Phase Velocity Of Waves Research Articles

Transverse surface wave in non-planar layered nearly incompressible elastic structure having imperfect contact

The prime motive of the present work is to bring out the emphatic impacts of planar boundary and non-planar boundary as well as imperfectness of the interface on the displacement components and phase velocity of Love-type wave (LTW) propagating in the layered structure. The layered structure essentially incorporates two dissimilar nearly incompressible elastic materials bonded imperfectly to each other having non-planar boundaries at the free surface and at the common interface. A linear spring model has been adopted to describe the imperfect bonding at the interface. The solution methodology features the applicability of variable separable technique along with Taylor’s series expansion that leads to establish dispersion relation and displacement components of LTW. The displacement components and phase velocity of LTW have been numerically computed, and their dependence on wave number have been graphically manifested. As a special case of the study, the dispersion relations for incompressible and isotropic elastic layered structures have been deduced. A comparative analysis between compressible, nearly incompressible and incompressible layered structures comprised of Neo–Hookean material, and isotropic layered structure has been performed to trace out the impact of imperfect bonding parameter on the phase velocity of LTW. The established result of dispersion relation for the considered geometrical structure, as a particular deduction, concur well with the result present in the literature.

Effects of physical parameters on shear wave in a porous piezoelectric model with imperfect interface

This study investigates the impact of interfacial imperfection on shear horizontal wave propagation in a microstructural coupled stress half-space beneath a porous piezoelectric layer adjacent to air. The validity of dispersion relations is shown by deriving special cases and comparing them with the classical dispersion relation of Love wave. Furthermore, a comparative analysis has been conducted to analyze the effect of various parameters on the phase velocity of shear wave by considering perfect and imperfect interfaces under electrically open and short conditions. The findings provide a theoretical framework for developing and designing underwater acoustic devices for sensing and nondestructive testing.

Active Tunable Elastic Metasurface for Abnormal Flexural Wave Transmission

An active elastic metasurface has more flexibility than a passively modulated elastic metasurface, owing to the manipulation of the phase gradient that can be realized without changing the geometrical configuration. In this study, a negative proportional feedback control system was employed to provide positive active control stiffness for adaptive unit cells, with the aim of achieving the active modulation of the phase gradient. The relationship between the control gain and the phase velocity of the flexural wave was derived, and the transfer coefficients and phase shifts of the flexural wave through the adaptive unit cells were resolved using the transfer matrix method. Finite element simulations for wave propagations in the adaptive unit cells were conducted, and they verified the analytic solutions. Based on this theoretical and numerical work, we designed active elastic metasurfaces with adaptive unit cells with sub-wavelength thicknesses according to the generalized Snell’s law. These metasurfaces show flexibility in achieving abnormal functions for transmitted waves, including negative refraction and wave focusing, and transforming guided waves at different operating frequencies by manipulating the control gain. Therefore, the proposed active metasurface has great potential in the fields of the tunable manipulation of elastic waves and the design of smart devices.

On propagation behavior of shear wave in piezoelectric-sandwiched structure

This paper delves into the analysis of shear wave propagation with a sandwiched structure comprising a piezoelectric layer and an elastic layer, with a transversely isotropic layer in between. The frequency equation has been derived following Biot’s theory. The dimensionless phase velocities numerical values are computed and visually depicted to demonstrate their dependencies on anisotropy, piezoelectricity, initial stress and porosity in a comparative manner. The explicit demonstration of the relationship between each parameter and the geometry has been presented. The observation shows that as porosity in the medium increases, the phase velocity also increases. Furthermore, the existence of medium anisotropy results in a decrease in the phase velocity of shear waves. Moreover, a correlation is observed where higher tensile initial stress within the medium leads to a corresponding reduction in the phase velocity of shear waves. We conclude that considered parameters (viz. piezoelectricity, anisotropy, porosity, initial stress and thickness of layers) affect the velocity profile of the shear waves significantly. This study holds practical significance in the development of innovative-layered composites, surface acoustic wave (SAW) devices and sensors utilizing intelligent piezoelectric devices for engineering purposes.

