我国境内乐夫波的相速度及地壳厚度计算

本文利用三个堪察加地震和两个阿拉斯加地震在我国某些地震台上所记录的乐夫波,进行了相位对比,用最小二乘法分别计算了各地区的乐夫波相速度。将观察的相速度与理论曲线相比较,得到各地区的地壳厚度。 理论曲线系根据多尔曼(Dorman)208模型的数据,采用β_1=3.53公里/秒,ρ_1=2.78克/厘米~3     

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.     

Love waves in inhomogeneous and anisotropic earth — I

Summary The frequency equation is derived for the propagation of Love waves in the earth's crust, composed of transversely isotropic layers and overlying anisotropic and inhomogeneous mantle. The exact boundary value problem is solved for a single layer and extended to multilayered media by generalizing theHaskell's technique. In fact the problem of deriving the frequency equation has been reduced to finding out the solution of the equation of motion subject to the appropriate boundary conditions. To illustrate the method, the author has derived frequency equations of Love waves for linear, exponential and generalized power law variation of vertical shear wave velocity with depth in the half space overlain by transversely isotropic inhomogeneous stratum.     

On love waves in inhomogeneous anisotropic elastic solids

Summary This paper consists of two parts. In the first part, the existence of Love waves in non-homogeneous and transversely-isotropic elastic layer over-lying a semi-infinite isotropic elastic solid has been investigated. The frequency equation for such waves has been derived. Numerical calculations giving the velocity of such waves has been made for different layer thicknesses. In the second part, a characteristic frequency equation has been calculated considering the lower boundary of the layer to be rigid. A numerical calculations has been made in this case also to represent the variation of wave number with velocity for different mode number.     

Love waves in a sedimentary layer lying over an anisotropic inhomogeneous half space

Summary The effects of anisotropy and inhomogeneity on the propagation of Love waves in a sedimentary layer, overlying the inhomogeneous and transversely isotropic half space, are studied in this paper. The results of numerical analysis show an appreciable variation of phase- and group-velocity of Love waves in low frequency region compared to high frequency region due to the presence of transverse isotropy and inhomogeneity in the half space. The higher values for phase velocity are found for the increasing values of anisotropy factor as well as for the greater power of density variation. However, the presence of higher anisotropy factor and inhomogeneity in the half space reduce group velocity considerably in the lower frequency region.     

On love waves in heterogeneous media

Summary Love waves in a half space with one homogeneous elastic layer overlying a semiinfinite medium having elastic properties varying with depth has been considered. The frequency equation for small wave lengths has been obtained, considering general variation, and has been shown to involve the first three derivatives of the rigidity of the heterogeneous medium at its interface with the homogeneous layer.     

A note on the approximate determination of the dispersion of Love waves in a laterally nonhomogeneous layer lying over a homogeneous half-space

Rayleigh's principle and the concept of the local wave number have been utilised for the approximate determination of the dispersion of Love waves propagating in a laterally heterogeneous layer lying over a homogeneous half-space. The shear wave velocity and the rigidity in the surface layer have been assumed to decrease with the increase of the lateral distance from the origin. The range of validity of the dispersion equation obtained by this method has been examined critically. It was found that: (a) for existence of Love waves the minimum value of shear wave velocity in the layer must be less than that in the matter below, and (b) the phase velocity of Love waves decreases with the increase of the lateral distance from the origin.     

On the frequency equation for love waves due to abrupt thickening of the crustal layer

Summary The effect of thickening of the crustal layer in mountainous region on the dispersion curve of Love waves has been studied. Perturbation method has been applied to obtain the modified frequency equation for Love waves through the surface of separation between a semi-infinite material and a layer the thickness of which abruptly increases throughout a certain length of the path. The effect is to decrease the phase velocity of the waves particularly in the low period range. It has been pointed out that by proper study, the amount of thickening may be obtained.     

Finite strain theory of love waves

Summary The propagation of Love waves is discussed on the basis of finite strain theory. The primary Love wave is found to be associated with a secondary Rayleigh wave and a tertiary Love wave. Numerical calculations are presented for two values of the wave-velocity; the results show that the theory of Love waves based on infinitesimal strain, is not applicable to short period waves.     

