Quality influencing factors of dispersion curves from short period dense arrays based on a convolutional neural network across the north section of the Xiaojiang fault area

The number of dispersion curves increases significantly when the scale of a short-period dense array increases.Owing to a substantial increase in data volume,it is important to quickly evaluate dispersion curve quality as well as select the available dispersion curve.Accordingly,this study quantitatively evaluated dispersion curve quality by training a convolutional neural network model for ambient noise tomography using a short-period dense array.The model can select high-quality dispersion curves that exhibit a≤10%difference between the results of manual screening and the proposed model.In addition,this study established a dispersion curve loss function by analyzing the quality of the dispersion curve and the corresponding influencing factors,thereby estimating the number of available dispersion curves for the existing observation systems.Furthermore,a Monte Carlo simulation experiment is used to illustrates the station-pair interval distance probability density function,which is independent of station number in the observational system with randomly deployed stations.The results suggested that the straight-line length should exceed 15 km to ensure that loss rate of dispersion curves remains<0.5,while maintaining the threshold ambient noise tomography accuracy within the study area.

A fast inversion method for ocean parameters based on dispersion curves with a single hydrophone

The dispersion characteristics of shallow water can be described by the dispersion curves,which contain substantial ocean parameter information.A fast ocean parameter inversion method based on dispersion curves with a single hydrophone is presented in this paper.The method is achieved through Bayesian theory.Several sets of dispersion curves extracted from measured data are used as the input function.The inversion is performed by matching a replica calculated with a dispersion formula.The bottom characteristics can be described by the bottom reflection phase shift parameter P.The propagation range and the depth can be inverted quickly when the seabed parameters are represented by on parameter P.The inversion results improve the inversion efficiency of the seabed parameters.Consequently,the inversion efficiency and accuracy are improved while the number of inversion parameters is decreased and the computational speed of replica is increased.The inversion results have lower error than the reference values,and the dispersion curves calculated with inversion parameters are also in good agreement with extracted curves from measured data;thus,the effectiveness of the inversion method is demonstrated.

Sequential Parameter Estimation Using Modal Dispersion Curves in Shallow Water

Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile（SSP） and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.

Effective Dispersion Curve and Pseudo Multimode Dispersion Curves for Rayleigh Wave

The hi-energy bands in the dispersion image are usually interpreted as the true dispersion phase velocities.However,the multiple dispersion modes of Rayleigh wave in layered media stack in space,producing the effective dispersion curve and the pseudo multimode dispersion curves in disper-sion image.The effective dispersion curve has the maximum energy with lower phase velocities than pseudo dispersion phase velocities,and thus is often misunderstood as the fundamental mode.Within the tolerable misfit,the effective dispersion curve can approach the true fundamental mode.Different from the true multimode dispersion curves,the pseudo multimode dispersion curves are related to the effective dispersion curve.A numerical model is adapted to simulate the true dispersion curves,effec-tive dispersion curve,and pseudo multimode dispersion curves.Their differences and mutual relations are demonstrated.

Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations

In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.

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.

Study on dispersion characteristics of terahertz waves in helical waveguides

Corresponding to the atmospheric transmission windows of the electromagnetic spectrum in the low terahertz range,the mode coupling and dispersion characteristics of two helically corrugated waveguides(HCW)in the frequency ranges of 90 GHz-100 GHz and 260 GHz-265 GHz are studied.Through analytic calculations and numerical simulations,dispersion curves and structural parameters of the two frequency ranges waveguides are obtained.A novel method was proposed to obtain the dispersion of the HCW from the eigenwave solution using a periodic boundary condition.The HCW in a frequency range of 90 GHz-100 GHz was fabricated and its dispersion performance was measured.By comparing the measured results with the theoretical and the simulated results,the validity of the analytical and simulation method is verified.Limited to our machining capability,the dispersion of the 260 GHz-265 GHz HCW was only simulated and calculated and it was found that the results agree well with each other.

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.

