Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.     

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.     

Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

The present paper is concerned with the propagation of shear waves in a homogeneous viscoelastic isotropic layer lying over a semi-infinite heterogeneous viscoelastic isotropic half-space due to point source. The inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of shear waves has been obtained using Green’s function technique. The dimensionless angular frequency has been plotted against dimensionless wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves. graphical user interface (GUI) software in MATLAB has been developed to show the effect of various inhomogeneity parameters on angular frequency. The topic can be of interest for geophysical applications in propagation of shear waves on the Earth’s crust.     

Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: convergence to an equivalent homogeneous porous medium

In this article, the quadrupole method is implemented in order to simulate the effects of heterogeneities on one dimensional advective and diffusive transport of a passive solute in porous media. Theoretical studies of dispersion in heterogeneous stratified media can bring insight into transport artefacts linked to scale effects and apparent dispersion coefficients. The quadrupole method is an efficient method for the calculation of transient response of linear systems. It is based here on the Laplace transform technique. The analytical solutions that can be derived by this method assists understanding of upscaled parameters relevant to heterogeneous porous media.First, the method is developed for an infinite homogeneous porous medium. Then, it is adapted to a stratified medium where the fluid flow is perpendicular to the interfaces. The first heterogeneous medium studied is composed of two semi-infinite layers perpendicular to the flow direction each having different transport properties. The concentration response of the medium to a Dirac injection is evaluated. The case studied emphasises the importance in the choice of the boundary conditions.In the case of a periodic heterogeneous porous medium, the concentration response of the medium is evaluated for different numbers of unit-cells. When the number of unit cells is great enough, depending on the transport properties of each layer in the unit cell, an equivalent homogeneous behaviour is reached. An exact determination of the transport properties (equivalent dispersion coefficient) of the equivalent homogeneous porous medium is given.     

二维地基波阻板隔振分析

本文采用了以薄层法层状半空间基本解答作为格林函数的边界元法,对均质弹性半空间和层状半空间中二维波阻板隔振设计进行了详细的参数分析。分析结果表明,均质弹性半空间和层状半空间内采用波阻板隔振均可取得较好的隔振效果;应保证波阻板具有合理的宽度和较小的埋深,才能得到理想的隔振效果;同时增加波阻板的厚度和模量是提高隔振效果的最有效的2种措施;此外,分层性对波阻板隔振效果也具有一定的影响。     

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.     

Love wave dispersion: A comparison of results for a semi-infinite medium with inhomogeneous layers and for its approximation by homogeneous layers

Love wave dispersion in various semi-infinite media consisting of inhomogeneous layers is discussed. The phase and group velocities are computed when shear wave velocity and density in each inhomogeneous layer are varying exponentially with depth. At the beginning one or two inhomogeneous layers over a homogeneous semi-infinite medium are considered. The dispersion results for these structures are compared with those for their approximations with homogeneous layers. Comparisons show that differences of phase and group velocities for the original models from those for their approximated models (i) increase with the increase of wave number and (ii) are larger for group velocity than for phase velocity. The difference is approximately proportional to the rate of change of parameters in the layers. Finally, dispersion curves are obtained for model IP3MC, which consists of many inhomogeneous and homogeneous layers over a homogeneous semi-infinite medium. The results are compared with the observed group velocity data across the Indian Peninsula.     

Stationary approximation of the magnetotelluric field in a halfspace with a vertical boundary and three-dimensional perturbing body

Summary Based on the generalized potential of a double layer, integral formulae have been derived for calculating the stationary approximation of the magnetotelluric field in a halfspace divided by a vertical boundary into two quarterspaces, one of which contains a three-dimensional perturbing body. The appropriate boundary integral equation and other surface integrals have been computed for a perturbing body in the shape of the three-dimensional prism located at the vertical boundary, or in contact with the said boundary. The exciting electrical field is assumed to be homogeneous and perpendicular to the vertical boundary. Isoline graphs of the electrical and magnetic fields on the surface of the halfspace have been plotted and their anomalies are discussed.     

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.     

中长周期数字化面波记录与中国东南地区地壳结构

本文使用适配滤波频时分析技术首次对中国数字地震台网的中长周期面波记录进行处理,获得穿过东南地区的82条勒夫波频散数据.使用随机反演理论,获得了东南沿海地区4°×4°网格的纯路径频散数据.这些频散的周期为1.95-68.27s,弥补了长周期面波所不能分辨的浅层结构.在网格反演的基础上,使用Harkrider的面波及演程序得出了中国东南地区的地壳和上地幔结构,浅部可分辨到1km,深部可达80km.在分辨率保证的前提下得出东南地区深至80km的三维剪切波速度结构.     

