Journal articles on the topic 'A Rayleigh wave'
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Qingling, Du, Liu Zhengping, and Liu Shijie. "Analysis of Influencing Factors and Numerical Simulation of Horizontal-to-Vertical Spectral Ratio Method." Journal of Earthquake and Tsunami 14, no. 01 (September 18, 2019): 2050004. http://dx.doi.org/10.1142/s1793431120500049.
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To improve the calculation accuracy of the horizontal-to-vertical spectral ratio (HVSR) method, this study theoretically analyzed the influencing factors of Rayleigh wave polarizability. The phase difference of the horizontal component and the phase difference of the vertical component are found to play a key role in calculating the polarizability. The influence mechanism of the superposition of body waves and different Rayleigh waves on the polarizability of the Rayleigh wave is derived. The effects of the body wave, amplitude, frequency and Rayleigh wave superposition of different sources on the polarizability are verified by numerical simulation. The results show that the body wave significantly interferes with the polarizability of the Rayleigh wave. When a signal contains more than one set of Rayleigh waves, the superposition of the same-source Rayleigh waves does not affect the ratio. However, the superposition of Rayleigh waves from different sources significantly interferes with the calculation of the polarizability. This provides a technical method and a theoretical basis for accurately extracting the Rayleigh wave polarizability dispersion curve from a seismic record signal. This would help improve the detection accuracy of the HVSR method for ground pulse signals.
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Gupta, Shishir, Rishi Dwivedi, Smita Smita, and Rachaita Dutta. "Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids." Engineering Computations 38, no. 8 (May 18, 2021): 3368–87. http://dx.doi.org/10.1108/ec-04-2020-0231.
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Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.
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Nobili, A., E. Radi, and C. Signorini. "A new Rayleigh-like wave in guided propagation of antiplane waves in couple stress materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2235 (March 2020): 20190822. http://dx.doi.org/10.1098/rspa.2019.0822.
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Motivated by the unexpected appearance of shear horizontal Rayleigh surface waves, we investigate the mechanics of antiplane wave reflection and propagation in couple stress (CS) elastic materials. Surface waves arise by mode conversion at a free surface, whereby bulk travelling waves trigger inhomogeneous modes. Indeed, Rayleigh waves are perturbations of the travelling mode and stem from its reflection at grazing incidence. As is well known, they correspond to the real zeros of the Rayleigh function. Interestingly, we show that the same generating mechanism sustains a new inhomogeneous wave, corresponding to a purely imaginary zero of the Rayleigh function. This wave emerges from ‘reflection’ of a bulk standing mode: This produces a new type of Rayleigh-like wave that travels away from , as opposed to along, the free surface, with a speed lower than that of bulk shear waves. Besides, a third complex zero of the Rayleigh function may exist, which represents waves attenuating/exploding both along and away from the surface. Since none of these zeros correspond to leaky waves, a new classification of the Rayleigh zeros is proposed. Furthermore, we extend to CS elasticity Mindlin’s boundary conditions, by which partial waves are identified, whose interference lends Rayleigh–Lamb guided waves. Finally, asymptotic analysis in the thin-plate limit provides equivalent one-dimensional models.
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Rosyidi, Sri Atmaja P. "Analisis Parameter Kecepatan Teoritik Dan Nilai Beda Fase Gelombang Rayleigh Lapisan Aspal Perkerasan Jalan Berdasarkan Teori Perambatan Gelombang Pada Media Yang Homogen Dan Isotropik." Semesta Teknika 8, no. 1 (March 5, 2016): 88–101. http://dx.doi.org/10.18196/st.v8i1.918.
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The Rayleigh wave is one of seismic waves which generated from the natural and artificial mechanical source in the earth or place on the subsurface, such as landslide, earthquake, explosion, traffic vibration, machine works, etc. The Rayleigh wave in a possible stratified of homogeneous media is a linear combination of Primary (P) and Vertically Shear (SV) waves, which satisfied the equations of elasticity with zero body forces and zero traction on the boundary of a half-space media. In the case of a homogeneous isotropic half-space there is a unique mode of the Rayleigh waves which propagates without being sustained by any sources or external loads. Almost 70 % of wave energy generated from the mechanical sources is the Rayleigh wave energy. Therefore, it is a potential characteristic of Rayleigh wave that is able to be used in engineering purposes. One of them is a spectrum analysis that is applied in transportation engineering in order to control the quality of asphaltic material. The aim of this paper is to predict the Rayleigh wave velocity parameters and phase different value of asphaltic layer based on a fundamental theory of Rayleigh wave propagation in a homogeneous isotopic. The results have been shown that the phase different value in homogenous isotropic media is strongly influenced by field spacing of wave measurement. The Rayleigh wave velocity parameters were easier obtained using the simple equation considering to various Poisson value.
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Bullitt, John T., and M. Nafi Toksöz. "Three-dimensional ultrasonic modeling of Rayleigh wave propagation." Bulletin of the Seismological Society of America 75, no. 4 (August 1, 1985): 1087–104. http://dx.doi.org/10.1785/bssa0750041087.
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Abstract The effects of topographic features on Rayleigh wave propagation and scattoring are investigated in the laboratory using three-dimensional ultrasonic models. Starting from simple steps, different topographic features are modeled. The effects of these features on Rayleigh wave transmission and scattering are examined as a function of wavelength and as a function of angle of incidence. In general, backscattered or reflected Rayleigh waves are small compared to transmitted waves. A significant fraction of the Rayleigh wave energy is scattered into body waves. Transmission and reflection coefficients (transmitted or reflected energy/incident energy) computed from spectral ratios vary strongly with incidence angle. At wavelengths equal to twice the step height, the fraction of incident energy scattered into body waves ranges from more than 90 per cent at normal incidence to about zero at near-grazing incidence. At each angle, transmission coefficients vary strongly with frequency. Because of frequency-dependent phase shifts, the transmitted and reflected waves are distorted. The effect of the steps on the propagation of Rayleigh waves is demonstrated by convolving synthetic dispersed wave trains with the impulse response of the scale models. The ocean-continent margin of the Western United States is modeled as a 60° ramp scaled to 60 km height. The Tibetan Plateau is modeled as a broad mesa scaled to 40 km height. In both models, azimuthal dependence of transmitted Rayleigh waves is similar to that observed at WWSSN stations for Rayleigh waves crossing the modeled terrestrial structures.
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Yang, Jun. "A note on Rayleigh wave velocity in saturated soils with compressible constituents." Canadian Geotechnical Journal 38, no. 6 (December 1, 2001): 1360–65. http://dx.doi.org/10.1139/t01-046.
