Phase Velocity Dispersion Curves Research Articles

Shear-wave velocity profiling of Jizan city, southwestern Saudi Arabia, using controlled-source spectral analysis of surface-wave measurements

Shear-wave velocity profiles are the main site-specific data for site classification, which are commonly used for the purposes of seismic microzonation and hazard assessment. The controlled-source spectral analysis of surface wave (CSSASW) dispersion measurements have been successfully performed to characterize seismic sites up to 30-m depths. This study utilizes the CSSASW application in Jizan City to obtain shear-wave velocity profiling at 14 sites distributed throughout the city using an electromagnetic vibrator. The recorded Rayleigh wave phase velocity dispersion curves are transformed to calculate the apparent velocity distribution in depth. Shear-wave velocities, calculated using theoretical relationships, can then be utilized to obtain design parameters for the soil strata. Shear-wave velocity varies from 216.97 to 829.59 m/s through Jizan City indicating the remarkable change of the near-surface sediments. The hard soil profiles of soft rock that were revealed by Vs values in this terrain (sites No. 7, 8, and 13) can be attributed to the existence of a dense layer of salt rock. Construction in such areas is prohibited due to the high susceptibility of large settlements in foundations as a consequence of salt dissolution. In the Sabkha terrains, all soil profiles were related to Vs, defined as stiff soils that were then modified to a softer class owing to their high liquefaction potential. These results should be considered before establishing important and strategic projects in the city.

Investigating the subsurface in a shallow water environment using array and single-station ambient vibration techniques

SUMMARYSingle-station and array ambient vibration techniques are widely used in onshore environments, in particular to retrieve the subsurface structure and shear-wave velocity profiles. We apply these techniques offshore in Lake Lucerne (Switzerland) using single-station and array Ocean Bottom Seismometer (OBS) data. This lake has experienced tsunamigenic subaquatic slope failures in the past and still has sediment-charged slopes that might fail in the presence of a seismic or aseismic trigger. The application of traditional onshore methods offshore brings additional challenges related to the processing of recorded data. To overcome these challenges, we perform multibeam bathymetry surveys to precisely locate the OBS on the lake floor and airgun shootings to determine the orientation of the horizontal components of the seismometer and to correct the time drift of the recorder. Then we obtain surface-wave phase velocity dispersion curves of Scholte and Love waves, and Scholte wave ellipticity curves at six subaquatic slopes. After the estimation of the dispersion curves, we deal with their modal identification using mode attribution analysis. The shear-wave velocity and thickness of the sedimentary layers at the investigated slopes are inferred using a transdimensional Bayesian inversion algorithm. The resolved velocity profiles show very low shear-wave velocities in shallow lake sediments and allow us to improve the understanding of the local stratigraphy. This research contributes to the assessment of stability and tsunamigenic potential of subaquatic slopes in Lake Lucerne.

Seismic Ambient Noise Imaging of a Quasi-Amagmatic Ultra-Slow Spreading Ridge

Passive seismic interferometry has become very popular in recent years in exploration geophysics. However, it has not been widely applied in marine exploration. The purpose of this study is to investigate the internal structure of a quasi-amagmatic portion of the Southwest Indian Ridge by interferometry and to examine the performance and reliability of interferometry in marine explorations. To reach this goal, continuous vertical component recordings from 43 ocean bottom seismometers were analyzed. The recorded signals from 200 station pairs were cross-correlated in the frequency domain. The Bessel function method was applied to extract phase–velocity dispersion curves from the zero crossings of the cross-correlations. An average of all the dispersion curves was estimated in a period band 1–10 s and inverted through a conditional neighborhood algorithm which led to the final 1D S-wave velocity model of the crust and upper mantle. The obtained S-wave velocity model is in good agreement with previous geological and geophysical studies in the region and also in similar areas. We find an average crustal thickness of 7 km with a shallow layer of low shear velocities and high Vp/Vs ratio. We infer that the uppermost 2 km are highly porous and may be strongly serpentinized.

Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach

A new solving procedure based on the Legendre polynomial series is developed to investigate the longitudinal guided waves in fractional order thermoelastic inhomogeneous hollow cylinders. Different from the available Legendre polynomial approach, integrals are calculated by the explicit and simple expressions to replace the numerical solutions. The solutions according to the global matrix method (GMM) are also derived for the first time to verify the effectiveness of the presented approach. Comparison of the CPU time indicates that the computational efficiency of the new solving procedure has a huge improvement. Then, the guided wave phase velocity dispersion curves, attenuation curves, displacement and temperature distributions for functionally graded hollow cylinders with different fractional orders, flexural orders, radius-thickness ratios and gradient fields are analyzed. It is found that the attenuation coefficients of flexural longitudinal modes rapidly decrease when the flexural torsional mode curve is close to the flexural longitudinal mode curve. Furthermore, notable influence of the flexural order on attenuation curves mainly occurs at the cut-off frequencies and mutation frequencies. In addition, a smaller radius-thickness ratio implies a larger attenuation, and the temperature amplitudes of flexural torsional mode are more and more close to those of longitudinal mode when the radius-thickness ratio decreases.

Site Characterization of Swiss Strong-Motion Stations: The Benefit of Advanced Processing Algorithms

ABSTRACTSince 2009, 91 new strong-motion stations were built for the renewal of the Swiss Strong Motion Network. Another nine stations will be installed until 2022. For each new station, an extensive site characterization study is performed to model the 1D seismic-velocity profile and, for some sites, the liquefaction potential. Geophysical (passive and active surface-wave methods) and geotechnical cone penetration test (CPT) with additional pore-pressure measurement (CPTu) and seismic CPT (SCPT) methods are used. Analyzing the passive and active recordings with a variety of established and advanced methods, the fundamental frequency of the site, the polarization of the wavefield, the Love- and Rayleigh-wave phase-velocity dispersion curves, and the Rayleigh-wave ellipticity function are retrieved. The liquefaction potential is assessed using CPTu. SCPT measurements are sometimes used to determine the shallow underground structure. The benefits of the combination of different appropriate methods are shown for two examples—the borehole station SBUS in Buochs and the upcoming borehole station SCME in Collombey-Muraz. At both the sites, the CPTu measurements show an elevated liquefaction potential. Combining the passive and active data, the dispersion curves for Love and Rayleigh waves and Rayleigh-wave ellipticity curves are retrieved over a wide-frequency range and inverted for the S-wave velocity profile, in which the shallow part is constrained by the active or SCPT data, the intermediate part by the dispersion curves of the passive methods, and the deepest part by the ellipticity information. For Buochs, the 1D SH-wave amplification functions modeled for the velocity profiles are compared with the empirical amplification for earthquake recordings. Finally, an overview of the site characterization results for 52 of the newly installed seismic stations is given.

Extending the formulation of the spatial autocorrelation (SPAC) method to strain, rotation and tilt

SUMMARYThe spatial autocorrelation (SPAC) method has been applied to ambient seismic noise measured by arrays of translational seismometers for inverting phase-velocity dispersion curves of Rayleigh or Love waves for shallow S-wave velocity structure. Recently, it is becoming possible to observe wave spatial gradients such as strain, rotation and tilt owing to the development of dense seismic networks and improving measurement technologies. Therefore, it is desirable to extend the formulation of the SPAC method to strain, rotation and tilt. This study presents analytical expressions of cross-spectra and coherence of the strain, rotation and tilt components that are measured on the free surface. According to the results, both Rayleigh and Love waves contribute to most components of strains. The exceptions are the areal strain and the vertical axial strain (ezz) on the free surface that are affected by only Rayleigh waves. Only Rayleigh waves contribute to the tilts and rotations around the horizontal axes on the free surface, too. On the other hand, only Love waves contribute to the rotation around the vertical axis. Therefore, different kinds of wave spatial gradients are helpful to separate Rayleigh and Love waves correctly. For practical applications, the analytical expression for the radial axial strain (err) component will be applied directly to distributed acoustic sensing data measured with straight sections of a fibre-optic cable. On the other hand, dense observations of rotation and tilt may still be difficult to carry out at present. However, an application of analytical formulations in this study to arrays of at least several three-component rotational seismometers is attractive because it enables us to separately estimate the phase velocities of Rayleigh and Love waves.

