Rayleigh Waves Research Articles

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.

Crustal and uppermost mantle structure near the Gloria Fault, North Atlantic, from ocean bottom seismometer surface wave observations

SUMMARY In this work, we present both 1-D and 3-D shear wave velocity (Vs) models of the oceanic crust and uppermost mantle below the Deep OCean Test ARray area, located ∼ 70 km north of the central section of the Gloria Fault, in the eastern North-Atlantic Ocean. The velocity models are inferred from the dispersion of surface waves recorded on ocean bottom seismometers. Dispersion measurements are obtained from the analysis of ambient seismic noise at short periods (< 14 s) and teleseismic surface waves at long periods (> 14 s) using the two-station method. The 1-D Vs model is inferred from the joint inversion of Rayleigh wave phase velocities and Love wave group and phase velocities. The 3-D tomographic model is obtained by inversion of 2-D Love wave group velocity maps as a function of depth, further constrained by the average of Love wave phase velocities obtained from ambient noise (4–9 s) and the average Rayleigh and Love wave phase velocities calculated from teleseismic data (14–44 s). The 1-D Vs model shows a sediment layer with a low velocity of 1.05 km s−1, similar to previous studies in the region. Below the sediments, we find an oceanic crust with velocities ranging from 3.3 to 4.5 km s−1. The model reaches an unusually high velocity of 4.9 km s−1 in a 20 km thick layer at depths between 16 and 36 km. We interpret this fast velocity layer as indicative of the presence of harzburgite, a residue of enhanced melting that might have been formed by the proximity between the Mid-Atlantic Ridge and the Azores mantle plume. At greater depths the velocity decreases, forming a low-velocity zone that reaches a minimum at ∼ 70 km depth, which we interpret as the maximum depth for the lithosphere–asthenosphere boundary. The 3-D model shows a structure that is mostly horizontally layered, with Vs isocontours at 3.5–4.5 km s−1 highlighting oscillations of the crustal structure with wavelengths of ∼25–30 km. These oscillations may be due to changes in the rate of mantle upwelling and magma supply rate.

Three-component high-resolution seismic time–frequency polarization filter

SUMMARY The analysis of earthquake recordings from three-component instruments can be challenging due to overlapping events. Time–frequency (TF) polarization methods are efficient tools for this purpose, which can discriminate these events. Previous polarization methods did not consider all three components simultaneously while transferring data to TF domain, which can cause inaccuracies in the reconstruction of wave amplitudes. Therefore, the three-component sparse adaptive S transform (3C-SAST) algorithm is preferred to other TF decompositions since it is mainly developed for polarization analysis purposes, and outperforms other TF methods. In this paper, we developed the 3C-SAST by adding a parameter to adjust the sparseness of the solution and make the resolution flexible. The developed TF decomposition is then used to extend the Morozov & Smithson method to TF domain, and devise a new TF polarization filter whose invertibility and resolution flexibility make it a promising tool for wavefield separation. This filter can eliminate the out-of-plane arrival energies and extract the Rayleigh waves for multicomponent data, which has application in Rayleigh wave tomography and seismological studies. We demonstrated the efficiency of the proposed method for seismic surface waves separation using synthetic signals and three-component teleseismic earthquake recording.

Rayleigh Wave Propagation With Rotation, Two Temperature With Diffusion in Context to Dual Phase Lag Thermoelasticity

Rayleigh Wave Propagation With Rotation, Two Temperature With Diffusion in Context to Dual Phase Lag Thermoelasticity

Shear-wave velocity determination by combining data from passive and active source field investigations in Kumamoto city, Japan

