A Semi-classical calculus of correlations

The method of passive imaging in seismology has been developped recently in order to image the Earth’s crust from recordings of the seismic noise. This method is founded on the computation of correlations of the seismic noise. In this article, we give an explicit formula for this correlation in the “semi-classical” regime. In order to do that, we define the power spectrum of a random field as the ensemble average of its Wigner measure; this allows phase-space computations: the pseudo-differential calculus and the ray theory. In this way, we get a formula for the correlation of the seismic noise in the semi-classical regime with a source noise which can be localized and non-homogeneous. After that, we show how the use of surface guided waves allows us to image the Earth’s crust.     

半无限介质内异质体方位探测数值研究

用数值模拟方法研究了地下异质体对波散射,分析了散射波对表面波相速度影响,结果表明：由相速度曲线扰动难以有效确定异质体方位。在表面波场中,散射波能量相对较小,不易辨别,以振源为中心,在测线上对称布置一组测点,通过两侧测点质点响应曲线比较,得到表面散射波场。在表面散射波场中,散射瑞利波是主要的,由散射瑞利波走时随测点位置变化可判断地下异质体的方位。最后,给出地下异质体方位测试方案。     

利用小波变换分析随机-均匀介质尺度特征

为研究复杂非均匀介质中非均匀体的尺度特征,建立了随机-均匀介质模型,利用小波变换方法,对随机-均匀介质3种地震波(直达波、散射波和反射波)的尺度特征进行了分析和研究。结果表明：3种地震波表现出不同的尺度特征,直达波表现出大尺度特征,散射波次之,反射波具有小尺度特征;随着模型参量横向自相关长度的增大,直达波的最佳尺度呈下降趋势,散射波和反射波的最佳尺度呈上升趋势。研究结果为利用小波变换分析地震剖面中地震波以及非均匀体的尺度特征提供了参考。     

Seismic response of 3D topographical irregularities under incoming elastic waves from point sources

We study some effects that produce 3D topographical irregularities under incoming elastic waves from point sources using the indirect boundary element method. This technique is based on the representation of elastic waves in terms of single-layer boundary sources. In this way reflected and diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. The field emited from the point source is computed with the moment tensor for a shear dislocation and analytical expressions of the elastodynamic 3D Green's functions. In this way we can construct a double couple with variable orientation. We compare the technique with that of Bouchon, who used the discrete wave number method for a shear dislocation in a halfspace with a triangular source function. We subsequently apply our method to simulate the seismic response of a mountain of ellipsoidal geometry. The source function that we have considered is a triangular pulse and we show results corresponding to the velocity registered over the surface of the irregularity and that of the halfspace. This motion is presented by means of snapshots showing the evolution of the wavefields that are present in the problem.     

Displacement ring load Green's functions for saturated porous transversely isotropic tri‐material full‐space

Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Earthquake waves in a random medium

Measurements are conducted with small samples in the laboratory and thus for all practical purposes the medium is macroscopically homogeneous. On the other hand, the uncertainties and the irregular changes in situ are macroscopic inhomogeneities. This work is an attempt to account for these stochastic changes in the elastic properties and density in a rational manner. The method used is that of Karal and Keller which is based on the use of the Green's function and neglect of third-order correlations. The resulting integral equations are solved by Laplace transform. The analysis indicates that the energy decay in the mean motion through random mode coupling introduces damping into even a purley'elastic medium and enhances the damping in a significant manner in a hysteretic viscoelastic medium. This consideration is important in relating the damping and dispersion characteristics of wave in situ to those measured in the laboratory. The formulation is extended to multilayer systems through transfer matrices and to arbitrary inputs by Fourier transform. Sample calculations are presented for single and multilayer systems to obtain response spectra and for the response to Gaussian and actual earthquake input motions.     

Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs

We present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three‐layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three‐layer‐spring medium. Although a closed‐form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi‐layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo‐3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements. Copyright © 2008 John Wiley & Sons, Ltd.     

