Modifications of the dispersion relations for surface waves in a layer on a half-space

Summary Dispersion relations for Love and Rayleigh waves in a layer on a half-space are modified by introducing quadratic slownesses instead of velocities. The advantages of this approach are demonstrated on analytical formulae for computing the group velocity.     

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.

     

瞬时偏振滤波技术压制X分量中的面波(英文)

瑞雷面波与体波在偏振上的差异使得利用偏振特征分离这两种波场成为可能。为克服滑动时窗法在应用中存在的一些问题,本文将工程地震和天然地震信号分析中的复数道技术与瞬时偏振分析技术引进到能源领域多分量地震勘探转换波记录中的面波压制处理。理论模拟与野外实测数据的处理试验显示了较好的压制面波、保留有效信号的去噪效果,证明了该技术值得在多分量数据处理中推广应用。     

Instantaneous polarization filtering focused on suppression of surface waves

The different characteristics of polarization of body and Rayleigh waves make it possible to separate these two types of waves by their characteristics and suppress the latter. The moving time-window analysis often is used in polarization filtering but it is difficult to determine a suitable time-window length, resulting in some problems, such as complex eigenvalues and non-convergence. For overcoming these disadvantages, in this paper, we introduce the concept of complex-trace analysis and conduct de-noise processing to suppress undesirable surface waves by instantaneous polarization analysis in the case of horizontal and vertical component seismic recordings from the Hauinan coal mine. The performance of the method is illustrated by examples with synthetic and field data and its effectiveness to remove surface waves from multi-component seismic data is demonstrated.     

Long waves due to a symmetrical wind stress on the surface of a rotating ocean

Abstract

The problem of unsteady long waves generated by any horizontal and symmetrically distributed, time-periodic surface wind on a rotating ocean is analysed for large times and distances. Uniform asymptotic estimates of the surface displacement in the unsteady state are obtained. The steady-state wave and velocity fields at any distance are also determined. Some characteristics of the unsteady and steady motions are described. Also noted are the features that distinguish the motion from its one-dimensional analogue for which a non-uniform analysis in the unsteady state along with a large-distance form of the surface elevation are already known.     

Analytical partial derivatives of the phase- and group velocities for Rayleigh waves propagating in a layer on a half-space

The dispersion relation for Rayleigh waves in a layer on a half-space is modified by introducing the quadratic wave number instead of the phase velocity. The implicit function theorem is then used to derive analytical formulae for the group velocity and for the phase- and group velocity partial derivatives with respect to the parameters of the medium. As two examples, the method is applied to the interpretation of dispersion curves for short-period Rayleigh waves observed in a sedimentary basin of the West Carpathians, and in the Moravo-Silesian region, Czech Republic.     

Absorption of strain waves in porous media at seismic frequencies

An understanding of strain wave propagation in fluid containing porous rocks is important in reservoir geophysics and in the monitoring in underground water in the vicinity of nuclear and toxic waste sites, earthquake prediction, etc. Both experimental and theoretical research are far from providing a complete explanation of dissipation mechanisms, especially the observation of an unexpectedly strong dependence of attenuationQ ^–1 on the chemistry of the solid and liquid phase involved. Traditional theories of proelasticity do not take these effects into account. In this paper the bulk of existing experimental data and theoretical models is reviewed briefly in order to elecidate the effect of environmental factors on the attenuation of seismic waves. Low fluid concentrations are emphasized. Thermodynamical analysis shows that changes in surface energy caused by weak mechanical disturbances can explain observed values of attenuation in real rocks. Experimental dissipation isotherms are interpreted in terms of monolayered surface adsorption of liquid films as described by Langmuir's equation.In order to describe surface dissipation in consolidated rocks, a surface tension term is added to the pore pressure term in the O'Connell-Budiansky proelastic equation for effective moduli of porous and fractured rocks. Theoretical calculations by this modified model, using reasonable values for elastic parameters, surface energy, crack density and their geometry, lead to results which qualitatively agree with experimental data obtained at low fluid contents.     

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.     

Analysis of Rayleigh waves in saturated porous elastic media by finite element method

A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.     

Propagation of guided waves in a fluid layer bounded by two viscoelastic transversely isotropic solids

The analysis of Stoneley wave propagation in a fracture is essential for the identification and evaluation of fracture parameters from the borehole Stoneley wave. Also, it is important for many geophysics considerations, e.g. for tremor and long-period events observed in volcanoes and geothermal areas. In this paper, we investigate the guided waves propagation in a fluid layer lying between two viscoelastic vertically transversely isotropic media. The viscoelastic mechanism models the attenuation due to the presence of fluid saturation in the rock. A model based on the superposition of three inhomogeneous partial plane waves: one in the fluid and two heterogeneous waves in the solid is developed. The dispersion equation is obtained for this case. A numerical solution is carried out to obtain the guided wave velocity and attenuation coefficient. The results of this investigation show that there is a strong correlation between the velocity dispersion and attenuation of Stoneley wave and the anisotropic parameters of the medium especially in a sandstone (fast) medium.     