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The problem of Rayleigh waves in a semi-infinite saturated soil medium is reconsidered in this study, with the purpose of clarifying existing confusion and limitations of available studies. By employing Biot's general formulation, which takes into account not only the compressibility of the solid and fluid constituents but also the viscous dissipation due to fluid flow, the secular equation for Rayleigh waves is rigorously derived and the velocity of Rayleigh waves is computed for several typical types of saturated soils. The results show that the velocity of Rayleigh waves in general is independent of frequency in the frequency range actually employed in engineering practice and is only slightly less than the shear wave velocity. The results confirm that current understanding of Rayleigh wave velocity achieved based on the classical theory of elasticity is acceptable and indicate that some results in the literature are incorrect.Key words: Rayleigh wave velocity, saturated soil, porous media, wave propagation, analytical method.
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Mackay, Tom G., and Akhlesh Lakhtakia. "Multiple Rayleigh waves guided by the planar surface of a continuously twisted structurally chiral material." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200314. http://dx.doi.org/10.1098/rspa.2020.0314.
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The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending on the structural period and orientation of the CTSCM. In the case of two Rayleigh waves, each wave possesses a different wavenumber. The Rayleigh wave with the larger wavenumber is more localized to the surface and has a phase speed that changes less as the angular frequency varies in comparison with the Rayleigh wave with the smaller wavenumber.
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Hamilton, Mark F., Yuri A. Il’insky, and Evgenia A. Zabolotskaya. "Rayleigh wave nonlinearity." Journal of the Acoustical Society of America 93, no. 4 (April 1993): 2384. http://dx.doi.org/10.1121/1.406074.
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Zhou, Jie, and Haiming Zhang. "Exact Rayleigh-Wave Solution from a Point Source in Homogeneous Elastic Half-Space." Bulletin of the Seismological Society of America 110, no. 2 (February 18, 2020): 783–92. http://dx.doi.org/10.1785/0120190197.
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ABSTRACT A Rayleigh wave, often the most visible component in the far-field seismograms, is an important type of seismic-wave motion associated with the Earth’s surface. In this study, we explore some of the general properties of the Rayleigh wave in a homogeneous elastic half-space. Starting from the displacement expressed in the form of a wavenumber integral in the frequency domain, we extract the contribution from the pole in the complex wavenumber plane to obtain the excitation formulae of the Rayleigh wave by the residue theorem for complex integrals. Numerical results are compared with the full wavefield solutions to validate our solutions. By examining the analytical expressions obtained, we explore some basic properties of Rayleigh waves such as the particle motion and geometrical spreading. We also demonstrate that these properties of the Rayleigh wave excited by a point source are slightly different from but mostly consistent with the well-known classical properties of plane Rayleigh waves.
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Narayan, J. P., and A. Kumar. "Quantification of Effects of Ridge and Valley Topography on the Rayleigh Wave Characteristics." Journal of Earthquake and Tsunami 12, no. 03 (August 12, 2018): 1850007. http://dx.doi.org/10.1142/s1793431118500070.
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The effects of ridge and valley on the characteristics of Rayleigh waves are presented in this paper. The research work carried out has been stimulated by the day by day increase of long-span structures in the hilly areas which are largely affected by the spatial variability in ground motion caused by the high-frequency Rayleigh waves. The Rayleigh wave responses of the considered triangular and elliptical ridge and valley models were computed using a fourth-order accurate staggered-grid viscoelastic P-SV wave finite-difference (FD) program. The simulated results revealed very large amplification of the horizontal component and de-amplification of the vertical component of Rayleigh wave at the top of a triangular ridge and de-amplification of both the components at the base of the triangular valley. The observed amplification of both the components of Rayleigh wave in front of elliptical valley was larger than triangular valley models. A splitting of the Rayleigh wave wavelet was inferred after interaction with ridge and valley. It is concluded that the large-scale topography acts as a natural insulator for the surface waves and the insulating capacity of the valley is more than that of a ridge. This insulation phenomenon is arising due to the reflection, diffraction and splitting of the surface wave while moving across the topography. It is concluded that insulating potential of the topography for the Rayleigh waves largely depends on their shape and shape-ratio.
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Wang, Meng, Yangguang Bu, Zhaojie Dai, and Shengyang Zeng. "Characterization of Grain Size in 316L Stainless Steel Using the Attenuation of Rayleigh Wave Measured by Air-Coupled Transducer." Materials 14, no. 8 (April 11, 2021): 1901. http://dx.doi.org/10.3390/ma14081901.
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Grain size is an important parameter in evaluating the properties of microstructures in metals. In this paper, the attenuation coefficient of Rayleigh waves is introduced to characterize grain size in heat treated 316L stainless steel. Rayleigh wave attenuation is measured using an angle beam wedge transducer as the transmitter and an air-coupled transducer as the receiver. The results show that the grain size in 316L stainless steel increases due to heat treatment time, the hardness decreases accordingly, and the attenuation coefficient of Rayleigh waves increases. This indicates that the Rayleigh wave attenuation is sufficient in distinguishing the changes in the properties of the heat-treated stainless steel. It is found that compared with the measurement method using an angle beam wedge receiver, the measured results are efficient, more stable and less influenced by the surface state when an air-coupled receiver is used. In addition, comparison results also show that the Rayleigh wave attenuation is more sensitive to changes in material properties than the longitudinal wave attenuation, as the wavelength of the Rayleigh wave is shorter than that of the longitudinal wave at the same frequency.
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Ikeda, Tatsunori, Toshifumi Matsuoka, Takeshi Tsuji, and Toru Nakayama. "Characteristics of the horizontal component of Rayleigh waves in multimode analysis of surface waves." GEOPHYSICS 80, no. 1 (January 1, 2015): EN1—EN11. http://dx.doi.org/10.1190/geo2014-0018.1.
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In surface-wave analysis, S-wave velocity estimations can be improved by the use of higher modes of the surface waves. The vertical component of P-SV waves is commonly used to estimate multimode Rayleigh waves, although Rayleigh waves are also included in horizontal components of P-SV waves. To demonstrate the advantages of using the horizontal components of multimode Rayleigh waves, we investigated the characteristics of the horizontal and vertical components of Rayleigh waves. We conducted numerical modeling and field data analyses rather than a theoretical study for both components of Rayleigh waves. As a result of a simulation study, we found that the estimated higher modes have larger relative amplitudes in the vertical and horizontal components as the source depth increases. In particular, higher-order modes were observed in the horizontal component data for an explosive source located at a greater depth. Similar phenomena were observed in the field data acquired by using a dynamite source at 15-m depth. Sensitivity analyses of dispersion curves to S-wave velocity changes revealed that dispersion curves additionally estimated from the horizontal components can potentially improve S-wave velocity estimations. These results revealed that when the explosive source was buried at a greater depth, the horizontal components can complement Rayleigh waves estimated from the vertical components. Therefore, the combined use of the horizontal component data with the vertical component data would contribute to improving S-wave velocity estimations, especially in the case of buried explosive source signal.
