Rayleigh Wave Attenuation Research Articles

Estimation of dispersion and attenuation of Rayleigh waves in viscoelastic inhomogeneous layered half-space based on spectral method

Estimation of dispersion and attenuation of Rayleigh waves in viscoelastic inhomogeneous layered half-space based on spectral method

Simulation study of Rayleigh wave inspection of subsurface white etching crack in bearing rollers

Abstract Rolling bearings are widely used in wind energy and electric vehicle industries. One of the premature failure mode due to the contact fatigue is White Etching Crack (WEC) in the subsurface. WEC occurs preferentially in the Hertzian contact region of bearings, preferentially around multi-phase inclusions containing aluminium, manganese, and sulfur. The formation process undergoes intense plastic deformation and recrystallization. Most of WECs are 100~300 μm below the contact surface in a butterfly shape. Its principal axis is 30°~50° to the rolling direction. Since the sample preparation is difficult, this simulation study enables to better understand the interaction between WEC and ultrasonic waves for a better measurement system design. Rayleigh surface wave penetrates to a depth of about an order of magnitude of one wavelength. Its energy is concentrated near the surface containing rich WEC information. The Rayleigh wave propagation process is first analyzed based on the grain scale model established. Then the immersion inspection of WEC is simulated based on the finite element method at 15 MHz in order to compromise between the detection accuracy and defect depth. Finally, by analyzing the time and frequency domain information of the scattered signals, the quantitative relationships between crack characteristics (depth, length and tilt angle) and those of Rayleigh waves (amplitude and attenuation) can be obtained. This study paves the way for the quantitatively characterization of WEC in bearing rollers with surface integrity evaluation possibility at early stage.

Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation

Novel Multi-Vibration Resonator with Wide Low-Frequency Bandgap for Rayleigh Waves Attenuation

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Metamaterial design enabling simultaneous manipulation of Rayleigh and Love waves

Studies on elastic metamaterials have expanded from manipulating bulk waves to surface waves, aiming to control the propagation of in-plane Rayleigh waves or anti-plane Love waves. Considering the coexistence of Rayleigh and Love waves in various scenarios, the objective of this study is to develop a metamaterial capable of simultaneously manipulating both types of waves. The proposed metamaterial consists of horizontal resonators with an oblique mounting angle relative to the wave propagation direction, as well as vertical resonators. Initially, analytical solutions for the dispersion of surface waves are derived, followed by Finite Element (FE) simulations to validate the analytically predicted dispersion and illustrate the corresponding wave modes, as well as the in-plane and out-of-plane displacement fields at specified frequencies. The present study reveals that the mounting angle of the horizontal resonators plays a crucial role in surface wave manipulation. By adjusting the mounting angle, three distinct objectives can be achieved: (i) the attenuation of Rayleigh waves alone; (ii) the independent attenuation of Rayleigh and Love waves, targeting different frequency ranges; and (iii) the simultaneous attenuation of both Rayleigh and Love waves.

Split-type seismic metamaterials with pseudo-surface wave weakening mechanism

Pseudo surface waves, as a type of propagating wave, are detrimental to the attenuation of seismic Rayleigh waves. A split seismic metamaterial (SSM) that can weaken pseudo surface wave modes and generate ultra wideband gaps of 12.92Hz is proposed. The split configuration of SSM can be obtained by separating the modes of different waves within the energy band curve, which can cause the surface waves inside the sound cone to move outward and weaken the pseudo surface wave modes inside the band gap. Combined with the frequency response curve, it is further demonstrated that the attenuation amplitude of SSM is larger than that of monolithic seismic metamaterials (MSM) within the same bandgap range. Afterwards, by studying the changes in bandgap through structural parameters, the method of a gradient array was used to fuse the characteristic frequency that can generate larger attenuation with the weakened pseudo surface wave mode frequency, resulting in greater attenuation. Finally, it is verified by experiments that SSM can provide ultra-wide low-frequency band gaps while also generating large attenuation accuracy, which provides a practical solution for the application of seismic metamaterials.