Retrieval and precise phase-velocity estimation of Rayleigh waves by the spatial autocorrelation method between distributed acoustic sensing and seismometer data

Summary In distributed acoustic sensing (DAS), optical fibre is used as sensors, which enables us to observe strain over tens of kilometres at intervals of several metres. S-wave velocity (Vs) structures of shallow sediments of high resolution have been obtained from surface wave dispersion curves by applying seismic interferometry to DAS data both onshore and offshore. However, it is known that there is a disadvantage to DAS seismic interferometry. In addition to Rayleigh waves, Love waves are also included. Consequently, the accuracy of the estimated phase velocities for Rayleigh waves is reduced due to the contamination of Love waves. To address this shortcoming, we suggest a spatial autocorrelation (SPAC) method between DAS and the vertical component of seismometer data. The SPAC method is equivalent to seismic interferometry and is useful for obtaining phase velocity dispersion curves of surface waves from the cross-correlation functions (CCFs) between the records of two receivers. The CCFs obtained from a combination of DAS and vertical seismometer data should contain only Rayleigh waves because Love waves have no vertical component. CCFs between DAS and vertical seismometer data are therefore expected to give more accurate phase velocities of Rayleigh waves than CCFs with DAS data only. In this study, we first formulated analytical expressions of cross-spectra for DAS and three-component seismometer data because seismic observation is generally carried out using a three-component seismometer. A new SPAC method is presented in the form of analytical expressions. We showed that our formulation only includes Rayleigh and not Love waves in the cross-spectra with DAS and the vertical-component seismometer data. We applied our SPAC method to actual DAS and vertical seismometer data recorded on the seafloor. Then, we compared our new SPAC method for DAS and vertical seismometer data with a conventional SPAC method for only DAS data. The results reveal that our new SPAC method can estimate the phase velocities of Rayleigh waves more accurately than the conventional method. In addition, the analytical formulations of the cross-spectrum between DAS and three-component seismometer data, which we obtained in this study, are expected to be useful for the estimation of accurate three-dimensional structures in the future, although this is not available at the moment due to the lack of an applicable dataset.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

PurposeThis paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.Design/methodology/approachThe analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.FindingsComputational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.Research limitations/implicationsThe results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.Practical implicationsThis investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.Originality/valueThis study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

On the temperature sensitivity of near-surface seismic wave speeds: application to the Groningen region, the Netherlands

SUMMARY Subsurface temperature measurements play a crucial role, for instance, in optimizing geothermal power plants and monitoring heat-storage systems. Previous studies have demonstrated that time-lapse variations in temperature can be correlated with variations in seismic wave speeds, offering the potential for temperature monitoring via seismic surveys. However, an apparent discrepancy has emerged between field and laboratory experiments. Field studies predominantly report positive correlations between temperature and seismic wave speeds, while laboratory experiments often show anticorrelations. This inconsistency underscores the need for a more comprehensive, physics-based understanding of temperature-induced wave speed changes. In this study, we strive to bridge the gap between field and laboratory findings by examining several mechanisms governing temperature-induced seismic wave speed changes, namely the intrinsic temperature dependency of elastic parameters and thermally induced elasticity. We present a physics-based modelling approach to identify the primary mechanisms responsible for temperature-induced seismic wave speed changes. By considering several end-member models, we find that intrinsic temperature dependency of elastic parameters (negative correlation) compete with thermal pressure effects (positive correlation). The precise initial and boundary conditions and physical parameters of the system under consideration will determine the weight of both effects. Temperature-related dilatation does not seem to play an important role. We apply our approach to loosely consolidated sediments in the shallow subsurface of the Groningen region, where subsurface temperature fluctuations are driven by seasonal atmospheric temperature fluctuations roughly between −5 and $30\, ^\circ$C. For these models, we predict seasonal temperature-induced changes in body-wave speeds of up to 8 per cent in the first few metres of the subsurface, high-frequency (above 2 Hz) surface wave phase velocity variations in the range of 1–2 per cent, and relative changes in site amplification on the order of 4 per cent. These findings contribute to a more comprehensive understanding of the intricate relationship between temperature and near-surface seismic properties, offering insights for applications as subsurface temperature monitoring systems.