Seismic site characterization and site response study of Nirsa (India)

The Nirsa block, a coal mining area, and an industrial town lies in the southern part of Dhanbad district, at the border between the Indian states of Jharkhand and West Bengal. This area manifests the significant seismic risk posed by earthquakes, natural as well as induced, of high enough seismic intensity VI and VII from regional and local earthquakes. Hence, it is indispensable to seismically characterize the top surficial layers to reduce the risk associated with earthquakes in this region. We characterize these layers, using ambient noise acquired from multichannel simulation with one receiver and single station method to subsequently invert for shear wave velocities, via iterative global search technique of the guided Monte Carlo method by fitting fundamental mode Rayleigh wave phase velocity dispersion curves and horizontal-to-vertical spectral ratios (HVSR). We survey the area to record a sufficient amount of ambient noise within the frequency range of 1–30 Hz at seventy-eight observation points, with uniform spacing of 250 m, covering a total area of about 4 km2. Our results reveal that the bedrock depth lies in the range of 19.5–2.7 m; while Vs30 values vary in the range of 250–950 m/s in the Nirsa region. The variations in fundamental resonance frequencies, obtained from HVSR curves, are found to be more scattered in the range between 2 and 23 Hz. The maps of fundamental resonance frequency, peak HVSRs’ amplitude, bedrock depth and Vs30 derived from this research exhibit good correlation with each other. The Vs30 prediction equation based on the fundamental resonance frequency (fr) and HVSR amplitude (A0) will help future studies to determine Vs30 of unknown regional sites. The efficacy of our results is reliable as there is good concurrence between shear wave velocity profiles, HVSR profiles and litholog data sets. Our results may prove to be important assets to agencies such as National Disaster Management Authorities and Geological Survey of India for construction of seismic microzonation maps in Nirsa.

Basic performance of a spatial autocorrelation method for determining phase velocities of Rayleigh waves from microtremors, with special reference to the zero-crossing method for quick surveys with mobile seismic arrays

SUMMARY We theoretically and empirically demonstrate the usability of the zero-crossing method for quick microtremor surveys in earthquake engineering (i.e. microtremor array surveys), namely shallow (< a few kilometres) surveys with small-scale (< 1 kilometre in radius) mobile seismic arrays with a short observation time (< a few hours). The zero-crossing method is a type of spatial autocorrelation (SPAC) method that determines phase velocities based on multiple frequencies at which the SPAC coefficient curve crosses zero. It is theoretically shown that the zero-crossing method is robust against incoherent noise and that the use of the first zero crossings (i.e. those at the lowest frequencies) is more robust against inadequate conditions of the microtremor wavefield than the use of later zero crossings (i.e. those at higher frequencies). We used microtremor array data with maximum array radii and observation durations of 400 m and 120 min on average, respectively, at 445 observation sites in the Kanto Plain, Japan, for validating the practicality of using the first zero crossings. As an illustration of the robustness against low signal-to-noise ratios (SNRs), we show that with the zero-crossing method, low-sensitivity (i.e. low-SNR) seismometers provide the same analysis results as those obtained with high-sensitivity seismometers, even when the power spectral densities for the low-sensitivity seismometers are close to the self-noise level. We then show that a reference phase velocity dispersion curve (RPVDC), created mainly based on the first zero crossings at each site, has a spatial distribution that well corresponds to the geology and topography and is consistent with that obtained in a previous study. We inverted five RPVDCs to model 1-D S-wave profiles and validated them using S-wave profiles obtained from velocity logs at nearby deep (e.g. hundreds of metres) boring wells. The accuracy of phase velocities at the later zero crossings for three-sensor/four-sensor arrays and all zero crossings for two-sensor arrays are statistically examined (maximum of 9805 data) based on a comparison with the RPVDCs. The disadvantage of the zero-crossing method is that it can only provide information on phase velocities at discrete wavelengths up to a maximum wavelength of 2.6r (i.e. corresponding to the first zero-crossing point), where r is the radius of a seismic array. Therefore, the RPVDCs were then used to examine the upper limit of the analysable wavelength ranges for the conventional SPAC method for microtremor array surveys. Based on a few hundred three-sensor/four-sensor arrays, it was found that for arrays with radii larger than several tens of metres, three-quarters of the upper limit wavelengths (ULWs) stayed within 5r. For arrays with radii smaller than this value, the ULWs strongly depended on the array radius; the ULWs dramatically increased with decreasing array radius. For example, for arrays with an r value of 0.6 m, half of 336 data ranged between 26r and 54r, and the maximum ULW reached 186r. This strong size dependence can be explained by differences in SNR.

