Surface Wave Attenuation Research Articles

Seismic metamaterial surface for broadband Rayleigh waves attenuation

Elastic metamaterials (EMMs) have been widely studied owing to their advantages in controlling the propagation of elastic waves. In the past decade, considerable efforts have been made to attenuate Rayleigh waves using EMMs. However, the complex nonlinear behaviour of soil renders the realisation of existing EMMs challenging in practical engineering. To overcome this limitation, we present a new seismic metamaterial surface (SMMS) to isolate Rayleigh waves over a broad frequency range of 3.2–19.2 Hz. First, we discuss the propagation velocity of Rayleigh waves in EMMs and determine a reasonable design range for the effective dynamic material properties of the SMMS for seismic surface wave attenuation. Then, we construct a unit cell and demonstrate that these properties, both in band gaps and negative bands, lie within this specified design range. The negative bands are initially introduced into Rayleigh wave mitigation. Finally, a new type of SMMS is presented and validated using numerical results and scaled experiments. The results show that the vertical deformation on the surface can be decreased by more than 96 %. The findings reported here open new avenues for protecting engineering structures from low-frequency seismic vibrations.

Influence of boundary conditions on acoustic emission propagation characteristics of Zelkova schneideriana

To study the propagation characteristics of acoustic emission signals in Zelkova schneideriana under different boundary conditions, three types of boundary conditions were generated by applying aluminum plates and sound-absorbing cotton on the surface of Zelkova schneideriana specimens. Firstly, the sudden and continuous acoustic emission (AE) sources were simulated by PLB (pencil–lead break) tests and signal generator on the specimen surface, and the AE signals were collected by 5 sensors equally spaced on the surface of the specimen, and the sampling frequency was set to 500 kHz. Then, the detailed signals of different frequency bands were obtained by wavelet decomposition, and TDOA (the time difference of arrival) and correlation analysis method were used to calculate the time difference of longitudinal wave and surface transverse wave and the corresponding propagation velocity, respectively. Finally, the pulse trains with different energy levels generated by the signal generator were used as AE sources to study the attenuation law of AE signal energy with distance under different boundary conditions. The results show that the boundary changes can lead to a significant increase in the surface transverse wave velocity, and have no significant effect on the longitudinal wave velocity. At the same time, the energy attenuation of surface and longitudinal waves is faster after the aluminum plate and sound-absorbing cotton are affixed, and the distance of longitudinal waves attenuation to 90% is reduced from 186 to 139 mm, and the distance of surface transverse waves propagation is reduced from 312 to 226 mm.

Forest trees as a natural metamaterial for surface wave attenuation in stratified soils

Forest trees have been shown to act as a natural metamaterial to attenuate elastic waves. However, the existing studies assumed that forest trees are located on homogeneous soils and did not consider the soil stratification that widely exists in natural strata. This study investigates the forest trees as a natural metamaterial to manipulate the propagation of elastic waves in stratified soils. A semi-analytical method is proposed to calculate the dynamic responses of a layered half-space coupled with arbitrary number of trees. A close-form Green’s function for a harmonic line load on a layered half-space is derived by the thin layer method, and subsequently used to determine the multiple scattered wavefield induced by forest trees as surface oscillators. The attenuation performance of forest trees on stratified soils is systematically investigated. Trees with a graded array of heights can provide a wide attenuation zone at frequencies below 80 Hz. Since the higher surface wave modes in a layered half-space can propagate forward without being affected by trees, the attenuation efficiency of trees on stratified soils is significantly lower than that of trees on corresponding homogeneous soils. The performance uncertainty induced by the randomness of the height, sizes, and spacing of trees is subsequently investigated through a Monte Carlo simulation. The forest trees can still obtain a significant attenuation efficiency at frequencies below 80 Hz even the randomness of tree properties being considered. The randomness in height and radius leads to significant uncertainty in attenuation performance, while the randomness in spacing results in reasonable uncertainty.