Geoacoustic Inversion Based on Modal Dispersion Curve for Range-Dependent Environment

A geoacoustic inversion method is proposed based on the modal dispersion curve of two-wideband explosive signals for range-dependent environment. It is applied to the wideband explosive sound source data from the South China Sea in 2012. The travel time differences of different modes at various frequencies and distances are extracted by warping transform. The mean bottom acoustic parameters are inverted by matching the theoretical modal time differences to that of the experimental data. The inversion results are validated by using other explosive signals at different distances.

Local Stress Measurement in Thin Aluminum Plates based on Zero-Group-Velocity Lamb mode

The stress state is critical to the reliability of structures,but existing ultrasonic methods are challenging to measure local stress.In this paper,zero-group-velocity(ZGV)Lamb mode was proposed to measure the local stress field in thin aluminum plates.The Lamb wave’s dispersive characteristics under initial stress were analyzed based on the FloquetBloch theory with Murnaghan hyperelastic material model.The obtained dispersion curves show that higher-order Lamb wave modes near the cut-off frequencies are sensitive to applied stress across the plate,indicating that the S1-ZGV mode has a rather high sensitivity to stress.Similar to conventional ultrasonic stress measurement,it is found that the frequency of the S1-ZGV mode changes near-linearly with the amplitude of applied stress.Numerical experiments were conducted to illustrate the feasibility of local stress measurement in a thin aluminum plate based on the S1-ZGV mode.Single and multiple localized stress fields were evaluated with the S1-ZGV method,and reconstructed results matched well with actual stress fields,proving that the ZGV Lamb wave method is a sensitive stress measurement technique in thin plates.

Novel mode-coupling vibrations of AlN thin film bulk acoustic resonator operating with thickness-extensional mode

The dispersion curves of bulk waves propagating in both AlN and ZnO film bulk acoustic resonators(FBARs)are presented to illustrate the mode flip of the thickness-extensional(TE)and 2nd thickness-shear(TSh2)modes.The frequency spectrum quantitative prediction(FSQP)method is used to solve the frequency spectra for predicting the coupling strength among the eigen-modes in AlN and ZnO FBARs.The results elaborate that the flip of the TE and TSh2 branches results in novel self-coupling vibration between the small-wavenumber TE and large-wavenumber TE modes,which has never been observed in the ZnO FBAR.Besides,the mode flip leads to the change in the relative positions of the frequency spectral curves about the TE cut-off frequency.The obtained frequency spectra can be used to predict the mode-coupling behaviors of the vibration modes in the AlN FBAR.The conclusions drawn from the results can help to distinguish the desirable operation modes of the AlN FBAR with very weak coupling strength from all vibration modes.

Properties of Ternary One Dimensional Plasma Photomic Crystals for an Obliquely Incident Electromagnetic Wave Considering the Effect of Collisions in Plasma Layers

An analytical study is presented on the modal dispersion characteristics, group velocity, and effective group, as well as the phase index of a ternary one dimensional plasma photonic crystal for an obliquely incident electromagnetic wave considering the effect of collisions in plasma layers. The dispersion relation is derived by using the transfer matrix method and the boundary conditions based on electromagnetic theory. The dispersion curves are plotted for both the normal photonic band gap structure and the absorption photonic band gap structure. It is found that the increase in the angle of incidence shifts the photonic band gap toward higher frequencies. Also, the cutoff frequency is independent of collisions.

Acoustoelastic effects on mode waves in a fluid-filled pressurized borehole in triaxially stressed formations

Based on the nonlinear theory of acoustoelasticity, considering the triaxial terrestrial stress, the fluid static pressure in the borehole and the fluid nonlinear effect jointly, the dispersion curves of the monopole Stoneley wave and dipole flexural wave prop- agating along the borehole axis in a homogeneous isotropic formation are investigated by using the perturbation method. The relation of the sensitivity coefficient and the velocity-stress coefficient to frequency are also analyzed. The results show that variations of the phase velocity dispersion curve are mainly affected by three sensitivity coefficients related to third-order elastic constant. The borehole stress concentration causes a split of the flexural waves and an intersection of the dispersion curves of the flexural waves polarized in directions parallel and normal to the uniaxial horizontal stress direction. The stress-induced formation anisotropy is only dependent on the horizontal deviatoric terrestrial stress and independent of the horizontal mean terrestrial stress, the superimposed stress and the fluid static pressure. The horizontal terrestrial stress ratio ranging from 0 to 1 reduces the stress-induced formation anisotropy. This makes the intersection of flexural wave dispersion curves not distinguishable. The effect of the fluid nonlinearity on the dispersion curve of the mode wave is small and can be ignored.