Along‐Strike Variations of Alaska Subduction Zone Structure and Hydration Determined From Amphibious Seismic Data

AbstractWe develop a 3‐D isotropic shear velocity model for the Alaska subduction zone using data from seafloor and land‐based seismographs to investigate along‐strike variations in structure. By applying ambient noise and teleseismic Helmholtz tomography, we derive Rayleigh wave group and phase velocity dispersion maps, then invert them for shear velocity structure using a Bayesian Monte Carlo algorithm. For land‐based stations, we perform a joint inversion of receiver functions and dispersion curves. The forearc crust is relatively thick (35–42 km) and has reduced lower crustal velocities beneath the Kodiak and Semidi segments, which may promote higher seismic coupling. Bristol Bay Basin crust is relatively thin and has a high‐velocity lower layer, suggesting a dense mafic lower crust emplaced by the rifting processes. The incoming plate shows low uppermost mantle velocities, indicating serpentinization. This hydration is more pronounced in the Shumagin segment, with greater velocity reduction extending to 18 ± 3 km depth, compared to the Semidi segment, showing smaller reductions extending to 14 ± 3 km depth. Our estimates of percent serpentinization from VS reduction and VP/VS are larger than those determined using VP reduction in prior studies, likely due to water in cracks affecting VS more than VP. Revised estimates of serpentinization show that more water subducts than previous studies, and that twice as much mantle water is subducted in the Shumagin segment compared to the Semidi segment. Together with estimates from other subduction zones, the results indicate a wide variation in subducted mantle water between different subduction segments.

Evaluation of Robustness of S-Transform Based Phase Velocity Estimation in Viscoelastic Phantoms and Renal Transplants.

Ultrasound shear wave elastography (SWE) methods are being used to differentiate healthy versus diseased tissue on the basis of their viscoelastic mechanical properties. Tissue viscoelasticity is often studied by analyzing shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. Recently, a unique approach using a generalized Stockwell transformation (GST-SFK) was proposed for the calculation of dispersion curves in viscoelastic media over expanded frequency band. In this work, the method's robustness was evaluated on data from five custom-made viscoelastic tissue-mimicking phantoms and sixty in vivo renal transplants. For each phantom, 15 shear wave motion data acquisitions were taken, while 10-13 acquisitions were acquired for renal transplants measured in the renal cortex. For each data-set mean and standard deviation (SD) of estimated phase velocity dispersion curves were studied. In addition, the viscoelastic parameters of the Zener model were examined, which were preceded by a convergence analysis. For viscoelastic phantoms scanned with a research ultrasound scanner, and for the in vivo renal transplants scanned with a clinical scanner, the decisive advantage of the GST-SFK method over the standard two-dimensional Fourier transform (2D-FT) method was shown. The GST-SFK method provided dispersion curve estimates with lower SD over a wider frequency band in comparison to the 2D-FT method. These advantages are relevant to the analysis of the mechanical properties of tissues in clinical practice to discriminate healthy from diseased tissue.

Broadband Love Wave Phase Velocity Maps Based on Modified Double‐Beamforming of Ambient Noise Cross‐Correlations

AbstractAmbient noise tomography has become a popular method in the past two decades to image the crust and uppermost mantle structure. To date, broadband Rayleigh wave signals can be obtained from ambient noise, which can be utilized to study the earth's interior structure from the surface down to ∼200–300 km depths. However, it is hard to extract intermediate‐ and long‐period (>50 s) Love wave signals from ambient noise using conventional data processing techniques for ambient noise. Array‐based data processing techniques can enhance weak signals. In this study, we adopt a modified algorithm of the double‐beamforming method to extract broadband Love wave signals from ambient noise. We validate the accuracy of the dispersion curves measured from our method by comparing them to those measured from the conventional method. Then, we use a finite frequency ambient noise tomography method to construct broadband Love wave phase velocity maps across the contiguous USA. These phase velocity maps are consistent with those obtained from conventional methods at short periods (<40 s). Finally, we analyze the resolution of our double‐beamforming method based on checkerboard tests and find that the resolution of phase velocity maps based on our method is close to the aperture of the subarrays used in our double‐beamforming method.