Love waves in the fiber-reinforced layer over a gravitating porous half-space

This paper aims to study the propagation of Love waves in fiber-reinforced layer lying over a gravitating anisotropic porous half-space. The closed form of dispersion equation has been derived for the Love waves in terms of Whittaker function and its derivative, which are further expanded asymptotically, retaining the terms up to second degree. The frequency equation shows that the transverse and longitudinal rigidity of reinforced material, as well as gravity and porosity of the porous halfspace have significant effect on the propagation of Love waves. The study reveals that the increment in width of reinforced layer decreases the phase velocity. For a particular width of the reinforced layer, it is also observed that the phase velocity increases with increasing porosity of the half-space, but it decreases with increasing gravity.     

Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties

The paper is concerned with the propagation of the Love waves in an inhomogeneous transversely isotropic fluid saturated porous layered half-space with linearly varying properties. The analysis is based on Biot's theory. Firstly, the dispersion equation in the complex form for the Love waves in an inhomogeneous porous layer is derived. Then the equation is solved by an iterative method. Detailed numerical calculation is presented for an inhomogeneous fluid saturated porous layer overlying a purely elastic half-space. The dispersion and attenuation of the Love waves are discussed. In addition, the upper and lower bounds of the Love wave speed are explored.     

Feasibility of determining Q of near-surface materials from Love waves

High-frequency (≥ 2 Hz) Multi-channel Analysis of Love Waves (MALW) provides a practical way to determine velocity of horizontally polarized shear (SH) waves for a layered earth model up to 30 m below the ground surface in many geological settings. The information used in the MALW method is phase of Love waves. Information on amplitude of Love waves is not utilized in the MALW method. In this paper we present a method that uses information on amplitude of high-frequency Love waves to estimate quality factors (Q_s) of near-surface materials. Unlike Rayleigh waves, attenuation coefficients (amplitude) of Love waves are independent of quality factors for P waves and are function of quality factors of Love waves. In theory, a fewer parameters make the inversion of attenuation coefficients of Love waves more stable and reduce the degree of nonuniqueness. We discussed sensitivity of an inversion system based on a linear relationship between attenuation coefficients and dissipation factors (1/Q_s). The sensitivity analysis suggested that damping and constraints to an inversion system are necessary to obtain a smooth and meaningful quality factor model when no other information is available. We used synthetic and real-world data to demonstrate feasibility of inversion of attenuation coefficients of high-frequency Love-wave data acquired with the MALW method for quality factors with a linear, damped and constrained system.     

面波偏振与中国大陆岩石层横向不均匀性

本文利用７个ＣＤＳＮ台站的长周期数字地震记录和奇异值分解方法，分析了在中国大陆内传播的基阶勒夫波的偏振方向，从而确定波到达台站时的入射方向对于大圆方向的偏离．５°-１０°的偏角是常见的，最大偏角可达２０°左右．尤其是４０ｓ以下的勒夫波，在大多数路径上都显著偏离．这些观测到的现象可以用勒夫波穿过不同大地构造单元界线发生的折射作出定性解释．青藏块体的边界和天山褶皱带可引起２０-６０ｓ（或更长）周期的勒夫波发生折射；华北与华南地块间及华北平原和鄂尔多斯地块间的速度差异一般影响２０-４０ｓ之间的勒夫波；扬子地台与东南沿海褶皱的差异主要影响２０ｓ以下的波；２０ｓ以下的短周期勒夫波往往表现出复杂的多重路径现象．     

Propagation of love waves in a two-layered heterogeneous halfspace

Summary This paper studies the propagation of Love waves in the following two-layered models: (i) a heterogeneous layer overlying a heterogeneous halfspace, (ii) a heterogeneous layer overlying homogeneous halfspace, (iii) a homogeneous layer overlying a homogeneous halfspace. The heterogeneities of the layer and halfspace are specified by different exponential functions of the depth. The dispersion curves have been drawn taking account of the actual variation of elastic parameters with depth in the Earth. The effects of the heterogeneities of the layer (crust) and halfspace (mantle) on dispersion curves have been discussed.     

Effect of anisotropy and inhomogeneity on Love wave dispersion

Summary An analysis is carried out of the Love wave propagation in a system consisting of an anisotropic, inhomogeneous layer bounded on either side by homogeneous, isotropic solid halfspaces. The period equation is obtained, which incorporates in it the effects of a typical variation of directional rigidities and density in the layer on dispersive properties of the Love waves. The conditions for the existence of the real roots of the frequency equation is brought out in the form of limits on phase velocity values. Corresponding to these values, the frequency equation is discussed in different wave length ranges. Numerical computation is done to analyse the variation of (i) Phase and Group velocity and (ii) Amplitudes (at different depths), with wave number. Conclusions on the significant results follow in the end.     

