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

Earthquake Science 2024年第1期37卷 13-35页

作者： Shaotong Wang Laiyu Lu The Institute of Geophysics China Earthquake AdministrationBeijing 100081China

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.

关键词： dispersion curve eigenvalue generalized reflection and transmission coefficient surface wave guide wave

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

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Earthquake Engineering and Engineering Vibration 2014年第1期13卷 13-21页

作者： Lu Jianqi Li Shanyou Li Wei Tang Lihua Key Laboratory of Earthquake Engineering and Engineering Vibration Institute of Engineering MechanicsChina Earthquake Administration Heilongjiang Provincial Water Conservancy Hydro Electric InvestigationDesign&Research Institute Earthquake Administration of Xinjiang Uyghur Autonomous Region

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.

关键词： damped least squares simulated annealing hybrid inversion dispersion curve Rayleigh wave

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

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Global Geology 2024年第1期27卷 56-62页

作者： ZHENG Chao WANG Yanlong ZHANG Baohui DU Lizhi College of Construction Engineering Jilin UniversityChangchun 130026China China Water Northeastern Investigation Design&Research Co.Ltd.Changchun 130021China Changchun Urban Investment Infrastructure Construction Project Management Consulting Co. LtdChangchun 130031China

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.

关键词： transient Rayleigh wave detection tunnel lining quality detection dispersion curve Rayleigh wave velocity profile

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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

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Earthquake Science 2023年第3期36卷 200-211页

作者： Si Chen Rui Gao Zhanwu Lu Yao Liang Wei Cai Lifu Cao Zilong Chen Guangwen Wang Institute of Geology Chinese Academy of Geological SciencesBeijing 100037China State Key Laboratory of Tibetan Plateau Earth System Environment and Resources(TPESER)Beijing 100101China SinoProbe Laboratory of Ministry of Natural Resources Beijing 100037China School of Earth Sciences and Engineering Sun Yat-Sen UniversityGuangzhou 510275China

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.

关键词： convolutional neural network ambient noise tomography dispersion curve

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Guided Wave Propagation in Multilayered Two-dimensional Quasicrystal Plates with Imperfect Interfaces

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Acta Mechanica Solida Sinica 2022年第4期35卷 694-704页

作者： Xin Feng Liangliang Zhang Zhiming Hu Han Zhang Yang Gao College of Science China Agricultural UniversityBeijing 100083China College of Engineering China Agricultural UniversityBeijing 100083China China State Key Laboratory of Acoustics Institute of AcousticsChinese Academy of SciencesBeijing 100190China

An analytical solution of the guided wave propagation in a multilayered twodimensional decagonal quasicrystal plate with imperfect interfaces is derived.According to the elastodynamic equations of quasicrystals(QCs),the wave propagating problem in the plate is converted into a linear control system by employing the state-vector approach,from which the general solutions of the extended displacements and stresses can be obtained,These solutions along the thickness direction are utilized to derive the propagator matrix which connects the physical variables on the lower and upper interfaces of each layer.The special spring model,which describes the discontinuity of the physical quantities across the interface,is introduced into the propagator relationship of the multilayered structure.The total propagator matrix can be used to propagate the solutions in each interface and each layer about the multilayered plate.In addition,the traction-free boundary condition on the top and bottom surfaces of the laminate is considered to obtain the dispersion equation of wave propagation,Finally,typical numerical examples are presented to illustrate the marked influences of stacking sequence and interface coeficients on the dispersion curves and displacement mode shapes of the QC laminates.

关键词： Two-dimensional QC materials Wave propagation dispersion curve State vector approach Propagator matrix Imperfect interface

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

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Applied Mathematics and Mechanics(English Edition) 2023年第12期44卷 2187-2206页

作者： Zinan ZHAO Nian LI Yilin QU Weiqiu CHEN Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province and Department of Engineering Mechanics Zhejiang UniversityHangzhou 310027China Huanjiang Laboratory Zhuji 311816Zhejiang ProvinceChina Suzhou HunterSun Electronics Co. Ltd.Suzhou 215124Jiangsu ProvinceChina School of Marine Science and Technology Northwestern Polytechnical UniversityXi’an 710072China

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.