Monte Carlo evaluation of microbial-mediated contaminant reactions in heterogeneous aquifers

Monte Carlo simulations are conducted to evaluate microbial-mediated contaminant reactions in an aquifer comprised of spatially variable microbial biomass concentrations, aquifer hydraulic conductivities, and initial electron donor/acceptor concentrations. A finite element simulation model is used that incorporates advection, dispersion, and Monod kinetic expressions to describe biological processes. Comparisons between Monte Carlo simulations of heterogeneous systems and simulations using homogeneous formulation of the same two-dimensional transport problem are presented. For the assumed set of parameters, physical aquifer heterogeneity is found to have a minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system; however, it noticeably changes the dispersion, skewness, and peakness of contaminant concentration distributions. Similarly, for low microbial growth rate, given favorable microbial growth characteristics, biological heterogeneity has minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system. On the other hand, when higher effective growth rates are assumed, biological heterogeneity and spatial heterogeneities in essential electron donor/acceptors reduce the efficiency of biotic contaminant reactions; consequently, model simulations derived from heterogeneous biomass distributions predict remediation time scales that are longer than those simulated for homogeneous systems. When correlations between physical aquifer and biological heterogeneities are considered, the assumed correlation affects predicted mean and variance of contaminant concentration and biomass distributions. For example, an assumed negative correlation between hydraulic conductivity and the initial biomass distribution produces a plume where less efficient biotic contaminant reactions occur at the leading edge of the plume; this is consistent with less degradation/transformation occurring over regions of higher groundwater velocities. However, the presence and absence of these correlations do not appear to affect the efficiency of microbial-mediated contaminant attenuation.     

Influence of small-scale heterogeneity on upward CO2 plume migration in storage aquifers

Recent advancements in experimental techniques allow sub-core-scale heterogeneities to be quantified in a high resolution. Based on the observations of heterogeneity distributions in natural core samples, we perform simulations to study the influence of small-scale heterogeneities on large-scale CO₂ migration during geological storage. We observe that even the heterogeneities at millimeter scale (the scale of a Representative Elementary Volume for sandstones) can affect large-scale buoyancy-driven upward CO₂ migration. For the representative examples we study, ignoring small-scale heterogeneities can lead to an overestimation of the migration speed by a factor of two.To analyze the cause of such overestimation, we introduce a dimensionless heterogeneity factor to characterize different levels of heterogeneity. The influence on CO₂ migration is quantified with respect to a variety of heterogeneity factors, correlation lengths, and fluid viscosity ratios for isotropic and anisotropic media. Our findings suggest that small-scale heterogeneities should not be ignored in core analysis, even for cores that appear relatively homogeneous and do not have distinguishable heterogeneous patterns. In addition, relative-permeability curves measured from core-flood experiments under high-flow-velocity conditions (a common practice to eliminate capillary end-effects) should not be directly used in modeling low-velocity CO₂ migration if small-scale heterogeneities are present.     

Simulation of seismic response in an idealized city

We study the seismic response of an idealized 2D ‘city’, constituted by ten non equally-spaced, non equally-sized, homogenized blocks (i.e. buildings or groups of buildings) anchored in a soft soil layer overlying a hard halfspace. Our results display strong response inside the blocks and on the ground which qualitatively match the responses observed in some earthquake-prone cities.     

勒夫波群速度频散与太平洋地壳及上地幔三维构造

应用现代适配滤波频时分析技术对SRO/GDSN长周期面波记录进行处理,获得穿过太平洋盆地的117条波路径的勒夫波频散数据。我们用改进的分格频散反演方法,从混合路径频散数据中提取出对应于构成整个太平洋盆地的10°×10°分格的纯路径频散数据。所获得的18s到215s范围内的28个周期的太平洋勒夫波群速度的横向分布,揭示了速度随海底年龄的增大而逐渐增加的总趋势,以及其它变化细节。例如,对于同一等年龄线区而言,北太平洋及南太平洋的群速度要比中太平洋的低0.1-0.3km/s。在分格模型反演的基础上得出的深至300km的三维剪切波速度结构提供了太平洋盆地地壳及上地幔横向不均匀性的详尽的描述。     

Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field where deformations are relatively small, a linear elastic constitutive behaviour is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model based on a subdomain formulation. First, the case of vibratory pile driving is considered, where the contributions of different types of waves are investigated for several penetration depths. In the near field, the soil response is dominated by a vertically polarized shear wave, whereas in the far field, body waves are importantly attenuated and Rayleigh waves dominate the ground vibration. Second, the case of impact pile driving is considered. A linear wave equation model is used to estimate the impact force during the driving process. Apart from the response of a homogeneous halfspace, it is also investigated how the soil stratification influences the ground vibration for the case of a soft layer on a stiffer halfspace. When the penetration depth is smaller than the layer thickness, the layered medium has no significant influence on ground vibrations. However, when the penetration depth is larger than the layer thickness, the influence of the layered medium becomes more significant. The computed ground vibrations are finally compared with field measurements reported in the literature.     