Spatial autocorrelation method for reliable measurements of two-station dispersion curves in heterogeneous ambient noise wavefields

SUMMARYThe microtremor survey method (MSM) is used to estimate S-wave velocity profiles from microtremors or ambient noise. Although array-based MSM analyses are usually used for shallow exploration purposes because of their robustness, the extraction of numerous phase-velocity dispersion curves by two-station microtremor analysis is attractive because those dispersion curves can be used to construct high-resolution phase-velocity maps by solving a least-squares problem. However, in exploration studies (>1 Hz), the reliability of two-station microtremor analysis can be affected by short data acquisition times and heterogeneous noise distributions mainly caused by anthropogenic noises. In this study, we propose a new approach to estimate surface wave dispersion curves between station pairs considering a heterogeneous ambient noise distribution based on the spatial autocorrelation method. We first estimated azimuthal variations of noise energy from the complex coherencies between all station pairs in a receiver array, and then estimated dispersion curves between station pairs. Our field example demonstrates that modelling the azimuthal noise energy distribution allows us to use not only the real parts of complex coherencies, but also the imaginary parts, which are usually neglected when assuming a homogeneous noise field. The simultaneous use of the real and imaginary parts of complex coherencies improves the reliability and continuity of phase-velocity estimations between station pairs. Because the stability of phase-velocity estimations depends on the azimuths between station pairs, we carefully selected between-station azimuths that produce stable phase velocities. Selected phase velocities at 8 Hz can be used to construct high-resolution phase-velocity maps with least-squares inversion. Because our approach does not require a regular receiver interval for two-station analysis, it allows for more flexible seismic array geometries. This is particularly important for MSM analyses in urban areas, where limited space is available to install seismic stations. We conclude that our proposed approach is effective in reconstructing high-resolution shallow structures in heterogeneous ambient noise fields.

Crustal Radial Anisotropy of the Iran Plateau Inferred From Ambient Noise Tomography

AbstractThis study presents a three‐dimensional (3D) model of the crustal and uppermost mantle shear wave velocity and radial anisotropy beneath the Iran Plateau constructed by Rayleigh and Love waves from ambient noise. We correlate three years of continuous seismic ambient noise data recorded in 98 stations to obtain cross correlation functions. Then, we measure Rayleigh (8–60 s) and Love (8–50 s) wave dispersion curves from these cross‐correlation functions to generate two‐dimensional dispersion maps using a fast marching surface tomography method. Finally, we build a quasi‐3D shear wave velocity and radial anisotropy model by jointly inverting Rayleigh and Love local phase velocity dispersion curves using a Bayesian Markov chain Monte Carlo inversion method. Observed radial anisotropy beneath Central Iran is weaker than adjacent areas. Negative radial anisotropy is observed in the shallow structures across our study region, which is most likely attributed to vertically aligned cracks in the upper crust. Strong positive radial anisotropy in the middle to the lower crust beneath the Zagros is imaged, which is associated with ductile shear zones in the crust. Radial anisotropy changes from positive values in the crust to negative values in the upper mantle beneath the Zagros, which may be evidence for the decoupling of the crust from the upper mantle beneath the Zagros.

High-Resolution Crustal S-wave Velocity Model and Moho Geometry Beneath the Southeastern Alps: New Insights From the SWATH-D Experiment

We compiled a dataset of continuous recordings from the temporary and permanent seismic networks to compute the high-resolution 3D S-wave velocity model of the Southeastern Alps, the western part of the external Dinarides, and the Friuli and Venetian plains through ambient noise tomography. Part of the dataset is recorded by the SWATH-D temporary network and permanent networks in Italy, Austria, Slovenia and Croatia between October 2017 and July 2018. We computed 4050 vertical component cross-correlations to obtain the empirical Rayleigh wave Green’s functions. The dataset is complemented by adopting 1804 high-quality correlograms from other studies. The fast-marching method for 2D surface wave tomography is applied to the phase velocity dispersion curves in the 2–30 s period band. The resulting local dispersion curves are inverted for 1D S-wave velocity profiles using the non-perturbational and perturbational inversion methods. We assembled the 1D S-wave velocity profiles into a pseudo-3D S-wave velocity model from the surface down to 60 km depth. A range of iso-velocities, representing the crystalline basement depth and the crustal thickness, are determined. We found the average depth over the 2.8–3.0 and 4.1–4.3 km/s iso-velocity ranges to be reasonable representations of the crystalline basement and Moho depths, respectively. The basement depth map shows that the shallower crystalline basement beneath the Schio-Vicenza fault highlights the boundary between the deeper Venetian and Friuli plains to the east and the Po-plain to the west. The estimated Moho depth map displays a thickened crust along the boundary between the Friuli plain and the external Dinarides. It also reveals a N-S narrow corridor of crustal thinning to the east of the junction of Giudicarie and Periadriatic lines, which was not reported by other seismic imaging studies. This corridor of shallower Moho is located beneath the surface outcrop of the Permian magmatic rocks and seems to be connected to the continuation of the Permian magmatism to the deep-seated crust. We compared the shallow crustal velocities and the hypocentral location of the earthquakes in the Southern foothills of the Alps. It revealed that the seismicity mainly occurs in the S-wave velocity range between ∼3.1 and ∼3.6 km/s.