Reconstructing the Green's function through iteration of correlations

Correlations of ambient seismic noise are now widely used to retrieve the Earth response between two points. In this study, we reconstruct the surface-wave Green's function by iterating the correlation process over the tail of the noise-based correlation function. It has been demonstrated that the so-called C³ function shows the surface-wave part of the Green's function. Using data from 150 continuously recording stations in Europe, the C³ results help in the extraction of the travel-times from noise-based measurements, especially through the suppression of effects caused by non-isotropic source distributions. We present the results of the next iterative step (i.e. C⁵), which show that some coherent signal is still present in the coda of the C³ function, and we investigate the evolution of the reconstruction of the Green's function throughout the iteration process. Finally, we discuss the interest of combining information from the different correlation functions to improve noise-based tomography analysis.     

Wave scattering and diffraction of subsurface cavities in layered half-space for incident SV-P and SH waves

A novel approach is proposed to deal with the problem of wave scattering and diffraction of subsurface cavities embedded in stratified half-space. The subsurface cavity with complex surroundings is treated as a substructure. The continuity condition at the interface between the substructure and the far field of stratified half-space is maintained by applying a free-field approach. As the boundary of the free-field ground is regular, the construction of the dynamic matrices and the evaluation of the wave input on the interface become considerably easier. Based on the previous work with some improvement, a novel approach for evaluation of Green's functions in stratified half-space is presented. The wave equation is decoupled into the one for SV-P wave components and the other one for SH wave component. The precise integration technique ensures high accuracy of the solution of wave equations. The layer merging technique and the dual form equation make it possible to obtain Green's function in closed-form solution of matrix equations. Numerical examples validate accuracy and efficiency of the proposed approach.     

青藏高原东北部寒潮次数时空变化特征研究

基于青藏高原东北部1961 - 2015年68个国家气象站点的逐日气温观测资料, 统计了各站月、 季、 年不同时间尺度的寒潮次数, 并用气候诊断方法分析了寒潮次数时空变化特征。结果表明： 在时间尺度上, 20世纪60年代至21世纪00年代, 寒潮各年代的年平均次数大致经历了“多 - 多 - 多 - 多 - 少”的变化过程; 1961 - 2015年青藏高原东北部寒潮年次数的平均值为2.6次, 以0.192次·（10a）^-1速率呈显著的减少趋势; 1981年为突变点, 2005 - 2015年为显著的减少时段, 而1961 - 2004年为较弱的减少时段; 春、 秋、 冬三季寒潮次数的平均值分别为0.7、 0.7、 1.2次, 秋季减少趋势通过了显著性检验, 2月和11月减少的趋势最为明显。在空间尺度上, 年度、 春季、 秋季寒潮次数显著减少的站点数量分别达19、 44和21个。寒潮年次数减少的这种变化特征与青藏高原地区20世纪80年代气候变暖以来气温明显升高的趋势基本一致。     

泥质砂岩动弹模阻尼及能量耗散特性试验研究

针对煤矿矿区受爆破地震波影响下泥质砂岩斜坡的稳定性问题,利用MTS 815试验机开展了波形为正弦波、频率1 Hz的岩石动三轴试验,对滞回圈应力—应变数据进行了准确分析,计算了泥质砂岩的动弹性模量及阻尼参数,以及在循环动力作用下单位体积能、单位弹性能、单位耗散能的演化规律。研究中发现耗散能与围压水平、动应力水平两者之间呈幂函数关系。对试验中出现的“突增或突减”现象进行了讨论和分析,初步归因于岩石具有蓄能的特性和动应力的“触发效应”、“累积效应”,并指出这与天然或爆破地震波能触发斜坡崩塌的机理是一致的。本试验旨在为受爆破地震波影响的泥质砂岩斜坡稳定性分析指明研究方向和提供基础性的研究指标。     

Three‐dimensional time‐harmonic fundamental solutions for a fluid‐saturated poroelastic half‐space with partially permeable free surface

By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Crustal structure beneath the Malawi and Luangwa Rift Zones and adjacent areas from ambient noise tomography

