A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

Application of transient Rayleigh wave in detection of tunnel lining void area

Transient Rayleigh wave detection is a high-precision nondestructive detection method.At present,it has been widely used in shallow exploration,but rarely used in tunnel lining quality detection.Through the tunnel lining physical model experiment,the layout defects of the double-layer reinforcement lining area were detected and the Rayleigh wave velocity profile and dispersion curve were analyzed after data process-ing,which finally verified the feasibility and accuracy of Rayleigh wave method in detecting the tunnel lining void area.The results show that the method is not affected by the reinforcement inside the lining,the shallow detection is less disturbed and the accuracy is higher,and the data will fluctuate slightly with the deepening of the detection depth.At the same time,this method responds quite accurately to the thickness of the concrete,allowing for the assessment of the tunnel lining’s lack of compactness.This method has high efficiency,good reliability,and simple data processing,and is suitable for nondestructive detection of internal defects of tun-nel lining structure.

Multi-Mode Guided Waves Based Reference-Free Damage Diagnostic Imaging in Plates

Probability-based diagnostic imaging(PDI)is one of the most well-known damage identification methods using guided waves.It is usually applied to diagnose damage in plates.The previous studies were dependent on the certain damage index(DI)which is always calculated from the guided wave signals.In conventional methods,DI is simply defined by comparing the real-time data with the baseline data as reference.However,the baseline signal is easily affected by varying environmental conditions of structures.In this paper,a reference-free diagnostic imaging method is developed to avoid the influence of environmental factors,such as temperature and load conditions.The DI is defined based on the mode conversion of multi-mode guided waves with realtime signals without baseline signals.To improve the accuracy of diagnosis,two terms are included in the reference-free DI.One is called energy DI,which is defined based on the feature of signal energy.The other is called correlation DI and is defined based on the correlation coefficient.Then the PDI algorithm can be carried out instantaneously according to the reference-free DI.The real-time signals which are used to calculate DI are collected by the piezoelectric lead zirconate titanate(PZT)transducers placed on both sides of a plate.The numerical simulations by the finite element(FE)method on aluminum plates with PZT arrays are performed to validate the effectiveness of the reference-free damage diagnostic imaging.The approach is validated by two different arrays:a circle network and a square network.The results of diagnostic imaging are demonstrated and discussed in this paper.Furthermore,the advantage of reference-free DI is investigated by comparing the accuracy of defined reference-free DI and energy DI.

Dispersion function of Rayleigh waves in porous layered half-space system

Rayleigh wave exploration is based on an elastic layered half-space model. If practical formations contain porous layers, these layers need to be simplified as an elastic medium. We studied the effects of this simplification on the results of Rayleigh wave exploration. Using a half-space model with coexisting porous and elastic layers, we derived the dispersion functions of Rayleigh waves in a porous layered half-space system with porous layers at different depths, and the problem of transferring variables to matrices of different orders is solved. To solve the significant digit overflow in the multiplication of transfer matrices, we propose a simple, effective method. Results suggest that dispersion curves differ in a low- frequency region when a porous layer is at the surface; otherwise, the difference is small.

Analysis of quality factors for Rayleigh channel waves

To facilitate investigation of the effect of imperfect elastic dissipation on the propagation of Rayleigh-type channel waves and use of their quality factors in investigations of the properties of coal seams, a simple method for calculating the quality factor QR is proposed in this paper. Introduction of complex velocities into the dispersion function allows calculation of the dispersion function of Rayleigh-type channel waves in coal seams. By the control variable method, we analyzed changes in QR with changes in coal seam thickness and P- and S-wave Q-factors within the coal seam and adjacent rock layers. The numerical results show that the trend of the QR curve is consistent with the group velocity curve. The minimum QR value occurs at the Airy phase frequency; the Airy phase frequency decreases as coal seam thickness increases. The value of QR increases with increasing QS2(quality factor for S wave in coal seam). We can compensate for the absorption of Rayleigh-type channel waves using the computed QR curve. Inversion of the QR curve can also be used to predict the thicknesses and lithologies of coal seams.