Surface wave attenuation by periodic hollow steel trenches with Bragg band gap and local resonance band gap

The use of phononic crystals and elastic metamaterials has been a significant concern as an efficient approach to attenuate the surface waves of ambient vibration and seismic vibration. In previous research, elastic metamaterials with periodic array of pillars or other forms of standing structures (such as H-fractal steel or built-up structural steel) erected on soil substrate can achieve a low frequency surface wave band gap (BG). However, such metamaterials with standing structures occupy land and affect the esthetics of cities, and buried metamaterials such as cross-like-cavity or hollow-cylinder structures with large size in soils necessitate continual maintenance for the stability of cavity soil structure. Thus, this study proposes two types of periodic hollow steel trenches exhibiting both a Bragg BG and a local resonance BG, the steel plates are used to support the soil on both sides of the trench to meet the stability requirements of cavity soil structure and avoid toppling or landslide of soils. The dispersion relations of periodic hollow steel trenches are calculated by using finite element method and the mechanism of generation for two kinds of BGs are interpreted by the eigenmodes. Furthermore, the effectiveness of periodic hollow steel trenches on isolating surface waves within the BGs is demonstrated in both frequency domain and time domain analysis. Several significant geometrical and material parameters on BGs that can affect the BG are studied as well. This study provides a new approach using the coupling effects of Bragg BG and local resonance BG to simultaneously attenuate the surface waves induced by the ambient and seismic vibration in a more practical way.

The 3D conical Radon transform for seismic signal processing

Recently, the attenuation of highly aliased broadband surface waves has received significant attention as their high-frequency and low-speed components render f- k x- k y filters ineffective. As a popular tool widely used in seismic signal processing, the 3D linear Radon ([Formula: see text]) transform does not match the surface wave events in the time domain. This leads to the dispersal of energy over ellipses on the zero-intercept slice, whereas the reflected events over the ellipses are reflected on each intercept slice of the 3D linear Radon transform (LRT) domain, decreasing the resolution in slowness. We have introduced a new type of Radon transform defined on circular cones called 3D conical Radon transform (CRT) for seismic signal processing. Unlike LRT, the CRT maps seismic data to surface integrals on circular cones in the 3D seismic records. Consequently, surface wave events are focused as points on the zero-intercept slice, whereas the reflected events are points on each intercept slice of the CRT domain, which significantly improves the resolution in slowness compared with the LRT. We determine the performance of the CRT for seismic signal processing for random noise attenuation, primary and multiple separations, and surface wave attenuation. Based on a comparison with the LRT, synthetic data and field data sets validate the effectiveness of the CRT method at improving the focusing properties.

Application of passive seismic interferometry for mapping mining waste storage facilities: A case study of Pyhäsalmi mine in Finland

Obtaining knowledge about the structural, geotechnical and hydrogeological conditions of mining waste storage facilities (e.g., tailing storage facilities, TSF) is an important task for mining waste management. From the existing applied geophysics techniques, high-resolution controlled source seismic methods are the most appropriate due to their superior spatial and depth resolution. However, the TSF areas are not often accessible for installation of seismic instruments and application of controlled source. Moreover, TSF areas in active mine sites are characterised by high-level of seismic and acoustic noise, produced by mining operations and other human activities at mine sites. In this study, we show that these problems can be addressed by utilizing passive seismic interferometry, in which cross-correlation of ambient seismic noise is used to obtain the Empirical Green's function (EGF's) of the studied medium. We used this method to evaluate seismic velocities in the TSF and in the near-surface bedrock at the site of the Pyhäsalmi underground mine in Finland. We used the ambient seismic noise recorded in two seismic experiments in the area. In the first experiment, the data were acquired in 2013 along a line 10 km long crossing the area of the underground mine. The second experiment was carried out in the TSF area in 2019. We obtained S-wave velocity models of both bedrock and the TSF by applying multichannel analysis of surface waves (MASW) to surface wave parts of Empirical Green's Functions (EGFs). The analysis of autocorrelation functions of passive seismic data recorded on the TSF surface allowed to us retrieve reflected arrivals from the boundaries inside the TSF. At the same time, we used amplitudes of surface wave parts of EGF's to obtain information about attenuation of surface waves in TSF. Our results show that passive seismic interferometry and interpretation of passive seismic data by different techniques can be a useful tool for inspection of TSF of active mines

