利用多重滤波方法提取面波频散曲线

多重滤波方法已被证明在分析面波的频散特性时是一种有效而快速的方法。本文用单个台站的单次地震事件记录,应用MFT(Multiple Filter Technique)方法提取了内华达地区的面波频散曲线并分析了其特征,认为其具有大陆基振型瑞利波频散曲线的典型特征。还利用广义反透射系数法快速计算了瑞利面波频散曲线,尤其是基阶瑞利波相速度及群速度频散曲线;并且在由振型叠加方法合成的理论地震图的基础上,通过比较理论频散曲线和MFT方法得到的频散曲线,研究了多重滤波的可靠性。     

瑞雷波"之"形速度-深度曲线的成因

本文通过对层状介质的瑞雷方程进行求解,验证了层状介质中瑞雷波的多阶性,讨论了各阶导波对频散曲线的影响．在此基础上,从两个方面对实测速度-深度曲线常出现的“之”字形进行了解释,提出了其中还有待进一步解决的问题及相应的建议．     

广义S变换在瑞利波频散曲线提取中的应用

虽然一些时频分析方法已经被用于频散曲线提取中,但是它们自身时频窗的缺陷使的所得频散曲线信息缺失或错误.本文首次尝试利用广义S变换分析瑞利波的频散特性.以半空间模型为例确定方法的可行性,频散曲线变化准确反映地层变化情况.不同炮检距设置对频散曲线有一定影响,采用大于勘测深度,小于4倍勘测深度可以得到较稳定的结果.最后,为了得到更加光滑稳定的频散曲线,提出了一种基于多道瑞利波的改进方法.用此方法对四种典型地层模型下的多道瑞利波数据进行分析,得到频散曲线光滑稳定,且比理论频散曲线和基于单道法获得频散曲线更能准确反映地层变化情况.这就为瑞利波勘探中的反演解释提供了更可靠依据.     

瑞雷波多阶模式频散曲线稀疏正则化反演方法研究

目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型进行稀疏性刻画,使反演结果更加符合地质实际;在反问题的数值实现上,针对稀疏正则化模型提出一种隐式迭代正则化算法,其迭代算子具有非膨胀特性,可以收敛到极小化问题的解.数值实验结果表明,新的反演方案具有计算效率高,模型"逐块"光滑的特性刻画好,对非高斯噪声鲁棒性强的特点.     

Multi-station analysis of surface wave dispersion

Methods based on multi-station recordings are presented for constructing the experimental dispersion curve of Rayleigh waves. Multi-station recording permits a single survey of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing near field and far field effects. A method based on the linear regression of phase angles measured at multiple stations is introduced for determining data quality and filtering criteria. This method becomes a powerful tool for on site quality control in real time. The effects of multiple modes and survey line parameters, such as near offset, receiver spacing, and offset range, are investigated. Parametric studies result in general guidelines for the field data acquisition. A case study demonstrates how to easily deploy commonplace seismic refraction equipment to simultaneously record data for P-wave tomographic interpretation and multi-station analysis of surface wave.     

Continental dispersion of seismic surface waves

Summary Continental dispersion curves for Love and Rayleigh waves have been determined by means of the Uppsala seismograph records for three earthquakes near the south coast of Turkey in April, 1957. To the authors' knowledge this is the first time dispersion curves have been determined for a relatively homogenous path across the whole of continental Europe and covering a good range of periods, namely from 3 to 86 sec for Love waves and from 5 to 61 sec for Rayleigh waves. The dispersion curves obtained are relevant to determinations of the average structure along the path traversed in particular, and to determinations of crustal structure of the European continent in general.

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Zusammenfassung Kontinentale Dispersionskurven für Love-und Rayleigh-Wellen wurden vermittels Registrierungen an der Station Uppsala von drei Erdbeben in der Nähe der Südküste der Türkei im April 1957 bestimmt. Soweit es den Autoren bekannt ist, wurden damit erstmalig Dispersionskurven für einen relativ homogenen Weg über das gesamte kontinentale Europa mit einem beträchtlichen Periodenbereich, der 3 bis 86 Sek für Love-Wellen und 5 bis 61 Sek für Rayleigh-Wellen umfasst, ausgearbeitet. Die erhaltenen Dispersionskurven haben ihre Bedeutung in der Festlegung der mittleren Krustenstruktur entlang dem durchlaufenen Wellenweg und überhaupt in der Festlegung der Krustenstruktur im Bereich des europäischen Kontinents.