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Polet, J., and H. Kanamori. "Upper-mantle shear velocities beneath southern California determined from long-period surface waves." Bulletin of the Seismological Society of America 87, no. 1 (February 1, 1997): 200–209. http://dx.doi.org/10.1785/bssa0870010200.
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Abstract We used long-period surface waves from teleseismic earthquakes recorded by the TERRAscope network to determine phase velocity dispersion of Rayleigh waves up to periods of about 170 sec and of Love waves up to about 150 sec. This enabled us to investigate the upper-mantle velocity structure beneath southern California to a depth of about 250 km. Ten and five earthquakes were used for Rayleigh and Love waves, respectively. The observed surface-wave dispersion shows a clear Love/Rayleigh-wave discrepancy that cannot be accounted for by a simple isotropic velocity model with smooth variations of velocity with depth. Separate isotropic inversions for Love- and Rayleigh-wave data yield velocity models that show up to 10% anisotropy (transverse isotropy). However, tests with synthetic Love waves suggest that the relatively high Love-wave phase velocity could be at least partly due to interference of higher-mode Love waves with the fundamental mode. Even after this interference effect is removed, about 4% anisotropy remains in the top 250 km of the mantle. This anisotropy could be due to intrinsic anisotropy of olivine crystals or due to a laminated structure with alternating high- and low-velocity layers. Other possibilities include the following: upper-mantle heterogeneity in southern California (such as the Transverse Range anomaly) may affect Love- and Rayleigh-wave velocities differently so that it yields the apparent anisotropy; higher-mode Love-wave interference has a stronger effect than suggested by our numerical experiments using model 1066A. If the high Love-wave velocity is due to causes other than anisotropy, the Rayleigh-wave velocity model would represent the southern California upper-mantle velocity structure. The shear velocity in the upper mantle (Moho to 250 km) of this structure is, on average, 3 to 4% slower than that of the TNA model determined for western North America.
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Nayak, Avinash, and Clifford H. Thurber. "Using multicomponent ambient seismic noise cross-correlations to identify higher mode Rayleigh waves and improve dispersion measurements." Geophysical Journal International 222, no. 3 (June 1, 2020): 1590–605. http://dx.doi.org/10.1093/gji/ggaa270.
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SUMMARY Ambient seismic noise cross-correlation with three-component sensors yields a nine-component empirical Green's tensor, in which four components of the radial–vertical plane contain Rayleigh waves. We exploit the retrograde elliptical nature of particle motion of the fundamental mode Rayleigh wave to correct the phase of the four radial–vertical components and stack them to obtain an average fundamental mode Rayleigh-wave time-series. This technique can suppress incoherent noise and wave packets that do not follow the targeted elliptical particle motion. The same technique can be used to isolate the first higher mode Rayleigh wave that follows prograde elliptical particle motion. We first demonstrate the effectiveness of the method on synthetic waveforms and then apply it on noise cross-correlations computed in Central California. Using this method, we isolate 1st higher mode Rayleigh waves on noise cross-correlations in the Great Valley, California, which provides new phase velocity constraints for estimating velocity structure in the sedimentary basin. We also obtain improved estimates of fundamental mode Rayleigh-wave dispersion for surface-wave tomography. The waveforms stacked assuming retrograde particle motion return at least ∼20 per cent more group velocity dispersion measurements satisfying a minimum signal-to-noise ratio (SNR) criterion than the individual components for periods ∼4–18 s. For equivalent group velocity measurements, SNR for the stacked estimate of the fundamental mode Rayleigh wave is on average 40 per cent greater than that measured on the individual components at periods less than 10 s. The technique also provides an easy way to detect large errors in sensor orientation.
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Sutherland, B. R. "Rayleigh Wave–Internal Wave Coupling and Internal Wave Generation above a Model Jet Stream." Journal of the Atmospheric Sciences 63, no. 3 (March 1, 2006): 1042–55. http://dx.doi.org/10.1175/jas3658.1.
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Abstract Linear theory for modes in a nonuniformly stratified, semi-infinite shear flow demonstrates that Rayleigh waves (stable waves propagating in fluid with spatially varying shear) couple with evanescent internal waves. If the bulk Richardson number (the squared ratio of the buoyancy frequency and shear) lies between 1/4 and 1, the waves have infinite e-folding depth for waves with critical relative horizontal wavenumbers. Fully nonlinear numerical simulations examine the effect of Rayleigh wave–internal wave coupling when the shear layer is localized and is thus Kelvin–Helmholtz unstable. Diagnostics examining profiles of the wave-induced mean flow show that if the bulk Richardson number is of order unity, significant momentum is extracted from a shear layer as a consequence of transport by waves. The work is extended to the study of unstable jet flows and applications of this work for internal wave generation by dynamic instability of the upper flank of the jet stream are discussed.
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Sharma, Mohan D. "Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity." Journal of Vibration and Control 26, no. 21-22 (March 2, 2020): 2070–80. http://dx.doi.org/10.1177/1077546320912069.
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Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.
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Su, Shan, and Bing Sheng Yan. "Fatigue Damage Characterization of Magnesium Thick Plate Using Nonlinear Rayleigh Wave." Applied Mechanics and Materials 130-134 (October 2011): 2006–9. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2006.
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In order to extend engineering application of nonlinear ultrasonic nondestructive testing technique in wave structure, an experimental technique for excitation and reception directly of Rayleigh wave by fixing piezoelectric sensor on the edge of the specimen is presented. Using the experimental system and procedure, the surface fatigue damage of AZ31 magnesium thick plate is detected by nonlinear Rayleigh waves. Although the experimental results have some dispersion, the ultrasonic nonlinearity parameters overall increase apparently with the fatigue cycles increasing, which demonstrates the Rayleigh wave nonlinearity parameters are sensitive for the changes of microscopic defects in the materials internal, and the experimental system and procedure are reliable. The Rayleigh wave nonlinearity parameters for the thick plate structure fatigue life prediction have potential engineering applications.
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Vinh, Pham Chi, Tran Thanh Tuan, and Le Thi Hue. "Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer." Vietnam Journal of Mechanics 39, no. 4 (December 27, 2017): 365–74. http://dx.doi.org/10.15625/0866-7136/10033.
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This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.
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Ju, Hai-yan, and Ming-fu Fu. "In-Plane Vibration Response of the Periodic Viaduct on Saturated Soil under Rayleigh Surface Wave." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/835460.