Average thickness of the deccan traps between Bombay and Koyna from dispersion of short-period Love waves

Summary Experimental dispersion curves of short-period Love waves due to three small shocks in the Koyna region and recorded at Bombay have been compared with theoretical computed curves. The results indicate that the average thickness of the traps overlying the granitic basement is about 1.25 km.     

Rayleigh波勘探中“之”字形频散曲线“起跳点”频率研究

当层状介质中存在低速层的时候,实际提取到的Rayleigh波频散曲线往往会发生“之”字形回折.已有研究表明,“之”字形回折与各模式的激发能量有关.特别的,“之”字形回折的“起跳点”(发生“之”字形回折的点)与介质参数有一定关系,因此在应用中它反映了介质的一些特征.但是,这一关系是怎样的还没有人进行详细研究.本文计算了三...     

Diffraction of a compressional wave by a rigid barrier in a liquid layer — Part II

Summary The problem of diffraction of compressional waves striking obliquely at a rigid barrier fixed in the surface of a liquid layer lying over a solid halfspace has been studied. Exact values for the amplitudes of the waves reflected in the solid halfspace have been obtained. The method of solution is based on the Wiener-Hopf technique.     

Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

The presence of porosity and reinforcement in a medium is an important factor affecting seismic wave propagation and plays vital role in many geophysical prospects. Also, the presence of salt and ore deposits, mountains, basins, mountain roots, etc. is responsible for the existence of corrugated boundary surfaces of constituent layers. Such facts brought motivation for the present paper which deals with the propagation of SH-wave in a heterogeneous fluid-saturated poroelastic layer with corrugated boundaries lying over an initially stressed fibre-reinforced elastic halfspace. Closed form of dispersion relation has been obtained and is found in well agreement to classical Love wave equation for isotropic case. The effect of corrugation, wave number, undulation, position parameter, horizontal compressive/tensile initial stress and heterogeneity on phase velocity has been analysed through numerical computation and graphical illustration. Moreover, comparative study exploring the effect of presence and absence of reinforcement in half-space on dispersion curve is the major highlight of the current study.     

Array performances for ambient vibrations on a shallow structure and consequences over <Emphasis Type="Italic">V</Emphasis><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript> inversion

Valuable information about one-dimensional soil structures can be obtained by recording ambient vibrations at the surface, in which the energy contribution of surface waves predominates over the one of other types of waves. The dispersion characteristics of surface waves allow the retrieval of the shear-wave velocity as a function of depth. Microtremor studies are usually divided in two stages: deriving the dispersion (or auto-correlation) curve from the recorded signals and inverting it to obtain the site velocity profile. The possibility to determine the dispersion curve over the adequate frequency range at one site depends on the array aperture and on the wavefield spectra amplitude that can be altered by filtering effects due to the ground structure. Microtremors are usually recorded with several arrays of various apertures to get the spectral curves over a wide frequency band, and different methods also exist for processing the raw signals. With the objective of defining a strategy to achieve reliable results for microtremor on a shallow structure, we analyse synthetic ambient vibrations (vertical component) simulated with 333 broadband sources for a 25-m deep soil layer overlying a bedrock. The first part of our study is focused on the determination of the reliable frequency range of the spectral curves (dispersion or auto-correlation) for a given array geometry. We find that the wavenumber limits deduced from the theoretical array re sponse are good estimates of the valid spectral curve range. In the second part, the spectral curves are calculated with the three most popular noise-processing techniques (frequency–wavenumber, high-resolution frequency–wavenumber and spa tial auto-correlation methods) and inverted indi vidually in each case. The inversions are performed with a tool based on the neighbour hood algorithm that offers a better estimation of the global uncertainties than classical linearised methods, especially if the solution is not unique. Several array apertures are necessary to construct the dispersion (auto-correlation) curves in the appropriate frequency range. Considering the final velocity profiles, the three tested methods are almost equivalent, and no significant advantage was found for one particular method. With the chosen model, all methods exhibit a penetration limited to the bedrock depth, as a consequence of the filtering effect of the ground structure on the vertical component, which was observed in numerous shallow sites.