Wave Dispersion Curves Research Articles

Guided waves propagation in arbitrarily stacked composite laminates: Between-layers incompatibility issue resolution using hybrid matrix strategy

Lamb waves (LWs) are widely used to achieve structural health monitoring of aeronautic composite structures. Composite materials are however anisotropic and LWs propagation characteristics depend on their propagation direction. Within one composite ply, when this direction coincides with the principal axis of the ply, they are not coupled with shear waves (SHWs) but become coupled with SHWs for any other direction. As composite materials are built up with layers at various orientations LWs and SHWs are coupled for some layers and uncoupled for some others when studying an arbitrary propagation direction. Transfer Matrix Method (TMM), Global Matrix Method (GMM), and Stiffness Matrix Method (SMM) are all methods allowing to predict guided waves (LWs and SHWs) behavior in composite materials. However those methods suffer from an incompatibility issue preventing them to manage cases when SHWs and LWs are coupled for some plies but uncoupled for some other plies. This issue is particularly frequent when dealing with metallic-composite plates or with composite plates made up with isotropic, orthotropic, and triclinic materials. In order to solve this incompatibility issue, a hybrid matrix strategy (HMS) is proposed here on the basis of SMM. The core idea of the HMS is to re-couple LWs and SHWs into hybrid guided waves when they are uncoupled in order to make them compatible with the general coupled waves cases. The numerical stability of HMS is proved theoretically and its effectiveness is validated through numerical investigations and using experimental data from the literature. The SMM-HMS framework can thus be considered as a state of the art benchmark approach for evaluating the performance of numerical methods dedicated to the computation of guided waves dispersion curves and can be confidently applied to any arbitrary composite material used in aeronautic and aerospace industries.

Dispersion curves of acoustoelastic borehole waves: the perturbation method with the correct formulation of the stresses around the borehole

SUMMARY The acoustoelastic model has been widely used to investigate the influence of formation stresses on the dispersion curves of borehole waves. The analytical perturbation method (PM), the finite-difference time-domain (FDTD) and the semi-analytical finite element (SAFE) are three common-used methods to calculate the dispersion curves. However, due to different interpretations of the PM and plane strain assumptions, the obtained dispersion curves are incompatible among existing PMs, which may misguide the interpretation of formation stresses. It is therefore necessary to untangle the applicability and limitations of PM. Considering that the conventional PMs are usually inaccurate at the low frequency or inconsistent with Hamilton’s principle, we develop a revised PM to obtain the dispersion curves of borehole waves propagating along a borehole surrounded by the triaxially stressed formation assumed as a monoclinic medium. The revised PM is more accurate, reasonable and logical than existing PMs. When the formation is subjected to low stresses, our finding is of great benefit for quickly computing dispersion curves, since the revised PM is much more efficient than the FDTD method; and there are small discrepancies between the flexural dispersions obtained by the revised PM and those obtained by the FDTD method. Nevertheless, the revised PM has two limitations. The first limitation is that the revised PM cannot be used to compute the Stoneley dispersion curves, which have been validated by comparison with SAFE and FDTD methods. The second limitation is that flexural dispersion curves show significant discrepancies in the high-frequency domain when the low-stress assumption does not hold, as compared to those obtained by the FDTD method.

Bolt Axial Stress Measurement Based on the Dual-Mode Electromagnetic Acoustic Transducer

To further simplify the bolt stress measurement process, the feasibility of using a dual-mode EMAT that excites both longitudinal and shear waves is investigated to achieve rapid and accurate measurement. The propagation characteristics of cylindrical guided waves in a rod are studied by a Semi-analytical Finite Element model. Through the combination of the theoretical formula and the finite element simulation, the non-uniform distribution of axial stress is directly used to calculate the time of flight of cylindrical guided waves without building any approximate model. The effect of stress distribution on guided wave modes with different energy concentration regions is analyzed. The propagation characteristics of guided waves and the theoretical values of group velocity of these two modes are studied by cylindrical guided wave dispersion curve and mode shape analysis. Then, by combining the static stress distribution inside the bolt with the theoretical formula, the influence of the different distributions of guided wave energy in the cross section of the two modes on the velocity ratio was analyzed. Finally, the feasibility of the theory is verified by the experiment. The result of the experiment in the aluminum bolt verified the effectiveness of the dual-mode EMAT on stress measurement and the novel ultrasonic testing models proposed in this paper.