A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.

High-resolution crustal velocity structure in the Shanxi rift zone and its tectonic implications

The Shanxi rift zone, located in the Trans-North China Orogen (TNCO) of the North China Craton (NCC), is wellknown for hosting large intraplate earthquakes in continental China. The TNCO is a suture zone formed by the amalgamation of the eastern and the western blocks of the NCC. After its formation, it was reactived and deformed by later tectonic activities, which result in complex lithospheric heterogeneities. Thus, the detailed crustal structure of the Shanxi rift zone is critical for understanding the tectonics and seismogenic mechanism in this area, which will shed new lights on the formation and dynamic evolution of the NCC. In this study, we applied ambient noise tomography based on 18 months continuous records from 108 seismic stations located in Shanxi and its surroundings, in order to constrain its detailed crustal structure. We measured 4437 Rayleigh wave phase velocity dispersion curves in the period of 5–45 s from the cross-correlation functions. Next, a surface wave direct inversion algorithm based on surface-wave ray tracing was used to resolve a 3-D S-wave velocity model in the upper 60 km with lateral resolution of ∼50–80 km. The tomographic images show that the sedimentary thickness of the Taiyuan Basin is less than 5 km. At depth of 0–10 km, we observe a good correlation between the imaged structural variations with geological and topographic features at the surface. For example, the center of rift shows low-velocity anomalies and the uplifting areas on both sides are characterized by high velocity anomalies. The western and eastern boundaries of the slow materials coincide with the faults that control the basin. The slow material extends from the shallow surface to depth of about 15 km but it getting smaller in shape at deeper depth. For the Taiyuan Basin, Linfen Basin, and Yuncheng Basin in the central and southern parts, the structure is dominant by slow materials in the upper crust but changes to strong high-velocity anomalies in the lower crust and the uppermost mantle at depth deeper than 25 km. We interprete these high-velocity anomalies to be associated with the cold remnant of the underplated basalt in the lower crust that were formed in early Tertiary before the basin was stretched. We also observe the low-velocity anomaly beneath the Datong volcanic area, which extends from the uppermost mantle to a depth of 20 km vertically and migrates from west to east laterally. It may reflect the upwelling channel of the magmatic material in Datong. Moreover, the strong low-velocity anomalies presented north of 38°N could be related to the heated crustal materials with paritial melting as a result of the intensive magmatic activities of the Datong Volcano since the Cenozoic. In our study region, seismicity mainly concentrates in the depth range of 5–20 km and we find that most earthquakes appear to occur in places where velocity changes from high to low rapidly, with slight higher concentration in the faster material areas. In summary, our high-resolution 3-D crustal velocity model provides important seismological constraints to understand the tectonic evolution and seismicity across the Shanxi rift zone.

Estimation of Ground Profiles Based on Microtremor Survey in the Bangkok Basin

Multiple earthquakes have been felt in high-rise buildings in Bangkok despite the epicenters being far away. Seismic wave recordings in the Bangkok basin show a low-frequency peak. This study uses horizontal-to-vertical spectral ratio (HVSR) analysis and array analysis of ambient vibration data to find the predominant period of the ground and the shear wave velocity profiles at five sites in Bangkok. The accuracy of the accelerometer used for the ambient data recording was verified by comparing results with velocity-meter results. The estimated predominant period was within 0.68–0.86 s. From the array records, dispersion curves of the Rayleigh-wave phase velocity were extracted and inverted for the deep layers. The results show that the shear-wave velocity of the top clay layer is low (82–120 m/s) at depths of 11–14.3 m. The low-frequency peak in the HVSR of the earthquake data, and the sediment layer with low shear-wave velocity implies that Bangkok is at risk of amplification of long-period earthquake waves.