The effect of viscosity of saturated soil on the surface wave attenuation by periodic in-filled trench

Investigations on the ambient vibration reduction by periodic wave barriers have been received more and more attention in recent years. However, the role of energy dissipation caused by the viscosity of soil is usually ignored in most of the previous studies. The surface wave attenuation in saturated viscoelastic soil by periodic in-filled trench is investigated in this study. Firstly, the constitutive model of saturated viscoelastic soil is constructed by introducing Kelvin viscoelastic model into the Biot's theory. Secondly, the complex band structure of surface waves propagating in periodic in-filled trench is calculated. A finite model for analyzing ambient vibration isolation is built, and the responses of the site under external excitation are numerically solved both in frequency domain and time domain. The roles of the viscosity of soil and the periodic barrier in the surface wave attenuation are comprehensively discussed, and some findings are obtained. Soil's viscosity reinforces the attenuation when the frequencies of surface waves fall in the attenuation zone. However, the contribution of the viscosity is not obvious. Contrary to the attenuation zone, soil's viscosity plays a key role in the attenuation when the frequencies of surface waves are out of the attenuation zone.

Seismic surface wave attenuation by resonant metasurfaces on stratified soil

AbstractThis study aims to theoretically and numerically investigate the dispersion relations of Rayleigh waves propagating through vertical oscillators periodically distributed on stratified media. The classical elastodynamics theory and an effective medium approximation method are adopted to describe the dynamic behavior of metasurfaces and hybridization between the local oscillators and the foundational surface wave modes. The Abo‐zena algorithm and delta‐matrix method are combined to simplify the Eigen equation to overcome the accuracy problem in solving the closed‐form dispersion laws and improve the computational efficiency. Subsequently, plane‐strain finite element (FE) models with three configurations are developed to confirm the analytical predictions and obtain further insight into the resonator‐Rayleigh wave coupling mechanism. The numerical results are in good agreement with the analytical solutions, revealing that only the foundational mode is strongly coupled with the vertical resonators at resonance, while the surface wave band gap reported in homogeneous media is crossed by the remaining higher‐order surface modes. The attenuation performance and mechanical behavior of a finite‐length metasurface are investigated, and it is demonstrated that the output surface ground motion can be significantly reduced in a narrow frequency band near resonance. Moreover, a graded resonant metasurface with decreasing frequency is simulated to assess the feasibility of broadband attenuation. In summary, the aforementioned analytical framework and numerical simulation results show that the vertical oscillators placed atop a stratified soil system can be designed as resonant metasurfaces for shielding seismic surface waves to protect multiple large infrastructures or special structures from earthquake hazards.

Forest Trees as a Natural Metamaterial for Surface Wave Attenuation in Stratified Soils

Forest Trees as a Natural Metamaterial for Surface Wave Attenuation in Stratified Soils

Terraced slopes as large scale natural seismic metasurfaces

In this work, a new type of metasurface which could be applied for surface waves attenuation is numerically examined. Terraced slopes are examined numerically for their applicability of attenuating surface waves. The calculations were performed by using the finite element method. The research includes an investigation for all the geometric parameters of the structure, and how its performance as a metasurface is being affected by the values of each parameter. The proposed terraced slopes can be found in many places either as a natural morphology of the ground or, in most cases, as an artificial ground formation. The findings of this work strongly indicate that the morphology of the sloped surface is fundamental regarding its potential of performing as a large-scale natural metasurface.