Shear Wave Velocities in the San Gabriel and San Bernardino Basins, California

AbstractWe construct a new shear velocity model for the San Gabriel, Chino and San Bernardino basins located in the northern Los Angeles area using ambient noise correlation between dense linear nodal arrays, broadband stations, and accelerometers. We observe Rayleigh and Love waves in the correlation of vertical (Z) and transverse (T) components, respectively. By combining Hilbert and Wavelet transforms, we obtain the separated fundamental and first higher mode of the Rayleigh wave dispersion curves based on their distinct particle motion polarization. Basin depths constrained by receiver functions, gravity, and borehole data are incorporated into the prior model. Our 3D shear wave velocity model covers the upper 3–5 km of the crust in the San Gabriel, Chino and San Bernardino basin area. The Vs model is in agreement with the geological and geophysical cross‐sections from other studies, but discrepancies exist between our model and a Southern California Earthquake Center community velocity model. Our shear wave velocity model shows good consistency with the CVMS 4.26 in the San Gabriel basin, but predicts a deeper and slower sedimentary basin in the San Bernardino and Chino basins than the community model.

An inversion method for evaluating ballastless track degradation based on multi-channel analysis of surface wave

Due to the heterogeneous properties of constituent materials, traditional Multi-channel analysis of surface wave (MASW) method is unsuitable for evaluating ballastless track as surface waves exhibit different dispersion patterns. To overcome this limitation, firstly, the implementation process of MASW was introduced, and the phase shift method was employed to perform dispersion analysis of multi-channel surface wave signals. Secondly, a wave field solution model of ballastless track was established using the time-domain finite-difference method. Subsequently, the stiffness matrix method was improved to account for the heterogeneous properties of the constituent materials and to calculate the theoretical surface wave dispersion curve of ballastless track, followed by the analysis of surface wave dispersion characteristics in ballastless track and the proposal of an inversion method. Finally, the optimal excitation central frequency and receivers’ deployment were analyzed in the MASW method, and the inversion analysis of ballastless track degradation were conducted. Results shown that the surface wave dispersion curve is more sensitive to CA mortar degradation at low frequencies and concrete slab degradation at high frequencies. Appropriate excitation central frequency and receivers’ deployment are essential for accurately extracting the surface wave dispersion curve from the dispersion energy of ballastless tracks. The inversion method proposed in this study provides a more accurate evaluation of ballastless track degradation compared to assuming ballastless track as a homogeneous structure during inversion analysis.

In situ estimation of effective rock elastic moduli by seismic ambient vibrations

In this study, we performed a non-invasive ambient noise investigation of unsaturated rock structures in the Bohemian Paradise (Bohemian Cretaceous Basin, Czech Republic). Our study focused on two key topics: 1) An in situ elastic moduli estimate of competent, horizontally deposited sandstone layers using ambient noise array measurements. Recordings were processed using an f-k array analysis, from which frequency-dependent Love and Rayleigh wave dispersion curves, as well as Rayleigh wave ellipticity, were retrieved. Data were inverted for the P- and S-wave velocity profiles, from which Young's and shear moduli were successfully estimated. 2) A study of the local response of the Kapelník rock tower. We analysed a dataset of ambient noise recordings obtained from the top of the tower and its foot. Information regarding tower oscillation frequencies and directions, together with amplification ratios, were retrieved from a particle motion polarisation analysis and from site-to-reference spectral ratios. Euler-Bernoulli beam theory was also employed for interpreting measured data using elastic moduli estimated from noise array measurements.

Study on Time-frequency Imaging of Ultrasonic Detection with Phase Shifted Fiber Bragg Grating Sensing

Abstract The influence of the wavelength difference between the laser source and the phase-shifted fiber Bragg grating (PS-FBG) on the intensity of the power demodulation system based on an adjustable laser source was studied experimentally, and the optimum of the output laser wavelength was determined. Then, the research on time-frequency imaging damage identification based on smooth pseudo-Wigner-Ville distribution was carried out. The Time of Flight of the acoustic wave signal was calculated and time compensation was made according to the Wigner-Ville distribution and the Lamb wave dispersion curve. The ultrasonic waves before and after damage were measured with spatially arranged PS-FBGs. The difference signals were processed in a window, and then the time-frequency energy of the normalized difference signal was imaged to assess the damage detection and location. Although the mode and group velocity of ultrasound measured by each fiber grating were different, the accurate location and identification of artificial damage in an aluminum alloy plate was realized by using only three PS-FBGs and a smooth Wigner time-frequency imaging method.