     

基于图像分析的双台面波相速度频散曲线快速提取方法

双台波形的互相关方法是面波相速度频散曲线提取的一种常用方法。传统的方法精度不高,效率较低。本文提出了一种基于图像分析的频散曲线快速提取方法,采用图像显示互相关振幅矩阵,且提出了快速追踪整条频散曲线的算法,并用Matlab编写了交互式的处理软件。基于这种方法编写的资料处理软件提高了双台相速度频散曲线提取的速度和精度,为大批量处理地震数据资料提供了坚实的软件基础。基于图像分析的方法可以更为清晰地展现出双台问的面波频散曲线的特征,对频散曲线的识别和分析也提供了更为有效的研究工具。     

横向非均匀介质多道瑞雷波频散曲线正演

作为近地表横波速度结构成像的主要手段之一,面波多道分析法的正问题研究对现场观测系统设计及后续反演计算具有重要意义.目前面波频散曲线的正演主要分为两类:一是对水平层状介质中面波的本征值问题进行求解,该类方法计算效率高但较难考虑地下介质在横向上的不均匀性;二是基于波动方程的全波场模拟,该类方法在理论上可考虑任意复杂的地质模...     

Age of East Antarctica from surface wave dispersion

Rayleigh wave dispersion measurements across East Antarctica give high phase velocities to periods as long as 75 sec. These are characteristic of the other Precambrian shields of the world.Publication number 1773, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024, USA.     

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory.     

面波频散测量的频时分析法

总结了面波频时分析(FTAN)的主要成果,如移动窗分析法、多重滤波法、残差频散测量法、时间变量滤波法,力图阐述各方法间的联系.对滤波参数的选择,详细介绍了常相对带宽、均等显示滤波、线性时间分辨、最佳滤波等,其中线性时间分辨是本文首次提出的新方法.对频时分析中的显示技术作了必要的讨论,最后介绍了如何利用频时分析方法作相速度测量.     

多地震叠加提取双台间面波频散信息

利用中国HIA台和哈撒克斯坦BRVK台的甚宽频地震仪记录的2011年日本MW9.0大地震及3次MW6——7强余震数据, 采用互相关法提取了双台间的瑞雷波群速度频散曲线．研究发现, 对于同一台记录的大地震和强余震激发的瑞雷波, 其主要能量的周期范围明显不同, MW9.0大地震面波主要能量周期长(70 s以上), 而强余震面波的主要能量周期相对较短（10——50 s）．单独利用大地震数据无法提取60 s以下的群速度频散, 而单独利用强余震数据无法提取100 s以上频散．将双台记录的特大地震、强余震数据进行互相关叠加, 可以提取出较为可靠的宽频带瑞雷波群速度频散曲线（10——200 s）．      

Spatial dispersion of surface waves at the free surface of a general anisotropic elastic medium

A new technique relates the wave velocity of the surface waves in anisotropic elastic medium to its elastic constants. Anisotropic propagation of surface waves is studied in a half-space occupied by a general anisotropic elastic solid. The phase velocity expressions of quasi-waves, in three-dimensional space, are used to derive the secular equation of surface waves. The complex secular equation is resolved, analytically, into real and imaginary parts and is then solved, numerically, for phase velocity along a given phase direction on the surface. The complete procedure is thus analogous to the one used for conventional Rayleigh waves in isotropic medium. A non-linear equation relates the ray direction of the surface waves to its phase direction on the (plane) surface of the medium. The analytical differentiation of secular equation yields the directional derivative of phase velocity. This derivative is used to calculate the wave velocity of surface waves. Spatial variations of phase velocity, wave velocity and ray direction over the free plane surface are plotted for the numerical models of crustal rocks with orthorhombic, monoclinic and triclinic anisotropies.     

Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation

Surface wave dispersion curve inversion is a challenging problem for linear inversion procedures due to its highly non-linear nature and to the large numbers of local minima and maxima of the objective function (multi-modality). In order to improve the reliability of the inversion results, we implemented and tested a two-step inversion scheme based on Genetic Algorithms (GAs). The proposed scheme performs several preliminary “parallel” runs (first step) and a final global run using the previously-determined fittest models as starting population.In this work we focus on the inversion of shear-wave velocity and layer thickness while fixing compressional-wave velocity and density according to user-defined Poisson's ratios and velocity–density relationship respectively. The procedure can nonetheless perform the inversion under different degrees of regularization, depending on the a priori information and the desired degree of freedom of the system.Thanks to the large number of considered models, in addition to the fittest model, a mean model and its accuracy are evaluated by means of a statistical approach based on the estimation of the Marginal Posterior Probability Density (MPPD).We tested the proposed GA-based inversion scheme on three synthetic models reproducing a complex structure with low-to-moderate velocity cover (also including a low-velocity channel) lying over hard bedrock. For all the considered cases the bedrock velocity and depth were properly identified, and velocity inversion was reconstructed with minor uncertainties.The performed tests also investigate the influence of the first higher mode, the reduction of the frequency range of the considered dispersion curve as well as the use of different number of strata. While a limited frequency range of the dispersion curve (maximum frequency reduced from 80 to 40 Hz) does not seem to significantly limit the accuracy of the retrieved model, the adoption of the correct number of strata and the addition of the first higher mode help better focus the final solution.In conclusion, the proposed approach represents an improvement of a purely GA-based optimization scheme and the MPPD-based mean model typically offers a more significant and precise solution than the fittest one.Results of the inversion performed on a field data set were validated by borehole stratigraphy.     