青藏高原中部Quasi-Love波的识别及其转换点揭示的东西向方位各向异性变化

目前人们利用4种基本的地震波现象研究地震各向异性,如横波双折射、面波散射、与传播方向有关的走时异常和PS转换波震相.本文利用面波散射产生的Quasi-Love（QL）波研究青藏高原上地幔顶部的各向异性结构特征.首先利用中国地震台网昌都（CAD）台记录的地震波形资料识别出产生QL波的路径,并利用合成地震记录和垂直偏振极性分析证实所观测到的为QL波,而不是高阶振型的Rayleigh波或其他体波震相;然后由Rayleigh波、Love波和QL波的群速度估算了各向异性结构横向变化的转换点;不同周期时,转换点的位置不同,这种频率依赖性还需要进一步的模拟研究.Love波向Rayleigh波耦合（产生QL波）的转换点位置揭示了青藏高原面波方位各向异性变化特征,并以南北向构造带的东西分段性、上地幔流引起的地球内力诱导岩石形变解释了青藏高原各向异性的东西向差异性.     

利用地震背景噪声提取西山村滑坡高频面波信号

滑坡体三维速度结构为滑坡治理、灾害防治、风险防范以及理解滑坡的动力学过程提供了关键信息,而高频面波成像是研究浅层速度结构的重要手段.本文详细介绍了利用2016年12月1日在四川理县西山村滑坡上布设的38个仪器记录的三分量连续地震噪声数据,提取1～5Hz的基阶Love波和Rayleigh波经验格林函数,分析了不同参数和处理方法对背景噪声互相关计算结果的影响.结果表明,1天左右的连续波形记录裁剪至1200s的时间长度,进行互相关叠加就可以得到较为稳定的经验格林函数.西山村滑坡体上Love波和Rayleigh波的群速度分别为约400m·s-1和700m·s-1,并且Love波信噪比高于Rayleigh波.此外,我们还利用聚束分析方法对噪声源的位置进行了分析,发现1～5Hz的背景噪声主要来自滑坡东南侧附近杂谷脑河水的搬运作用.这些高频面波数据和噪声源位置为获取滑坡浅层三维速度结构提供了重要输入,同时也为研究滑坡体速度结构随时间的变化提供了基础.     

东北地区背景噪声的Rayleigh和Love波相速度层析成像

本文利用中国数字地震台网位于东北地区的122个宽频地震台站的18个月记录的三分量连续地震噪声数据,采用互相关方法提取了Rayleigh和Love波经验格林函数,并利用时频自动分析技术获取了相应的相速度频散曲线.通过反演频散曲线,获得了Rayleigh和Love波周期为8~35s的二维相速度分布.结果表明,东北地区相速度的分布存在横向和垂向的不均匀性.短周期的相速度分布同地表地质构造密切相关,松辽盆地及山间沉积盆地呈现低速异常,而大兴安岭、小兴安岭及东部的一些山岭显示高速异常.随着周期的增加,位于中间的松辽盆地变为高低速相间,两侧的造山带呈现低速异常.这种异常的转变,可能是受构造活动或者莫霍面深度的影响.另外,在周期为20~35s频段内,Rayleigh和Love波同一周期的相速度在松辽盆地和位于吉林地区的郯庐断裂带表现不一致,表明可能存在径向各向异性.     

Surface waves in magneto-elastic initially stressed conducting media

Summary The object of the present paper is to investigate the magneto-elastic surface waves in an initially stressed conducting medium. The theory of magneto-elastic surface waves in an initially stressed conducting medium has firstly been deduced and then it has been employed in investigating the particular cases of surface waves such as (i) Rayleigh waves (ii) Love waves and (iii) Stoneley waves. The wave-velocity equations obtained in different cases are in agreement with the corresponding classical results when the solid is initially unstressed and the magnetic field is absent or the material is non-magnetic.     

Dispersion of love waves in non-uniform channels lying over homogeneous half-spaces

Summary Earth's crust has non-uniformity in lateral as well as in vertical directions. In some tectonically significant areas, extremely rapid Love waves velocity variations have been observed. To study Love waves dispersion characteristics in such areas, two non-uniform channels with exponential velocity and rigidity variations in vertical and lateral directions are considered. Theoretical dispersion curves are presented to understand quantitatively the effect of non-uniformity in different directions by using ray theory techniques.Theoretical Geophysics Group, National Geophysical Research Institute, Hyderabad-7 (A.P. India.-NGRI Contribution No. 72-359.