Surface Wave Velocity Research Articles

Deep learning-based inversion of soil and rock compaction density utilizing Falling Weight Deflectometer (FWD) and Surface Waves

Methods relying on a single dynamic parameter to estimate the material density for the compaction quality testing of earth-rock dams and roadbed projects, present certain limitations in terms of applicability, testing accuracy, and work efficiency. The theory of elastic wave propagation reveals that the compaction density of the medium results from the combined interaction of multiple material properties. This study proposes a method that utilizes the transient surface wave method and a vehicle-mounted Falling Weight Deflectometer (FWD) to jointly enhance the accuracy of soil and rock material compaction detection. The transient surface wave method is employed to extract surface wave velocity and compressional wave velocity. The analysis of the FWD signal involves extracting dynamic parameters closely related to material density, including stiffness coefficients, central frequencies, and stiffness impedances, from time-domain, frequency-domain, and mechanical impedance analyses. A fully connected deep neural network is introduced to intelligently estimate the compaction density. The deep learning model is optimized by selecting the optimal activation function and optimization algorithm, as well as additional tuning. Extensive testing shows that deep learning model produce results closely approximating the true compaction density values. The average relative errors for the wet density and the dry density are 2.9% and 2.85%, respectively, meeting the quality control requirements for density testing. The proposed approach enables rapid detection and control of the compaction quality of soil and rock materials, providing a new method for the in-situ rapid detection of compaction quality.

Phase velocity shifts of shear surface waves in flexoelectric wave-guide clamped on piezomagnetic base

Surface acoustic wave devices featuring periodic layers of piezomagnetic and piezoelectric-flexoelectric layers are subject to intense investigation. In miniaturized devices, large strain gradients are possible that produce significant flexoelectric fields in piezoelectric components. In the present theoretical research, surface acoustic wave transference has been manifested in a flexoelectric waveguide clamped over a piezomagnetic base. This endeavor involves the formulation and solution of coupled magneto-electro-elastic field equations governing the structure’s behavior. Coupled magneto-electro-elastic field equations for the structure have been derived and solved utilizing analytical techniques. By accounting for pertinent boundary conditions, the dispersion relations characterizing the velocity of surface waves, both in scenarios with and without electrodes have been obtained. Based on proper numerical examples, the frequency and phase velocity spectrum have been plotted offering insights into key parameters i.e. modal frequency, phase velocity, and wave attenuation. The outcomes of the theoretical study may be helpful in providing insights into mechanical wave propagation in coupled piezoelectric/piezomagnetic structures.

Dipolar Huygens-Kerker radiation for surface waves.

Exotic dipolar radiation with zero light emission in one direction but maximal light emission in the opposite direction was envisioned by Huygens in 1690, and it could emerge in vacuum if the ratio between the source's electric and magnetic dipole moments fulfills the Kerker condition as revealed by Kerker in 1983. Due to its intricate connection with both the Huygens principle and Kerker condition, this radiation phenomenon is suggested to be termed as dipolar Huygens-Kerker radiation, and at this moment, the ratio is termed as the Huygens-Kerker ratio. However, the dipolar Huygens-Kerker radiation remains underexplored in non-vacuum matters, inside which the source locates, especially for surface waves. Here we find that the dipolar Huygens-Kerker radiation of surface waves in principle could occur in non-vacuum matters and is essentially featured with the same normalized radiation pattern, which is closely related to the inclination factor that appears in the Fresnel-Kirchhoff diffraction theory. Moreover, the corresponding Huygens-Kerker ratio is intrinsically determined by the phase velocity of excited surface waves. To be specific, the Huygens-Kerker ratio is proportional to the phase velocity for transverse-magnetic surface waves but becomes inversely proportional to the phase velocity for transverse-electric surface waves.

Azimuthal Variation in the Surface-Wave Velocity in the Arabian Plate

Azimuthal Variation in the Surface-Wave Velocity in the Arabian Plate

Numerical Investigation of Evaluating the Degree of Damage in Concrete Plate Cold Joints through Surface Wave Dispersion Velocity Profiles

