Propagation Of Love Waves Research Articles

Supersonic Love waves in strong piezoelectrics of symmetry mm2

A study has been made of the Love wave propagation on piezoelectric substrates of symmetry mm2. It has been shown that under certain conditions the velocity of the Love wave exceeds that of shear horizontal (SH) bulk waves in the substrate. This occurs when the slowness curve of SH bulk waves in the substrate either has a concavity or is convex with nearly zero curvature. For such “supersonic” Love waves to appear, it is also required that the substrate as well as the layer be specially oriented and that their material constants fulfill a number of inequalities. Numerical computations have been carried out for a number of structures. The results of numerical computations have been compared with approximate analytical estimations.

Love waves in piezoelectric coupled solid media

The propagation of Love waves in a piezoelectric lamina bonded ontoa semi-infinite solid medium is investigated in this paper. The dispersivecharacteristics and the mode shapes of the deflection and the electricpotential in the thickness direction of the piezoelectric layer aretheoretically derived. Numerical simulations show that the phase velocitiesinitiate at the shear wave velocity of the host medium and tend towards theBleustein-Gulyayev surface wave velocity for the piezoelectric layer at highwavenumbers for the first mode. The first two mode shapes of the electricpotential correspond to a half-cosine and a full-cycle sinusoidaldistribution, respectively, and become distorted as the wavenumber increases.These findings are significant in the application of inter-digital transducersfor surface wave excitation in structural health monitoring.

Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure

The propagation behavior of Love waves in a layered piezoelectric structure with an initial stress is investigated in this article. It involves a thin piezoelectric layer bonded perfectly to an elastic substrate. Solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate by solving the coupled electromechanical field equations. The phase velocity equations of the Love wave propagation and the stress fields in the layered piezoelectric structure are obtained for electrical open and short cases on the free surface, respectively. The effect of the initial stress on the phase velocity, the stress fields and the coupled electromechanical factor are discussed, respectively. Three sets of piezoelectric layer–elastic substrate systems are considered, i.e. BaTiO 3 ceramic layer–borosilicate glass substrate, PZT-5H ceramic layer–borosilicate glass substrate, and PZT-5H ceramic layer–SiO 2 glass substrate. It is seen that the phase velocity of the Love wave propagation decreases with the increase of the magnitude of the initial stress. The coupled electromechanical factor increases remarkably, as the magnitude of the initial the stress is greater than 100 MPa. This is useful for the design of acoustic surface wave devices.

Modelling of the mass sensitivity of the Love wave device in thepresence of a viscous liquid

This paper describes a new theoretical model for the analysis of themass sensitivity of the Love wave device. We use this model along withcalculations from perturbation theory to calculate sensitivity. The model isbased on Love wave propagation in an isotropic, non-piezoelectric quartzsubstrate over-layered by a silica waveguiding layer and immersed in aviscous liquid. The analysis considers power flow in the three-layered system,comprising the quartz substrate, the silica over-layer and the viscous liquid.The model fully accounts for the first time for the power that flows throughthe liquid phase and assesses its effect on mass sensitivity. Mass sensitivityvalues were obtained by determining the displacement field throughout theviscous liquid and the Love waveguide device. The resulting velocity field wasused to generate a number of trial functions that had solutions assumingstress and strain continuity at the boundaries, and the complex dispersionrelation was evaluated numerically. The resulting wavevector k and propagationconstant β values were used to calculate the power in both the Love wavedevice and the liquid layer and the velocity amplitude at the surface. Themodel predicts that the mass sensitivity of the Love wave device will increasein the presence of a viscous solution due to power flow into the liquid.

The Propagation of a Layer-Confined Love Wave in Layered Piezoelectric Structures

The Propagation of a Layer-Confined Love Wave in Layered Piezoelectric Structures

On SH waves in a pre-stressed layered half-space for an incompressible elastic material

The propagation of Love waves along the boundary between a half-space and a layer of different pre-stressed material is examined for incompressible isotropic elastic materials. The secular equation is obtained for a general strain-energy function and analysed for particular deformations and materials. For the neo-Hookean strain-energy function, numerical results are obtained to illustrate the dependence of the wavespeed on the wave number and on the deformation.

Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium

In this paper, Love waves in a non-homogeneous orthotropic elastic medium under changeable initial stress has been studied. Fourier transform method has been applied to find the dispersion equation. It has been shown that the velocity of Love waves lies between two quantities which are dependent on the non-homogeneities of two media. When the medium is isotropic and the initial stress is absent, the dispersion equation obtained is in agreement with the corresponding results. The effect of non-homogeneity and the initial stress are illustrated by figures.

Investigation of thin film shear modulus from spatially resolved measurement of Love wave velocity

The investigation of transversely polarized surface acoustic waves (SAWs) is strongly hindered by their missing out-of-plane oscillation component because commonly applied measurement techniques are based on access to that component. Nevertheless, these waves are very interesting for accurate extraction of thin film elastic properties as well as for SAW devices and sensor applications. In this contribution we report a new development of spatially resolved SAW analysis. The scanning acoustic force microscope (SAFM) has been extended in its sensitivity to in-plane polarized waves. A nonlinear mechanism could be found that couples the in-plane surface oscillations to torsional cantilever vibrations. This mechanism is used to transfer the rf SAW signals to kHz frequencies and to measure the SAW phase velocity. The new technique has been applied to study the Love wave propagation in the layered system fused silica on ST-cut quartz. The phase velocity could be derived from measurements of the phase shift along a propagation distance in the micron range. The obtained velocities show a clear spatial variation at elastic changes within the investigated surface. This is used to investigate the shear modulus of the layer material by numerically solving the inverse problem of SAW propagation.

窪みのある大陸性地殻構造におけるラブ波伝播

窪みのある大陸性地殻構造におけるラブ波伝播

High-Gradient Modeling for Love Wave Propagation in Geological Materials

Based on a microstructural approach, geological material, owing to its discrete nature, can be represented by an equivalent continuum of the high-gradient type. The high-gradient continuum differs from the perfectly elastic continuum by having a characteristic length scale that is an intrinsic property of the material. Using the high-gradient stress-strain relationship, we formulate a fourth-order wave equation to describe the propagation of a Love-wave in a two-layer medium. We employ Hamilton's principle to derive the additional boundary conditions involved in the differential equation. The differential equation is then solved to study the effects of characteristic length on the wave propagation in geological material. Comparisons are made between the predicted and observed wave velocities in a two-layer geological medium during an earthquake.

Propagation of Love waves in a transversely isotropic fluid-saturated porous layered half-space

The dispersion equation for Love wave propagation in a layer lying over a half-space is derived. Both media are assumed to be transversely isotropic fluid-saturated poroelastic solids with principal axes perpendicular to the surface. The analysis is based on the Biot’s theory. The dissipation due to fluid viscosity is considered and therefore the dispersion equation is complex and intractable analytically. An iterative procedure is developed to solve this equation. Two situations are discussed in detail: (i) an elastic layer overlying a poroelastic half-space and (ii) a poroelastic layer lying over an elastic half-space. Dispersion curves and attenuation curves of Love waves are plotted for these two cases. In addition, the upper and lower bounds of Love wave speeds are also explored.

Design considerations for the acoustic waveguide biosensor

Love waveguide devices utilize shear-horizontal waves which propagate on the top layer of a coated SSBW acoustic device. Initially, attention was focused on the selection of a material which would effectively guide the Love wave. Silica and polymethyl methacrylate were used as guiding layers and the mass sensitivity of the corresponding sensors was tested in air. Low-shear-acoustic-velocity polymer overlayers were found to guide the Love wave most effectively with a maximum sensitivity of . The polymer waveguide sensor was further used to detect protein adsorption on the polymer surface from IgG solutions within the concentration range of 1 - . Radiolabelled IgG was applied to the device surface in order to calibrate the wave response to protein surface mass density. Finally, the effect of the acoustoelectric interaction on liquid-based applications was studied by utilizing a three-layer waveguide geometry. It was found that the evaporation of a 50 nm gold layer on the polymer overlayer can be used to eliminate acoustoelectric interactions without interfering with the Love wave propagation. After activation with protein A and IgG, the above system was used successfully to detect the direct binding of 400 ppb atrazine.