Crustal Shear Wave Velocity Structure Using Dispersion of Rayleigh Wave Beneath Sumatra Stations

The structure of the earth's crust is a fundamental and very important topic in seismology, because the crustal structure can be used as initial information to study the surface conditions of an area. One method to determine the structure of the earth's crustal layers is by analyzing the dispersion of surface waves, because surface waves are very sensitive to S waves. The shear wave velocity as a result of Rayleigh wave velocity inversion can provide the information of the subsurface material properties in the earth that can be study the structure of the earth's crust. The inversion results using the SVAL program can provide the Rayleigh wave dispersion curve with group velocity which shows the station on the island of Sumatra is higher than the velocity on the island of Nias. The structure beneath the island of Sumatera was formed earlier than the island of Nias. The thickness of the crust varies in the Sumatra region, the thickness of the crust on the island of Sumatra (BKNI, LHMI, MNAI and PMBI) is 28 km and 33 km. Specifically on the island of Nias, the thickness of the crust is 19 km. S-wave velocity in the crust is 3.1 km/s to 3.7 km/s.

On the direct estimation of bedrock depth and time-weighted average VS from surface waves dispersion and HVSR curves

The engineering bedrock depth (h) and time-weighted average shear wave velocity till that depth (VS,h) are recognized to be of primary relevance for earthquake hazard assessment. In fact, in contemporary seismic construction codes, they are regarded as proxys for the site response evaluation. Therefore, time-, cost-efficient and reliable investigation strategies are required for their determination, particularly when numerous surveys have to be interpreted for the reconstruction of the geological setting in large study areas and within micro-zonation studies. With this aim a workflow based on the application of a recently published linear wavelength-depth transformation (WD transform) is evaluated in this paper. The workflow allows to directly derive both h and VS,h from surface waves dispersion and HVSR curves, avoiding the formal solution of the inverse problem,. Obtained results show for the first time the effectiveness and reliability of the proposed workflow for various bedrock depths and overlying velocity structures, and discuss advantages and drawbacks in its application in relation to the uncertainty of the inversion techniques.

Lithospheric deformation in Mongolia revealed by anisotropic Rayleigh wave tomography: Implications for the mechanism of intracontinental orogeny

The Mongolian Plateau is situated in the eastern part of the Central Asian Orogenic Belt that was formed during the Paleozoic era. In the Cenozoic era, the plateau has been reactivated, leading to significant topographic uplift, volcanism, and seismic activity. Several destructive earthquakes, ranging from magnitudes 6 to 8, have occurred in the 20th century. But the mechanism of these neotectonics remains unclear. To better understand these processes, we determined S wave velocity and azimuthal anisotropy in the crust and upper mantle under Mongolia using Rayleigh wave dispersion curves. Our findings indicate that the lithosphere is dominated by NW-SE fast velocity directions (FVDs). However, we observed different patterns in two specific regions. The lithospheric anisotropy under the Hangay Dome is weak, suggesting that it is accompanied by significant mantle upwelling under the dome. On the other hand, the FVDs in the Gobi Desert exhibit a circular pattern that wraps around the Ordos Block, which may have been caused by past and present deformation imposed on the stable block. These results offer new insights into the lithospheric deformation and dynamics of the Mongolian Plateau.

Surface wave dispersion curve inversion using mixture density networks

SUMMARYIn many seismological, environmental and engineering applications a detailed S-wave velocity model of the shallow subsurface is required. This is generally achieved by the inversion of surface wave dispersion curves using various inversion methods. The classical inversion approaches suffer from several shortcomings, such as inaccurate solutions due to local minima or large computation times in case of a wide parameter space. A number of machine learning (ML) approaches have been suggested to tackle these problems, which however do not provide probabilistic solutions and/or constrain layer number and layer thickness to a fixed value. In this study, we develop a novel neural network (NN) approach in order to characterize the shallow velocity structure from Love and Rayleigh wave dispersion curves. The novelty of our method lies in the simultaneous estimation of layer numbers, layer depth and a complete probability distribution of the S-wave velocity structure. This is achieved by a two-step ML approach, where (1) a regular NN classifies the number of layers within the upper 100 m of the subsurface and (2) a mixture density network outputs the depth estimates together with a fully probabilistic solution of the S-wave velocity structure. We show the advantages of our ML approach compared to a conventional neighbourhood inversion and a Markov chain Monte Carlo algorithm. Our ML approach is then applied to dispersion curves extracted from recorded noise data in Munich, Germany. The resulting velocity profile is in accordance with lithologic information at the site, which highlights the potential of our approach.