This study aims to develop a technology for assessing the interfacial condition of cold joints in concrete plates, focusing on the dispersion velocity profile of surface waves. The methodology employs a small impact hammer embedded with a piezoelectric element and a displacement receiver strategically positioned on either side of the seam. In this initial investigation, numerical models were constructed using ANSYS LS-DYNA. The cold joint zone was simulated by randomly removing elements with a predetermined void ratio. Displacement waveforms at the sensor node underwent analysis using a short-time Fourier Transform and the reassigned method to derive the dispersive velocity profile of surface waves. The study delves into the impacts of varying test-line lengths, impact durations, and void distributions. Numerical findings indicate that cold joints are detectable with a void ratio of 40% or greater. For the 60% and 80% void ratios, surface wave velocities register notably lower for wavelengths below 0.1 m and 0.2 m, respectively. Under the same porosity ratio for surface-observable cold joints, if their extension depth is smaller, the wave velocity on the dispersion curve will be lower than that of a fully penetrated cold joint. The current study reveals that a contact duration of 60 μs and an impactor-receiver distance of 0.82 m yield the most distinguishable results for detecting the extension and porosity ratio of a cold joint. Accompanied by tests with a hammer with a contact duration of 20 μs, additional information about the joint can be unveiled. Finally, various void distributions in the cold joint predominantly influence the wave velocity at shorter wavelengths.

Regional noise source location based on the time delays between station pairs from ambient noise interferometry

Identifying the location of a potential noise source assists in understanding the characteristics of the seismic or volcanic activity and provides valuable information for hazard assessment. Unlike the conventional waveform-based techniques that rebuild the source energy into the possible source region, we apply a simplified method to determine the absolute location of the noise source based on the station-pair time-delays from ambient noise interferometry. Synthetic tests demonstrate the robustness of the method and the locating precision is mainly influenced by the signal-to-noise ratio of the synthetic waveforms, and the higher frequency bandwidth source signals are more likely to result in accurate detection of the source. An application at the Central Tien Shan indicates that our method is capable of locating the known virtual source from the empirical Green’s functions. Furthermore, assuming a surface wave velocity, the depth of the source can be generally recovered from ambient noise interferometry in a simplified 3-D homogeneous model. The new method sheds light on applications of ambient noise interferometry for locating potential sources, making it suitable for detecting time-dependent behavior.

Effect of Anisotropy on Residual Stress Measurement of 316L Stainless Steel by Ultrasonic Surface Wave

Fe–Cr alloys are widely used in power, petroleum, and manufacturing industries for their good resistance to corrosion and oxidation at high temperatures. Ultrasound is the only nondestructive method so far to measure the residual stress of in-service components. However, for parts with material anisotropy, such as materials processed by rolling, the measurement accuracy is highly restrained. In this paper, a rolled 316L stainless steel sample is used to study the influence of texture on the measurement of residual stress by ultrasonic surface wave. The experimental results show that the propagation velocity of surface waves in the sample has anisotropic characteristics. The wave velocity parallel to the rolling direction (0°) is the maximum, and the wave velocity perpendicular to the rolling direction (90°) is the minimum, thereby affecting the measurement accuracy. It is found that reducing the frequency of surface waves can reduce the influence of anisotropy. Therefore, a low-frequency method and modified formula are used to improve the measurement accuracy. The maximum error in the rolling direction is reduced from 21.3 to 3.6 MPa, and the maximum relative error is also reduced from 45.4 to 9.0%. The modified formula can further reduce the influence of anisotropy, with the maximum error value further reduced to 2.3 MPa, the maximum relative error reduced to 4.9%, and the surface wave detection accuracy effectively improved.

Study on the film thickness and surface wave velocity of the thin liquid film formed by a round jet obliquely impinging on a horizontal plate

For a thin liquid film (in a supercritical flow) prior to the formation of a non-circular hydraulic jump formed by a round jet obliquely impinging on a horizontal plate, the time-averaged film thickness and the surface wave velocity are extracted based on the measured transient film thickness. On the one hand, the effect of many factors, including the jet velocity, impingement angle, azimuthal angle, liquid viscosity, and surface tension, on the time-averaged film thickness and surface wave velocity are discussed. When the jet Reynolds number increases to about 1.4×104, the film thickness profile suddenly increases, and the transition of liquid flow from laminar to turbulent occurs. Meanwhile, a rapid increase is observed downstream of the turbulent film thickness profile. The influence of surface tension on the time-averaged film thickness and surface wave velocity is negligible for thin liquid films before non-circular hydraulic jumps. Nonetheless, the surface tension has a significant influence on the interface profile of non-circular hydraulic jumps. Furthermore, a “crescent” kink region upstream of the jump can be identified when the surface tension is lower than 40.6 mN/m. On the other hand, experimental results are used to verify the prediction accuracy of existing approximate solutions. The laminar approximate solution with a quadratic boundary layer velocity profile can accurately predict the film thickness distribution of most laminar thin liquid films, except downstream of the thin liquid films with a dynamic viscosity higher than 9.71 mPa s. The surface wave velocities are found to be close to the predicted surface velocities of the approximate solutions.