Nonlinear Love waves in a ferroelastic film on an elastic substrate

A theory of nonlinear acoustic Love wave propagation in a ferroelastic film on an elastic substrate is presented. The main stress in this work is put upon the investigation of the properties of the nonlinear acoustic waves in films close to the phase transition, which is different from previously reported works on this subject. The parameters of the striction superstructure (elastic domains) nucleating close to the paraelastic - ferroelastic phase transition are estimated for real ferroelectric films. In the framework of the asymptotic approach the effective nonlinear Schrödinger equation for the envelope of the Love wave is derived and the possibility of bright- and dark-soliton formation is discussed. It is demonstrated that for a change of career wave wavenumber the transition between stable wave propagation and the modulation instability is realized. It is found that the strong dispersion of the soft Love wave near the ferroelastic phase transition is responsible for such a transition.

Nonstationary love waves of the SH-type in an anisotropic elastic medium. A kinematic approach

In this paper, the propagation of Love waves in anisotropic elastic media is studied. These waves are a similar to the transverse surface SH waves in the isotropic case. Necessary conditions for the existence of Love waves of this polarization type near the surface Σ of an anisotropic elastic body are deduced. The algorithm developed here makes it possible to find the direction (s) of transverse surface wave propagation (at every point on the surface Σ). The algorithm employed is illustrated by some special anisotropic cases. The space-time method is used to construct the asymptotics of Love waves for those types of anisotropic media the eikonal equation of which is valid on the surface of an elastic body.

The influence of local irregularities on the propagation of Love waves

The propagation of Love waves in models with local irregularities (a canyon or an alluvial valley) related to general waste deposit problems in environmental geophysics is numerically investigated. The investigation is based on a direct boundary element method for calculating wave fields and on a Green's function technique for evaluating transmission, reflection and ‘diffraction’ coefficients for Love waves, incident on a local surface or subsurface irregularity in layered media. The present model studies reveal that the influence of local irregularities on the propagation of Love waves depends both on the geometry and material properties of the local irregularities and on the dynamic parameters of the incident Love waves. Local irregularities lead to strong scattering of Love waves whose wavelengths are comparable to the characteristic sizes of the irregularities. For Love waves having wavelengths which are very large compared to the characteristic sizes of irregularities the influence of these irregularities are negligible. In addition, Love waves incident on a local irregularity always undergo mode conversion. Part of the energy of the incident Love wave will covert to other Love wave modes and body waves. With respect to the application of surface waves in environmental geophysics, two results may be stressed: (i) Though the conversion of Love waves to body waves has been qualitatively anticipated in the past, its enormous strength quantified by the diffraction coefficients is interesting; (ii) Love waves are more sensitive to local velocity changes than to local density changes. For in situ measurements, this result leads to the conclusion that density is a less relevant quantity, although it may better characterize the material inside a waste deposit than velocity.

The propagation of Love and Rayleigh waves in the Andean Region

El patrón distintivo desde la fuente sísmica de un campo irradiado de ondas sísmicas se modifica profundamente al pasar por una región irregular como la Cordillera de los Andes de América del Sur. La onda Lg guiada por la corteza útil en la discriminación de fuentes sísmicas, pero, aun para una sola fuente, las amplitudes de ondas de periódo corto como Lg pueden variar significativamente. La Cordillera de los Andes de Bolivia forma una parte de la cadea de los Andes, que se originó en los dos principales ciclos orogénicos del Fanerozoico, un Ciclo Preandino Precámbrico-Paleozoico Superior y el Ciclo Andino Mesozoico-Cenozoico. Durante el último Ciclo, cuatro sistemas del arco magmático se desarrollaron sucesivamente hacie el este: un arco Jurásico-Cretácico Temprano en la Cordillera Costera de Chile, un arco Cretácico Medio en el Valle Longitudinal de Chle, un arco Cretácico Tardío-Paleogénico en la Precordillera Chilena y el arco Mioceno-Holoceno en la Cordillera Occidental (Omarini et al., 1991; Dorbath et al., 1993; Scheuber et al., 1994). En la región del Cabalgamiento Andino Principal entre la Cordillera Oriental (o Real) y las Sierras Subandinas en Bolivia septentrional, hay superposición de aproximadamente 230 km de edad Neogena (Roeder, 1988). Las areniscas cloríticas Permicas marinas cerca de Copacabana sobre el Lago Titicaa y las diamicititas, areniscas, cuarcitas y lutitas Ordovícico.Silúricas apretadamente plegadas, expuestas abundantemente en los cortes del camino entre Cochabamba y Caracollo, se encuetran a elevaciones desde 3800 m a 4500 m sobre el nivel del mar. El sistema de fallas de la Cordillera Real, en el borde sudoccidental, marca un límite subvertical, con buzamiento al sudoeste, que separa dos unidades de velocidad contrastante hasta una profundidad de 140 km. La profundiad de Moho debajo del Altiplano fue encontrada por Dorbath et al. (1993) aproximadamente a 60 km y, debajo de la Cordillera Real, aproximadamente a 50 km. Más al sur, a través del Sur de Bolivia y Norte de la Argentina, Wigger et al. (1994) encontraton que la profundidad al Moho debajo del Altiplano es aproximadamente de 72 km y, debajo de la Cordillera Real aproximadamente a 65 km. La propagación de las ondas de Love y de Rayleigh de periódo corto, a lo largo de un perfil que atraviesa estas unidades del Altiplano y de la Cordillera Real de Bolivia septentrional, ha sido analizada por el método de elementos finitos. Un resultado preliminar es que, sin tener en cuenta la absorción, a un periódo de 2 s, 91.69% de la energía del modo fundamental de la onda Love y 98.60% de la energía del modo fundamental de la onda Rayleigh son transmitidos.