Single-point dispersion measurement of surface waves combining translation, rotation and strain in weakly anisotropic media: theory

SUMMARY A new approach is proposed for measuring the dispersion relation of surface waves in weakly anisotropic media using a single station, which consists of translational displacement and rotation or strain. The azimuth-dependent surface wave dispersion curve can be directly obtained by using the amplitude ratio of translational displacement to rotation or strain. Using observations from earthquakes from a variety of azimuths allows us to characterize the anisotropy of subsurface media. The amplitude ratio gives the localized azimuth-dependent dispersion relations of the formation beneath a receiver without requiring knowledge of the source or structure along the path. The theory shows that in anisotropic media the coupled quasi-Rayleigh wave and quasi-Love wave will result in elliptically polarized rotational motions. In addition, rotational motion information allows the determination of backazimuth even in general anisotropic media. We carry out numerical experiments, investigate the effects of noise and degree of anisotropy and demonstrate the potential for field studies.

Active and passive seismic methods for site characterization in Nuweiba, Gulf of Aqaba, Egypt

Nuweiba is located on the western coast of the Gulf of Aqaba (GoA), which represents the southern part of the Gulf of Aqaba - Dead Sea transform fault (GoA-DST). The GoA is characterized by high seismic activity and is the source of the November 22, 1995, Nuweiba earthquake, with a moment magnitude of Mw 7.3. This seismic unrest caused extensive damage in the city of Nuweiba due to the strong shaking caused by the earthquake. In addition, soil amplification triggered by the thick soft-sediments of the Wadi Watir delta beneath the city amplified the destructive power of the event. Therefore, an assessment of the effect of the Wadi Watir sediments on the ground motion at Nuweiba is very important for future construction, seismic hazard assessment, and seismic risk mitigation. Accordingly, the goal of the current study is to define the amplification characteristics of the Wadi Watir deposits using microtremor and surface wave data sets. The horizontal-to-vertical spectral ratio (HVSR) technique is applied to the microtremor data and Multichannel Analysis of Surface Waves (MASW) is applied to the surface wave data. The data are processed to obtain the distribution of the fundamental resonance frequency (F0), the depth of the geophysical bedrock using joint inversion of the Rayleigh wave dispersion curve and ellipticity peak, the shear wave velocity structure, the time-averaged shear-wave velocity in the topmost 30 m (Vs30), and the shear wave transfer function. The results of the HVSR show that F0 in the northern part of the city is 4.2–5.2 Hz and 0.5–0.8 Hz in the middle of the city. Bedrock depth is found to be in the range of 27 and 199 m. The one-dimensional velocity structure obtained from the MASW measurements has resolved two sedimentary layers within the upper 15 m. The Vs30 ranges between 207 and 556 m/s, according to the Vs30 the soil in the study area is categorized into soil classes B and C according to Eurocode 8. The obtained shear wave transfer functions show that the highest amplification factors are observed in the middle part of the study area.

A Local Seismic Project near the Dalk Glacier Area, Larsemann Hills, East Antarctica: Toward Subice Imaging and Icequake Monitoring

Abstract During the 2019–2020 field season of the 36th Chinese National Antarctic Research Expedition, two seismic arrays were deployed in the Dalk Glacier area of Larsemann Hills, East Antarctica. The arrays consisted of 100 short-period nodal stations and were intended to investigate the physical properties and seismic events in the region, with the goal of enhancing our understanding of the glacier’s structure and dynamics. With these data, we use horizontal-to-vertical spectral ratio (HVSR) analysis to estimate the ice thickness. Noise cross-correlation functions and multimode dispersion curves of Rayleigh waves were extracted from the vertical-component ambient noise data to illuminate near-surface glacial structures. Teleseismic events with Mw >5.5 and two typical kinds of icequakes were observed via visual inspection. These initial results improve the understanding of the physical properties of the ice sheet as well as the glacial seismicity in Dalk Glacier.