Dynamic response of utility tunnel during the passage of Rayleigh waves

The modeling methodologies and calculation of dynamic response of underground structure under Rayleigh waves is investigated in this paper. First the free field responses under Rayleigh waves are analyzed and the numerical results agree well with the theoretical results. Then, the approximate Rayleigh waves are put forward based on the preliminary re- search, and Rayleigh wave field is obtained through fast Fourier transform technique. Taking a utility tunnel as an example, its dynamic responses under Rayleigh waves is calculated by ABAQUS. The results demonstrate that bending deformation is the main component of structural deformation and the deformation at the top of the structure is about twice as much as that at bottom of the structure. The effect of soil-structure interface and the buried depth of underground structure are also investi- gated via parameter analysis. For the shallow buffed underground structures, Rayleigh waves can be the key factor to control the responses and damage of the structure.

Group velocity distribution of Rayleigh waves and crustal and upper mantle velocity structure of the Chinese mainland and its vicinity

Based on the long period digital surface wave data recorded by 11 CDSN stations and 11 IRIS stations, the dispersion curves of the group velocities of fundamental mode Rayleigh waves along 647 paths, with the periods from 10 s to 92 s, were measured by multi-filter. Their distribution at 25 central periods within the region of 18~54N, 70~140E was inverted by Dimtar-Yanovskaya method. Within the period from 10 s to 15.9 s, the group velocity distribution is laterally inhomogeneous and is closely related to geotectonic units, with two low velocity zones located in the Tarim basin and the East China Sea and its north regions, respectively. From 21 s to 33 s, the framework of tectonic blocks is revealed. From 36.6 s to 40 s, the lithospheric subdivision of the Chinese mainland is obviously uncovered, with distinct boundaries among the South-North seismic belt, the Tibetan plateau, the North China, the South China and the Northeast China. Four cross-sections of group velocity distribution with period along 30N, 38N, 90E and 120E, are discussed, respectively, which display the basic features of the crust and upper mantle of the Chinese mainland and its neighboring regions. There are distinguished velocity differences among the different tectonic blocks. There are low-velocity-zones (LVZ) in the middle crust of the eastern Tibetan plateau, high velocity featured as stable platform in the Tarim basin and the Yangtze platform, shallow and thick low-velocity-zone in the upper mantle of the North China. The upper mantle LVZ in the East China Sea and the Japan Sea is related to the frictional heat from the subduction of the Philippine slab and the strong extension since the Himalayan orogenic period.

A method for inversion of layered shear wavespeed azimuthal anisotropy from Rayleigh wave dispersion using the Neighborhood Algorithm

Seismic anisotropy provides important constraints on deformation patterns of Earth＇s material. Rayleigh wave dispersion data with azimuthal anisotropy can be used to invert for depth-dependent shear wavespeed azimuthal anisotropy, therefore reflecting depth-varying deformation patterns in the crust and upper mantle. In this study, we propose a two-step method that uses the Neighborhood Algorithm （NA） for the point-wise inversion of depth-dependent shear wavespeeds and azimuthal anisotropy from Rayleigh wave azimuthally anisotropic dispersion data. The first step employs the NA to estimate depth- dependent Vsv （or the elastic parameter L） as well as their uncertainties from the isotropic part Rayleigh wave dispersion data. In the second step, we first adopt a difference scheme to compute approximate Rayleigh-wave phase velocity sensitivity kernels to azimuthally anisotropic parameters with respect to the velocity model obtained in the first step. Then we perform the NA to estimate the azimuthally anisotropic parameters Gc/L and Gs/L at depths separately from the corresponding cosine and sine terms of the azimuthally anisotropic dispersion data. Finally, we compute the depth-dependent magnitude and fast polariza- tion azimuth of shear wavespeed azimuthal anisotropy. The use of the global search NA and Bayesian analysis allows for more reliable estimates of depth-dependent shear wavespeeds and azimuthal anisotropy as well as their uncertainties.We illustrate the inversion method using the azimuthally anisotropic dispersion data in SE Tibet, where we find apparent changes of fast axes of shear wavespeed azimuthal anisotropy between the crust and uppermost mantle.

The acoustoelastic effect on Rayleigh waves in elastic-plastic deformed layered rocks

On the basis of the acoustoelastic theory for elastic-plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect： the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic-plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.