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In this study, the in-plane vibration response of the periodic viaduct on saturated soil under Rayleigh surface wave is studied. The Floquet transform method is used to decompose Rayleigh surface wave into a set of spatial harmonic waves. Considering the periodic condition of the viaduct, the wave number domain dynamic response of the periodic viaduct on saturated soil subjected to Rayleigh surface wave excitation is obtained by the transfer matrix method. Then the space domain dynamic response is retrieved by means of the inverse Floquet transform. Numerical results show that when the periodic viaduct is undergoing in-plane vibration, there exist three kinds of characteristic waves corresponding to axial compression, transverse shear, and bending vibration. Furthermore, when the frequency of Rayleigh wave is within the pass band of the periodic viaduct, the disturbance propagates over a very long distance and the attenuation of the wave motion far from the source is determined by the characteristic wave with the smallest attenuation, while the vibration attenuates rapidly and propagates in a short distance when the frequency of excitation source is in the range of band gap of periodic structure.
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Meyers, Patrick, Daniel C. Bowden, Tanner Prestegard, Victor C. Tsai, Vuk Mandic, Gary Pavlis, and Ross Caton. "Direct Observations of Surface‐Wave Eigenfunctions at the Homestake 3D Array." Bulletin of the Seismological Society of America 109, no. 4 (June 25, 2019): 1194–202. http://dx.doi.org/10.1785/0120190026.
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Abstract Despite the theory for both Rayleigh and Love waves being well accepted and the theoretical predictions accurately matching observations, the direct observation of their quantifiable decay with depth has never been measured in the Earth’s crust. In this work, we present observations of the quantifiable decay with depth of surface‐wave eigenfunctions. This is done by making direct observations of both Rayleigh‐wave and Love‐wave eigenfunction amplitudes over a range of depths using data collected at the 3D Homestake array for a suite of nearby mine blasts. Observations of amplitudes over a range of frequencies from 0.4 to 1.2 Hz are consistent with theoretical eigenfunction predictions. They show a clear exponential decay of amplitudes with increasing depth and a reversal in sign of the radial‐component Rayleigh‐wave eigenfunction at large depths, as predicted for fundamental‐mode Rayleigh waves. Minor discrepancies between the observed eigenfunctions and those predicted using estimates of the local velocity structure suggest that the observed eigenfunctions could be used to improve the velocity model. Our results confirm that both Rayleigh and Love waves have the depth dependence that they have long been assumed to have. This is an important direct validation of a classic theoretical result in geophysics and provides new observational evidence that classical seismological surface‐wave theory can be used to accurately infer properties of Earth structure and earthquake sources.
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Singh, Baljeet, and Baljinder Kaur. "Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions." Journal of Vibration and Control 26, no. 21-22 (February 20, 2020): 1980–87. http://dx.doi.org/10.1177/1077546320909972.
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The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.
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Chang, Dong Mei, and Xue Feng Liu. "Eigenfunctions of Rayleigh Wave in Viscoelastic Halfspace." Applied Mechanics and Materials 598 (July 2014): 486–89. http://dx.doi.org/10.4028/www.scientific.net/amm.598.486.
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In this paper, the eigenfunctions of Rayleigh wave in viscoelastic halfspace is studied. By comparing the eigenfunctions of Rayleigh wave in viscoelastic halfspace and the corresponding elastic halfspace, we found the penetration depth of Rayleigh wave in viscoelastic halfspace is always larger than in the corresponding elastic halfspace. But the difference is small. The ratio of penetration depth and wave length under different cases is calculated, the results show penetration ability of Rayleigh wave in viscoelastic halfspace is always stronger than the corresponding elastic case, and penetration ability of Rayleigh wave gets weaker when the Poisson's ratio is smaller. The penetration ability of Rayleigh wave is stronger when the Q value is smaller. The study in the paper is meaningful for the further research of Rayleigh wave in viscoelastic media.
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Kumar, Rajneesh, and Vandana Gupta. "Effect of phase-lags on Rayleigh wave propagation in thermoelastic medium with mass diffusion." Multidiscipline Modeling in Materials and Structures 11, no. 4 (November 9, 2015): 474–93. http://dx.doi.org/10.1108/mmms-12-2014-0066.
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Purpose – The purpose of this paper is to study the propagation of Rayleigh waves in thermoelastic medium with mass diffusion. Design/methodology/approach – The field equations for the linear theory of homogeneous isotropic thermoelastic diffusion medium are taken into consideration by using dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree. Findings – From the polynomial equation, Rayleigh wave root is found. The secular equation is resolved into a polynomial form to find the roots and therefore to find the existence and propagation of Rayleigh wave. The existence of Rayleigh wave in the assumed model depends on the values of various parameters involved in the secular equation. These roots are resolved for phase velocity and attenuation of the inhomogeneous propagation of Rayleigh wave. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Particular cases of the interest are also deduced from the present investigation. Originality/value – Governing equations corresponding to DPLT and DPLD models of thermoelastic diffusion are formulated to study the wave propagation and their dependence on various material parameters. In this paper effects of thermal and diffusion phase lags on the phase velocity, attenuation and on particle paths are observed and depicted graphically.
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He, Fang Ding, Guang Jun Guo, Zhi Gang Dou, and Yang Yang. "Study on the Dispersion Curves of Rayleigh Wave in Foundation of Obstacles." Applied Mechanics and Materials 90-93 (September 2011): 2193–99. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.2193.
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It is difficult to accurately identify dispersion curves of Rayleigh wave for the foundation with obstacles. Displacement curve of time-domain of half-space foundation have been obtained with the finite element in the paper. Then time-domain curve have been transformed Rayleigh wave dispersion curves. Rayleigh wave dispersion curves have been analysed in half-space foundation with water drain pipes. The results show that, there are reflection waves at the receiving signals in front of the obstacles, there are no reflection waves behind the obstacles basically. The location and spacing of the sensor have a greater impact on the results. The results provide the reference for the recognition of dispersion curves and disposition patterns of the sensors.
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Li, Jing, Sherif Hanafy, Zhaolun Liu, and Gerard T. Schuster. "Wave-equation dispersion inversion of Love waves." GEOPHYSICS 84, no. 5 (September 1, 2019): R693—R705. http://dx.doi.org/10.1190/geo2018-0039.1.
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We present a theory for wave-equation inversion of Love-wave dispersion curves, in which the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to inversion of Rayleigh-wave dispersion curves, the complicated Love-wave arrivals in traces are skeletonized as simpler data, namely, the picked dispersion curves in the [Formula: see text] domain. Numerical solutions to the SH-wave equation and an iterative optimization method are then used to invert these dispersion curves for the S-wave velocity model. This procedure, denoted as wave-equation dispersion inversion of Love waves (LWD), does not require the assumption of a layered model or smooth velocity variations, and it is less prone to the cycle-skipping problems of full-waveform inversion. We demonstrate with synthetic and field data examples that LWD can accurately reconstruct the S-wave velocity distribution in a laterally heterogeneous medium. Compared with Rayleigh waves, inversion of the Love-wave dispersion curves empirically exhibits better convergence properties because they are completely insensitive to the P-velocity variations. In addition, Love-wave dispersion curves for our examples are simpler than those for Rayleigh waves, and they are easier to pick in our field data with a low signal-to-noise ratio.
