Rayleigh-type Surface Waves Research Articles

Motion of the particles due to viscoelastic surface waves of an assigned frequency

The motion of the material particles due to viscoelastic properties of the half-space is considered when the propagating surface wave has an assigned frequency. The detailed examination shows that for Rayleigh waves in classical elasticity as well as for the viscoelastic Rayleigh-type surface waves the sense of the particle path along the ellipse is retrograde on the surface of the half-space and changes into direct only once at depth about one seventh to one quarter of the wavelength. When there is a viscoelastic surface wave that does not satisfy the adopted four criteria for behaviour at infinity (the case of viscoelastic Rayleigh-type surface wave) but only two of them, this additional wave is direct on the surface of the half-space and does not change or may change many times the sense of the particle path along the ellipse with the distance from the stress-free surface of the half-space. In contrast to the elastic case, the ellipse axes in the viscoelastic case are not parallel and orthogonal to the surface of the half-space, respectively. Their orientation depends on the magnitude of the viscous part of the Lamé moduli and tends to a constant at great depth. The numerical computations in the paper refer to some typical values of the complex Lamé moduli and to some real materials.

Size Effects on Surface Elastic Waves in a Semi-Infinite Medium with Atomic Defect Generation

The paper investigates small-scale effects on the Rayleigh-type surface wave propagation in an isotopic elastic half-space upon laser irradiation. Based on Eringen’s theory of nonlocal continuum mechanics, the basic equations of wave motion and laser-induced atomic defect dynamics are derived. Dispersion equation that governs the Rayleigh surface waves in the considered medium is derived and analyzed. Explicit expressions for phase velocity and attenuation (amplification) coefficients which characterize surface waves are obtained. It is shown that if the generation rate is above the critical value, due to concentration-elastic instability, nanometer sized ordered concentration-strain structures on the surface or volume of solids arise. The spatial scale of these structures is proportional to the characteristic length of defect-atom interaction and increases with the increase of the temperature of the medium. The critical value of the pump parameter is directly proportional to recombination rate and inversely proportional to deformational potentials of defects.

On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space

In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a first-order linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the first-order differential system follows. On this basis, the Rayleigh-type surface waves are studied, and the dispersion condition is found.

Influence of a superficial field of residual stress on the propagation of surface waves—Applied to the estimation of the depth of the superficial stressed zone

In this study, we were interested in the dispersion of surface waves caused by the presence of a micrometric field of residual stress on the surface of an amorphous medium. We have shown that in relation to surface waves, a stressed structure like this is comparable to a layer on substrate type structure. The design and implementation of SAW-IDT MEMS sensors enabled quasi-monochromatic Rayleigh-type surface waves to be generated and the dispersion phenomenon to be studied over a wide range of frequencies for different superficial fields of residual stress. The thicknesses of the stressed cortical zones were estimated with good accuracy using an inverse method.

Shallow-to-deep shear wave velocity profiling by surface waves in complex ground for enhanced seismic microzonation of Las Vegas, Nevada

Shear-wave velocity (VS) profiles were developed using the spectral analysis of Rayleigh-type surface waves (SASW) method for 12 sites in the Las Vegas Valley, Nevada, an urban area that is situated on a deep alluvium-filled basin. The objective of the study was to develop VS profiles to depths of 100m or deeper to support earthquake site response analyses. To that end, a “minivib” Vibroseis was used in conjunction with an instrumented hammer source, allowing development of deep VS profiles, while also maintaining resolution at shallow depths. The results from optimization by linearized inversion compared well with those from simulated annealing followed by linearized inversion. Data from one site known to have a shallow, high-velocity inclusion were analyzed with the benefit of this independent information, which permitted the depth of the inclusion to be estimated closely. Overall, the VS profiles obtained are consistent with an existing earthquake microzonation of the Valley.

On Rayleigh-type surface waves in an initially stressed incompressible elastic solid

In this paper, we apply the theory of the superposition of infinitesimal deformations on finite deformations in an initially stressed hyperelastic material to the study of the propagation of surface waves in an initially stressed incompressible half-space subjected to a pure homogeneous deformation. This is based on a theory of initial stress in elastic solids due to Shams et al. (2011, Initial stresses in elastic solids: constitutive laws and acoustoelasticity. Wave Motion, 48, 552–567). The initial stress is not itself associated with a finite-elastic deformation and this contrasts with the situation in which the initial stress is a pre-stress that is accompanied by a finite deformation. A general formulation of the equations governing incremental motions is provided and then specialized to two-dimensional motions in a principal plane of the underlying (homogeneous) deformation with a uniform initial stress that is coaxial with the finite deformation. With this specialization, the combined effect of initial stress and finite deformation on the speed of Rayleigh waves is discussed and illustrated graphically with the main emphasis on the effect of initial stress.