Thermodynamic properties of 3C-SiC

In the present paper, we report on the results of various thermodynamic properties of 3C-SiC at high pressure and temperature using first principles calculations. We use the plane-wave pseudopotential density functional theory as im- plemented in Quantum ESPRESSO code for calculating various cohesive properties in ambient condition. Further, ionic motion at a finite temperature is taken into account using the quasiharmonic Debye model. The calculated thermody- namic properties, phonon dispersion curves, and phonon densities of states at different temperatures and structural phase transitions at high pressures are found to be in good agreement with experimental and other theoretical results.

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave racliation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.

Application of passive source surface-wave method in site engineering seismic survey

Site engineering seismic survey provides basic data for seismic effect analysis. As an important parameter of soil, shear-wave velocity is usually obtained through wave velocity testing in borehole. In this paper, the passive source surface-wave method is introduced into the site engineering seismic survey and practically applied in an engineering site of Shijingshan District. By recording the ubiquitous weak vibration on the earth surface, extract the dispersion curve from the surface-wave components using the SPAC method and obtain the shear-wave velocity structure from inversion. Over the depth of 42 m under- ground, it totally consists of five layers with interface depth of 3.31, 4.50, 7.23, 17.41, and 42.00 m; and shear-wave velocity of 144.0, 198.3, 339.4, 744.2, and 903.7 m/s, respectively. The inversion result is used to evaluate site classification, determine the maximum shear modulus of soil, provide basis for further seismic hazard analysis and site assessment or site zoning, etc. The result shows that the passive source surface-wave method is feasible in the site engineering seismic survey and can replace boreholes,shorten survey period, and reduce engineering cost to some extent.

Nondestructive determination of film thickness with laser-induced surface acoustic waves

The application of surface acoustic waves（SAWs） for thickness measurement is presented. By studying the impact of film thickness h on the dispersion phenomenon of surface acoustic waves, a method for thickness determination based on theoretical dispersion curve v（ fh） and experimental dispersion curve v（ f） is developed. The method provides a series of thickness values at different frequencies f, and the mean value is considered as the final result of the measurement. The thicknesses of six interconnect films are determined by SAWs, and the results are compared with the manufacturer＇s data.The relative differences are in the range from 0.4% to 2.18%, which indicates that the surface acoustic wave technique is reliable and accurate in the nondestructive thickness determination for films. This method can be generally used for fast and direct determination of film thickness.

Mechanism analysis of radiation generated by the beam-plasma interaction in a vacuum diode

When we were studying the vacuum switch,we found that the vacuum diode can radiate a broadband microwave.The vacuum diode is comprised of a cathode with a trigger device and planar anode,there is not a metallic bellows waveguide structure in this device,so the radiation mechanism of the vacuum diode is different from the plasma filled microwave device.It is hard to completely imitate the theory of the plasma filled microwave device.This paper analyzes the breakdown process of the vacuum diode,establishes the mathematical model of the radiating microwave from the vacuum diode.Based on the analysis of the dispersion relation in the form of a refractive index,the electromagnetic waves generated in the vacuum diode will resonate.The included angle between the direction of the electromagnetic radiation and the initial motion direction of electron beam is 45 degrees.The paper isolates the electrostatic effect from the beam-plasma interaction when the electromagnetic radiation occurs.According to above analyses,the dispersion relations of radiation are obtained by solving the wave equation.The dispersion curves are also obtained based on the theoretical dispersion relations.The theoretical dispersion curves are consistent with the actual measurement time-frequency maps of the radiation.Theoretical deduction and experiments indicate that the reason for microwave radiating from the vacuum diode can be well explained by the interaction of the electron beam and magnetized plasma.

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.