Rayleigh waves in viscoelastic piezoelectric half-space with cladding structures: An analytic Legendre-Laguerre polynomial method

Piezoelectric materials are widely used in surface acoustic wave devices. Many piezoelectric materials themselves have viscoelastic properties, and their surface wave characteristics, especially the attenuation characteristics still needs to be explored. This article proposes a Legendre-Laguerre orthogonal polynomial method to solve the Rayleigh wave problems in a viscoelastic piezoelectric half space with a covering layer. The proposed method compensates for the inherent shortcomings of traditional Laguerre polynomials in solving layered half spaces: the normal stress and electric displacement are discontinuous. The correctness of the method was verified through literature comparison and finite element simulation. At the same time, by utilizing the orthogonality of the Legendre-Laguerre polynomial, the integral analytical formula encountered in the solution process is derived, which improves the computational efficiency by more than ten times. Through the analysis and discussion of the dispersion and attenuation curves, it is found that the piezoelectric effect can suppress the attenuation of Rayleigh waves; the piezoelectric and viscous properties of the covering layer mainly affect attenuation at high frequencies, while those of the half space layer mainly affect attenuation at low frequencies of high-order modes.

Comparison of Near-Surface Attenuation from Surface Array-Based Seismic Noise Data and Borehole Weak-Motion Recordings at the STIN Test Site in Northeastern Italy

Abstract Seismic wave attenuation and the related shear-wave quality factor (QS) in the near surface are crucial parameters for ground motion simulations and seismic hazard assessments. Although recent approaches developed to calculate QS from seismic noise acquired by surface arrays have been accepted for practice, additional testing and comparison of results estimated using various geophysical methods are still necessary to verify the reliability of such techniques. This work presents the results of an experiment conducted at the STIN site in northeastern Italy, which is equipped with a 100 m deep instrumented borehole. A seismic noise campaign was implemented by installing a temporary independent local surface array of seismological stations. The gathered data were used to initially estimate the shear-wave velocity (VS) profile and frequency-dependent Rayleigh-wave attenuation, and subsequently determine the QS factor via a linearized inversion method. The study compares these findings with the VS and QS values derived from analyzing weak-motion events recorded by two permanent seismic sensors positioned at the top and bottom of the well. The results confirm the potential of the inversion procedure used to obtain QS from local-scale seismic noise arrays as a promising approach for conducting attenuation studies at the local level in less geologically complex sites.

Rayleigh wave attenuation tomography based on ambient noise interferometry: methods and an application to Northeast China

SUMMARY Although ambient noise interferometry has been extensively utilized for seismic velocity tomography, its application in retrieving attenuation remains limited. This study presents a comprehensive workflow for extracting Rayleigh wave amplitude and attenuation from ambient noise, which consists of three phases: (1) retrieval of empirical Green's functions (EGFs), (2) selection and correction of amplitude measurements and (3) inversion of attenuation, site amplification and noise intensity terms. Throughout these processes, an ‘asynchronous’ temporal flattening method is used to generate high-quality EGFs while preserving relative amplitudes between stations. Additionally, a novel ‘t-symmetry’ criterion is proposed for data selection along with the signal-to-noise ratio. Furthermore, 2-D sensitivity kernels are utilized to estimate the focusing/defocusing effect, which is then corrected in amplitude measurements. These procedures are designed to deliver reliable attenuation measurements while maintaining flexibility and automation. To validate the effectiveness of the proposed noise-based attenuation tomography approach, we apply it to a linear array, NCISP-6, located in NE China. The obtained results correlate reasonably well with known geological structures. Specifically, at short periods, high attenuation anomalies delineate the location of major sedimentary basins and faults; while at longer periods, a notable rapid increase of attenuation is observed beneath the Moho discontinuity. Given that attenuation measurements are more sensitive to porosity, defect concentration, temperature, melt and volatile ratio than seismic velocities, noise-based attenuation tomography provides important additional constraints for exploring the crustal and upper mantle structures.