We present the 1D subsoil structure and local site effects at KUMA strong ground motion station in Kumamoto City, Japan. We analyze data from a field campaign conducted in the framework of the Blind Prediction BP1 test of the 6th IASPEI/IAEE International Symposium: Effects of Surface Geology on Seismic Motion. In parallel with other participants of the BP1 test, we process data from passive and active source measurements aiming to determine the shear-wave velocity, Vs, structure and the site response at KUMA station. Passive measurements are associated to five microtremor arrays. In each array, seven seismometers have been deployed in a common-center triangle shape, recording microtremors simultaneously for 1 to 2 h. The vertical component of microtremors was analyzed using the spatial autocorrelation (SPAC) method. Cross-correlation coefficients were computed for all station pairs available for each array. By fitting the average SPAC’s coefficients to the first-kind zero-order Bessel function, J0, and assuming that microtremors primarily comprise fundamental mode Rayleigh waves, phase velocity dispersion curves were determined. Phase velocity values for frequencies > 15 Hz were obtained from data of a close-by active source geophone profile. We integrated the data with those of the passive measurements and obtained an experimental phase velocity dispersion curve. The resulting curve shows low velocity variation, from 150 to 200 m/s, in the surface layers, whereas significant dispersion appears in frequencies below 2.5 Hz. By inverting this curve, we achieved to determine the 1D shear-wave velocity structure at KUMA station. Site response characteristics were determined by applying the Horizontal-to-Vertical-Spectral-Ratios method. Significantly amplified peaks in the frequency range between 0.3 to 1.5 Hz dominate HVSR spectral ratios. These peaks correspond to resonant frequencies of soils and originate from different impedance contrasts within the substratum of the site.Graphical

Seismic attenuation tomography of Eastern Europe from ambient seismic noise analysis

SUMMARY The Eastern-Europe region (EER), is a complex geotectonic area that captures part of the Alpine-Himalayan Orogen, the subduction of multiple NeoTethys Branches and part of the East European Craton. It is one of the most exciting geological areas in Europe due to a diversity of tectonic processes acting within it: extensional basin evolution, oceanic subduction, post-collisional volcanism, as well as active crustal deformation associated with the push of the Adria plate or the pull of the actively detaching Vrancea slab. This makes EER an excellent natural laboratory to study the behaviour of the lithosphere–asthenosphere system in a heterogeneous tectonic setting. To investigate the lateral heterogeneity and physical properties of the crust in the EER, we use ambient seismic noise data recorded by the vertical components of broad-band stations that have been operational between 1999 and 2020 in Eastern Europe and surrounding regions. We used this significant amount of data and the latest processing techniques of the ambient seismic noise field based on the continuous wavelet transform to compute cross-correlations between various station pairs, turning every available seismic station into a virtual source. The coda of the interstation cross-correlograms were used to determine coda quality factors (Qc) of Rayleigh waves in four different period ranges (3.0–5.0, 5.0–10.0, 10.0–20.0 and 20.0–30.0 s) and to invert them in the 2-D space, constructing the highest resolution attenuation tomography of the region. Our results reveal high attenuation features throughout the northeast Pannonian region, the Bohemian Massif, the East Carpathians and the Moesian Platform. Nevertheless, our findings do not emphasize a close correlation between the depth of sedimentary basins and attenuation features identified at longer periods. In addition, Qc variations are larger at short periods, indicating higher heterogeneity in the uppermost crust of Eastern Europe. Our findings demonstrate the higher efficiency of noise correlation approaches relative to earthquake data analyses investigating Qc at low frequencies.

An approximate formula for the Rayleigh wave velocity in the machined surface with residual stress

The present paper is concerned with the Rayleigh wave propagation in the machined surface with a thin damaged layer with residual stress. We assume that the layer and the half-space are bonded perfectly to each other. Biot’s theory of small deformations influenced by initial stress forms the basis for this study. With the help of the effective boundary condition method, a third-order approximate secular equation of Rayleigh waves is established for the case that the layer and half-space are both orthotropic. In addition, an explicit third-order approximate formula for the Rayleigh wave velocity is derived from the secular equation. By considering a sample of silicon wafer by fine grinding with fine abrasive grains, the accuracy of the approximate formula has been verified. This study is meant to serve as the mathematical foundation for non-destructive testing of residual stress in the practical applications.

