黏弹性EDA介质中地震波的衰减特性研究

本文首先由Christoffel方程推导出黏弹性EDA介质中均匀、 非均匀P波、 SV波和SH波的相速度表达式, 然后参照极端各向异性介质的相关计算方法, 推导出EDA介质中均匀、 非均匀地震波相衰减系数和群衰减系数的表达式, 并通过数值计算分析了相速度、 相衰减系数、 群衰减系数与裂隙方位的关系. 结果表明: 均匀介质中SH波的相速度和相衰减系数均可指示裂隙的走向; 非均匀介质中SH波相衰减系数随非均匀角的增大而增大, 且其对称轴与介质对称轴的夹角也相应增加; 由于地震波振幅的衰减随岩石物理性质的变化比地震波速度的变化更为灵敏, 而且携带了更多的岩石物理性质信息, 因此可用来探明裂隙走向、 密度及含水特性, 进而应用于预测、 预防地下工程地质灾害事故.      

Horizontal impedances for radially inhomogeneous viscoelastic soil layers

A study of the dynamic impedances of horizontally excited, radially inhomogeneous, infinite viscoelastic soil layers with a circular hole, and of piles embedded in a medium represented by such layers is made considering the shear modulus of the material to increase radially within a narrow annular boundary zone. Unlike a previous study in which the boundary zone was presumed to be massless, in the present study the inertia effects of this zone are taken into account. The impedances are evaluated over wide ranges of the parameters involved and the sensitivity of the results is assessed. The results are also compared with those obtained for similarly excited homogeneous layers and for vertically excited inhomogeneous layers. For purposes of analysis, the inhomogeneous boundary zone is represented by a series of concentric rings of constant properties, and the transfer matrix technique is used to evaluate the results. The analysis and the computer program used to implement it are applicable to layers of arbitrary radial variation of material properties.     

Low‐frequency normal wave propagation in a periodically layered medium with weak contrast in elastic properties

We derive the phase velocity dispersion and the scattering for wave vertically propagating in a periodically weak‐contrast horizontally layered medium with arbitrary number of layers in a period. Phase velocity dispersion is defined as the frequency dependence of vertical travel time, and scattering is defined as a reflection coefficient at the interface between the multilayered system and the corresponding Backus medium. Low‐frequency approximation is used to define a dynamic effective medium with frequency‐dependent phase velocity. The results are compared with those obtained earlier for a gradient medium. We show that the low‐frequency weak‐contrast approximation is valid for models with realistic contrasts in elastic properties.     

Surface Wave Group Velocity Tomography Imaging from Ambient Noise for Fujian Province and Its Adjacent Areas

Two-month continuous waveforms of 108 broadband seismic stations in Fujian Province and its adjacent areas are used to compute noise cross-correlation function (NCF). The signal quality of NCF is improved via the application of time-frequency phase weighted stacking. The Rayleigh and Love waves group velocities between 1s-20s are measured on the symmetrical component of the NCF with the multiple filter method. More than 5,000 Rayleigh wave dispersion curves and about 4,000 Love wave dispersion curves are obtained and used to invert for group velocity maps. This data set provides about 50km resolution that is demonstrated with checkerboard tests. Considering the off great circle effect in inhomogeneous medium, the ray path is traced based on the travel time field computed with a finite difference method. The inverted group velocity maps show good correlation with the geological features in the upper and middle crust. The Fuzhou basin and Zhangzhou basin showed low velocity on the short period group velocity maps. On the long period group velocity maps, the low velocity anomaly in the high heat flow region near Zhangzhou and clear velocity contrast across the Zhenghe-Dapu faults, which suggests that the Zhenghe-Dapu fault might be a deep fault.     

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.     