Crustal shear wave velocity structure beneath the Malawi and Luangwa Rift Zones (MRZ and LRZ, respectively) and adjacent regions in southern Africa is imaged using fundamental mode Rayleigh waves recorded by 31 SAFARI (Seismic Arrays for African Rift Initiation) stations. Dispersion measurements estimated from empirical Green's functions are used to construct 2-D phase velocity maps for periods between 5 and 28 s. The resulting Rayleigh wave phase velocities demonstrate significant lateral variations and are in general agreement with known geological features and tectonic units within the study area. Subsequently, we invert Rayleigh wave phase velocity dispersion curves to construct a 3-D shear wave velocity model. Beneath the MRZ and LRZ, low velocity anomalies are found in the upper-most crust, probably reflecting the sedimentary cover. The mid-crust of the MRZ is characterized by an ~3.7% low velocity anomaly, which cannot be adequately explained by higher than normal temperatures alone. Instead, other factors such as magmatic intrusion, partial melting, and fluid-filled deep crustal faults might also play a role. Thinning of the crust of a few kilometers beneath the rifts is revealed by the inversion. A compilation of crustal thicknesses and velocities beneath the world's major continental rifts suggests that both the MRZ and LRZ are in the category of rifts beneath which the crust has not been sufficiently thinned to produce widespread syn-rifting volcanisms.     

The influence of the depth of the ground water table on free field road traffic-induced vibrations

This paper describes the influence of seasonal variations of the ground water table on free field traffic-induced vibrations. The passage of a truck on two types of road unevenness is considered: a joint in a road pavement consisting of concrete plates and a speed bump with a sinusoidal profile. Free field vibrations are computed with a two-step solution procedure, where the computation of the vehicle axle loads is decoupled from the solution of the road–soil interaction problem. The impedance of the soil is calculated using a boundary element method, based on the Green's functions for a dry layer on top of a saturated half-space. It is demonstrated that, in the low-frequency range of interest, wave propagation in the saturated half-space can be modelled with an equivalent single phase medium as an alternative to Biot's poroelastic theory for saturated porous media. The relation between the free field velocity and the depth of the ground water table is dominated by three phenomena: (1) the compressibility of the soil decreases due to the presence of the pore water, (2) the ground water table introduces a layering of the soil which may cause resonance of the dry layer and (3) refracted P-waves in the dry layer interfere with surface waves. If the depth of the ground water table is large with respect to the wavelength of the vibrations in the soil, the response tends to the response of a dry half-space. The average free field velocity is equal to the velocity in the absence of ground water. If the depth of the ground water table is small with respect to the wavelength of the vibrations in the soil, the response tends to the response of a saturated half-space and resonance of the dry layer does not occur. The average free field velocity is smaller than the velocity in the absence of ground water. The interference of refracted P-waves and surface waves causes an additional oscillation of the response as a function of the excitation frequency and the distance between the road and the receiver. Copyright © 2004 John Wiley & Sons, Ltd.     

Acceleration of near-field scattering from an inhomogeneous spherical shell

The three dimensional scattering of near-field, from a point source, is studied for acceleration in the time domain. The perturbation method is applied to define the acceleration for the first order scattering from a weak inhomogeneity in a homogeneous surrounding. A body force, arising from the interaction between the primary waves and the inhomogeneity, acts as the source generating the scattered motion. The acceleration of scattered waves is related to the velocity and density fluctuations of the inhomogeneity. No restrictions are placed on the inhomogeneity size or locations of the source and receiver. Decoupling of scattered motion enables the identification of different phases. Integral expressions are derived for the scattering acceleration due to the incidence of near-field wave (from an impulsive point force) at a radially inhomogeneous volume element. These integrals are solved further for scattering from an inhomogeneous spherical shell. The accelerations for back scattering are obtained as a special case. These accelerations are simple analytically solvable expressions in closed form. Only spherical asymmetry ofP wave velocity inhomogeneity can affect the scatteredS acceleration. ScatteredP acceleration is affected by the gradient ofS wave velocity inhomogeneity. The back scattering of near-field from a spherical shell, is independent of radial inhomogeneity ofP wave velocity. Inhomogeneity with smoothly perturbedS wave velocity does not back-scatter any acceleration. Accelerations are computed numerically for scattering from a part of inhomogeneous spherical shell. Hypothetical models are considered to study the effects of the distances of spherical shell from source, receiver, its thickness and its position relative to the direction of impulsive force.     