关键词： AlN film mode flip frequency spectrum quantitative prediction(FSQP) dispersion curve mode-coupling vibration

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Effects of spatial aliasing on frequency wavenumber domain inversion of Rayleigh-wave dispersion curve

Effects of spatial aliasing on frequency wavenumber domain i...

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中国科学院地质与地球物理研究所2013年度（第13届）...

作者： Li Ziwei Liu Xuewei School of Geophysics and Information Technology China University of Geosciences(Beijing)

Near surface velocity structure and high-density structure profiles can be built by inverting the dispersion curve extracted from the Rayleigh-wave in seismic shot gathers.The accurate extraction of Rayleigh-wave dispersion curve can ensure the accuracy near surface structure inversion.However, spatial aliasing will affect dispersion curve extraction and the inversion of dispersion curve because of large receiver intervals in seismic shot gathers. Using a theoretical model,we find that the spatial aliasing causes high frequency information lack on the dispersion curve by large receiver intervals.We also find that high frequency dispersion curve is more sensitive to shear wave velocity of shallow layers.The joint inversion with the isopath layered and damped least squares is applied on both synthetic model and real data with different receiver intervals.Both of the tests demonstrate that the high frequency lack on dispersion curve increases the relative error of inversion,and harms the inversion stability due to the spatial aliasing.

关键词： Rayleigh-wave receiver interval spatial aliasing dispersion curve sensitivity

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Young's modulus determination of low-k porous films by wide-band DCC/LD LSAW

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Journal of Semiconductors 2011年第10期32卷 26-31页

作者：白茂森傅星 Dante Dorantes 金宝印胡小唐 State Key Laboratory of Precision Measuring Technology and Instruments School of Precision Instrument and Opto-Electronics EngineeringTianjin University

Low-k interconnection is one of the key concepts in the development of high-speed ultra-large-scale integrated（ULSI） circuits.To determine the Young＇s modulus of ultra thin,low hardness and fragile low-k porous films more accurately,a wideband differential confocal configured laser detected and laser-generated surface acoustic wave（DCC/LD LSAW） detection system is developed.Based on the light deflection sensitivity detection principle, with a novel differential confocal configuration,this DCC/LD LSAW system extends the traditional laser generated surface acoustic wave（LSAW） detection system＇s working frequency band,making the detected SAW signals less affected by the hard substrate and providing more information about the thin porous low-k film under test.Thus it has the ability to obtain more accurate measurement results.Its detecting principle is explained and a sample of porous silica film on Si（100） is tested.A procedure of fitting an experimental SAW dispersion curve with theoretical dispersion curves was carried out in the high frequency band newly achieved by the DCC/LD LSAW system.A comparison of the measurement results of the DCC/LD LSAW with those from the traditional LSAW shows that this newly developed DCC/LD LSAW can dramatically improve the Young＇s modulus measuring accuracy of such porous low-k films.

关键词： nano-porous low-k film surface acoustic wave differential confocal Young＇s modulus dispersion curve wide band

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

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Plasma Science and Technology 2017年第1期19卷 20-28页

作者：季曾超陈仕修高深 School of Electrical Engineering Wuhan University Wuhan 430072 People's Republic of China

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.

关键词： beam-plasma interaction dispersion relation dispersion curve wide band microwave radiation

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

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Chinese Physics B 2018年第9期27卷 457-461页

作者：肖夏孔涛戚海洋秦慧全 School of Microelectronic Tianjin Key Laboratory of Imaging and Sensing Microelectronic Technology Tianjin University

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.

关键词： thickness measurement dispersion curve surface acoustic waves layered structure

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