Tectonic Activities Description in the Ongoing Collision Zone of the Eurasia-Arabia Plates Using 2D Surface Waves Tomography

In order to better understand the regional tectonic activities of the continent-continent ongoing collision-compressed edge zone of the Eurasian-Arabic plates, 2D tomography maps of the Caucasus territory using the Rayleigh waves were generated. The 2D tomography images of this study, illustrate the large variety in surface wave propagation velocity in different complex geologic units of the Caucasus. To draw the 2D tomography maps, we accomplished a 2D-linear inversion procedure on the Rayleigh wave dispersion curves for the periods of 5 to 70 s (depth= ~180 km). To conduct this, local-regional data from ~1300 earthquakes (M≥3.9) recorded by the 49 broadband stations from 1999 to 2018 in a wide area with complicated tectonic units were used. In comparison with results of previous studies in Caucasus, the tomography maps for the long-periods (T= 50-70 s; depth ~180 km) are more influenced by the velocity structure of the uppermost mantle which demonstrate the ultralow and ultrahigh-velocity anomalies. The results for the medium-periods (30≤T≤45 s), the low-velocity zones coincide with areas thought to be correlated with underplating of the lower crust (e.g. shallow LAB), while, the high-velocity zones are usually demonstrating the presence of a normal continental crust over a stable and thick or oceanic-like lid. Short-periods (5≤T≤25 s) are more influenced by the ever-evolving deformations of the geological units, sedimentary basins, volcanic complexes, uplifts, and reveals a low-velocity small zone, on the NW slope of the Aragats volcano (depth= ~7 km), which is different from the results of other studies.

Multiple Voronoi Partition Improves Multimodal Dispersion Imaging From Ambient Noise: A Case Study of LASSO Dense Array

AbstractRecent studies on the frequency‐Bessel transform (F‐J) method demonstrate the ability of the array‐based method to extract higher‐mode surface wave dispersion curves from ambient noise, which provides a new opportunity to reveal more accurate underground structures. However, problems with the subarray selection for three‐dimensional imaging remain. On the one hand, we need the subarray to be large enough such that the F‐J method can capture high‐quality dispersion curves, and on the other hand, we want the subarray to be small enough to maintain a sufficient horizontal resolution. To solve this problem, we propose a strategy that randomly and repeatedly partitions the subarray based on Voronoi diagrams. We call this the FJ‐VoroTomo method. The FJ‐VoroTomo method does not require tedious parameter tuning and can measure high‐quality dispersion while maintaining horizontal resolution. More importantly, this method can quantitatively analyze the uncertainty of the measured dispersion curves. In this work, we use the noise cross‐correlation functions from the LArge‐n Seismic Survey in Oklahoma array as an example to demonstrate the dispersion and its uncertainty obtained by the FJ‐VoroTomo method and evaluate the three‐dimensional S wave velocity structure beneath this dense array. We hope that by using this strategy, the multimodal surface wave method can be more feasible in dense arrays that are currently widely used.

Structure Along the Martian Dichotomy Constrained by Rayleigh and Love Waves and Their Overtones

AbstractUsing seismic recordings of event S1222a, we measure dispersion curves of Rayleigh and Love waves, including their first overtones, and invert these for shear velocity (VS) and radial anisotropic structure of the Martian crust. The crustal structure along the topographic dichotomy is characterized by a fairly uniform vertically polarized shear velocity (VSV) of 3.17 km/s between ∼5 and 30 km depth, compatible with the previous study by Kim et al. (2022), https://doi.org/10.1126/science.abq7157. Radial anisotropy as large as 12% (VSH > VSV) is required in the crust between 5 and 40 km depth. At greater depths, we observe a large discontinuity near 63 ± 10 km, below which VSV reaches 4.1 km/s. We interpret this velocity increase as the crust‐mantle boundary along the path. Combined gravimetric modeling suggests that the observed average crustal thickness favors the absence of large‐scale density differences across the topographic dichotomy.