Simulation of the crosshole method in isotropic and anisotropic media

The crosshole seismic method was simulated using a finite element model with a diagonal mass matrix and a direct integration of the equations of motion in the time domain. The results were compared to those of a more efficient but also more restricted formulation using discrete Green's functions. The effects of the type of excitation, the shape of the applied pulse and the position of the receiver with respect to the source on the shape of the recorded motions were investigated for isotropic and cross anisotropic soil deposits. The computed times of arrival of the different waves were compared to those predicted using curved ray path theory to assess the accuracy of this much simpler procedure as a means to interpret the experimental data and determine the soil properties. Copyright © 1999 John Wiley & Sons, Ltd.     

Structure of young East Pacific Rise lithosphere from ambient noise correlation analysis of fundamental- and higher-mode Scholte-Rayleigh waves

Inter-station Green's functions estimated from ambient noise studies have been widely used to investigate crustal structure. However, most studies are restricted to continental areas and use fundamental-mode surface waves only. In this study, we recover inter-station surface (Scholte-Rayleigh) wave empirical Green's function (EGFs) of both the fundamental- and the first-higher mode using one year of continuous seismic noise records on the vertical component from 28 ocean bottom seismographs deployed in the Quebrada/Discovery/Gofar transform faults region on the East Pacific Rise. The average phase-velocity dispersion of the fundamental mode (period band 2–30 s) and the first-higher mode (period band 3–7 s) from all EGFs are used to invert for the 1-D average, shear-velocity structure in the crust and uppermost mantle using a model-space search algorithm. The preferred shear-velocity models reveal low velocities (4.29 km/s) between Moho and 25 km depth below sea-surface, suggesting the absence of a fast uppermost mantle lid in this young (0–2 Myr) oceanic region. An even more pronounced low-velocity zone, with shear velocities ～3.85 km/s, appears at a depth between 25–40 km below sea-surface. Along with previous results, our study indicates that the shear velocity in the uppermost oceanic mantle increases with increasing seafloor age, consistent with age-related lithospheric cooling.     

Formation of galactic shocks and the vertical structure of the gaseous disk of the galaxy in a “turbulent” interstellar medium

The effects on the formation of Galactic shocks and the vertical structure of the Galactic disk due to thermal processes in a cloudy interstellar medium as it flows through a spiral density wave in the plane of the Galactic disk are considered. The evolution of the gas is fundamentally different, depending on the thermal properties of the medium. For example, if it is compressed in the horizontal direction (parallel to the Galactic plane) by the gravitational forces of the spiral density waves responsible for the formation of spiral arms, an isothermal and adiabatic medium is swept out in the vertical direction. However, on the contrary, a medium whose volume loss function increases fairly rapidly with density and temperature is further compressed under the action of the overall gravitational field of the galaxy. This effect is referred to as “self-focusing,” and may serve as an additional mechanism to explain the recently discovered anticorrelation between the width of the atomic hydrogen layer in the Galaxy and the gas density. The difference in the vertical behavior of media with different thermal properties can be used as an indicator of the thermal properties of a particular component of the interstellar gas (atomic or molecular). Attention is drawn to the fact that Galactic shocks themselves represent a mechanism that can heat the ensemble of clouds, i.e., increase the dispersion of cloud velocities. The vertical structure of a Galactic shock front is constructed, which is in qualitative agreement with the “bow shock” inferred from radio data.     

ABAQUS动力无限元人工边界研究

针对动力场天然无限地基的数值模拟与地震波输入问题进行了一些有意义的研究,评述了现有动力计算常用无限元的优缺点,详细阐述了ABAQUS无限元理论体系框架,并加以改进,提出一种考虑外域地震动影响的ABAQUS动力无限元人工边界。采用等效边界力的叠加原理,对入射波和散射波分开处理,视入射波和散射波在边界上互不影响,将输入地震动转化为作用于有限元无限元交界面上的等效应力的方法来解决外源波的入射问题。算例验证结果表明：内源振动和固定边界会出现失真和扰动现象,同时该计算结果与黏弹性边界的计算结果对比可知,该方法对外行散射波的过滤作用优于黏弹性边界。因此,改进的ABAQUS动力无限元人工边界理论方法有效且具有一定的稳定性。