Tunable topological interface states and resonance states of surface waves based on the shape memory alloy

Topological interface state(TIS)of elastic wave has attracted significant research interest due to its potential prospects in strengthening acoustic energy and enhancing the signal accuracy of damage identification and quantification.However,previous implementations on the interface modes of surface waves are limited to the non-adjustable frequency band and unalterable mode width.Here,we demonstrate the tunable TIS and topological resonance state(TRS)of Rayleigh wave by using a shape memory alloy(SMA)stubbed semi-infinite one-dimensional(1D)solid phononic crystals(PnCs),which simultaneously possesses the adjustable mode width.The mechanism of tunability stems from the phase transformation of the SMA between the martensite at low temperature and the austenite at high temperature.The tunable TIS of Rayleigh wave is realized by combining two bandgap-opened PnCs with different Zak phases.The TRS with adjustable mode width is achieved in the heterostructures by adding PnCs with Dirac point to the middle of two bandgap-opened PnCs with different Zak phases,which exhibits the extraordinary robustness in contrast to the ordinary Fabry–Perot resonance state.This research provides new possibilities for the highly adjustable Rayleigh wave manipulation and find promising applications such as tunable energy harvesters,wide-mode filters,and high-sensitivity Rayleigh wave detectors.

Numerical simulation for recognition of coalfield fire areas by Rayleigh waves

Effective recognition of a coalfield fire area improves fire-fighting efficiency and helps avoid potential geological hazards. Coalfield fire areas are hard to detect accurately using general geophysical methods. This paper describes simulations of shallow, buried coalfield fires based on real geological conditions. Recognizing the coalfield fire by Rayleigh wave is proposed. Four representative geological models are constructed, namely; the non-burning model, the pseudo-burning model, the real-burning model, and the hidden-burning model. Numerical simulation using these models shows many markedly different characteristics between them in terms of Rayleigh wave dispersion and Eigen displacement. These characteristics, as well as the shear wave velocity obtained by inverting the fundamental dispersion, make it possible to distinguish the type of the coalfield fire area and indentify the real and serious coalfield fire area. The results are very helpful for future application of Rayleigh waves for the detection of coalfield fire area.

Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects

This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most important features of nanostructures,surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions.Concrete expressions of the dispersion equation are derived,and numerical results are provided to examine the effects of several surface-related parameters,including the surface elasticity,surface piezoelectricity,surface dielectricity,surface density,as well as surface residual stress,on the dispersion modes and phase velocity.The size-dependent dispersion behaviors occurring with surface effects are also predicted,and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.

周期性堆载体Rayleigh波减振特性分析及试验研究

为了揭示周期性堆载体Rayleigh波的振动作用波特性,实现对低频表面波的有效衰减,研究了衰减域内的减振机理及效果。首先,构建传输模型,确定了合适的堆载几何尺寸。其次,基于复频散曲线和频域曲线,分析了堆载高度和弹性模量影响下振动波的作用规律及其衰减效果。最后,开展缩尺扫频试验,调取X、Z方向的加速度数据绘制频域曲线,并与复频散曲线做进一步对比分析,研究了各衰减域减振机理。结果表明:扫频试验结果出现了X、Z方向衰减域不一致的现象,不同方向的衰减域恰好与复频散曲线中的衰减域内作用波型一致,X方向会出现一个低频段衰减域,Z方向会在第2衰减域终止频率时出现衰减减弱趋势;进一步说明周期性堆载体可以激发出水平极化共振衰减域和Bragg散射衰减域;而高度是影响伪表面波的重要因素,表现为高度高,容易在第1衰减域内产生伪表面波,高度低,容易在第2衰减域内产生伪表面波;弹性模量是影响高速伪表面波的重要因素,表现为当其达到混凝土弹性模量单位数量级(10 GPa)时,第3衰减域可能会出现高速伪表面波作用范围,否则,将直接进入SV波和P波耦合作用的凋落波模态。研究结果将进一步启发环境隔振领域利用表面波阻块开展减振工作。

基于谱元法的Rayleigh波频散特征计算与模态叠加耦合机理研究

为了提升Rayleigh波勘探成层结构力学参数的精细化水平,基于谱元法,构建了弹性层状半无限结构的Rayleigh波频散方程。针对半无限土基和“上软下硬”这2种规则成层结构,运用谱元法与快速矢量传递法对比计算了Rayleigh波多阶模态的频散曲线。结果表明:谱元法与解析法计算结果之间的相对误差在0.05%以下,具有较高的计算精度。在此基础上,进一步针对“上硬下软”的典型路面结构、含“软夹层”和含“硬夹层”的复杂成层结构,结合谱元法,推导了表面位移的计算方法,通过分解Rayleigh波各模态相速度对表面位移能量的贡献,建立了一种基于谱元法确定复杂成层结构中Rayleigh波多模态叠加耦合机理的半解析方法,此方法确定的Rayleigh各阶模态叠加耦合频散特征与速度-应力有限差分方法仿真结果之间具有很好的吻合度,表明基于谱元法计算Rayleigh波频散曲线并以此揭示成层结构中Rayleigh波模态叠加耦合机理是合理、可行的。