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Ivanov, Julian, Richard D. Miller, Daniel Feigenbaum, Sarah L. C. Morton, Shelby L. Peterie, and Joseph B. Dunbar. "Revisiting levees in southern Texas using Love-wave multichannel analysis of surface waves with the high-resolution linear Radon transform." Interpretation 5, no. 3 (August 31, 2017): T287—T298. http://dx.doi.org/10.1190/int-2016-0044.1.
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Shear-wave velocities were estimated at a levee site by inverting Love waves using the multichannel analysis of surface waves (MASW) method augmented with the high-resolution linear Radon transform (HRLRT). The selected site was one of five levee sites in southern Texas chosen for the evaluation of several seismic data-analysis techniques readily available in 2004. The methods included P- and S-wave refraction tomography, Rayleigh- and Love-wave surface-wave analysis using MASW, and P- and S-wave cross-levee tomography. The results from the 2004 analysis revealed that although the P-wave methods provided reasonable and stable results, the S-wave methods produced surprisingly inconsistent shear-wave velocity [Formula: see text] estimates and trends compared with previous studies and borehole investigations. In addition, the Rayleigh-wave MASW method was nearly useless within the levee due to the sparsity of high frequencies in fundamental-mode surface waves and complexities associated with inverting higher modes. This prevented any reliable [Formula: see text] estimates for the levee core. Recent advances in methodology, such as the HRLRT for obtaining higher resolution dispersion-curve images with the MASW method and the use of Love-wave inversion routines specific to Love waves as part of the MASW method, provided the motivation to extend the 2004 original study by using horizontal-component seismic data for characterizing the geologic properties of levees. Contributions from the above-mentioned techniques were instrumental in obtaining [Formula: see text] estimates from within these levees that were very comparable with the measured borehole samples. A Love-wave approach can be a viable alternative to Rayleigh-wave MASW surveys at sites where complications associated with material or levee geometries inhibit reliable [Formula: see text] results from Rayleigh waves.
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Xu, Meng Jiao, and Jian Wu. "Application of Multi-Channel Transient Rayleigh Wave in Geological Exploration." Applied Mechanics and Materials 638-640 (September 2014): 397–401. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.397.
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Rayleigh wave exploration has broad application in engineering geological investigation, underground cave detection, highway nondestructive testing, etc. On the basis of introduction about the principle of transient Rayleigh wave exploration, the process of multi-channel transient Rayleigh wave exploration and data processing with an engineering example are stated. Compared to the field drilling histogram, reasonable explanation for the local deviation from the Rayleigh wave exploration result is given. Besides, the advantages and disadvantages of multi-channel transient Rayleigh wave exploration are also discussed, indicating a widely applicability of the Rayleigh wave exploration and some problems that need further research.
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Κρητικάκης, Σ. Γ., Α. Βαφείδης, and J. C. Gourry. "RAYLEIGH SURFACE WAVE ANALYSIS AND APPLICATION AT THE MONFALCONE LANDFILL, AND AT THE INDUSTRIAL AREA OF PORTO PETROLI, GENOA, NORTHERN ITALY." Bulletin of the Geological Society of Greece 36, no. 3 (January 1, 2004): 1234. http://dx.doi.org/10.12681/bgsg.16466.
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During the last few years, the dispersion of Rayleigh surface waves has been intensively studied as an alternative to contemporary geotechnical and environmental geophysical techniques. Nowadays, Rayleigh surface wave analysis (SASW, MASW) is widely used for the determination of S-wave velocity distribution with depth. This work aims to the description of the Rayleigh surface wave analysis methodology as well as to the presentation of its application on seismic data from geophysical surveys, carried out for the purposes of the HYGEIA European project, in two polluted areas: a) In the area of Monfalcone, northern Italy and b) in the industrial area of Porto Petroli, Genoa. Rayleigh surface wave analysis proved very useful in locating the lateral and vertical extent of the heterogeneous soil in Monfalcone and in mapping the bedrock relief in Porto Petroli through Swave velocity determination.
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Langston, Charles A. "Scattering of long-period Rayleigh waves in Western North America and the interpretation of coda Q measurements." Bulletin of the Seismological Society of America 79, no. 3 (June 1, 1989): 774–89. http://dx.doi.org/10.1785/bssa0790030774.
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Abstract The codas of long-period Rayleigh waves recorded at WWSSN and Canadian network stations in Western North America from eight underground explosions at NTS are examined in an effort to separate scattering and anelastic attenuation effects. Coda behavior of 0.1 and 0.2 hz Rayleigh waves follows coda characteristics seen in studies of short-period S waves. Coda decay rate is seen to be a stable observation over most stations in Western North America and is consistent with the hypothesis that backscattered surface waves from heterogeneities contained within the western half of the continent form the Rayleigh wave coda. The basic data observables of coda level and decay are interpreted using several plausible models. The single scattering model yields a coda Q consistent with previously determined Rayleigh anelastic attenuation coefficients. Separation of anelastic and scattering Q is possible using an energy flux model and shows that scattering Q is one to two orders of magnitude higher than anelastic Q. However, an energy flux model that incorporates a layer of scatterers over a homogeneous half-space shows that all Rayleigh-wave attenuation can be explained purely by scattering effects which include Rayleigh- to body-wave conversion. Coda can be fit equally well by these mutually incompatible models. It is not likely that the mechanisms of scattering or anelastic attenuation can be addressed by coda observations of a single homogeneous data set.
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Schaal, Christoph, Suzhou Zhang, Himadri Samajder, and Ajit Mal. "An analytical study of the scattering of ultrasonic guided waves at a delamination-like discontinuity in a plate." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 16 (March 24, 2017): 2947–60. http://dx.doi.org/10.1177/0954406217700176.
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Interface delaminations between individual plies in a composite, or disbonds of face sheets in honeycomb structures often remain undetected. Using guided ultrasonic waves (Rayleigh and Lamb waves) such hidden defects can be detected. In this work, an analytical framework that considers propagating, nonpropagating and evanescent waves to analyze the scattering of an incident ultrasonic wave at a delamination-like discontinuity is presented. Wave conversion at the interface of the damage is quantified in terms of the power flows of the individual waves. The analytical solutions are compared with results from numerical simulations. For an incident Lamb wave, excellent agreement is found. However, it is shown that the analytical solution for an incident Rayleigh wave has significant differences from the numerical results, due to the incomplete nature of the Rayleigh wave-field in the half-space. Even though this study is performed for isotropic waveguides, the method can be extended to transversely isotropic laminates by substituting the corresponding expressions for the dispersion equations, as well as displacement and stress fields.