Multi-Mode Imaging of Ambient Background Noise for Karst Detection in the Limestone Area Based on Frequency-Bessel Transform

In response to the challenges of karst geophysical exploration in an environment with strong external interference, this paper proposes a new method, namely the frequency-Bessel transform method, for extracting multi-order dispersion curves of surface waves from background noise to characterize karst. The observation noise data of the Wuhan karst development area are used as an example, where the dolomitic limestone and limestone mixed with dolomite of the Jialing River Formation of the middle lower Triassic are widely developed in the observation area. The frequency-Bessel transform method involves performing a Bessel integral transformation on the cross-correlation coefficient of background noise in the frequency domain. Firstly, by synthesizing theoretical noise data and comparing it with the spatial autocorrelation method—which is currently the main method for extracting the fundamental dispersion curve of surface waves—it is verified that the frequency-Bessel transform method can extract the higher-mode dispersion curve. Then, by taking the actual measured single-point noise data as an example, the effect of applying the frequency-Bessel transform to the actual noise data is tested, and the inversion of the fine structure of the strata by the addition of higher-mode dispersion, the use of the damped least squares inversion method, and the joint inversion of fundamental and higher-mode dispersion curves are analyzed. The higher-mode dispersion curve of Rayleigh surface wave extracted by the frequency-Bessel transform is much clearer, and the 2D shear wave velocity structure profile obtained from inversion explains the karst development area, karst strip area, and thickness of the Quaternary overburden. The inferred results match with the actual borehole data. Multi-mode imaging of background noise based on the frequency-Bessel method can be applied to depict karst in complex backgrounds, and has significant potentiality in the field of ambient seismic noise tomography, providing a new idea and method for karst detection in near-surface engineering.

Surface-wave dispersion curves extraction method from ambient noise based on U-net++ and density clustering algorithm

It is crucial to accurately and rapidly extract dispersion curves of surface waves from ambient noise recordings for inverting the subsurface shear (S) wave velocity structures. Conventional manual picking methods are labor-intensive and affected by subjective factors related to seismologists. The existing deep learning methods can automatically and efficiently extract dispersion curves from dispersion spectrograms with a single branch. However, extracting dispersion curves from phase-velocity dispersion spectrograms with multiple branches remains challenging due to complex label-making processes and extensive label-preparation times. Notably, phase velocities typically display a positive correlation with periods and are slightly higher than group velocities. Given the significance of this empirical relationship, we present an intelligent surface-wave dispersion curves extraction method based on U-net++ and density clustering algorithm. Initially, guided by domain knowledge that dispersion curves are smooth, a global searching method is employed to automatically label group-velocity dispersion curves from group-velocity dispersion spectrograms. Subsequently, the group-velocity dispersion curves undergo transformation into probability images of the curves using a Gaussian function. The U-net++ then nonlinearly converts group-velocity dispersion spectrograms into probability images of group-velocity dispersion curves within a high-dimensional space. Following this, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is applied to obtain multi-mode phase-velocity dispersion curves from phase-velocity dispersion spectrograms. We then remove invalid dispersion values in the multi-mode phase-velocity dispersion curves based on the empirical relationship between phase and group velocities, ultimately obtaining the phase-velocity dispersion curve corresponding to the group-velocity dispersion curve. Our proposed method has been tested using synthetic data and 3D real-world data collected near Lake Chao in Anhui Province. The test results show that our approach effectively extracts both group-velocity and phase-velocity dispersion curves. Inverted S-wave velocity structures based on extracted dispersion curves in real-world data can characterize the Tan-Lu fault zone, demonstrating the effectiveness of our proposed method.

Lead Zirconate Titanate Transducers Embedded in Composite Laminates: The Influence of the Integration Method on Ultrasound Transduction.

In the context of an embedded structural health monitoring (SHM) system, two methods of transducer integration into the core of a laminate carbon fiber-reinforced polymer (CFRP) are tested: cut-out and between two plies. This study focuses on the effect of integration methods on Lamb wave generation. For this purpose, plates with an embedded lead zirconate titanate (PZT) transducer are cured in an autoclave. The embedded PZT insulation, integrity, and ability to generate Lamb waves are checked with electromechanical impedance, X-rays, and laser Doppler vibrometry (LDV) measurements. Lamb wave dispersion curves are computed by LDV using two-dimensional fast Fourier transform (Bi-FFT) to study the quasi-antisymmetric mode (qA0) excitability in generation with the embedded PZT in the frequency range of 30 to 200 kHz. The embedded PZT is able to generate Lamb waves, which validate the integration procedure. The first minimum frequency of the embedded PZT shifts to lower frequencies and its amplitude is reduced compared to a surface-mounted PZT.