Determination of Shear Wave Velocity and Depth to Basement Using Multichannel Analysis of Surface Wave Technique

Abstract The dispersive characteristics of Rayleigh type surface waves were utilized to estimate shear wave velocity (Vs) profile followed by imaging the shallow subsurface granitic layers in the heart of Hyderabad. The reliability of Multichannel Analysis of Surface Waves (MASW) depends on the accurate determination of phase velocities for horizontally traveling fundamental mode Rayleigh waves. Multichannel recording leads to effective identification and isolation of various factors of noise. Calculating the 1-D shear wave velocity (Vs) field from surface waves ensures high degree of accuracy irrespective of cultural noise. The main advantage of mapping the bed rock surface with shear wave velocity (Vs) is the insensitivity of MASW to velocity inversion besides being free from many constraints such as contrast in physical properties etc. Modeling of surface waves data results a shear wave velocity (Vs) of 250-750 m/s covering the top soil to weathering and up to bedrock corresponding to a depth range of 10-30 m. Further, the computed N values (which is an indicator of site characteristic) based on the harmonic shear wave velocity up to a depth of 5 m is found to be quite high (> 25-30) well above 5 indicating the site to be safe and strong enough and not prone to liquefaction. A pair of selected set of results over granites are presented here as a case study highlighting the salient features of MASW.

Noise Reduction Technique Applied to the Multichannel Analysis of Surface Waves

AbstractThis paper shows the presence of noises and technique to reduce these noises during the surface wave analysis. The frequency‐dependent properties of Rayleigh‐type surface waves can be used for imaging and characterizing the shallow subsurface. Interference by coherent source‐generated noise inhibits the reliability of shear‐wave velocities determined through inversion of the phase velocities of Rayleigh waves. Among these interferences by non‐planar, non‐fundamental mode Rayleigh waves (noise) are body waves, scattered and non‐source‐generated surface waves, and higher‐mode surface waves. For the reduction of noise, the filtering technique is implemented in this paper for the multichannel analysis of surface wave method (MASW). With the de‐noising technique during the MASW method, more robust and reliable outcome is achieved. The significance of this paper is to obtain pre‐awareness about noises during surface wave analysis and take better outcomes with de‐noising performance in near surface soil investigations.

Rayleigh-type surface quasimodes in general linear elasticity

Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudo-differential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

Liquefaction Hazard Assessment of Earth Quake Prone Area: a Study Based on Shear Wave Velocity by Multichannel Analysis of Surface Waves (MASW)

The shear wave velocity (VS) profile based on the dispersive characteristics of fundamental mode of Rayleigh type surface waves indicate underground stiffness change with depth as well as near surface stiffness. The most important utility of shear wave velocity (VS) is to estimate the liquefaction hazard potential of an area particularly in seismically active region. Rayleigh type surface waves were utilized to estimate the velocity (VS) of shallow subsurface covering a depth range of 30–50 m employing multichannel analysis of surface waves. The liquefaction hazard map predicts an approximate percentage of an area that will have surface manifestation of liquefaction during an earth quake. The surface wave data acquired in an earth quake prone region of Jabalpur (Seismic zone III), India, yields a velocity (VS) range of 200–750 m/s corresponding to the subsurface depth of 30–35 m. The results were analyzed for possible liquefaction hazard in the study area and presented here besides the N values.

The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone

The work deals with the far field asymptotics of the classical solution for the problem of diffraction by an impedance cone. The incident acoustic plane wave completely illuminates the semi-infinite conical surface. The scattered field contains different components in the asymptotics, namely, the spherical wave from the vertex of the cone, the reflected waves, and, under some conditions, also the surface waves of Rayleigh type. We give integral representations for the scattering diagram of the spherical wave. The uniform (with respect to the observation direction) asymptotic expression for the wave field is also addressed and described by the parabolic cylinder ansatz.

Multichannel analysis of surface waves for bedrock depth estimation over granites, Hyderabad, India

The dispersive characteristics of Rayleigh type surface waves were utilized to estimate shear wave velocity (Vs) profile followed by imaging the shallow subsurface granitic layers near Hyderabad India. The reliability of Multichannel Analysis of Surface Waves (MASW) depends on the accurate determination of phase velocities for horizontally traveling fundamental mode Rayleigh waves. Multichannel recording leads to effective identification and isolation of various factors of noise. Calculating the 1-D shear wave velocity (Vs) field from surface waves ensures high degree of accuracy irrespective of cultural noise. The main advantage of mapping the bed rock surface with shear wave velocity (Vs) is the insensitivity of MASW to velocity inversion besides being free from many constraints such as contrast in physical properties etc. Modeling of surface waves data results a shear wave velocity (Vs) of 250-750 m/sec covering the top soil to weathering and up to bedrock corresponding to a depth range of 10-30 m. A pair of selected set of results over granites are presented here as a case study highlighting the salient features of MASW.

