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.

An analytical study on the Rayleigh wave generation in a stratified structure

In this paper,an analytical method is used to investigate the Rayleigh wave generation in a stratified structure and the wave generation in a dry sandy layer constrained between the couple stress and inhomogeneous orthotropic half-spaces.This study is devoted to analyzing the impact of various effective parameters associated with the media on the phase velocities of the wave.The displacement components for each medium are derived by implementing the separable variable method.The frequency equa-tion is secured by using the displacement components in the boundary conditions,imposed at the interfaces between the layer and half-spaces.Moreover,the secured equation is the relation between the phase velocity and the wave number.Numerical computations are performed,and graphical representations are demonstrated between the phase velocity and the wave number for both phase velocities with different values of the parameters.The comparison between the phase velocities is observed for the same value of each pa-rameter.

All-parameters Rayleigh wave inversion

Since S-wave velocity of the subsurface is an important parameter in near surface applications,many studies have been conducted for its estimation.Among the various methods that use surface waves or body waves,Rayleigh wave inversion is the most popular.In practice,the densities and P-wave velocities of different layers are usually assumed to be known to avoid ill-posed problems,as they have less influence on the dispersion curves.However,improper assignment of these two groups of parameters leads to inaccurate estimation of the S-wave velocity profile.In order to address this problem,the all-parameters Rayleigh wave inversion strategy is proposed in which the S-wave velocities,layer thicknesses,densities and P-wave velocities of different layers are included as the unknown parameters for inversion.Meanwhile,the transitional Markov Chain Monte Carlo(TMCMC)algorithm is applied for the implementation of all-parameters Rayleigh wave inversion.One simulated example and two real-test applications are demonstrated to verify the capability of the proposed method in the estimation of the S-wave velocity profile,the densities and the P-wave velocities.Furthermore,it is verified that the proposed method achieved more accurate S-wave velocity profile estimation than the traditional approach.

Generalized Rayleigh Wave Dispersion in a Covered Half-space Made of Viscoelastic Materials

Dispersion of the generalized Rayleigh waves propagating in a covered halfspace made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity.The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration.Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time,long-term values and the mechanical behaviour of the viscoelastic material around the initial state of the deformation.Numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov.As the result of this discussion,in particular,how the rheological parameters influence the dispersion of the generalized Rayleigh waves propagating in the covered half-space under consideration is established.

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.

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 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.

Bayesian Rayleigh wave inversion with an unknown number of layers

Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.

Effect of lateral heterogeneity on 2-D Rayleigh wave ZH ratio sensitivity kernels based on the adjoint method: Synthetic and inversion examples

The ratio between vertical and radial amplitudes of Rayleigh waves(hereafter,the Rayleigh wave ZH ratio)is an important parameter used to constrain structures beneath seismic stations.Some previous studies have explored crust and upper mantle structures by joint inversion of the Rayleigh wave ZH ratio and surface wave dispersion.However,all these studies have used a 1-D depth sensitivity kernel,and this kernel may lack precision when the structure varies a great deal laterally.Here,we present a systematic investigation of the two-dimensional(2-D)Rayleigh wave ZH ratio kernel based on the adjoint-wavefield method and perform two synthetic tests using the new kernel.The 2-D ZH ratio kernel is consistent with the traditional 1-D sensitivity kernel but has an asymmetric pattern with a preferred orientation toward the source.The predominant effect caused by heterogeneity can clearly be seen from kernels calculated from models with 2-D heterogeneities,which confirms the necessity of using the new 2-D kernel in some complex regions.Inversion tests using synthetic data show that the 2-D ZH ratio kernel has the potential to resolve small anomalies as well as complex lateral structures.

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.

Application of artificial bee colony algorithm in Rayleigh wave inversion

In order to solve the problems of multi-parameter,multi-extreme and multi-solution in the nonlinear iterative optimization process of Rayleigh wave inversion,the artificial bee colony(ABC)algorithm is selected for global nonlinear inversion.The global nonlinear inversion method does not rely on a strict initial model and does not need to calculate the derivative of the objective function.The ABC algorithm uses the local optimization behavior of each individual artificial bee to finally highlight the global optimal value in the colony,and the convergence speed is faster.While searching for the global optimal solution,an effective local search can also be performed to ensure the reliability of the inversion results.This paper uses the ABC algorithm to perform Rayleigh wave dispersion inversion on the actual seismic data to obtain a clear undergrounding of shear wave velocity profile and accurately identify the location of the high-velocity interlayer.It is verified that the ABC algorithm used in the inversion of the Rayleigh wave dispersion curve is stable and converges quickly.