Shear-wave velocity models in and around north-east India by modelling Rayleigh wave group velocity dispersion data

Shear-wave velocity models in and around north-east India by modelling Rayleigh wave group velocity dispersion data

The propagation of the multi-physical fields coupled Rayleigh wave on the half-space with a gradient piezoelectric semiconductor layer

The propagation of the multi-physical fields coupled Rayleigh wave on the half-space with a gradient piezoelectric semiconductor layer

Depth profiling of residual stress distribution in surface treated metallic structures using nonlinear ultrasonics

Robotic hammer peening (RHP) is a cold-working technique to improve the fatigue life of metallic structures by inducing compressive residual stress in the near-surface region. Measuring the depth profiling of residual stress distribution plays an important role in process design towards the advanced manufacturing of metallic structures. This study investigates the use of the nonlinear ultrasonic method to measure the residual stress profiles through the frequency-dependent penetration depth approach. Stainless steel specimens were treated with varying RHP intensities, and their morphological evolutions were characterized with a step-profilometer. The amplitudes of the second and third harmonic components of the longitudinal critically refracted (LCR) and Rayleigh waves were measured and analyzed. The effect of the surface roughness on the acoustic nonlinearity parameters before and after polishing at various peening intensities was briefly discussed. The results show a large variation in the acoustic nonlinearity parameter at the surface layer, indicating the potential of the proposed nonlinear ultrasonics for the measurement of depth profiling of residual stress.

Shock waves generated by toroidal bubble collapse are imperative for kidney stone dusting during Holmium:YAG laser lithotripsy

Holmium:yttrium–aluminum-garnet (Ho:YAG) laser lithotripsy (LL) has been the treatment of choice for kidney stone disease for more than two decades, yet the mechanisms of action are not completely clear. Besides photothermal ablation, recent evidence suggests that cavitation bubble collapse is pivotal in kidney stone dusting when the Ho:YAG laser operates at low pulse energy (Ep) and high frequency (F). In this work, we perform a comprehensive series of experiments and model-based simulations to dissect the complex physical processes in LL. Under clinically relevant dusting settings (Ep = 0.2 J, F = 20 Hz), our results suggest that majority of the irradiated laser energy (>90 %) is dissipated by heat generation in the fluid surrounding the fiber tip and the irradiated stone surface, while only about 1 % may be consumed for photothermal ablation, and less than 0.7 % is converted into the potential energy at the maximum bubble expansion. We reveal that photothermal ablation is confined locally to the laser irradiation spot, whereas cavitation erosion is most pronounced at a fiber tip-stone surface distance about 0.5 mm where multi foci ring-like damage outside the thermal ablation zone is observed. The cavitation erosion is caused by the progressively intensified collapse of jet-induced toroidal bubble near the stone surface (<100 μm), as a result of Raleigh-Taylor and Richtmyer-Meshkov instabilities. The ensuing shock wave-stone interaction and resultant leaky Rayleigh waves on the stone surface may lead to dynamic fatigue and superficial material removal under repeated bombardments of toroidal bubble collapses during dusting procedures in LL.

Machine learning enhanced characterization of surface defects using ultrasonic Rayleigh waves