Depth of Sudden Velocity Changes Derived From Multi‐Mode Rayleigh Waves

AbstractTo integrate structural subsurface models and smooth seismic velocity models, they need to share common features and resolutions. Here, we propose a new approach, Depth Assessment from Rayleigh Wave Ellipticities (DARE), for estimating the depth of sudden velocity changes from ambient‐noise multi‐mode Rayleigh waves applicable to a wide range of frequencies. At frequencies where multi‐mode Rayleigh waves have an extremum in ellipticity, the phase velocity can be used to estimate the depth of sudden velocity changes. We test our approach theoretically, numerically, and on real data from two geothermal sites by extracting Rayleigh wave ellipticities and phase velocities from three‐component beamforming of ambient noise using the python code package B3AMpy. For a small‐scale array, our approach validates the depth of quaternary sediments predicted by geological models. For deeper velocity changes, high uncertainties remain but the general trend of inclining boundaries can be recovered well. We demonstrate that, if impedance contrasts are larger than three, our approach is valid for multiple layers, laterally heterogeneous models, and a wide range of Poisson ratios.

Resonant generation of propagating second-harmonic spin waves in nano-waveguides

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

Constraints on the Calibration of Borehole Volumetric Strainmeters Using Rayleigh Wave Vertical Seismic Acceleration

ABSTRACT To ensure the accuracy and reliability of crustal strain measurements requires in situ sensor calibration. In this study, a seismogeodetic approach for the calibration of volumetric strain is introduced. The protocol, which relies on the dilatational character of Rayleigh waves, combines observational and theoretical analyses based on the near-surface properties of the Rayleigh wave vertical seismic acceleration. The calibration coefficient is estimated for a Rayleigh wave dominant period of 15–20 s using strain data and strong-motion records of acceleration from 62 global events (Mw≥7). The approach shows a good agreement with tidal calibration estimates for a Poisson ratio of 0.22–0.27 and Rayleigh wave phase velocity of 3–4 km·s−1. The protocol is straightforward, it requires no sophisticated simulation but only the numerical comparison of a similarly located accelerometer, and offers an alternative or a complement to tidal calibration.

Supermirrors and spin wave amplifications

Superradiance, a phenomenon of multiple facets, normally occurs in classical/quantum physics under extreme conditions. Here, we present its manifestation in spin waves under a practical condition. We show that an interface between a current-free ferromagnetic region and a current-flow ferromagnetic region can be a spin wave supermirror whose reflection coefficient is larger than 1. The super-reflection is the consequence of current-induced spectrum inversion where phase and group velocities of spin waves are in the opposite directions. An incident spin wave activates a backward propagating refractive wave inside the current-flow region. The refractive spin wave re-enters the current-free region to constructively interfere with the reflective wave. It appears that the current-flow region coherently emits reflective waves, leading to a super-reflection. The process resembles superradiance of a spinning black hole through the Hawking radiation process or Dicke superradiance of cavity photons inside population inverted media.

FUNCTIONAL ASSESSMENT OF WAVE PROPAGATION IN IMPERFECT CYLINDER MATERIALS

This work provides a theoretical framework to investigate the shear wave propagation properties within an Electrostrictive cylindrical layered structure. The structure is made up of a concentric, Functionally Assessed Electrostrictive Material (FAEM) cylindrical layer of limited width and an inadequately bonded Electrostrictive material cylinder. The FAEM layer has a constant functional gradient in the radial direction, and flaws at the interface are taken seriously, mirroring actual circumstances involving structural and electrical degradation. The fundamental electromechanical connected Bessel's equations are used to simplify field differential equations by mathematical modifications. Relationships for shear wave propagation under electrically short and open circumstances are established analytically. The acquired findings are verified against predefined standards and a particular issue instance. The impact of variables on the phase velocity of shear waves, including functional range and imperfection parameters, is shown through numerical simulations and graphical displays. The research also establishes boundaries for electrically short and open circumstances, taking into account the shear defect that exists between the inner and outer cylindrical layers.

Modeling of shear horizontal waves propagation in magneto-electro-elastic substrate loaded with complex conductive fluid

In this study, the dissipation and dispersion of shear horizontal (SH) wave in magneto-electro-elastic (MEE) materials overlying an elastic half-space loaded with a complex conductive fluid have been investigated. The complex dispersive relation of SH waves for magnetic short and magnetic open cases has been derived using an exact analytical approach. The derived dispersive relations have been theoretically and graphically validated against previous work. The study explores the impact of geometrical parameters, frequency, conductivity, and permittivity of the complex conductive fluid on the phase velocity and attenuation of SH waves.