地震面波产生的地震动转动分量研究

本文利用弹性波动理论对地面转动分量，即瑞利（Rayleigh)波和乐夫（Love)波产生的转动分量进行了研究，给出了相应的计算公式和计算方法，特别注意到面波的散射效应对转动分量的影响，并将这一特性引入到转动分量的求取中，使问题的解决更切合于实际，最后选取实际地震记录，利用得到的公式计算出地震面波产生的转动分量。     

Surface waves in a micropolar elastic solid containing voids

The present paper investigates the effect of voids on the propagation of surface waves in a homogeneous micropolar elastic solid medium which contains a distribution of vacuous pores (voids). The general theory for surface wave propagation in micropolar elastic media containing voids has been presented. Particular cases of surface waves (Rayleigh’s, Love’s and Stoneley’s) in micropolar media which contain vacuous pores have been deduced from the above general theory. Discussions have been made in each case to highlight the effect of voids and micropolar character of the material medium separately. Their joint effect has also been studied in details. Modulation of Rayleigh wave velocity has been studied numerically. It is observed that Love waves are not affected by the presence of voids.     

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.     

弹性介质中瑞雷面波有限差分法正演模拟

为研究瑞雷面波的形成机理及传播规律,促进瑞雷面波资料处理方法的发展,本文根据弹性波方程,采用交错网格有限差分数值求解算法,对浅层各向同性弹性介质进行了包括瑞雷面波和体波在内的全波场模拟. 提出了变系数吸收边界条件并将之应用于正演模拟,使边界条件的处理简单而高效,同时给出了角点的处理方法. 对工程勘察中常见的连续和层状介质模型进行了模拟,获得了更加接近实际情况的地震记录. 结合模拟记录,探讨了瑞雷面波的形成条件,同时讨论了震源埋深对面波能量的影响.     

Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.     

桩身材料阻尼对波传播特性影响的小波分析方法

理论计算及实测资料表明,反射波法基桩动测激振信号近似为半周期正弦波,不同激振方式产生的桩顶速度脉冲信号宽度不同,相应频率成分也就不同。桩身内阻尼对不同频率谐波的幅值衰减及频散规律不同,使得不同激振方式产生的复合脉冲在同一桩中会有不同变化规律,为了使不同激振方式测试资料具有可比性,应采用相同频带进行对比。为此利用小波分析的时-频特性,通过对测试信号进行时频分解,就桩身内阻尼对不同频带信号的吸收系数及波速的影响规律进行了研究。对实测资料分析的结果表明,预制桩不同频带信号波速变化不大,但衰减系数随频率增大近似线性增加。     

Magneto-acoustic-gravity waves in the horizontal magnetic field

Abstract

In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained.

Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed.     

Finite-difference modeling of surface waves in poroelastic media and stress mirror conditions

During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surfacewave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggeredgrid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh (R1) waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method.     

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.     

Conditional statistics of Reynolds shear stress in flow over 2D dunes in the presence of surface waves

This study presents the analysis of the velocity fluctuations to describe the conditional statistics of Reynolds shear stress in flow over two‐dimensional dunes in the presence of surface waves of varying frequency. The flow velocity measurements over the dunes are made using a 16‐MHz 3D acoustic Doppler velocimeter. The joint probability distributions of the normalized stream‐wise and vertical velocity fluctuations at different vertical locations are calculated in the trough region of a selected dune in quasi‐steady region of the flow. Third‐order moments of the stream‐wise and vertical velocity components over one dune length are also calculated throughout the flow depth for understanding the effect of surface waves on relative contributions to the Reynolds shear stress due to the four quadrant events. The structure of instantaneous Reynolds stresses is analysed using quadrant analysis technique. It has been shown that the contributions of second and fourth quadrant events to the Reynolds shear stress increase with increase in the frequency of surface waves. In fact, the largest contribution to turbulent stresses comes from the second quadrant. The cumulant discard method is applied to describe the statistical properties of the covariance term u′w′. Conditional statistics and conditional sampling are used to compare the experimental and theoretical relative contributions to the Reynolds shear stress from the four quadrant events. Copyright © 2013 John Wiley & Sons, Ltd.