The surface wave attenuation zone of periodic composite in-filled trenches and its isolation performance in train-induced ground vibration isolation

The mitigation of surface wave is the primary concern in ground vibration isolation due to the energy of wave propagation in the soil being concentrated in the surface wave. Herein, a composite in-filled trench composed of expanded polystyrene (EPS) and concrete was proposed and arranged as a periodic structure. The surface wave attenuation zone of the proposed periodic composite in-filled trenches and its application to the isolation of train-induced ground vibration were investigated in this paper. A field test of ground vibration induced by an elevated intercity railway was conducted in order to obtain acceleration data and their corresponding dominate frequencies. Then, a two-dimensional finite element mode using COMSOL was developed to reveal the dispersion relationship and attenuation zones of the surface wave in layered ground. The influence of the different parameters of the periodic composite in-filled trenches on the reduction performance of train-induced ground vibration was analyzed numerically. The results indicate that an effective reduction performance of the proposed periodic composite in-filled trenches can be achieved when their attenuation zone coincides with the frequencies of the surface waves. Moreover, the proposed composite periodic structure illustrated an improvement in ground vibration isolation compared to periodic in-filled trenches comprising concrete or EPS only.

Assessment of small-strain characteristics for vibration predictions in a Swedish clay deposit

Environmental vibrations induced by human activities such as traffic, construction or industrial manufacturing can cause disturbance among residents or to vibration sensitive equipment in buildings. In Sweden, geological formations of soft clay overlying a stiff bedrock are soil conditions prone to ground vibrations that are encountered both in urban areas and along parts of the national railway network. This paper presents an extensive investigation of the small-strain soil properties for the prediction of environmental ground vibrations in a shallow clay where the bedrock is situated at 7.5 m depth. The small-strain properties are estimated using available empirical correlations, bender elements, seismic cone penetration tests, seismic refraction and inversion of surface wave dispersion and attenuation curves. The results are synthesised into a dynamic layered soil model which is validated by measurements at the soil's surface at source-receiver distances up to 90 m in the frequency range 1–80 Hz. Analyses of uncertainties in the estimated values of wave speeds and material damping are performed by model investigations, indicating that surface wave tests overestimate the damping compared to bender element tests. The properties of the topmost unsaturated part of the soil is found to have a significant influence on the response at large distances, caused by critically refracted P-waves resonating in the top layer.

Propagation and attenuation of Rayleigh and pseudo surface waves in viscoelastic metamaterials

The development of seismic metamaterials has attracted much research interest in the past decade. Efforts have been made by using experimental and theoretical approaches to isolate buildings and structures susceptible to elastic surface wave damage. However, most seismic metamaterials were designed without considering the viscoelastic effect that widely exists in nature. In this work, we investigate the propagation and attenuation of the Rayleigh and pseudo surface waves (PSWs) in two types of viscoelastic seismic metamaterials, namely, pillared and inclusion-embedded metamaterials, by analyzing the complex band structures and transmission spectra. The complex band structure developed in this work reveals for the first time the existence of PSWs and their propagation properties in inclusion-embedded metamaterials at the surface. These PSW modes are hidden in the traditional ω(k) technique, therefore showing the usefulness of the complex band structure approach. Introducing viscosity to the substrate of both types of seismic metamaterials will enhance the attenuation of both the Rayleigh wave and PSW. For inclusion-embedded metamaterials, the viscoelastic effect in the soft coating layer can have a specific influence only on the PSW. PSWs show advantages to minimize the relative attenuating effect in general. The results in this work will open up great possibilities for designing and optimizing seismic metamaterials in practice.

Diagnostics of Reinforcement Conditions in Concrete Structures by GPR, Impact-Echo Method and Metal Magnetic Memory Method

It is important to use adequately reliable non-destructive methods that would be capable of determining the reinforcement conditions in concrete structures. Three different methods: ground penetrating radar, impact-echo method, and metal magnetic memory method were used for testing laboratory-prepared reinforced concrete beams (with a reinforcing bar of the same diameter along its whole length, reinforcing bar locally impaired, and reinforcing bar interrupted). The ground-penetrating radar proved the correlation of signal parameters with the reinforcing bar condition. An impairment/interruption reinforcing bar appeared in the record from measurements in the transversal and longitudinal direction by changes of the observed depth of the reinforcing bar from the concrete surface and direct wave attenuation. The impact-echo method proved that the shifts of the dominant frequencies from the response signal correspond with the impairment/interruption of the reinforcing bar. Results of diagnostics by the metal magnetic memory method were presented by a magnetogram of the magnetic field strength and field gradient on the measured distance. The changes in the magnetic field strength proved different stress concentration zones due to the reinforcing bar condition. The used non-destructive methods showed that they are capable of indicating the different reinforcement conditions in reinforced concrete beams. This paper indicates in which cases and for what reason it is appropriate to use these three methods and in what way they differ from each other.