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Lianngenga, R., L. P. Duhawma, and L. Thangmawia. "Symmetric and antisymmetric vibration in elastic plate with voids immersed in a liquid." International Journal of Computational Materials Science and Engineering 07, no. 03 (September 2018): 1850017. http://dx.doi.org/10.1142/s2047684118500173.
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The problem of the symmetric and antisymmetric vibrations are attempted for the elastic plate with voids immersed in a liquid. The frequency equations are derived and deduced for the cases of plate wave, flexural and Rayleigh waves. It is also derived the cases when the liquid is replaced by vacuum/air. The two modes of vibration for the modified symmetric, antisymmetric, plate, flexural and Rayleigh waves in the considered medium are discussed. Numerically and analytically, the phase speeds and attenuations of symmetric and antisymmetric vibration, plate wave, flexural and Rayleigh waves are computed for a particular model. The effects of voids parameters on the phase speeds are also discussed.
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Athanasopoulos, Nikolaos, Edgar Manukyan, Thomas Bohlen, and Hansruedi Maurer. "Time–frequency windowing in multiparameter elastic FWI of shallow seismic wavefield." Geophysical Journal International 222, no. 2 (May 15, 2020): 1164–77. http://dx.doi.org/10.1093/gji/ggaa242.
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SUMMARY Full-waveform inversion of shallow seismic wavefields is a promising method to infer multiparameter models of elastic material properties (S-wave velocity, P-wave velocity and mass density) of the shallow subsurface with high resolution. Previous studies used either the refracted Pwaves to reconstructed models of P-wave velocity or the high-amplitude Rayleigh waves to infer the S-wave velocity structure. In this work, we propose a combination of both wavefields using continuous time–frequency windowing. We start with the contribution of refracted P waves and gradually increase the time window to account for scattered body waves, higher mode Rayleigh waves and finally the fundamental Rayleigh wave mode. The opening of the time window is combined with opening the frequency bandwidth of input signals to avoid cycle skipping. Synthetic reconstruction tests revealed that the reconstruction of P-wave velocity model and mass density can be improved. The S-wave velocity reconstruction is still accurate and robust and is slightly benefitted by time–frequency windowing. In a field data application, we observed that time–frequency windowing improves the consistency of multiparameter models. The inferred models are in good agreement with independent geophysical information obtained from ground-penetrating radar and full-waveform inversion of SH waves.
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Zhu, Xu Fang, and Bing Yan. "Researching on Characteristics of Rayleigh Waves." Applied Mechanics and Materials 721 (December 2014): 472–75. http://dx.doi.org/10.4028/www.scientific.net/amm.721.472.
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Rayleigh wave is a secondary wave characterized by low frequency and strong energy, propagating mainly along the interface of medium and rapid attenuation of energy with increase in interface distance. The same as reflected wave and refracted wave, Rayleigh wave also contain subsurface geological information. In this paper, the concept of the Rayleigh wave, wave equation, dispersion equation, the frequency bulk characteristics and the application of the actual data are used to indicate the characteristics of Rayleigh wave and its application.
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Haney, Matthew M., and Victor C. Tsai. "Rayleigh-wave ellipticity in weakly heterogeneous layered media." Geophysical Journal International 228, no. 2 (October 4, 2021): 1313–23. http://dx.doi.org/10.1093/gji/ggab395.
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SUMMARY We derive approximate expressions for the ellipticity (i.e. horizontal-to-vertical or vertical-to-horizontal ratio) of Rayleigh waves propagating in a layered medium. The approximation is based on the generalized energy equation for Rayleigh waves, which has been used previously to obtain perturbational results for ellipticity. For a medium with weakly heterogeneous layers, we obtain an approximation from the perturbational result by taking the background medium to be homogeneous. The generalized energy equation also requires an auxiliary function and we discuss how the various possible functions are related to the homogeneous Rayleigh-wave eigenfunction. The analysis reveals that, within the weak approximation, the product of ellipticity and squared phase velocity is linearly related to squared shear wave velocity in the subsurface. We show the accuracy of the approximation with a simple layer-over-half-space model and then demonstrate its utility in a linear inversion scheme for shear wave velocity.
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Mohseni, Hasan, and Ching-Tai Ng. "Rayleigh wave propagation and scattering characteristics at debondings in fibre-reinforced polymer-retrofitted concrete structures." Structural Health Monitoring 18, no. 1 (January 30, 2018): 303–17. http://dx.doi.org/10.1177/1475921718754371.
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Structural health monitoring is of paramount importance to ensure safety and serviceability of structures. Among different damage detection techniques, guided wave–based approach has been the subject of intensive research activities. This article investigates the capability of Rayleigh wave for debonding detection in fibre-reinforced polymer-retrofitted concrete structures through studying wave scattering phenomenon at debonding between fibre-reinforced polymer and concrete. A three-dimensional finite element model is presented to simulate Rayleigh wave propagation and scattering at the debonding. Numerical simulations of Rayleigh wave propagation are validated with analytical solutions. Absorbing layers by increasing damping is employed in the fibre-reinforced polymer-retrofitted concrete numerical model to maximise computational efficiency in the scattering study. Experimental measurements are also carried out using a three-dimensional laser Doppler vibrometer to validate the three-dimensional finite element model. Very good agreement is observed between the numerical and experimental results. The experimentally and analytically validated finite element model is then used in numerical case studies to investigate the wave scattering characteristic at the debonding. The study investigates the directivity patterns of scattered Rayleigh waves, in both backward and forward directions, with respect to different debonding size-to-wavelength ratios. This study also investigates the suitability of using bonded mass to simulate debonding in the fibre-reinforced polymer-retrofitted concrete structures. By enhancing physical understanding of Rayleigh wave scattering at the debonding between fibre-reinforced polymer/concrete interfaces, this study can lead to further advance of Rayleigh wave–based damage detection techniques.
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Dbibih, Fatima-Ezzahraa, Meddy Vanotti, Valerie Soumann, Jean-Marc Cote, Lyes Djoumi, and Virginie Blondeau-Patissier. "Measurement of PM10 and PM2.5 Using SAW Sensors-Based Rayleigh Wave and Love Wave." Engineering Proceedings 6, no. 1 (May 17, 2021): 81. http://dx.doi.org/10.3390/i3s2021dresden-10129.
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Particulate matter (PM) is reported to be dangerous and can cause respiratory and health issues. Regulations, based on PM concentration, have been implemented to limit human exposition to air pollution. An innovative system with surface acoustic wave (SAW) sensors combined with a 3 Lpm cascade impactor was developed by our team for real time mass concentration measurements. In this study, we compare the PM sensitivity of two types of SAW sensors. The first one consists of delay lines based on Rayleigh waves propagating on a Lithium Niobate Y-X 128° substrate. The second one is a based-on Love waves on AT-Quartz. Aerosols were generated from NaCl for PM2.5 and from Silicon carbide for PM10. The sensors’ responses was compared to a reference sensor based on optical measurements. The sensitivity of the Rayleigh wave-based sensor is clearly lower than the Love wave sensor for both PMs. Although less sensitive, Rayleigh wave sensors remain very promising for the development of self-cleaning sensors using RF power due to their high electromechanical factor. To check the performance of our system in real conditions, we tested the sensitivity to PM from cigarette smoke using Rayleigh SAW. The PM2.5 stage showed a phase shift while the PM10 did not respond. This result agrees with previous studies which reported that the size of particles from cigarette smoke varies between 0.1 to 1.5 µm. A good correlation between the reference sensor’s response and the phase variation of SAW sensors was obtained.