Methodology for Determining the Correct Ultrasonic Pulse Velocity in Concrete

Quite often, concrete strength parameters must be determined in the shortest possible time. Due to the strong correlation between concrete’s mechanical and acoustic properties, ultrasonic devices can be used for this purpose. However, the ultrasonic pulse velocity (UPV) is influenced by a variety of factors, including the curing and exploitation conditions of the concrete, the presence of reinforcement, and other various physical factors. Ignoring these factors may contribute to the misinterpretation of the measurement data when determining the strength of the concrete. Typically, all these factors are analyzed independently. This publication consolidates the findings obtained from our research efforts and field expertise over the past two decades. It outlines the elaborated UPV measurement methodology based on the integration of a four-argument function: the hydration process phase of the hardened cement paste (or concrete aged three days and older), hardening (curing) condition, concrete moisture level, and ambient temperature. To understand the interactions of the key factors, different ultrasonic devices were used to measure the velocities of longitudinal and surface waves in concrete by applying direct and indirect transmission methods when concrete specimens were tested under different moisture and temperature conditions.

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory. In semi-infinite space, a nondispersive Rayleigh wave mode exists, and the eigendisplacement decays exponentially with depth. In a layered model with increasing layer velocity, the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer. If the phase velocity is the same as the P- or S-wave velocity of the layer, which is called the critical mode or critical phase velocity of surface waves, the general solution of the wave equation is not a homogeneous (expressed by trigonometric functions) or inhomogeneous (expressed by exponential functions) plane wave, but one whose amplitude changes linearly with depth (expressed by a linear function). Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode, owing to the singularity at the critical phase velocity. In this study, based on the classical framework of generalized reflection and transmission coefficients, the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity. Therefore, the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem. The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models. In contrast to the normal mode, the eigendisplacement associated with the critical phase velocity exhibits different characteristics. If the phase velocity is equal to the S-wave velocity in the bottom half-space, the eigendisplacement remains constant with increasing depth.

Определение диэлектрических свойств воды в тонком слое

A technique is proposed for determining the dielectric properties of water in a nanoscale layer at frequencies corresponding to orientation polarization. The method is based on the registration of the change in the velocity of elastic surface waves resulting from the interaction with a thin layer of a liquid. It was assumed that the dispersion of the dielectric permittivity of water in the thin layer is described by the Debye's equations of dielectric relaxation. In order to demonstrate the capabilities of the proposed method, the values of the real part of the dielectric permittivity of adsorbed water at various frequencies f (43.2; 64.8; 108; 129.6, 194.4, 302.4, 388.8 MHz) were experimentally determined at a fixed thickness of the adsorption layer h (2.2; 2.8; 3.7; 13 nm). The determination of the value of the imaginary part of the dielectric permittivity as well as the calculation of the time of dielectric relaxation, static, and high-frequency dielectric permittivities was enabled by the use of the experimental values and Debye's equations. A comparison was made between the dielectric properties of adsorbed water and those of water in the bulk liquid phase. The high-frequency dielectric permittivity of adsorbed water was found to be lower than that of water in the bulk liquid phase, while the static dielectric permittivity was significantly higher. The dielectric relaxation time of adsorbed water is dependent on the thickness of the adsorption layer and is significantly longer than that of water in the bulk liquid phase.

Formation Model for Acoustic Characteristics of Solid Media with Ordered Fracturing

Introduction. The development of new structural materials and improvement of existing technologies for the production of new products on their basis lead to the emergence of new types of medium discontinuities. Therefore, the development of new models of discontinuities that take the previously ignored parameters into account seems to be relevant for the purposes of nondestructive testing and structural measurements. This concerns, e.g., the roughness of adjacent surfaces of microcrack ordered sets.Aim. Theoretical substantiation for the processes of elastic waves propagation through an elastic medium containing an ordered lattice of microcracks with boundary conditions in the linear slip approximation, modified by taking into account the parameters of micro-convexities of microcrack rough boundaries. Database formation for experimental studies aimed at determining the physical and mechanical characteristics of structural materials.Materials and methods. The acoustic characteristics of materials were determined based on the derivation and solutions of dispersion equations describing the formation and propagation of effective longitudinal, transverse, and Rayleigh surface elastic waves in elastic media with ordered cracking. Their values were also used to determine the effective speed of Rayleigh surface waves.Results. The conducted simulation of elastic wave formation processes showed that an increase in the concentration of microcracks leads to a decrease in the phase velocities of effective longitudinal, transverse, and surface waves, as well as to an increase in the attenuation coefficients at given ultrasound frequencies and material parameters.Conclusion. The radius of the microsphere that replaces the surface micro-convexity and the roughness parameter Rz have a significant impact on the formation of physical and mechanical characteristics of materials, which are determined by the results of ultrasonic measurements. The developed model can be recommended as a basis for interpreting the results of ultrasonic measurements.