Analysis of Seismic Signals Generated by Vehicle Traffic with Application to Derivation of Subsurface Q-Values

AbstractCorrect identification and modeling of anthropogenic sources of ground motion are of considerable importance for many studies, including detection of small earthquakes and imaging seismic properties below the surface. To understand signals generated by common vehicle traffic, we use seismic data recorded by closely spaced geophones normal to roads at two sites on San Jacinto fault zone. To quantify the spatiotemporal and frequency variations of the recorded ground motions, we develop a simple analytical solution accounting for propagation and attenuation of surface waves. The model reproduces well-observed bell-shaped spectrograms of car signals recorded by geophones close to roads, and it can be used to estimate frequency-dependent Q-values of the subsurface materials. The data analysis indicates Q-values of 3–40, for frequencies up to 150 Hz for road-receiver paths at the two examined sites. The derived Q-values are consistent with attenuation factors of surface waves previously obtained with other methods. The analytical results and analysis procedure provide a highly efficient method for deriving Q-values of shallow subsurface materials.

An estimation of the axial structure of surface-wave produced plasma column

An analytical expression to predict the axial distribution of electron density along the surface-wave sustained plasma column has been derived. The model is based on the square root approximation of the dispersion relation that gives a linear roll-off of electron density distribution in the plasma column. The point is to use a more tractable analytical approximation of dispersion relation of surface waves. An expression of attenuation coefficient, which includes the collisional loss, has been applied in studying the structure of the surface-wave produced plasma column. The derived attenuation model predicts a linear axial attenuation of electron density, as well as a nonlinear relation between the glass permittivity dependent frequency sensitivity and the wavenumber. The nonlinearity arises from non-negligible dielectric thickness. This result is consistent with early Aliev's results of the electron density profile, which correspond to the volume collisional absorption regime of surface wave sustained plasmas. The combined effects of surface-wave amplitude attenuation due to collisions and frequency dependence of group velocity cause an axial decrease in the surface wave axial power flux as the wave moves away from the launcher. A short analysis of the sensitivity of the normalized frequency to the permittivity of the glass based on the quasistatic approximation of the dispersion relation of surface waves is given.

Near-Field Body-Wave Extraction From Ambient Seafloor Noise in the Nankai Subduction Zone

Ambient noise correlation is capable of retrieving waves propagating between two receivers. Although waves retrieved using this technique are primarily surface waves, the retrieval of body waves, including direct, refracted, and reflected waves, has also been reported from land-based observations. The difficulty of body wave extraction may be caused by large amplitudes and little attenuation of surface waves excited by microseisms, indicating that body wave extraction using seafloor records is very challenging because microseisms are generated in ocean areas and large amplitudes of surface waves are presumably observed at the seafloor. In this study, we used a unique dataset acquired by dense arrays deployed in the Nankai subduction zone, including a permanent cabled-network of 49 stations, a borehole sensor, and 150 temporary stations, to attempt to extract near-field body waves from ambient seafloor noise observed by multivariate sensors of broadband and short-period seismometers, differential pressure gauges (DPGs), and hydrophones. Our results show thatPwaves are extracted only in the DPG-record correlations at a frequency of 0.2–0.5 Hz, which can be seen up to a separation distance of two stations of 17 km with an apparent velocity of 3.2 km/s. At 1–3 Hz,Pwaves are observed only in the vertical-record correlations up to a separation distance of 11 km with an apparent velocity of 2.0 km/s. These velocity differences reflect the vertical velocity gradient of the accretionary prism, because thePwaves at low frequencies propagate at relatively long distances and therefore the turning depth is greater. Moreover, the long-period and short-periodPwaves are observed at the slope and flat regions on the accretionary prism, respectively. To investigate the retrieved wavefield characteristics, we conducted a two-dimensional numerical simulation for wave propagations, where we located single sources at the sea surface above the flat and slope bathymetry regions. Based on our observations and simulations, we suggest that the retrieval of near-field body waves from ambient seafloor noises depends on the relative amplitudes ofPand other surface waves in the ambient noise wavefield, and those are controlled by the subseafloor velocity structure, seafloor topography, and water depth.