On the anomalous polarization of Love and Rayleigh elastic waves in a layered medium

The propagation of Love and Rayleigh waves with any smooth front in an arbitrary layered medium close to an isotropic half-space is considered. The first order ray approximation is used for a description of anomalies of such waves. Bibliography 8 titles.

薄い堆積盆地の地震動特性

We propose a very simple method to calculate the secondary Love wave generated at the edge of the two-dimensional (2-D) sediment-filled valley. From engineering point of view, we consider the seismic response due to horizontally incident plane SH wave. The rectangular sediment-filled valley is used in the analyses. In our approach, we neglect the displacement and stress distribution along the depth in the Love wave propagation and convert the 2-D sediment-filled valley to the one-dimensional (1-D) vertical stratified media. Considering the Love wave propagation in the layered media, Haskell matrix technique is used for such geological structure. The physical meaning and applicability of our approach is discussed in comparison with the formulation by Hisada. From some demonstrations, it has been shown that the validity of our method is confirmed.

Maslov theory for surface wave propagation on a laterally heterogeneous earth

SUMMARY The usual JWKB ray-theoretical description of Love and Rayleigh surface wave propagation on a smooth, laterally heterogeneous earth model breaks down in the vicinity of caustics, near the source and its antipode. In this paper we use Maslov theory to obtain a representation of the wavefield that is valid everywhere, even in the presence of caustics. The surface wave trajectories lie on a 3-D manifold in 4-D phase space (θ, φ, kθ, kφ), where θ is the colatitude, φ is the longitude, and kθ and kφ are the covariant components of the wave vector. There are no caustics in phase space; it is only when the rays are projected onto configuration space (θ, φ), the mixed spaces (kθ, φ) and (θ, kφ), or momentum space (kθ, kφ), that caustics occur. The essential strategy is to employ a mixed-space or momentum-space representation in the vicinity of configuration-space caustics, where the (θ, φ) representation fails. By this means we obtain a uniformly valid Green's tensor and an explicit asymptotic expression for the surface wave response to a moment tensor source.

水平方向不均質媒質におけるラブ波の伝搬様式

Propagation of Love waves across a symmetrical mountain root structure with a high dip angle is investigated by use of the finite difference method. The structure is modelled by a set of steps of the Moho discontinuity, and has crustal thicknesses of 35 and 87.5km at the thinnest and thickest portions over a distance of 250km, respectively. The dip angle of the Moho discontinuity is about 20°. The important and interesting results obtained are as follows:(1) The phase velocities for the downdip propagation are higher than those for the updip propagation in the period range 18-37s. They are inverse in the period range 38-46s.(2) The phase velocities for the downdip propagation oscillate several times in the period range 18-46s, while the phase velocities for the updip propagation increase monotonously with increasing period in the period range 22-46s.(3) At the periods of 18, 26 and 38s, the phase velocities for the downdip propagation accord with those for the updip propagation.(4) The average phase velocity dispersion curve across the mountain root structure shows the middle one between the dispersion curves for the downdip and updip propagations.(5) The average dispersion curve across the mountain root structure does not show the middle one between two typical dispersion curves for the thinnest (S-structure) and thickest (D-structure) crustal structures.(6) The average dispersion curve is close to that for the D-structure at short periods and approaches that for the S-structure at long periods.