供有益帮助.在某些弹性层状介质模型中,例如存在低速夹层和强波阻抗差异地层模型,Rayleigh波相邻两条频散曲线彼此会非常靠近,产生看似彼此"交叉"的现象,即"osculation"现象,但对于黏弹性介质中的这种现象并没有进行相关的研究.本文利用Muller法计算层状黏弹性介质Rayleigh波频散方程,基于层状介质模型中Rayleigh波频散和衰减曲线连续的性质,结合本征位移曲线特征,分析二层黏弹性介质模型中Rayleigh波频散曲线"交叉"现象以及"交叉"点附近的波动特性.结果表明:与弹性介质相比,黏弹性介质中Rayleigh波的波动特性存在明显差异,随着介质对地震波的损耗越来越强,将导致Rayleigh波频散曲线发生"交叉"现象. 相似文献
15.
I. Vardoulakis 《地震工程与结构动力学》1981,9(4):329-342
The present analysis deals with harmonic Rayleigh-type and transverse surface waves in a half-space of incompressible material with constant density and with shear modulus linearly increasing with depth. This model is proposed for describing the response of a half-space of submerged, dense sand to small strain vibrations of many cycles. It is shown that a discrete spectrum of polynomial solutions is always possible which makes the eigenvalue problem more tractable. 相似文献
16.
弹性层状半空间中凸起地形对入射平面SH波的放大作用 总被引：7，自引：0，他引：7
对Wolf理论进行拓展,使之可解决凸起地形对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中凸起地形对入射平面SH波的放大作用问题。本文模型的显著特点之一是考虑了层状半空间的动力特性以及层状半空间和凸起地形的阻尼;特点之二是计算精度高。文中以基岩上单一土层中半圆凸起地形对入射平面SH波的放大作用为例进行了数值计算分析。研究表明,基岩上单一土层中凸起地形对入射平面SH波放大作用和均匀半空间中凸起地形有着本质的差别;土层动力特性不仅影响凸起地形地表位移的幅值,还会影响地表位移的频谱;阻尼会显著降低凸起地形对高频波的放大作用。 相似文献
17.
Christos Vrettos 《地震工程与结构动力学》1999,28(12):1525-1540
The vertical and rocking response of rigid rectangular foundations resting on a linear-elastic, compressible, non-homogeneous half-space soil model is studied. The non-homogeneity is described by a continuous yet bounded increase of shear modulus with depth. The mixed boundary value problem is solved by means of the semi-analytical method of the subdivision of the foundation/soil contact area whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green's functions for the particular soil model. Impedance functions are given for representative values of the non-homogeneity parameters, the Poisson's ratio and the foundation geometry over a wide range of frequencies. Significant features associated with the soil non-homogeneity are pointed out. Copyright © 1999 John Wiley & Sons Ltd. 相似文献
18.
Christos Vrettos 《地震工程与结构动力学》1991,20(10):961-977
An analytical solution is presented for the response of a non-homogeneous, compressible, elastic half-space to a time-harmonic vertical point load on its surface. The shear modulus is assumed to increase continuously with depth. The model is chosen so as to describe uniformly deposited cohesionless soils. Expressions for displacements and stresses in the interior of the half-space medium are derived by means of Hankel transforms and contour integration. Selected numerical results are presented to demonstrate the influence of non-homogeneity. Finally, some effects are pointed out to be used in connection with vibration tests for subsoil investigation. 相似文献
19.
The spectral analysis of surface waves (SASW) method is an in situ, seismic method for determining the shear wave velocity (or maximum shear modulus) profile of a site. The SASW test consists of three steps: field testing, evaluation of dispersion curve by phase unwrapping method, and determination of shear modulus profile by inversion process. In general, field testing and dispersion curve evaluation are regarded as simple work. However, because of characteristic of Fourier transform used in the conventional phase unwrapping method, dispersion curve is sensitive to background noise and body waves in the low frequency range. Furthermore, under some field conditions such as pavement site, the usual phase unwrapping method can lead to erroneous dispersion curve. To overcome problem of the usual phase unwrapping method, in this paper, a new method of determining dispersion curve for SASW method was applied using time–frequency analysis based on harmonic wavelet transform as an alternative method of a current phase unwrapping method. To estimate the applicability of proposed method to SASW method, numerical simulations at various layered soil and pavement profiles were performed and the dispersion curves by proposed method are more reliable than those by the usual phase unwrapping method. 相似文献
20.
Approximation to Cutoffs of Higher Modes of Rayleigh Waves for a Layered Earth Model 总被引：2，自引：0，他引：2
A cutoff defines the long-period termination of a Rayleigh-wave higher mode and, therefore is a key characteristic of higher
mode energy relationship to several material properties of the subsurface. Cutoffs have been used to estimate the shear-wave
velocity of an underlying half space of a layered earth model. In this study, we describe a method that replaces the multilayer
earth model with a single surface layer overlying the half-space model, accomplished by harmonic averaging of velocities and
arithmetic averaging of densities. Using numerical comparisons with theoretical models validates the single-layer approximation.
Accuracy of this single-layer approximation is best defined by values of the calculated error in the frequency and phase velocity
estimate at a cutoff. Our proposed method is intuitively explained using ray theory. Numerical results indicate that a cutoffs
frequency is controlled by the averaged elastic properties within the passing depth of Rayleigh waves and the shear-wave velocity
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