Surface Wave Attenuation in Multilayer Structures With Lossy Media and Impedance Surfaces

A methodology for analyzing the attenuation constant of surface wave propagating in general multilayer structures is proposed. The multilayer structure may include any number of layers, that can be made up of lossy dielectric, magnetic-material, and impedance surfaces. The non-linear characteristic equation (transverse resonance equation - TRE) of the multilayer structure is defined by utilizing transmission line (TL) theory. Consequently, the root(s) of the TRE is/are computed which indicates the complex propagation constant of that characteristic equation. The obtained results are validated over the completely shielded waveguide structures where the full wave simulation is possible. The proposed approach is employed to analyze and discuss the propagation and attenuation constant of surface wave modes in several representative examples. The analysis is carried out in the frequency range from 1 to 12 GHz.

Rayleigh Wave Attenuation Tomography in the Crust of the Chinese Mainland

AbstractIn this study, we report a first major effort to measure surface wave amplitudes and to map attenuation structures of the Chinese mainland with dense modern broadband seismic networks in the country. We developed a method of phase‐matched filtering to automatically extract fundamental‐mode Rayleigh waves and to measure the spectral amplitudes. The results are compatible with those from the previous manual method with great improvement in efficiency. Using the automatic method, we extracted a large quantity of the amplitudes of Rayleigh waves at periods of 10 and 20 s recorded by 141 broadband stations from the China Digital Seismograph Network and 656 broadband stations from the China Regional Seismic Network. We performed tomographic inversions using the method of two‐station amplitude ratios and obtained images of the surface wave attenuation maps at periods of 10 and 20 s for the Chinese mainland. The tomographic model resolution reaches 1–2° in central and eastern China, 3–5° in western China, and 5° in the southeastern margin of the Tibetan Plateau and northeastern China. The tomographic results demonstrate good correspondence with geological structures. The distribution of strong historical earthquakes indicates that in the Chinese mainland, these earthquakes occurred mainly in high‐attenuation areas or the junctions between high‐ and low‐attenuation areas.

An experimental study of gravity waves through segmented floating viscoelastic covers

With climate changes and global warming, the extent of Marginal Ice Zone (MIZ) in the polar region is widening, and there is now more research attention on the wave interactions with broken ice covers within the zone to gain insights into its future sea conditions. Towards this objective, the dispersion and attenuation of surface waves propagating through segmented floating viscoelastic covers was investigated experimentally in this study. The covers were made of oil-doped Polydimethylsiloxane (PDMS) material, with different curing agent percentages to vary their rheological properties. For stiffer covers, the measurements showed that the effect of segmentation on wavelength modification was significant, and the dispersion relation agreed generally with the existing theoretical predictions for discrete floating elastic segments despite the presence of the additional viscosity for the material. At the same time, the earlier empirical formula based on the concept of “equivalent rigidity” to represent the segmented elastic cover, did not work well for the conditions investigated. With more flexible covers, however, the effect of segmentation became insignificant for thin cover thickness. Given the present experimental conditions, we confirmed that the effect of scattering was negligible, and the wave attenuation should be attributed to the various dissipative mechanisms. An empirical relation for the attenuation was established based on the experimental results, to quantitatively relate the attenuation coefficient to the incident wave characteristics and cover properties. The relation identifies a significant inverse relationship with the viscosity of cover material, and thus confirms the essential role of viscoelastic representation for the attenuation predictions.