EFFECTS OF A SLOPING THERMOCLINE AND RAYLEIGH FRICTION ON EQUATORIALLY TRAPPED KELVIN WAVES

Based on the observed equatorial ocean dynamic characteristics, the effects of a sloping thermocline and Rayleigh friction on the equatorially trapped free Kelvin waves were theoretically studied with a linear one and one half layer reduced gravity model, the multiple scale method and a small parameter expansion technique. Assuming that main thermocline depth (MTD) variations are slow, i.e. the changes of MTD over one wavelength are smaller than that of the wave amplitude and that wave reflections are negligible, the authors showed by their analytical results that the wavelengths and amplitudes of Kelvin waves are significantly modified by the MTD variations and Rayleigh friction. The results also showed that for an eastward shallowing thermocline, the zonal velocity of the Kelvin waves varies with thermocline depth to the power -7/8. The eastward shallowing of the thermocline depth strengthens Kelvin wave entrapment at the equator. Rayleigh friction reduces the Kelvin wave’s eastward velocity while the thermocline acts in the opposite way. The friction causes dispersion of the Kelvin wave, whose dissipation factor does not depend on its wavelength. The friction increases the lateral decay length and causes phase lines of Kelvin waves to slant westward in parabolic arcs.

Scattering of Rayleigh waves by a shallow circular alluvial valley: High-frequency solution

A high-frequency analytical solution for scattering of Rayleigh waves by a shallow circular alluvial valley was derived using wave function expansion method, and the solution was utilized to analyze the effects of incident frequency, width of the valley, and depth of the valley, etc, on the wave scattering. Numerical results showed that, because of the alluvial valley, the distribution of surface displacement at the side where wave arrives becomes relatively complicated, but the displacement amplitude is not large; the distribution of the surface displacement at far side is relatively simple, but the displacement amplitude is relatively large, and in most cases the amplitude is larger than that at the alluvium.

Phase velocity maps of Rayleigh waves in the Ordos block and adjacent regions

We analyze continuous waveform data from 257 broadband stations of the portable seismic array deployed under the "China Seismic Array-northern part of NS seismic belt" project as well as data from a permanent seismic network from January 2014 to December 2015. The phase velocity dispersion curve of 7,185 Rayleigh waves is obtained with a method based on the image analysis of phase velocity extraction, and the inversion is obtained. The period of Rayleigh wave phase velocity distribution has a range of 5–40 s, and minimum resolution close to 20 km. The results show that the phase velocity structure image well reflects the geological structural characteristics of the crust and uppermost mantle, and that the phase velocity distribution has obvious lateral heterogeneity. The phase velocity of the 5–15 s period is closely linked to the surface layer and sedimentary layer, the low-velocity anomalies correspond to loose sedimentary cover, and the high-velocity anomalies correspond to orogenic belts and uplifts and the boundary between high and low velocity anomalies is consistent with the block boundary. The phase velocity of the 5–15 s period is strongly affected by the crust layer thickness, the northeastern Tibetan plateau has low-velocity anomalies in the middle to lower crust, the west side of the Ordos block is consistent with the northeastern Tibetan plateau, which may imply the material exchange and fusion in this area. The velocity variation is inversely related to the Moho depth in the 40 s period of Swave, and the lateral velocity heterogeneity represents the lateral variation of the Moho depth. The Ordos block and the northern margin of Sichuan basin are located in the uppermost mantle at this depth, and the depth in the transition zone is still located in the lower crust.

Characterization of surface damage of a solid plate under tensile loading using nonlinear Rayleigh waves

This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesium alloy plate specimen.Rayleigh waves are generated and detected with wedge transducers,and the NPs are measured at different stress levels.The results show that there is a significant increase in the NPs with monotonic tensile loads surpassing the material’s yielding stress.The research suggests an effective nondestructive evaluation method to track the surface damage in metals.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave,also known as surface acoustic wave(SAW),solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth.Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation.A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates.It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius,confirming the existence of surface acoustic waves is irrelevant to coordinate system.On the other hand,the solutions can be treated as plane waves in regions far away from the source.Furthermore,the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.