Identification of Elastic Properties of Composites by Inversion of Ultrasonic Guided Wave Data

Given the inherent manufacturing variabilities and potential for in-service damage of composite parts, the identification of the elastic properties of composites is important to ensuring the safety and the proper performance of the part. The primary objective of this manuscript is to determine, nondestructively, the elastic properties of composite parts, whether as in-situ components that are part of a larger system, or as laboratory coupons. The proposed technique is based on multimode and dispersive ultrasonic guided waves propagating along a single direction, and the inversion of their phase velocity dispersion curves. The inversion procedure utilizes an efficient Semi-Analytical Finite Element method to solve the forward problem, and a Simulated Annealing algorithm as the optimization tool. The method is particularly well-suited for the characterization of composite laminates. In particular, the manuscript presents experimental evidence of the effectiveness of this technique, that was suggested earlier in a solely numerical work previously conducted by the authors. The test results show that reasonable accuracy can be obtained in the identification of four in-plane and three out-of-plane engineering constants of a quasi-isotropic laminate and a highly anisotropic laminate utilizing the single wave propagation direction. Non-obvious sensitivities of certain wave modes to particular constants are explained on the basis of stress coupling phenomena that are revealed by the SAFE wave propagation models. The study gives experimental evidence of the suitability of ultrasonic guided wave inversion schemes to identify the engineering constants of laminated composites, with the potential to properly characterize parts in-situ, because of the insensitivity of guided waves to boundary conditions located outside of the transmitter–receiver path.

Phase Velocity Estimation With Expanded Bandwidth in Viscoelastic Phantoms and Tissues.

Ultrasound shear wave elastography (SWE) is a technique used to measure mechanical properties to evaluate healthy and pathological soft tissues. SWE typically employs an acoustic radiation force (ARF) to generate laterally propagating shear waves that are tracked in the spatiotemporal domains, and algorithms are used to estimate the wave velocity. The tissue viscoelasticity is often examined through analyzing the shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. A number of available methods to estimate dispersion exist, which can differ in resolution and variance. Moreover, most of these techniques reconstruct dispersion curves for a limited frequency band. In this work, we propose a novel method used for dispersion curve calculation. Our unique approach uses a generalized Stockwell transformation combined with a slant frequency-wavenumber analysis (GST-SFK). We tested the GST-SFK method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. In addition, we evaluated the method on numerical shear wave motion data with different amounts of white Gaussian noise added. Additionally, we performed tests on data from custom-made tissue-mimicking viscoelastic phantom experiments, ex vivo porcine liver measurements, and in vivo liver tissue experiments. We compared results from our method with two other techniques used for estimating shear wave phase velocity: the two-dimensional Fourier transform (2D-FT) and the eigenvector (EV) method. Tests carried out revealed that the GST-SFK method provides dispersion curve estimates with lower errors over a wider frequency band in comparison to the 2D-FT and EV methods. In addition, the GST-SFK provides expanded bandwidth by a factor of two or more to be used for phase velocity estimation, which is meaningful for a tissue dispersion analysis in vivo.

A Weighted Average Phase Velocity Inversion Model for Depth-Resolved Elasticity Evaluation in Human Skin In-Vivo.

In current surface acoustic wave (SAW) elastography field, wavelength-depth inversion model is a straightforward and widely used inversion model for depth-resolved elasticity profile reconstruction. However, the elasticity directly evaluated from the wavelength-depth relationship is biased. Thus, a new inversion model, termed weighted average phase velocity (WAPV) inversion model, is proposed to provide depth-resolved Young's modulus estimate with better accuracy. The forward model for SAW phase velocity dispersion curve generation was derived from the numerical simulations of SAWs in layered materials, and inversion was implemented by matching the measured phase velocity dispersion curve to the one generated from the forward model using the least squares fitting. Three two-layer agar phantoms with different top-layer thicknesses and one three-layer agar phantom were tested to validate the proposed inversion model. Then the model was demonstrated on human skin at various sites (palm, forearm and back of hand) in-vivo. In multi-layered agar phantoms, depth-resolved elasticity estimates provided by the model have a maximal total inversion error of 15.2% per sample after inversion error compensation. In in-vivo human skin, the quantified bulk Young's moduli (palm: 212 ± 78 kPa; forearm: 32 ± 11 kPa and back of hand: 29 ± 8 kPa) are comparable to the reference values in the literature. The WAPV inversion model can provide accurate depth-resolved Young's modulus estimates in layered biological soft tissues. The proposed model can predict depth-resolved elasticity in layered biological soft tissues with a reasonable accuracy which traditional wavelength-depth inversion model cannot provide.

