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.

Characteristics of dispersion curves for Love channel waves in transversely isotropic media

Coal seams have a pronounced bedding structure with developed cracks and exhibit signifi cant anisotropy.However,few studies have examined the frequency dispersion properties of channel waves in anisotropic coal seams.In this study,numerical solutions are calculated using the generalized reflection–transmission coefficient method for the dispersion curves of Love channel waves in vertical transversely isotropic(VTI)and horizontal transversely isotropic(HTI)medium models.Moreover,the frequency dispersion characteristics of Love channel waves in several typical transversely isotropic models are analyzed.We fi nd that the dispersion curves for isotropic and VTI media diff er signifi cantly.In addition,the phase and Airy-phase velocities in VTI media are higher than those in isotropic media.Thus,neglecting this difference in practical channel wave detection will result in large detection errors.The dispersion curves for the isotropic and HTI media do not differ signifi cantly,and the Airy-phase velocities of various modes are similar.The group-velocity curve for a coal seam model containing a dirt band is found to be extremely irregular.The fundamental-mode Airy phase is not pronounced,but the fi rst-mode Airy phase can be clearly observed.Hence,fi rst-mode channel waves are suitable for detecting dirt bands.

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.

Investigating Stability Properties for Transition Metal Carbonate Precursors Using Universal Cluster Expansion Technique(UNCLE)as Cathodes for Li-Ion Batteries

The universal cluster expansion technique was used in this study to determine the binary phase diagrams for the transition metal carbonate precursors MCO3(M:Mn,Ni,Co).The use of mixed cathode materials in lithium-ion batteries such as NMC(Ni,Mn and Co)formulations,is a strategic approach to optimize performance,enhance safety and address cost and environmental considerations in the rapidly evolving field of energy storage.This study focuses on the cost issue related to lithium ion batteries by investigating the manganese rich NMC since manganese is more abundant and cost-effective.We doped MnCO3 with nickel and doped MnCO3 with cobalt then ran cluster expansion calculations to generate binary phases.The binary phase diagrams generated indicated that doping MnCO3 with nickel favours the Mn-rich side,while doping MnCO3 with cobalt favours 50%Mn-rich and 50%Co-rich.We further extracted the most stable structures from both binary diagrams and determined their electronic,mechanical and vibrational stabilities using DFT(density functional theory)calculations within the LDA(local gradient approximation)with Hubbard parameter(U).The electronic properties revealed that both materials are semiconductors due to their narrow energy band gap obtained while the mechanical properties showed that structures are mechanically stable since their necessary conditions for trigonal and triclinic systems were satisfied.

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.

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.

Electron Dispersion in Liquid Alkali and Their Alloys

Ashcroft＇s local empty core （EMC） model pseudopotential in the second-order perturbation theory is used to study the electron dispersion relation, the Fermi energy, and deviation in the Fermi energy from free electron value for the liquid alkali metals and their equiatomic binary alloys for the first time. In the present computation, the use of pseudo-alloy-atom model （PAA） is proposed and found successful. The influence of the six different forms of the local field correction functions proposed by Hartree （H）, Vashishta Singwi （VS）, Taylor （T）, lehimaru-Utsumi （IU）, Farid et al. （F）, and Sarkar et al. （S） on the aforesaid electronic properties is examined explicitly, which reflects the varying effects of screening. The depth of the negative hump in the electron dispersion of liquid alkalis decreases in the order Li --→ K, except for Rb and Cs, it increases. The results of alloys are in predictive nature.

Processing Seismic Ambient Noise Data to Obtain Reliable Surface Wave Dispersion Measurements

Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing and its development history over the past several years, with the intention to explain and justify this development through salient examples. The ambient noise data processing procedure can be divided into four principal phases： ① single station data preparation; ② cross- correlation and temporal stacking; ③ measurements of dispersion curves （ performed with frequency-time analysis for both group and phase speeds） ; ④ quality control, including SNR analysis and selection of the acceptable measurements. In addition, we provide a specific solution for a better use of the seismic station data to ambient noise study.

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.

Studies on phase and group velocities from acoustic logging

It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence （STC） method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.

Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm （SFLA）, into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

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.

2.5D boundary element simulation of wave propagation in a vertical fluid-filled borehole with irregular shape

In this paper, a boundary element formulation in the wave-number space domain for solving the wave equation for a borehole with arbitrary shape in acoustic logging problems is presented. The problem is treated as a two-dimensional medium with the discrete wave- number method in the vertical direction. The method is validated by comparing the results obtained by this method with those obtained by the finite-difference method. The method is used to study the effect on wave propagation in a vertical borehole of a vertical fracture. For a monopole source, the dispersion curves for Stoneley waves yield three branches. For dipole and quadrupole sources, different orientations of the source yield different results. When the dipole source is orthogonal to the fracture, the dispersion curve is similar to that of the open hole, while the curves are quite different when the source is parallel to the fracture. These characteristics enable us to determine the orientation of the vertical fracture.