Circular Crested Lamb Waves in a Fluid Saturated Incompreesible Porous Plate

The propagation of circular crested waves in a fluid saturated incompressible porous plate is analyzed. The frequency equations, for symmetric and anti‐symmetric waves, connecting the phase velocity with wave number are derived. At short wave length limits the frequency equations for symmetric and antisymmetric waves in a stress free plate reduce to Rayleigh type surface wave frequency equation and the finite thickness plate appears as a semi‐infinite medium. The results at various steps are compared with the corresponding results of classical theory and finally the variations of phase velocity, attenuation coefficient with wave number and displacements amplitudes with distance from the boundary of the plate is presented graphically and discussed.

Propagation of Rayleigh-type surface waves in a transversely isotropic piezoelectric layer on a piezomagnetic half-space

Propagation of Rayleigh-type surface waves in a piezoelectric-piezomagnetic layered half-space is investigated. The materials are assumed to be transversely isotropic crystals. The dispersion relations have been numerically derived and computed by considering the coupling piezoelectric and piezomagnetic behaviors. The phase velocities are obtained for four kinds of electric-magnetic boundary conditions at the free surface. The variations of mechanical displacements, electric and magnetic potentials along the thickness direction of the layer are obtained. The effects of different electric-magnetic boundary conditions on the phase velocity and mode shapes of displacements, electric and magnetic potentials have been discussed. The results show that the lowest mode is Rayleigh mode and that the phase velocities of the higher modes tend to the shear wave velocity of the piezoelectric layer as the frequency increases. The electric boundary conditions dominate the phase velocity. The magnetic boundary conditions have a significant effect on the mode shapes of the displacements, electric and magnetic potentials of the first mode. It is also found that piezoelectric material properties have an important effect on wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezoelectric and piezomagnetic materials.

Surface wave propagation in a fluid saturated incompressible porous half-space lying under two layers of different liquids

Abstract A study of surface wave propagation in a fluid saturated incompressible porous half-space lying under a double-layer consisting of non-homogeneous and homogeneous liquids is presented. The frequency equation connecting the phase velocity with wave number is derived. Special cases as: (i) Rayleigh type surface waves in an incompressible poro-elastic half-space lying under a uniform layer of a homogeneous liquid, (ii) Rayleigh type surface waves in an incompressible poro-elastic half-space lying under a uniform layer of a non-homogeneous liquid and (iii) Rayleigh type surface waves propagating along the free surface of a fluid saturated incompressible porous elastic half-space, are investigated. Numerical results with graphical presentations of the variations of phase velocity with wave number for different cases are also included.

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.

Elastic waves along a cylindrical borehole in a poroelastic medium saturated by two immiscible fluids

The propagation of elastic waves along a cylindrical borehole filled with/without liquid and embedded in an infinite porous medium saturated by two immiscible fluids has been studied. The theory of porous media saturated by two immiscible fluids developed by Tuncay and Corapcioglu (1997) is employed. Frequency equations determining the phase velocity of axial symmetric waves are obtained. It is found that the surface waves along cylindrical borehole are dispersive. The dispersion equation of Rayleigh-type surface waves along the boundary of a poroelastic solid half-space saturated by two immiscible fluids is also obtained. Some special cases have been deduced and the dispersion curves are obtained numerically for a peculiar model. It is found that the density of fluids affects the Rayleigh mode.

Inversion of SASW dispersion curves based on maximum flexibility coefficients in the wave number domain

Spectral analysis of surface waves (SASW) is a nondestructive in-situ testing method that is used to determine stiffness profiles of soil and pavement sites based on dispersion characteristics of Rayleigh-type surface waves. Inversion of the Rayleigh wave dispersion curve of a site provides information on the variation of shear-wave velocity with depth. In the inversion procedures currently used for SASW tests, the field dispersion curve is matched with a theoretical dispersion curve obtained for the fundamental mode of surface wave propagation. In order to overcome difficulties associated with the presence of multi-modes in SASW signals, a new inversion method based on the maximum vertical flexibility coefficient is introduced in this paper. Unlike root-searching methods, the new method easily identifies the predominant propagation modes. In this new approach, the simplex method is used to match field and theoretical dispersion curves automatically. The purpose of this paper is to present the details of the new method and to demonstrate its advantages.

Rayleigh modes in anisotropic, heterogeneous poroelastic layers

The generalized Rayleigh type surface waves are studied in a multilayered medium consisting of anisotropic poroelastic solid layered stack beneath a fluid layer and overlying a heterogeneous elastic solid half-space. The heterogeneity, considered, is of vertical type. The interface between solid layer and half-space is treated as an imperfect interface and suitable boundary conditions are applied thereat. The technique of transfer matrix is used to obtain the dispersion equation in compact and convenient form. Numerical results are obtained for particular models. The effects of anisotropy and heterogeneity on the surface waves speed are discussed.