Bayesian eikonal tomography using Gaussian processes


 Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the ambient-noise tomography setting. However, the results of eikonal tomography are crucially dependent on the way in which phase delay measurements are predicted from data, a point which has not been thoroughly investigated. In this work, I provide a rigorous formulation for eikonal tomography using Gaussian processes (GPs) to smooth observed phase delay measurements, including uncertainties. GPs allow the posterior phase delay gradient to be analytically derived. From the phase delay gradient, an excellent approximate solution for phase velocities can be obtained using the saddlepoint method. The result is a fully Bayesian result for phase velocities of surface waves, incorporating the nonlinear wavefront bending inherent in eikonal tomography, with no sampling required. The results of this analysis imply that the uncertainties reported for eikonal tomography are often underestimated.

Observation of Analog Flatland Cherenkov Radiations on Metasurfaces

AbstractRecent theoretical studies have suggested the existence of a lower‐dimensional version of the Cherenkov radiation, known as “flatland Cherenkov radiation” (FCR). FCR is generated by leakage from a surface‐wave waveguide while being entirely confined in a plane. Here, a metasurface platform is proposed for generating and observing FCR, which is characterized by alternated regions of capacitive and inductive surface impedance, supporting transverse electric (TE) and magnetic (TM) surface waves (SWs), respectively. For experimental demonstration, a microwave setup is presented, and measured results are compared with numerical simulations and theoretical predictions. The study shows that the phase velocities of different SWs can be controlled by structural designs, and suitably fast TE SWs can excite FCR in the form of slower TM SWs. FCR has unique properties such as directionality, tunability, and subwavelength confinement. The proposed platform has important potential to enable nanophotonic applications based on 2D optics, such as agile waveguiding and scanning.

Influence of orientation of fibres on surface wave in fibre‐induced anisotropic elastic medium

AbstractAn isotropic elastic solid reinforced with a family of parallel fibres behaves anisotropic to any deformation. With orientation of all fibres along a coordinate axis in rectangular Cartesian system, this anisotropy reduces to transverse isotropy. Else with arbitrary orientation of fibre‐family, induced anisotropy lacks any symmetry. In this composite medium with arbitrary anisotropy, three‐dimensional wave motion decaying with depth propagates as a surface wave along all directions on plane boundary. Real phase velocity for this surface wave lies implicit in a system of three equations with complex coefficients. An appropriate transformation of this system yields a real characteristic equation, which is solved to get the anisotropic phase velocity of generalised surface wave. This phase velocity defines a complex slowness vector, which is used to calculate the particle motion at any point in the medium. Effects of fibre‐orientation are analysed, numerically, on the phase velocity and polarisation of surface wave. For example, in the reinforced fibres alters the contours of particle motion through increased ellipticity. However, in the presence of fibres, the decay of particle motion with depth slows down.

Determining subsurface temperature & lithospheric structure from joint geophysical-petrological inversion: A case study from Ireland

High quality maps of the geothermal gradient and temperature are essential when assessing geothermal potential for a region. However, determining geothermal potential is a challenge as direct measurements of in situ temperature are sparse and individual geophysical methods are sensitive to a range of parameters, not solely temperature. Here, we develop a novel approach to determine the geothermal gradient using a new joint geophysical-petrological inversion where seismic velocities and density in the mantle are related to temperature and bulk composition within a thermodynamic framework. Large datasets of phase velocities of seismic surface-waves are now incorporated into the inversion, and provide essential constraints on the lithospheric thickness and temperature, which shape the crustal geotherms to a significant extent. We also include all available measurements of the surface heat flow, radiogenic heat production (RHP) and thermal conductivity within the crust, to further constrain the temperature and geothermal gradient, in particular in the top few kilometres of the crust. We use Ireland as a case study and show how our new methodology can reproduce the results of previous work but also improve on them, thanks to the complementary sensitivities of the full range of data. Lithospheric and crustal thicknesses have primary controls on the temperature gradient, with areas of thinner lithosphere showing higher geothermal gradients. In some locations, anomalously warm geotherms result from high RHP within crustal granitic rocks, mudstone and shales. RHP is above continental averages across all Ireland, likely due to a crust with mostly felsic lithology. The new methodology provides a robust workflow for determining the geothermal potential in areas with limited direct temperature measurements, facilitating knowledge creation for the transition to sustainable energy sources and energy self-sufficiency.