Rayleigh waves are successfully employed for the characterization of surface defects through the utilization of both time and frequency domain analysis. However, a significant challenge arises when attempting to cover a broad range of the defect depth to Rayleigh wavelength ratio with a single method. This paper presents an enhanced methodology that integrates optimized machine learning (ML) algorithms to expand the coverage of defect depth assessment. An experimentally validated numerical model is firstly established to simulate the interaction of Rayleigh waves with surface defects and utilized to generate a significant quantity of labeled Rayleigh wave signals. The features of received Rayleigh wave patterns are effectively extracted and serve as indicators of defect parameters. The ML framework encompasses the extraction and selection of optimal features, the construction of model architecture, and the tuning of hyperparameters. Three dimensionality optimization techniques—principal component analysis, correlation coefficient analysis, and expert knowledge integration—are compared. Additionally, six machine learning models (decision tree, support vector machine, k-nearest neighbors, random forest, gradient-boosting machine, and artificial neural network) are optimized using particle swarm optimization and subjected to comparison. The results reveal that: (1) principal component analysis yields the highest performance, suggesting the potential for feature dimensionality reduction without relying on expert knowledge; (2) among the models examined, the random forest model and artificial neural network with hyperparameter tuning demonstrate superior performance in predicting defect depth; and (3) the optimized machine learning methods consistently outperform empirical approaches in accurately predicting defect depths across a wide range. Furthermore, the proposed method shows promise for extension to determine additional parameters associated with surface defects, including their width and angle of inclination.

Magma and hydrothermal sources below the northern part of Paramushir Island (Kuril Arc) inferred from ambient noise tomography

Paramushir is the northernmost island of the Kuril Arc comprising several Holocene volcanoes, of which two are presently active: Ebeko and Chikurachki. We present the first crustal-scale three-dimensional seismic shear-wave velocity model of the northern part of Paramushir derived with the use of data of 20 temporary stations operated in 2021–2022 and one permanent station. The continuous seismic data were used to obtain the Rayleigh wave dispersion curves for periods ranging from 0.5 s to 12 s through computing ambient seismic noise cross-correlation functions. Then the 3D shear wave velocity distribution was constructed by seismic tomography. The synthetic tests demonstrate that the model has sufficient resolution down to 7–10 km depth. We observe a series of low-velocity anomalies at the depths of 4–6 km below the volcano-origin Vernadsky Ridge. They may likely represent magma reservoirs that are responsible for Holocene eruptions along the ridge. These anomalies are overlain by the high-velocity anomalies associated with the rigid cover consisting of an upper-crustal granite-granodiorite body and consolidated magma intrusions. Along the eastern flank of Ebeko we reveal a thin low-velocity anomaly at a depth of ∼1 km that can be interpreted as a water-saturated layer. The contact of this layer with hot magma intrusions leads to the formation of a large amount of steam that is ejected during the frequent phreatic eruptions of Ebeko and from numerous fumaroles in the summit area. On the other hand, this layer, which is following down to the Pacific Coast, might be promising for the geothermal energy exploitation.

Transient scattering of a Rayleigh wave by a cluster of subwavelength resonators—Towards asymptotic modeling of seismic surface metabarriers

A seismic metabarrier (intended for surface waves mitigation effect) is modeled as a cluster of single-degree-of-freedom resonator units deposited on the surface of an isotropic homogeneous elastic half-space. It is assumed that each resonator has a frictionless flat rigid base of diameter much smaller than the wavelength of an incoming surface wave. The slow-motions asymptotic method is applied for constructing the first-order asymptotic model of multiple time-dependent scattering of a pulsed Rayleigh wave with respect to the vertical displacements of the resonators (including their rigid bases and inertial elements) and the normal contact forces (time-dependent integral characteristics of the contact reactions beneath the resonator bases). Both the stationary and transient multiple scattering scenarios are considered. The variation of the amplitude reduction factor due to the model parameters variation is studied in detail.

A nonlocal strain gradient theory for wave propagation analysis in transversely isotropic elastic medium

This paper has the objective of studying the propagation of surface waves in a transversely isotropic medium based on nonlocal strain gradient theory (NSGT). A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory and classical theory. It has also been concluded that there exist escape frequency and cut-off frequency for the wave propagating in size-dependent materials based on the NSGT. Dispersion equation for the propagation of Rayleigh-type waves at the free surface has been derived. The effect of the nonlocal parameter, the strain gradient parameter on the Rayleigh wave propagation is considered through some numerical examples.