Global Rayleigh Wave Attenuation and Group Velocity from International Seismological Centre Data

This paper presents a study of global Rayleigh wave attenuation and group velocity at a period of around 20 s using data from the International Seismological Centre (ISC) bulletin. Rayleigh waves at this period are sensitive to the crustal structure beneath continents and the uppermost mantle beneath oceans. Tomographic imaging reveals strong continental-ocean contrasts due to this. Oceanic group velocities are high but vary with seafloor depth, while oceanic attenuation shows mid-ocean ridges. Subduction zone regions display high attenuation but little velocity reduction, indicating scattering attenuation. Low attenuation regions are associated with the Earth’s major cratonic regions, but there are no associated velocity changes. This implies that intrinsic attenuation is low and scattering dominates. Cratonic crustal scatterers have been annealed. A new surface wave magnitude scale is constructed that is valid from near-source to near-antipode distances.

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.

Novel techniques for in situ estimation of shear-wave velocity and damping ratio through MASW testing – I: a beamforming procedure for extracting Rayleigh-wave phase velocity and phase attenuation

SUMMARY A robust, in situ estimate of shear-wave velocity VS and the small-strain damping ratio DS (or equivalently, the quality factor QS) is crucial for the design of buildings and geotechnical systems subjected to vibrations or earthquake ground shaking. A promising technique for simultaneously obtaining both VS and DS relies on the Multichannel Analysis of Surface Waves (MASW) method. MASW can be used to extract the Rayleigh wave phase velocity and phase attenuation data from active-source seismic traces recorded along linear arrays. Then, these data can be inverted to obtain VS and DS profiles. This paper introduces two novel methodologies for extracting the phase velocity and attenuation data. These new approaches are based on an extension of the beamforming technique which can be combined with a modal filter to isolate different Rayleigh propagation modes. Thus, the techniques return reliable phase velocity and attenuation estimates even in the presence of a multimode wavefield, which is typical of complex stratigraphic conditions. The reliability and effectiveness of the proposed approaches are assessed on a suite of synthetic wavefields and on experimental data collected at the Garner Valley Downhole Array and Mirandola sites. The results reveal that, under proper modelling of wavefield conditions, accurate estimates of Rayleigh wave phase velocity and attenuation can be extracted from active-source MASW wavefields over a broad frequency range. Eventually, the estimation of soil mechanical parameters also requires a robust inversion procedure to map the experimental Rayleigh wave parameters into soil models describing VS and DS with depth. The simultaneous inversion of phase velocity and attenuation data is discussed in detail in the companion paper.

Pine-like elastic metamaterials for urban seismic Rayleigh wave attenuation

Preventing urban regions from seismic wave destruction is of paramount significance because it is closely related to urban lifeline and prosperity of cities. Almost all conventional seismic resistance approaches rely on the stiffness and strength of buildings, which require excessive structural components with additional self-weights. In this study, we propose a pine-like seismic metamaterial for efficient attenuation of surface Rayleigh waves. The pine arrays in suburban regions demonstrate an ability to convert Rayleigh waves to shear bulk waves or attenuate waves on the surface via local resonation. This property originates from a gradient design of pine arrays, where a scale ratio is defined to tune the geometric properties of each pine unit. Specifically, a gradient pine array with a scale ratio smaller than one can interact with the Rayleigh waves and convert them to shear waves that propagate deep to underground. The transmission ratio of the entire system indicates a broadband wave attenuation at subwavelength scale. It reveals that the pine is able to couple with a certain elastic Rayleigh wave whose wavelength is much larger than the lattice constant, which is rarely achieved in any conventional civil engineering structures such as open trench barriers and filled trench barriers. Additionally, a numerical model of an urban region and suburban pine array is established and analyzed. Infrastructures and structures in a city that suffer direct Rayleigh wave interference run into a high risk of structural destruction as compared to urban structures protected with suburban metamaterial pine arrays. Finally, two real earthquake wave signals are used to validate the efficiency of the pine arrays in dissipating earthquake energy. The approach in this paper can be extended to deal with more complex naturally available structures for examining the elastic wave attenuation abilities of these novel structures.