Ambient noise tomography of the Aegean region of Türkiye from Rayleigh wave group velocity

We have studied Rayleigh wave group velocities beneath the Aegean region of Türkiye using ambient noise tomography. Noise data were gathered from 43 broadband seismic stations belonging to three permanent broad-band arrays. The cross-correlation method was used to estimate empirical Green’s functions. Group velocities of the fundamental mode Rayleigh waves were determined using multiple filter technique. We measured dispersion for each station pair in a period range of 2–12 s and computed maps of group velocity distribution using the fast marching surface tomography method. The group velocity maps correlate well with the geological and tectonic features of the region, displaying low velocities for the Quaternary alluvial basins, moderate velocities for Cretaceous rocks, and high velocities for the regions where gneiss and granitoid rocks outcrop. Low velocity anomalies may be associated with the grabens and horsts formed by faulting and to deep mantle flow. We detect potential offshore geothermal zones in Izmir and Candarli Bay. The information from broad-band networks improves the resolution of crustal surface wave velocity structures, particularly for shallow depths. This improvement will support the assessment of seismic hazard, as the shallow layers of the crust contribute significantly to seismic activity.

Characterizing polycrystalline microstructures by reconstructing grain boundaries and velocity map from ultrasonic surface wave field

An ultrasonic material characterization method is proposed to reconstruct the polycrystalline microstructures from the field-measurement of ultrasonic surface waves. Two wavenumber–frequency domain filters are developed to extract specific wave components for the reconstructions. One is the evanescent-pass filter that can be used to reconstruct the grain boundaries. The other is the directional filter to map the surface wave velocity along a specific direction. The method is validated by numerical simulations, as well as by experiments, on an additively manufactured sample. Sub-wavelength resolution can be achieved by the proposed method if sufficient data is captured spatially within one wavelength of the surface wave.

Plasma surface ionization wave interactions with single channels

The study of plasma surface ionization waves (SIWs) in recent years has primarily focused on planar surfaces and periodic two dimensional structures. In application, substrates are likely to have non-planar morphology such as cracks, pores, and steps. Additionally, targets for the applications of medicine or catalysis may have targets with heterogeneous composition. This classification of targets are brought under the umbrella of complex interfaces. In this work, plasma SIWs were incident on a complex target consisting of a single channel cut into glass slides. The SIW velocities for the in-channel portion of the wave and radially propagating portion of the wave were tracked. It was found that surface wave velocities are not significantly affected by channel geometry, but primarily increase with pulse energy. A third propagation direction for the SIW is characterized in the azimuthal direction relative to the radial portion of the wave. Channel geometry is found to greatly effect the area treated by the plasma but not the propagation velocity of the surface wave. Surface wave morphology and the impact on application is also discussed. A simple model was introduced to understand the mechanisms behind SIW escape from a channel. It was found that the ratio of pulse energy to a geometry dependent minimum energy can predict the escape angle of a SIW from single channels.

On the Accuracy of Surface-Wave Dispersion Measurements from Horizontal-Component Ambient Noise Cross Correlations

Abstract At present, both Rayleigh and Love waves can be extracted from cross-correlations of ambient noise in ambient noise tomography (ANT). It has been demonstrated that accurate Rayleigh-wave dispersion curves can be extracted from vertical-component noise when noise sources are evenly distributed in space. However, because the rotation of horizontal components alters the distributions of effective sources in horizontal–horizontal cross correlations between a pair of stations, it is still not completely sure if dispersion curves of Rayleigh and Love waves extracted from horizontal-component noise data are accurate for ANT. In this study, through numerical simulations, we demonstrate that surface-wave phase velocities extracted from the horizontal–horizontal cross-correlation functions (CCFs) systematically deviate from structural phase velocity even when noise sources are evenly distributed in space. The deviations of phase velocities quickly increase with decreasing station separations of CCFs when station separations are shorter than three wavelengths. Further analysis on field data recorded at seismic stations in the contiguous United States confirms the existence of the phase-velocity deviations of Rayleigh and Love waves when they are measured from horizontal–horizontal CCFs. Because the deviations become smaller with increasing station separations and are less than 0.25% at station separations longer than three wavelengths, we suggest that it is best to only select those CCFs with station separations longer than three wavelengths in ANT when measuring phase velocities of surface waves from horizontal-component CCFs, such as Love waves from radial–radial CCFs.