Directional sources and distributed acoustic sensing deployments for near-surface characterization

Active near-surface surveys using distributed acoustic sensing (DAS) have been practically limited to 2D inline acquisitions followed by Rayleigh-wave dispersion analysis. In this study, we analyze different acquisition setups and the subsurface properties that can be estimated from them. First, we find a surface survey dedicated to Love-wave acquisition. We use a horizontal source and common-receiver sorting of the DAS data for a pure Love-wave velocity dispersion analysis yielding an S-wave velocity profile. Common-receiver sorting has the added benefit of practically eliminating the effect of the gauge length. Next, downhole DAS is used in a vertical seismic profile-type survey to recover a 1D P-wave velocity through checkshot analysis. Finally, we find that the horizontal portion of a fiber deployed in a deviated borehole records high-frequency data from surface sources. We use first arrivals for diving-wave tomography, yielding a 2D P-wave velocity model above and below the fiber. We validate the inversion results of all acquisitions through a comparison with geophone-derived velocity models. We conclude that source orientation plays a crucial role and should be considered during survey planning in conjunction with DAS directivity. As anticipated, fiber coupling can strongly influence the signal-to-noise ratio and needs to be adequately planned. In vertical boreholes, infilling offers a viable solution for deployment in existing wells. For deviated boreholes, installation inside the casing yields suboptimal coupling, but more adequate deployment protocols may yield high-frequency data useful for velocity model building and imaging. From a practical point of view, the acquisitions that we describe are difficult to justify due to their operational costs and limitations. Nonetheless, they highlight the potential of DAS in going beyond traditional analysis.

Contactless estimation of soil moisture using leaky Rayleigh waves and a fully convolutional network

AbstractSoil moisture is a key factor that influences various aspects of ecosystem functioning. Measuring soil moisture without installing any objects in the soil is desirable because it allows for accurate characterizations of soil moisture while minimizing impacts on soil structure and ecology. In this study, we explored the potential of leaky Rayleigh waves as a proxy to contactlessly estimate soil moisture. We developed an ultrasonic system containing a transducer, receivers, and acoustic barrier. The specimens of sand, silt, and clay were utilized. Experiments were conducted over 4 months. We used a widely used soil‐embedded moisture sensor to compare and develop relationships between leaky Rayleigh waves and soil moisture. Our results showed that as soil moisture increased, the velocity and amplitude of leaky Rayleigh waves decreased because water molecules attracted to the soils led to their attenuation. However, their magnitudes were not considerable except for very dry soils. To overcome these limited relations to estimate soil moisture from leaky Rayleigh waves, we constructed authentic images based on the observed leaky Rayleigh waves and used them as inputs for a fully convolutional network. We found that the combination of the ultrasonic system and deep learning approach developed in this study were suitable for estimating soil moisture without soil disturbances (RMSE = 0.01 m3 m−3). This study suggests that leaky Rayleigh waves have the potential to serve as a reliable proxy for determining soil moisture without the need for physical contact.

Wavefield Modeling and Analysis of Lightning Quakes Measured by a Distributed Acoustic Sensing Array

ABSTRACT Lightning-induced seismic waves, termed “lightning quakes,” are frequent natural sources in many storm-prone regions. Lightning quakes have been clearly observed in numerous environments by both seismic and acoustic instruments, for example, by distributed acoustic sensing (DAS) array. Despite these numerous observations, the physical nature of lightning quake wavefields detected by ground-based arrays remains poorly understood. The possibility of electroseismic (ES) conversion due to lightning’s powerful electromagnetic fields was, until now, unstudied. This investigation uses 3D numerical simulations of acoustic-to-seismic and ES wavefields alongside a novel data-driven azimuthal strain-rate variation analysis technique to robustly reveal the complex nature of lightning quakes. We show that lightning quakes begin as airborne acoustic waves before coupling with the solid earth as air-coupled Rayleigh waves and Love waves that are generated by local sources near the receiver, such as topography or urban infrastructure. These conclusions suggest thunder observations from a DAS array can be used to infer the structure of the near surface around the receiver, but care needs to be taken in understanding the role of local sources. An estimate of the Rayleigh- and Love-wave phase velocities is produced using a novel data analysis method unique to DAS. Furthermore, we demonstrate that electroseismic coupling does not play a significant role in the lightning quake wavefields. Although these simulations do not fully capture the realistic frequency of the electroseismic coupled wavefield, theory suggests that the wavefield is high frequency and thus quickly attenuated in the saturated near-surface soils. Electroseismic coupled wavefields from lightning may be detectable very close to the bolt.