Attenuation of Rayleigh and pseudo surface waves in saturated soil by seismic metamaterials

Seismic metamaterials have received extensive research interest due to their bandgap properties, simplicity in design principles, and stability in response. They have been developed to protect buildings or architectures susceptible to damage from surface elastic waves. In practice, the ground soil is generally a multiphase medium, and the influence of its permeability and viscosity on seismic metamaterials is not yet clear. In this work, we developed a formulation that combines Biot’s theory and Bloch-Floquet theorem to investigate the complex band structures and transmission properties of Rayleigh and pseudo surface waves (PSWs) for pillared and inclusion-embedded seismic metamaterials in saturated soil. It is shown that the ratio of fluid viscosity and permeability η/κ have an impact on the surface wave attenuation and the performances of seismic metamaterials, where the smaller ratio benefits the surface wave broadband attenuation and metamaterials attenuating effects. The complex band structures reveal that inclusion-embedded metamaterials can support the propagation of PSWs having a phase velocity higher than that of the transverse bulk waves. The PSWs are significantly affected by the rubber viscosity due to the mode displacements concentrated in the rubber coatings. The higher viscosity of metamaterials also allows for broadband attenuation of Rayleigh surface waves. The results of this study will present an appropriate way to design viscoelastic seismic metamaterials in saturated soil for low-frequency surface wave attenuation.

A novel buried periodic in-filled pipe barrier for Rayleigh wave attenuation: Numerical simulation, experiment and applications

Surface wave is a major concern in ambient vibration mitigation. To this end, a novel shallow buried periodic in-filled pipe barrier is proposed. Complex dispersion analysis is conduced to evaluate the decay of surface waves and the influence of material damping. Through a combination of numerical simulations and lab-scale experiments, the effectiveness and robustness of surface wave attenuation are verified. Result shows that the proposed periodic in-filled barrier exhibits excellent performance in low-frequency surface wave attenuation. Both the energy dissipation induced by material damping and local resonance of in-filled pipes contribute to surface wave attenuation. The influence of viscosity also enhances wave attenuation and it should be taken into full account in practice. In addition, these novel wave barriers are suitable for passive isolation as well as active isolation. To further widen the attenuation zones, the gradient layouts of in-filled pipes could be a good alternative considering the limited barrier width. Besides, the feasibility of periodic in-filled barriers to train-induced vibration mitigation is preliminary verified by analyzing the measured acceleration record in the time-domain. Thanks to the subwavelength size and shallow depth, these novel wave barriers are convenient for construction and cost-effective, thus showing great potential in ambient vibration mitigation.

Low-frequency and wide bandgap seismic metamaterials for Rayleigh wave attenuation

This study introducesa seismic metamaterial (SM) for mitigating low-frequency seismic Rayleigh waves when embedded in the ground.. Dispersion curves and vibration modes of a unit cell incorporatingthe SM were calculated using the Bloch theorem and sound cone method in a numerical model. The lowest frequency of the bandgaps (BGs) is 1.6 Hz, with the maximum absolute bandwidth reaching 18 Hz, matching the seismic wave considered in this study. Furthermore, a comprehensive analysis of vibrational modes revealed the mechanism responsible for BG formation. Numerical simulations in both the time and frequency domains confirmed the attenuation of Rayleigh waves by finite models containing SMs, along with theconversion of Rayleigh waves into body waves. Additionally, the effects of material and geometric parameters on BG frequency range is discussed. Complex SM structures were devised by combining two distinct SMs with varying geometric parameters, achieving a complete broadband attenuation range. Finally, realistic seismic Rayleigh wave propagation through complex SMs was simulated, conclusively validating their effectiveness in providing broadband attenuation.

Attenuation of Rayleigh waves due to three-dimensional surface roughness: A comprehensive numerical evaluation.