改进的等效半空间法及瑞雷波频散曲线反演

层状模型的理论频散曲线表明,层状模型表面瑞雷波同一频率对应的相速度具有多值特点,这就是所谓的瑞雷波多阶性. 面波的多阶性导致了实测频散曲线的复杂性,当地层中存在软弱夹层时这一问题尤为突出,从而给实测频散曲线的解释带来了困难. 本文从工程实用的角度出发,根据等效半空间理论,提出了一种计算理论频散曲线的新算法——改进的等效半空间法,避开了面波多阶性这一复杂问题. 由此方法计算得到的面波相速度并不同于某个具体阶数的面波,而是对多阶面波的综合反映. 按照改进的等效半空间法编制了拟合反演程序,并在工程中进行了运用,取得较好的效果.     

The dispersion of surface waves and crustal structure in African continent

Summary In this study has been interpreted the Love- and Rayleigh-waves of Agadir earthquake on February 29, 1960 recorded at Lwiro and Skopje earthquake on July 26, 1963 recorded at Pretoria and Windhoek by long period Columbia type seismographs, and determined the crustal structure in Africa with dispersion of both Love- and Rayleigh-waves along the paths on two different directions. The obtained results are compared each other and with those founded recently by several investigators for Africa and Europe. Herewith has been showed that the average thickness of the crust in Africa is thinner than in Europe and the thickness in direction from Skopje to Pretoria is more than that from Agadir to Lwiro.

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Zusammenfassung In diesem Artikel wurden die Love- und Rayleigh-Wellen vom Erdbeben in Agadir vom 29. Februar 1960, aufgezeichnet in Lwiro, und vom Erdbeben in Skopje vom 26. Juli 1963, aufgezeichnet in Pretoria und Windhoek von langperiodischen Columbia-Seismographen, untersucht und somit mit Dispersion von beiden Love- und Rayleigh-Wellen der Aufbau der Erdkruste in Afrika bestimmt. Die erhaltenen Resultate wurden miteinander und mit anderen Werten, die bis heute von verschiedenen Autoren für Afrika und Europa bestimmt wurden, verglichen. Somit wurde vorgelegt, dass die Erdkruste in Afrika im allgemeinen dünner ist als in Europa und dass die Schicht in der Richtung von Skopje zu Pretoria dicker ist als in der Richtung von Agadir zu Lwiro.

     

Retrieving lateral variations from surface wave dispersion curves‡

Surface wave analysis is usually applied as a 1D tool to estimate V_S profiles. Here we evaluate the potential of surface wave analysis for the case of lateral variations. Lateral variations can be characterized by exploiting the data redundancy of the ground roll contained in multifold seismic data. First, an automatic processing procedure is applied that allows stacking dispersion curves obtained from different records and which retrieves experimental uncertainties. This is carried out by sliding a window along a seismic line to obtain an ensemble of dispersion curves associated to a series of spatial coordinates. Then, a laterally constrained inversion algorithm is adopted to handle 2D effects, although a 1D model has been assumed for the forward problem solution. We have conducted different tests on three synthetic data sets to evaluate the effects of the processing parameters and of the constraints on the inversion results. The same procedure, applied to the synthetic data, was then tested on a field case. Both the synthetic and field data show that the proposed approach allows smooth lateral variations to be properly retrieved and that the introduction of lateral constraints improves the final result compared to individual inversions.     

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.     

On the problem of the existence and uniqueness of a discrete,surface, optimum wiener filter,applied to the filtering of geophysical fields

Summary Proof is given of the existence and uniqueness of a discrete, surface, optimum (in the Wiener sense) filter for filtering geophysical fields considering a spectral approach to the construction of the said filter. It is also shown that the filtration coefficients and the filtration errors of the filter, constructed with the help of statistical estimates of the required spectral densities, converge towards their theoretical values. From the mathematical point of view, this paper concludes the building-up of the mathematical model of the discrete Wiener optimum surface filtration, suitable for geophysical fields.     

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.