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.

Rayleigh Waves Propagation in an Infinite Rotating Thermoelastic Cylinder

In this paper,we investigated the inuence of rotating half-space on the propagation of Rayleigh waves in a homogeneous isotropic,generalized thermo-elastic body,subject to the boundary conditions that the surface is traction free.In addition,it is subject to insulating thermal conduction.A general solution is obtained by using Lame’potential’s and Hankel transform.The dispersion equations has been derived separately for two types of Rayleigh wave propagation properties by solving the equations of motion with appropriate boundary conditions.It is observed that the rotation,frequency and r exert some influence in the homogeneous isotropic medium due to propagation of Rayleigh waves.The frequency equation has been derived of homogeneous properties by solving the equations of motion with appropriate boundary conditions.It has been found that the frequency equation of waves contains a term involving the rotating.Therefore,the phase velocity of Rayleigh waves changes with respect to this rotating.When the rotating vanishes,the derived frequency equation reduces to that obtained in classical generalized thermo-elastic case which includes the relaxation time of heat conduction.In order to illustrate the analytical development,the numerical solution is carried out and computer simulated results in respect of Rayleigh wave velocity and attenuation coefficient are presented graphysically.A comparative and remarkable study has been carried out through various graphs to deliberate the consequences of different parameter on the frequency equation.The obtained results can be very useful in the design and optimization of Rayleigh wave.

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.

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.

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.

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.

A comparative analysis of seismic response of shallow buried underground structure under incident P,SV and Rayleigh waves

In this study,A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P,SV and Rayleigh waves are established,based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input.After verifying the calculation accuracy,a comparative study on seismic response of a shallow-buried,double-deck,double-span subway station structure under incident P,SV and Rayleigh waves is conducted.The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves.The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves.At the bottom of the side wall,the top and bottom of the center pillar of the underground structure,the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close,and are significantly larger than the calculation result under the incidence of P wave.At the center of the side wall and the top floor of the structure,the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave.In addition,the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions,and the magnification effect in the vertical direction is more significant.Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves,sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.

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.

Rayleigh waves from correlation of seismic noise in Great Island of Tierra del Fuego,Argentina:Constraints on upper crustal structure

In this study, the ambient seismic noise cross-correlation technique is applied to estimate the upper structure of the crust beneath Great Island of Tierra del Fuego（TdF）, Argentina, by the analysis of shortperiod Rayleigh wave group velocities. The island, situated in the southernmost South America, is a key area of investigation among the interaction between the South American and Scotia plates and is considered as a very seismically active one. Through cross-correlating the vertical components of ambient seismic noise registered at four broadband stations in TdF, we were able to extract Rayleigh waves which were used to estimate group velocities in the period band of 2.5-16 s using a timefrequency analysis. Although ambient noise sources are distributed in homogeneously, robust empirical Green＇s functions could be recovered from the cross-correlation of 12 months of ambient noise, The observed group velocities were inverted considering a non-linear iterative damped least-squares inversion procedure and several 1-D shear wave velocity models of the upper crust were obtained.According to the inversion results, the S-wave velocity ranges between 1.75 and 3,7 km/s in the first10 km of crust, depending on the pair of stations considered. These results are in agreement to the major known surface and sub-surface geological and tectonic features known in the area. This study represents the first ambient seismic noise analysis in TdF in order to constraint the upper crust beneath this region.It can also be considered as a successful feasibility study for future analyses with a denser station deployment for a more detailed imaging of structure.

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.

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.

Dispersive behavior of high frequency Rayleigh waves propagating on an elastic half space

When the wavelength of Rayleigh wave is comparable with nanometers,Rayleigh wave will become dispersive.Such an interesting phenomenon cannot be predicted by the classical theory of elastodynamics.In order to reveal the internal mechanism and influencing factors of the dispersion,a model of Rayleigh wave propagating on an elastic half space is established and analyzed by a new theory of surface elastodynamics,in which the surface effect characterized by both the surface energy density and surface inertia is introduced.Two intrinsic nano-length scales,including the ratio of bulk surface energy density to bulk shear modulus and the ratio of surface mass density to bulk mass density,are achieved.It is found that when the wavelength of Rayleigh wave is comparable with the two intrinsic nano-lengths,the surface effect becomes significant.As a result,dispersion of Rayleigh wave happens and even two Rayleigh waves with different wave speeds may appear.Furthermore,it is found that the effect of surface energy density would enhance the wave speed,while that of surface inertia would reduce it.With the increase of wavelength,both effects gradually disappear and the Rayleigh wave speed degenerates to the classical one.The results of this paper are not only helpful to understand the dispersive mechanism of elastic waves,but also helpful for the fine design and measurement of nanowave devices.

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.

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.

Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation

The simulation of Rayleigh waves is important in a variety of geophysical applications.The computational challenge is the fact that very fine mesh is necessary as the waves are concentrated at the free surface and decay exponentially away from the free surface.To overcome this challenge and to develop a robust high order scheme for the simulation of Rayleigh waves,we develop a mortar discontinuous Galerkin method with staggered hybridization.The use of the mortar technique allows one to use fine mesh in only a local region near the free surface,and use coarse mesh in most of the domain.This approach reduces the computational cost significantly.The staggered hybridization allows the preservation of the strong symmetry of the stress tensor without complicated construction of basis functions.In particular,the basis functions are piecewise polynomial without any continuity requirement,and the coupling of the basis functions is performed by using carefully chosen hybridized variables.The resulting scheme is explicit in time,and only local saddle point system are solved for each time step.We will present several benchmark problems to demonstrate the performance of the proposed method.

REFLECTION AND TRANSMISSION OF OBLIQUELY INCIDENT RAYLEIGH SURFACE WAVES BY A VISCOELASTIC INTERPHASE

The reflection and transmission of obliquely incident Rayleighsurface waves by an in- terphase between two quarter spaces ofidentical or different materials, have been investigated. Themechanical behavior of the interphase is represented by a thinviscoelastic layer. By using the full space Green's functions due toa spatially harmonic line load, the mathematical statement of the3-dimen- sion problem is reduced to a 2-dimension system of singularintegral equations. The far-field behavior of the scattered wavesleads to the definition of reflection and transmission coefficients,R and T.

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.

Propagation of waves in an electro-microstretch generalized thermoelastic semi-space

The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed： （i） reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and （ii） propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case （i）, the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case （ii）, the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plot- ted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.

Modeling of Rayleigh wave dispersion in Iberia

Phase and group velocities of 15-70 s Rayleigh waves propagating across the Iberian Penin- sula have been transformed into local dispersion curves by linear inversion of travel times. The procedure permits that the waveform dispersion to be obtained as a continuous period-dependent velocity function at grid points belonging to the area probed by the waves, thus providing phase- and group-velocity contour maps for several periods within the interval of interest. The regionalization process rests on a homoge- neous initial data set in which the number of observations remains almost constant for all periods of reference. Damped least-squares inversion of the local dispersion curves for shear-wave velocity structure is performed to obtain depth-dependent S-wave velocity profiles at the grid points covering the model region. The reliability of the results should improve significantly owing to the use of phase and group velocities simultaneously. On this basis, we have built horizontal depth sections that give an updated view of the seismic velocity structure of the peninsula at lithospheric and upper mantle depths （20--200 km）. After averaging all the pure-path S-wave velocities previously determined at each grid point, the velocity- depth models so obtained for major tectonic units allow the comparison between the Hercynian basement and other areas of Mesozoic folding and Tertiary hasins