The phenomenon of Rayleigh wave attenuation due to surface roughness has been well studied theoretically in the literature. Three scattering regimes describing it have been identified-the Rayleigh (long wavelength), stochastic (medium wavelength), and geometric (short wavelength)-with the attenuation coefficient exhibiting a different behavior in each. Here, in an extension to our previous work, we gain further insight with regard to the existing theory, in three dimensions, using finite element (FE) modeling, under a unified approach, where the same FE modeling techniques are used regardless of the scattering regime. We demonstrate good agreement between our FE results and the theory in all scattering regimes. Additionally, following this demonstration, we extend the results to cases that lie outside the limits of validity of the theory.

Rayleigh Wave Attenuation by a Nonlinear Metasurface with Both Vertical and Horizontal Resonators

It is well known that earthquakes are one of the most catastrophic geological disasters. In recent years, the use of metasurfaces to suppress the propagation of seismic surface waves to protect surface buildings has received extensive attention. However, most of the previous research works are on linear metasurfaces and the effect of vertical resonators. In this work, we propose a nonlinear metasurface, which consists of a linear elastic semi-infinite space with vertical nonlinear and horizontal linear resonators attached to its top surface. Our study shows that the interaction between the dynamics of the resonators and the waves of the semi-infinite space creates a hybrid Rayleigh wave propagating along the surface. First, the dispersion of the hybrid Rayleigh wave is derived analytically. Then, numerical calculations are conducted and the effect of the coupling of the vertical and horizontal resonators on the dispersion is discussed. Afterward, a finite-element simulation is performed to verify the analytical predictions. The results demonstrate that an ultra-wide bandgap for the hybrid Rayleigh wave can be achieved by the designed nonlinear metasurface. This work may help promote the application of metasurfaces in the field of earthquake protection.

Acoustoelectric Effect for Rayleigh Wave in ZnO Produced by an Inhomogeneous In-Depth Electrical Conductivity Profile.

The acousto-electric (AE) effect associated with the propagation of the Rayleigh wave in ZnO half-space was theoretically investigated by studying the changes in wave velocity and propagation loss induced by in-depth inhomogeneous changes in the ZnO electrical conductivity. An exponentially decaying profile for the electrical conductivity was attributed to the ZnO half-space, for some values of the exponential decay constant (from 100 to 500 nm), in order to simulate the photoconductivity effect induced by ultra-violet illumination. The calculated Rayleigh wave velocity and attenuation vs. ZnO conductivity curves have the form of a double-relaxation response as opposed to the single-relaxation response which characterizes the well-known AE effect due to surface conductivity changes onto piezoelectric media. As to the author's knowledge, this is the first time the double-relaxation AE effect has been theoretically predicted.

Broadband Rayleigh wave attenuation utilizing an inertant seismic metamaterial

In this work, a concept of constructing inertant seismic metamaterials for Rayleigh wave attenuation using inerter-based vibration absorbers (IDVAs) is proposed. The dynamic behaviors of the vibration absorbers are controlled by an inertant mechanical network, while three typical oscillator configurations are considered in the design of the proposed inertant seismic metamaterial. An expanded effective medium method is developed to obtain the dispersion of Rayleigh waves, which is separated into three branches by two broad Rayleigh wave band gaps at low frequencies. The influences of the inertance-to-mass ratio as well as the stiffness ratio on the Rayleigh wave propagation are thoroughly discussed. The results show that the multiple-resonance IDVAs can efficiently open low frequency band gaps of the inertant seismic metamaterial without having to increase the mass of the resonators. Band gaps of the low-frequency Rayleigh waves can be further merged to form an extra wide one by adding dissipative mechanisms, which further enhance the attenuation of the Rayleigh waves. Specifically, by analyzing the corresponding displacement fields, it is observed that the seismic energy propagating as Rayleigh surface waves is converted to that propagating as bulk waves not concentrated to the surface, which offers a protected area behind the inertant seismic metamaterials for the facilities located at the surface of the half space. This work provides a new approach for seismic vibration isolations utilizing inertant seismic metamaterials that can be applied in protecting large infrastructures or civil engineering architectures.