Metamaterial control of the surface acoustic wave streaming jet

The phenomenon of surface acoustic wave (SAW) streaming, where a streaming jet is created, occurs when an SAW propagating on the surface of a solid interacts with water, and underpins the increasingly important area of SAW microfluidics. A key characteristic of the streaming jet is the Rayleigh angle, i.e. the angle at which the jet is formed relative to the surface normal of the solid, which is determined by the ratio of the velocity of the acoustic wave in the fluid and in the solid. Although the ability to dynamically tune this angle would offer a novel tool for microfluidic control, the SAW velocity is normally fixed by the characteristics of the solid and liquid material properties. In this paper we show, using finite element method modelling, that changing the SAW Rayleigh wave phase velocity by patterning a metamaterial array, consisting of square annular holes, onto the surface of an SAW device can change the acoustic streaming Rayleigh angle by approximately a factor of two, in good agreement with calculations based on the change in velocity.

Characterization of relativistic electron bunch duration and traveling wave structure phase velocity based on momentum spectra measurements

The Accelerator Research Experiment at Sinbad (ARES) linac at DESY aims to generate and characterize ultrashort electron bunches (fs to sub-fs duration) with high momentum and arrival time stability for the purpose of applications related to accelerator research and development, e.g., development of advanced and compact diagnostics and accelerating structures, test of new accelerator components, medical applications studies, machine learning, etc. During its commissioning phase, the bunch duration characterization of the electron bunches generated at ARES has been performed with an rf-phasing technique relying on momentum spectra measurements, using only common accelerator elements (rf accelerating structures and magnetic spectrometers). The sensitivity of the method allowed highlighting different response times for Mo and Cs2Te cathodes. The measured electron bunch duration in a wide range of machine parameters shows excellent agreement overall with the simulation predictions, thus demonstrating a very good understanding of the ARES operation on the bunch duration aspect. The importance of a precise experimental determination of the phase velocity of the first traveling wave accelerating structure after the electron source, for which we propose a simple new beam-based method precise down to a variation of one part per ten thousand respective to the speed of light in vacuum, is emphasized for this purpose. A minimum bunch duration of 20 fs rms, resolution-limited by the space charge forces, is reported. This is, to the best of our knowledge, around 4 times shorter than what has been previously experimentally demonstrated based on rf-phasing techniques with a single rf structure. The present study constitutes a strong basis for future time characterization down to the sub-fs level at ARES, using dedicated X-band transverse deflecting structures. Published by the American Physical Society 2024

Relations between group, energy, and phase velocities of surface electromagnetic waves in half-infinite bianisotropic homogeneous media

Relations between group, energy, and phase velocities of surface electromagnetic waves in half-infinite bianisotropic homogeneous media

Novel techniques for in situ estimation of shear-wave velocity and damping ratio through MASW testing part II: a Monte Carlo algorithm for the joint inversion of phase velocity and phase attenuation

SUMMARY This paper deals with in situ characterization of the small-strain shear-wave velocity VS and damping ratio DS from an advanced interpretation of Multi-channel Analysis of Surface Waves (MASW) surveys. A new approach based on extracting Rayleigh wave data using the CFDBFa method has been discussed in the companion paper. This paper focuses on mapping the experimental Rayleigh wave phase velocity and attenuation into profiles of VS and DS versus depth, which is achieved through a joint inversion procedure. The joint inversion of phase velocity and attenuation data utilizes a newly developed Monte Carlo global search algorithm, which implements a smart sampling procedure. This scheme exploits the scaling properties of the solution of the Rayleigh eigenvalue problem to modify the trial earth models and improve the matching with the experimental data. Thus, a reliable result can be achieved with a limited number of trial ground models. The proposed algorithm is applied to the inversion of synthetic data and of experimental data collected at the Garner Valley Downhole Array site, as described in the companion paper. In general, inverted soil models exhibit well-defined VS profiles, whereas DS profiles are affected by larger uncertainties. Greater uncertainty in the inverted DS profiles is a direct result of higher variability in the experimental attenuation data, the limited wavelength range at which reliable values of attenuation parameters can be retrieved, and the sensitivity of attenuation data to both DS and VS. Nonetheless, the resulting inverted earth models agree well with alternative in situ estimates and geological data. The results stress the feasibility of retrieving both stiffness and attenuation parameters from active-source MASW testing and the effectiveness of extracting in situ damping ratio estimates from surface wave data.