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Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 74, no. 14 (April 3, 1995): 2729–32. http://dx.doi.org/10.1103/physrevlett.74.2729.
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Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 75, no. 9 (August 28, 1995): 1873. http://dx.doi.org/10.1103/physrevlett.75.1873.
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Liu, Zhaolun, Jing Li, Sherif M. Hanafy, and Gerard Schuster. "3D wave-equation dispersion inversion of Rayleigh waves." GEOPHYSICS 84, no. 5 (September 1, 2019): R673—R691. http://dx.doi.org/10.1190/geo2018-0543.1.
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The 2D wave-equation dispersion (WD) inversion method is extended to 3D wave-equation dispersion inversion of surface waves for the shear-velocity distribution. The objective function of 3D WD is the frequency summation of the squared wavenumber [Formula: see text] differences along each azimuth angle of the fundamental or higher modes of Rayleigh waves in each shot gather. The S-wave velocity model is updated by the weighted zero-lag crosscorrelation between the weighted source-side wavefield and the back-projected receiver-side wavefield for each azimuth angle. A multiscale 3D WD strategy is provided, which starts from the pseudo-1D S-velocity model, which is then used to get the 2D WD tomogram, which in turn is used as the starting model for 3D WD. The synthetic and field data examples demonstrate that 3D WD can accurately reconstruct the 3D S-wave velocity model of a laterally heterogeneous medium and has much less of a tendency to getting stuck in a local minimum compared with full-waveform inversion.
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Chmiel, M., A. Mordret, P. Boué, F. Brenguier, T. Lecocq, R. Courbis, D. Hollis, X. Campman, R. Romijn, and W. Van der Veen. "Ambient noise multimode Rayleigh and Love wave tomography to determine the shear velocity structure above the Groningen gas field." Geophysical Journal International 218, no. 3 (May 24, 2019): 1781–95. http://dx.doi.org/10.1093/gji/ggz237.
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SUMMARY The Groningen gas field is one of the largest gas fields in Europe. The continuous gas extraction led to an induced seismic activity in the area. In order to monitor the seismic activity and study the gas field many permanent and temporary seismic arrays were deployed. In particular, the extraction of the shear wave velocity model is crucial in seismic hazard assessment. Local S-wave velocity-depth profiles allow us the estimation of a potential amplification due to soft sediments. Ambient seismic noise tomography is an interesting alternative to traditional methods that were used in modelling the S-wave velocity. The ambient noise field consists mostly of surface waves, which are sensitive to the Swave and if inverted, they reveal the corresponding S-wave structures. In this study, we present results of a depth inversion of surface waves obtained from the cross-correlation of 1 month of ambient noise data from four flexible networks located in the Groningen area. Each block consisted of about 400 3-C stations. We compute group velocity maps of Rayleigh and Love waves using a straight-ray surface wave tomography. We also extract clear higher modes of Love and Rayleigh waves. The S-wave velocity model is obtained with a joint inversion of Love and Rayleigh waves using the Neighbourhood Algorithm. In order to improve the depth inversion, we use the mean phase velocity curves and the higher modes of Rayleigh and Love waves. Moreover, we use the depth of the base of the North Sea formation as a hard constraint. This information provides an additional constraint for depth inversion, which reduces the S-wave velocity uncertainties. The final S-wave velocity models reflect the geological structures up to 1 km depth and in perspective can be used in seismic risk modelling.
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Kaur, Baljinder, and Baljeet Singh. "The Effect of Rotation on Propagation of Rayleigh Wave in an Incompressible Monoclinic Elastic Solid." Journal of Mechanics 36, no. 4 (May 4, 2020): 485–95. http://dx.doi.org/10.1017/jmech.2020.2.
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ABSTRACTIn this paper, the Rayleigh wave propagation is investigated in rotating half-space of incompressible monoclinic elastic materials which are subjected to the impedance boundary conditions. In particular, the explicit secular equation of the Rayleigh wave is obtained. The main objective of this paper is to illustrate the dependence of dimensionless speed of Rayleigh wave on rotation, anisotropy and impedance parameters. An algorithm in MATLAB software is developed to solve the secular equation of Rayleigh wave. The speed of Rayleigh wave is plotted against rotation, anisotropy and impedance parameters.
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Haney, Matthew M., and Victor C. Tsai. "Perturbational and nonperturbational inversion of Rayleigh-wave velocities." GEOPHYSICS 82, no. 3 (May 1, 2017): F15—F28. http://dx.doi.org/10.1190/geo2016-0397.1.
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The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.
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Roy, Indrajit, D. P. Acharya, and Sourav Acharya. "Rayleigh Wave In A Rotating Nonlocal Magnetoelastic Half-Plane*." Journal of Theoretical and Applied Mechanics 45, no. 4 (December 1, 2015): 61–78. http://dx.doi.org/10.1515/jtam-2015-0024.
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AbstractThis paper investigates the propagation of Rayleigh surface waves in a rotating semi-infinite solid medium, permeated by an initial magnetic field in the context of linear nonlocal elasticity. Frequency equations are derived and the combined effect of magnetic field and rotation on Rayleigh wave propagation, based on the linear theory of nonlocal elasticity has been studied. Effects of magnetic field, as well as rotation on Rayleigh wave propagation in a nonlocal medium, have also been analyzed in details as special cases. Numerical calculations, graphs and discussions presented in this paper lead us to some important conclusions. Fourier double integral transform technique has been applied to solve the problem.
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Kumar, Rajneesh, and Tarun Kansal. "Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium." Advances in Applied Mathematics and Mechanics 3, no. 2 (April 2011): 219–38. http://dx.doi.org/10.4208/aamm.10-m1016.
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AbstractThis paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.
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Du, Qingling, Zhengping Liu, Shijie Liu, Li Zhang, and Wenfu Yu. "A study of the lateral heterogeneity with the ellipticity of Rayleigh waves derived from microtremors." Geophysical Journal International 225, no. 3 (February 24, 2021): 2020–34. http://dx.doi.org/10.1093/gji/ggab075.