A New Method for Selecting the Phase and Group Velocity Dispersion Curves of Rayleigh and Love Surface Waves: Real Data Case of Central Anatolia, Turkey (Türkiye)

We propose a new method to select the dispersion curve of Rayleigh and Love surface waves obtained from local and regional earthquakes. This method is efficient for the crustal tomography studies and the Central Anatolia is chosen to test it. The single-station method utilizing both seismograms and accelerograms is used for the group velocities from local earthquakes while the two-station approach utilizing the cross correlograms is employed for the group and phase velocities using both local and regional earthquakes. The proposed method is made of two stages. The first stage based on the multiple filter technique – MFT is designed for an automatic selection of the desired dispersion curve. In case of the single-station approach, the MFT diagrams are computed for both Rayleigh and Love seismograms or accelerograms. An algorithm based on several selection criteria is employed to extract the corresponding group velocity dispersion curve from the MFT diagram. In case of the two-station method, the MFT diagrams are computed for both Rayleigh and Love cross correlograms. The latter algorithm developed for the MFT diagram is again applied to the cross correlogram to select the respective two-station group velocity dispersion curve. To select the corresponding two-station phase velocity dispersion curve, another algorithm is developed where the joint inversion of phase and group velocities is employed. The RMS value quantifying the misfit between the selected and inverted dispersion curves is found minimum when the selected phase velocity curve is compatible with the group velocity curve extracted via the MFT. The selection procedures defined up until this point constitute the first stage. In the second stage, phase and group velocity gathering around base pathways is performed. This way it is possible to compute the averages and standard deviations for the observed pathways traversing the similar geology. The outliers determined by using the averages and standard deviations are eliminated from the data set and this elimination is performed for phase and group velocities, separately.

Nonlinear ultrasonic techniques to quantify oxidation damage in carbon/carbon composite material

This research applies linear and nonlinear ultrasonic (NLU) techniques to quantify oxidation damage in a carbon/carbon (C/C) composite material cut from an automotive friction disc ring. The oxidation as a result of gasification of carbon at high temperatures (T >∼ 500 °C) is a major degradation mechanism in C/C composites. This is the first research to successfully use a dry-contact mediator wedge setup for nonlinear ultrasonic applications, enabling repeatable in-situ Rayleigh wave measurements on slow wave velocity materials where submersion is impractical. The samples are subjected to thermal damage by exposure to a high temperature atmosphere over multiple holding times, and the oxidation damage is visualized using scanning electron microscopy (SEM). The sample mass is recorded and both linear (velocity and attenuation) and nonlinear (β′) ultrasonic measurements are performed after each holding time. Superior sensitivity to early stage oxidation affirms the suitability of nonlinear Rayleigh wave measurements for the quantification of thermally induced oxidation damage in C/C composites, while the double mediator wedge setup is well suited for high attenuation, slow wave velocity materials, demonstrating potential applicability for in-situ condition monitoring. The results show that a systematic oxidation starts after 3 min of exposure to the temperature in this C/C composite. The oxidation induced fiber–matrix debonding, matrix defects (appearing to be microcracking), and void growth are consistently detected by the Rayleigh wave velocity and acoustic nonlinearity. In addition to the higher sensitivity, the nonlinearity parameter has the capability of selectively measuring the strength related damage such as the observed fiber–matrix debonding, while the wave velocity can detect the oxidation voids. A combined use of these two parameters can provide useful information on the microstructural evolution in C/C composites subjected to high temperatures.