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 buried underground structures, Rayleigh waves can be the key factor to control the responses and damage of the structure.

High-resolution Rayleigh wave phase velocity maps from ambient noise tomography in North China

We presented high-resolution Rayleigh wave phase velocity maps at periods ranging from 5 s to 30 s in the northeast part of the North China Craton (NNCC). Continuous time-series of vertical component between October 2006 and December 2008, recorded by 187 broadband stations temporarily deployed in the NNCC region, have been cross-correlated to obtain estimated fundamental mode Rayleigh wave Green’s functions. Using the frequency and time analysis technique based on continuous wavelet transformation, we measured 3 667 Rayleigh wave phase velocity dispersion curves. High-resolution phase velocity maps at periods of 5, 10, 20 and 30 s were reconstructed with grid size 0.25°× 0.25°, which reveal lateral heterogeneity of shear wave structure in the crust and upper mantle of NNCC. For periods shorter than 10 s, the phase velocity variations are well correlated with the principal geological units in the NNCC, with low-speed anomalies corresponding to the major sedimentary basins and high-speed anomalies coinciding with the main mountain ranges. Within the period range from 20 s to 30 s, high phase velocity observed in eastern NCC is coincident with the thin crust, whereas low phase velocities imaged in central NCC is correlated to the thick crust. However, the low-velocity anomaly in the Beijing-Tianjin-Tangshan region displayed in the 20 s and 30 s phase maps may be associated with fluids.

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((54(N, 70(~140(E 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 30(N, 38(N, 90(E and 120(E, 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.

Stepwise joint inversion of surface wave dispersion,Rayleigh wave ZH ratio,and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio(i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity(v_S) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast(e.g., due to the existence of crustal interfaces) and v_P/v_S ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the v_S model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute v_S model and then incorporate receiver function data in the joint inversion to obtain a finer v_S model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal v_S structures and with little initial model dependency.

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 depthdependent 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 polarization 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.

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.

Methods to increase the depth and precision of transient Rayleigh wave exploration

In order to increase the exploration depth of Rayleigh wave, new idea that dif-ferent from the former principles in data acquisition was applied. Suitable data acquisition parameter was given out on the basis of large amount of experiments. By reducing the group interval, the low frequency signal are enhanced instead of been attenuated. Fur-thermore, to solve the problem that the precision of Rayleigh wave exploration method count much to the signal-to-noise ratio, some preprocessing methods were put forward. By using zero shift rectifying, digital F-K filtering and cutting, noises can be effectively eliminated.

Modeling of Rayleigh wave dispersion in Iberia

越过伊比利亚人半岛宣传的 1570 个 s 瑞利波浪的阶段和组速度被旅行时间的线性倒置转变了成本地分散曲线。在格子作为连续时期依赖者速度功能要获得的波形分散削尖属于区域的过程许可证在兴趣的间隔以内为几个时期由波浪，因此提供的阶段速度和组速度轮廓地图探查了。区域化进程在观察的数字为引用的所有时期在仍然保持几乎不变的一个同类的起始的数据集合上休息。为砍波浪速度结构的本地分散曲线的抑制最少平方的倒置被执行在盖住模型区域的格子点获得深度依赖者 S 波浪速度侧面。结果的可靠性应该同时由于阶段和组速度的使用显著地改善。在这个基础上，我们造了在 lithospheric 和上面的披风深度(20200 km ) 给半岛的地震速度结构的一个更新的看法的水平深度节。在平均以前在每个格子点决定的所有纯路径的 S 波浪速度以后，速度深度当模特儿因此获得因为主要构造单位允许在 Hercynian 地下室和中生代合拢和第三级的盆的另外的区域之间的比较。