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SUMMARY We examine the potential of frequency-dependent Rayleigh wave ellipticity, derived from microtremors, for the investigation of heterogeneous subsurface structure. Based on numerical simulation, we analyse the effects of interference waves in microtremors, primarily the various propagation directions of the Rayleigh waves, linear polarization waves and white noise, on the ellipticity frequency-dependent estimation of the Rayleigh waves. A data processing scheme to separate the Rayleigh waves from the interference waves is proposed and verified by synthetic data. We performed a field experiment in the mountainous areas of Southwest China to show that the ellipticity frequency dependence of Rayleigh waves in the period range of 0.05–5 s can be estimated from the microtremor records with the proposed data processing scheme. In addition, the method is feasible for investigating lateral heterogeneity within the top several hundred metres in the mountain regions. The study also reveals that the features of the ellipticity anomaly of a local heterogeneity are related to the propagation directions of the Rayleigh waves, and to reduce the ambiguity of the anomaly, the propagation direction of the waves picked for the ellipticity estimation should be consistent with (along or opposite to) that of the survey line. Then, to eliminate the effects of the phase differences due to the propagation direction, or time, the ellipticity for each location should be estimated by a single event rather than multiple events from the derived Rayleigh wave arrivals.
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Chael, Eric P. "An automated Rayleigh-wave detection algorithm." Bulletin of the Seismological Society of America 87, no. 1 (February 1, 1997): 157–63. http://dx.doi.org/10.1785/bssa0870010157.
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Abstract The desire to operate denser networks in order to monitor seismic activity at lower thresholds leads to greater emphasis on automated data processing. An algorithm for detecting and characterizing long-period Rayleigh-wave arrivals has been developed and tested. The routine continuously monitors all directions of approach to a station, in a manner similar to beamforming. The detector is based on cross-powers between the Hilbert-transformed vertical and rotated horizontal signals, so it is sensitive to both the power and polarization properties of the three-component wave field. Elliptically polarized Rayleigh arrivals are enhanced, while linearly polarized Love waves and body phases are suppressed. A test using one month of data from station ANMO demonstrated that this technique can, with high reliability, detect Rayleigh arrivals that are visible on the records. The measured arrival times and azimuths are accurate enough to permit automated association of the detections to events in a bulletin.
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Zhang, Zhen-Dong, and Tariq Alkhalifah. "Wave-equation Rayleigh-wave dispersion inversion using fundamental and higher modes." GEOPHYSICS 84, no. 4 (July 1, 2019): EN57—EN65. http://dx.doi.org/10.1190/geo2018-0506.1.
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Recorded surface waves often provide reasonable estimates of the S-wave velocity in the near surface. However, existing algorithms are mainly based on the 1D layered-model assumption and require picking the dispersion curves either automatically or manually. We have developed a wave-equation-based inversion algorithm that inverts for S-wave velocities using fundamental and higher mode Rayleigh waves without picking an explicit dispersion curve. Our method aims to maximize the similarity of the phase velocity spectrum ([Formula: see text]) of the observed and predicted surface waves with all Rayleigh-wave modes (if they exist) included in the inversion. The [Formula: see text] spectrum is calculated using the linear Radon transform applied to a local similarity-based objective function; thus, we do not need to pick velocities in spectrum plots. As a result, the best match between the predicted and observed [Formula: see text] spectrum provides the optimal estimation of the S-wave velocity. We derive S-wave velocity updates using the adjoint-state method and solve the optimization problem using a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Our method excels in cases in which the S-wave velocity has vertical reversals and lateral variations because we used all-modes dispersion, and it can suppress the local minimum problem often associated with full-waveform inversion applications. Synthetic and field examples are used to verify the effectiveness of our method.
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Liu, Xue Feng, and You Hua Fan. "A New Formula for the Rayleigh Wave Velocity." Advanced Materials Research 452-453 (January 2012): 233–37. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.233.
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The formula for the Rayleigh wave velocity in isotropic elastic half-space is studied by many researchers. In their deductions, Cardan’s formula of cubic equations is often used. Based on another formula instead of Cardan’s formula, a new formula for the Rayleigh wave velocity that does not contain complex number is presented here. Our new formula is more reasonable as both the parameters and Rayleigh wave velocity are real. And the computer time can be reduced since there is no complex computation. With this new formula, the variation of Rayleigh wave velocity with the parameters is computed. It shows that Rayleigh wave velocity decreases with the increase of Poission’s ratio when S-wave velocity is fixed.
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Nakahara, Hisashi, Kentaro Emoto, and Takeshi Nishimura. "Extending the formulation of the spatial autocorrelation (SPAC) method to strain, rotation and tilt." Geophysical Journal International 227, no. 1 (June 5, 2021): 287–302. http://dx.doi.org/10.1093/gji/ggab217.
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SUMMARY The spatial autocorrelation (SPAC) method has been applied to ambient seismic noise measured by arrays of translational seismometers for inverting phase-velocity dispersion curves of Rayleigh or Love waves for shallow S-wave velocity structure. Recently, it is becoming possible to observe wave spatial gradients such as strain, rotation and tilt owing to the development of dense seismic networks and improving measurement technologies. Therefore, it is desirable to extend the formulation of the SPAC method to strain, rotation and tilt. This study presents analytical expressions of cross-spectra and coherence of the strain, rotation and tilt components that are measured on the free surface. According to the results, both Rayleigh and Love waves contribute to most components of strains. The exceptions are the areal strain and the vertical axial strain (ezz) on the free surface that are affected by only Rayleigh waves. Only Rayleigh waves contribute to the tilts and rotations around the horizontal axes on the free surface, too. On the other hand, only Love waves contribute to the rotation around the vertical axis. Therefore, different kinds of wave spatial gradients are helpful to separate Rayleigh and Love waves correctly. For practical applications, the analytical expression for the radial axial strain (err) component will be applied directly to distributed acoustic sensing data measured with straight sections of a fibre-optic cable. On the other hand, dense observations of rotation and tilt may still be difficult to carry out at present. However, an application of analytical formulations in this study to arrays of at least several three-component rotational seismometers is attractive because it enables us to separately estimate the phase velocities of Rayleigh and Love waves.
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Singh, Baljeet, Asha Sangwan, and Jagdish Singh. "Nonlocal effects on Rayleigh-type surface wave in a micropolar piezoelectric medium." Vietnam Journal of Mechanics 44, no. 1 (March 30, 2022): 1–13. http://dx.doi.org/10.15625/0866-7136/16539.
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The properties of Rayleigh-type surface wave in a linear, homogeneous and transversely isotropic nonlocal micropolar piezoelectric solid half-space are explored. Dispersion relations for Rayleigh-type surface wave are derived for both charge free and electrically shorted cases. Using an algorithm of iteration method in MATLAB software, the wave speed of Rayleigh wave is computed for relevant material constants. The effects of nonlocality, angular frequency, micropolarity and piezoelectricity are illustrated graphically on the propagation speed of Rayleigh wave.