ANISOTROPIC Q AND VELOCITY DISPERSION OF FINELY LAYERED MEDIA1

When a seismic signal propagates through a finely layered medium, there is anisotropy if the wavelengths are long enough compared to the layer thicknesses. It is well known that in this situation, the medium is equivalent to a transversely isotropic material. In addition to anisotropy, the layers may show intrinsic anelastic behaviour. Under these circumstances, the layered medium exhibits Q anisotropy and anisotropic velocity dispersion. The present work investigates the anelastic effect in the long-wavelength approximation. Backus's theory and the standard linear solid rheology are used as models to obtain the directional properties of anelasticity corresponding to the quasi-compressional mode qP, the quasi-shear mode qSV, and the pure shear mode SH, respectively. The medium is described by a complex and frequency-dependent stiffness matrix. The complex and phase velocities for homogeneous viscoelastic waves are calculated from the Christoffel equation, while the wave-fronts (energy velocities) and quality factor surfaces are obtained from energy considerations by invoking Poynting's theorem. We consider two-constituent stationary layered media, and study the wave characteristics for different material compositions and proportions. Analyses on sequences of sandstone-limestone and shale-limestone with different degrees of anisotropy indicate that the quality factors of the shear modes are more anisotropic than the corresponding phase velocities, cusps of the qSV mode are more pronounced for low frequencies and midrange proportions, and in general, attenuation is higher in the direction perpendicular to layering or close to it, provided that the material with lower velocity is the more dissipative. A numerical simulation experiment verifies the attenuation properties of finely layered media through comparison of elastic and anelastic snapshots.     

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.     

声波测井中的相速度与群速度讨论(英文)

声波测井过程中获取的速度到底是相速度还是群速度,目前仍存在一些争议,本文从理论分析和数值模拟的角度,使用三种模型对这一问题进行了研究。首先,构造一个相速度与群速度可调的稳态声波传播模型——不同声速的两个平面波叠加模型,利用慢度时间相关(STC)方法提取声波波速,数值模拟结果表明,无论相速度较大或是群速度较大,STC方法提取出来的波速都是相速度;其次,通过频散分析和割线积分得到刚性壁圆柱流体模型中的频散曲线与分波波形,使用STC方法得到的速度与相速度的频散曲线吻合较好,而直接读取波至获得的速度与群速度的频散曲线趋势一致;最后,利用频散分析和实轴积分方法,获得偶极子在慢地层中激发的模式及全波波形,得到的结果再次验证了刚性壁圆柱流体模型中的结论。     

On the guided and surface shear horizontal waves in monoclinic transversely periodic layers and halfspaces with arbitrary variation of material properties across the unit cell

The paper outlines analytically and exemplifies numerically the basic aspects, characterizing dispersion spectra of the shear horizontal (SH) waves in transversely periodic layers and half-spaces with a monoclinic functionally graded unit cell. On introducing the background, the ’quasi-orthorhombic’ formulation is pointed out. Further analytical consideration bypasses explicit intricacy of the wave solutions in continuously varying media and relies only on a few basic traits of the governing equation of SH motion. An elementary reasoning pinpoints the key features of the Floquet eigenmodes and their link to the traction-free boundary conditions in question. This simple grounds suffices to generalize the remarkable property, previously restricted to the orthorhombic piecewise homogeneous periodic stacks, which implies that the SH dispersion spectrum for a unit cell, assumed free of traction at the faces, is embedded into the spectrum for the finite periodic structure of these unit cells and contains the locus of surface-wave solutions for the semi-infinite periodic structure. The conclusion is valid for an arbitrary continuous and/or discrete transverse periodic inhomogeneity. Numerical results, presented for the case of continuously inhomogeneous unit cell, are based on the Peano series of multiple integrals.     

Love waves in an inhomogeneous interstratum

Summary The propagation of Love waves in an inhomogeneous interstratum, whose rigidity and density follow generalized power law variation, lying between two homogeneous half-spaces has been considered. The characteristic frequency equations have been obtained. The computational results for some special cases are presented in the form of dispersion curves showing the variation of phase and group velocity of Love waves with wave number.     

Calculation of Rayleigh-wave phase velocities due to models with a high-velocity surface layer

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.     

各向异性介质中扭转波分裂的实验观测

实验室可以产生两种振动模式的横波,一种是剪切振动,另一种是扭转振动,在各向同性介质中两模式的横波速度是相同的,但它们的振动特性不一样,前者表现出很强的偏振特性,后者为无偏振特性.实验测试表明无偏振特性的扭转波在各向异性介质中传播时也会出现两种速度不同的扭转波,速度值与剪切横波的快慢横波速度值一致.用扭转波换能器接收时,这快慢扭转波的波形振幅不受各向异性方位影响.通过两块均匀的各向异性样品,用实验观测揭示了各向异性介质中扭转波的一些传播特征.     