Shear wave structure of southern Sweden from precise phase-velocity measurements of ambient-noise data

SUMMARY Rayleigh-wave phase-velocity tomography of southern Sweden is presented using ambient seismic noise at 36 stations (630 station pairs) of the Swedish National Seismic Network. We analyse 1 yr (2012) of continuous recordings to get the first crustal image based on the ambient-noise method in the area. Time-domain cross-correlations of the vertical component between the stations are computed. Phase-velocity dispersion curves are measured in the frequency domain by matching zero crossings of the real spectra of cross-correlations to the zero crossings of the zeroth-order Bessel function of the first kind. We analyse the effect of uneven source distributions on the phase-velocity dispersion curves and correct for the estimated velocity bias before tomography. To estimate the azimuthal source distribution to determine the bias, we perform inversions of amplitudes of cross-correlation envelopes in a number of period ranges. Then, we invert the measured and bias-corrected dispersion curves for phase-velocity maps at periods between 3 and 30 s. In addition, we investigate the effects of phase-velocity bias corrections on the inverted tomographic maps. The difference between bias-corrected and -uncorrected phase-velocity maps is small (<1.2 per cent), but the correction significantly reduces the residual data variance at long periods where the bias is biggest. To obtain a shear velocity model, we invert for a 1-D velocity profile at each geographical node. The results show some correlation with surface geology, regional seismicity and gravity anomalies in the upper crust. Below the upper crust, the results agree well with results from other seismological methods.

The lithospheric structure underneath the Circum Black Sea: Teleseismic receiver functions and Rayleigh wave phase velocity analysis

• Lithospheric structure beneath Circum Black Sea is revealed using joint inversion. • Moho depth increases southward from 35 to 40 km along Black Sea coastline. • Lithospheric depth increases southward beneath east of Black Sea (90–130 km). In this paper, the lithospheric structure underneath the Circum Black Sea is investigated on the basis of teleseismic receiver functions and Rayleigh wave phase velocity analyses. A joint inversion of P- and S-wave receiver functions are performed by using an iterative algorithm, similar to the simulated annealing method. The array method is employed to obtain the Rayleigh wave inter-station phase velocity dispersion curves. The dataset recorded during 2010–2020 by sixteen broadband stations, operated by several seismological agencies, includes more than 450 events (Mw ≥ 5.8). The Moho depth increases northward from 35 km to 40 km along both coastlines. Following the velocity models, it is suggested that the crust structure beneath the stations is the continental type. The lithosphere-asthenosphere boundary ranges from ~ 90 km to ~ 120 km from the east coast of the East Black Sea basin, while it is low-sloping (from ~ 100 km to ~ 93 km) for the west coast of the West Black Sea basin, and it is nearly 90 km along with the Pontides. The average P-wave and S-wave velocities inferred from the models indicate the continental lithosphere around the Black Sea coastal region. According to these results, tectonically, it points out that the southward subduction exists in the eastern part of the East Black Sea region beneath the Pontides, while it is not observed in the westernmost Black Sea region.

Estimation of the Lamb wave phase velocity dispersion curves using only two adjacent signals

Lamb waves are used in various non-destructive testing (NDT) and structural health monitoring (SHM) applications due to their velocity sensitivity to the properties of the material and their propagation over the entire thickness of the object over a long distance with low attenuation. However, the interpretation of the received signals is complex due to the Lamb waves dispersion nature, multiple mode generation, reflections and other. This work presents a novel method for the Lamb waves fundamental modes phase velocity dispersion evaluation and reconstruction of these curves segments using only two signals measured at two close points. The carried out investigation using simulated signals has shown that the proposed method works with an extremely high accuracy - the mean relative error from the true values is less than 0.01%. The proposed method has been experimentally verified in two different mediums: isotropic – aluminium plate and anisotropic GFRP plate. The obtained results have indicated have that the mean relative error from the true values is less than 1% in the aluminium case. The comparison of the results obtained in the GFRP plate case has indicated that the proposed method allows to reconstruct the phase velocity dispersion curves segments in the object of complex structure.