Experimental determination of Rayleigh-wave mode velocities using the method of wave number analysis

A method is presented to determine experimentally phase and group velocity dispersion curves of propagating Rayleigh-wave modes. Through the application of the Fourier transform method wave number spectra of surface displacements due to wave propagation along a line are constructed. The dominant peaks in the wave number spectra together with their corresponding wave numbers are identified. From the latter the phase velocities, which correspond to the wave modes present, are calculated. The phase and group velocity dispersion curves of wave modes are determined from repeated experiments with different frequencies of excitation. This method to determine the frequency-dependent Rayleighwave velocities solves the problem of non-linear phase changes between surface points in contrast to the conventional phase difference methods which assume linear phase changes.     

Finite difference modeling of seismic wave propagation in monoclinic media

Reported in the present paper are the results of the study of propagation of SH waves in the plane of mirror symmetry of a monoclinic multilayered medium with displacement normal to the plane. Dispersion equation has been obtained analytically ussing Haskell’s matrix method, while the finite-difference method has been employed to model the SH-wave propagation to study its phase and group velocities. The stability analysis has been carried out to minimize the exponential growth of the error of finite difference approximation in order to make the finite difference method stable and convergent. Further, variations of phase velocity with respect to both wave number and dispersion parameter for different stability ratios in monoclinic media have been examined and shown graphically. The effect of change of stability ratio on the group velocity of the wave propagation has been also investigated. Likewise, the effects of change of dispersion parameter on phase velocity and the variation of frequency with increase of wave number have been graphically represented and discussed.     

基于Remez迭代算法求解差分系数的双相介质自适应有限差分正演模拟

利用传统有限差分方法对基于Biot理论的双相介质波动方程进行数值求解时,由于慢纵波的存在,数值频散效应较为明显,影响模拟精度.相对于声学近似方程及普通弹性波方程,Biot双相介质波动方程在同等数值求解算法和精度要求条件下,其地震波场正演模拟需要更多的计算时间.本文针对Biot一阶速度-应力方程组发展了一种变阶数优化有限差分数值模拟方法,旨在同时提高其正演模拟的精度和效率.首先结合交错网格差分格式推导Biot方程的数值频散关系式.然后基于Remez迭代算法求取一阶空间偏导数的优化差分系数,并用于Biot方程的交错网格有限差分数值模拟.在此基础上把三类波的平均频散误差参数限制在给定的频散误差阈值和频率范围内,此时优化有限差分算子的长度就能自适应非均匀双相介质模型中的不同速度区间.数值频散曲线分析表明:基于Remez迭代算法的优化有限差分方法相较传统泰勒级数展开方法在大波数范围对频散误差的压制效果更明显;可变阶数的优化有限差分方法能取得与固定阶数优化有限差分方法相近的模拟精度.在均匀介质和河道模型的数值模拟实验中将本文变阶数优化有限差分算法与传统泰勒展开算法、最小二乘优化算法进行比较,进一步证明其在复杂地下介质中的有效性和适用性.     

A Fast Method of Computing Group-Velocity Partial Derivatives for Love Waves Propagating in a Layer on a Half-Space

The dispersion relation for Love waves in a layer on a half-space is modified by introducing the wave number and its square instead of the phase velocity. The implicit function theorem is then used to derive the analytical formulae for the group velocity and for the phase- and group-velocity partial derivatives with respect to the parameters of the medium. The formulae are compared with those obtained by Novotný (1971) where the traditional formulation of the dispersion relation was used.     

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.     

On the propagation of certain types of surface waves in a non-homogeneous elastic layer

Summary The propagation of a certain type of surface waves in a non-homogeneous elastic layer of finite thickness lying in welded contact with a semi-infinite homogeneous elastic medium has been investigated in this paper. The surface wave is characterised by the fact that the dilatation and the vertical displacement component are both zero. It has been proved that such disturbance can propagate only when the phase velocity of the wave is greater than the shear wave velocity and the group velocity is inversely proportional to the phase velocity.