Phase Velocity Estimation Research Articles

Sonic P-wave attenuation based on fluid pressure differential between joint and matrix

When P-wave compresses in-situ rocks saturated with fluid, there is a fluid pressure differential between compliant joints and stiff matrix. The pressure differential automatically drives a mesoscale squirt between joint wall and matrix interior. This mechanism is likely to dominate sonic P-wave attenuation in the field. A new model of P-wave attenuation based on the mesoscale squirt is established, in which the first porosity is represented by matrix pores while the second porosity is represented by joint. Sonic log of a sandstone reservoir in Saudi Arabia is used to illustrate the model. Both estimated phase velocity and measured quality factor of sonic P-wave are accurately simulated. The results show that for the sandstone reservoir, the relative second porosity is 5%, inter-joint distance is 0.1 m, squirt permeability at very low frequencies is about half of Darcy permeability of the matrix, and joint gap is 800 μm (quadruple grain diameter of 200 μm). Surprisingly, the model of joint-matrix squirt is also capable of reproducing seismic P-wave attenuation measured in the shallow crust of southern California. Therefore, mesoscale squirt across the joint wall is probably the underlying mechanism of attenuation for sonic and seismic P-waves shallower than 10 km.

Multiple Ionospheric Descending Layers Over Arecibo

AbstractObservations using Arecibo Observatory's highly sensitive Incoherent Scattering Radar (AO‐ISR) show ionospheric descending layers from as high as ∼400 km, much higher than earlier studies, with continuity down to 90 km. The AO‐ISR was operated to observe the ion‐line and plasma‐line with coded‐long‐pulse for high temporal and spatial resolution of 35/10 s and 300 m, respectively, during 01–06 February 2019. We found multiple layering structures descending from 400 to 90 km in all these six days. These layers are traditionally called intermediate descending layers (IDLs) (>130 km and below F‐peak), upper semi‐diurnal daytime and nighttime layers (110–130 km), and lower diurnal layers (<110 km). We have denoted the new daytime descending layers above the hmF2 as top‐side descending layers (TDLs). All these layers are collectively named ionospheric descending layers (IonDLs) since all of them are connected with some discontinuity at the F1‐peak (i.e., 170 km), except for the daytime lower‐diurnal layer. The most pronounced IonDLs occur in the twilight times. IonDLs mainly occur in shear zones of the vertical ion drifts and are favored by downward ion drifts, and their descent speeds increase with increasing altitude. The estimated phase velocities of the waves in the F‐region are comparable with the descending speed of the IonDLs. Furthermore, IonDLs/IDLs occur with and without spread‐F events but intensified spread‐F events raise their beginning altitude. The TDLs and IDLs are driven by gravity waves with periods of 1.5–4 hr.

Retrieval and precise phase-velocity estimation of Rayleigh waves by the spatial autocorrelation method between distributed acoustic sensing and seismometer data

Summary In distributed acoustic sensing (DAS), optical fibre is used as sensors, which enables us to observe strain over tens of kilometres at intervals of several metres. S-wave velocity (Vs) structures of shallow sediments of high resolution have been obtained from surface wave dispersion curves by applying seismic interferometry to DAS data both onshore and offshore. However, it is known that there is a disadvantage to DAS seismic interferometry. In addition to Rayleigh waves, Love waves are also included. Consequently, the accuracy of the estimated phase velocities for Rayleigh waves is reduced due to the contamination of Love waves. To address this shortcoming, we suggest a spatial autocorrelation (SPAC) method between DAS and the vertical component of seismometer data. The SPAC method is equivalent to seismic interferometry and is useful for obtaining phase velocity dispersion curves of surface waves from the cross-correlation functions (CCFs) between the records of two receivers. The CCFs obtained from a combination of DAS and vertical seismometer data should contain only Rayleigh waves because Love waves have no vertical component. CCFs between DAS and vertical seismometer data are therefore expected to give more accurate phase velocities of Rayleigh waves than CCFs with DAS data only. In this study, we first formulated analytical expressions of cross-spectra for DAS and three-component seismometer data because seismic observation is generally carried out using a three-component seismometer. A new SPAC method is presented in the form of analytical expressions. We showed that our formulation only includes Rayleigh and not Love waves in the cross-spectra with DAS and the vertical-component seismometer data. We applied our SPAC method to actual DAS and vertical seismometer data recorded on the seafloor. Then, we compared our new SPAC method for DAS and vertical seismometer data with a conventional SPAC method for only DAS data. The results reveal that our new SPAC method can estimate the phase velocities of Rayleigh waves more accurately than the conventional method. In addition, the analytical formulations of the cross-spectrum between DAS and three-component seismometer data, which we obtained in this study, are expected to be useful for the estimation of accurate three-dimensional structures in the future, although this is not available at the moment due to the lack of an applicable dataset.

On seismic gradiometric wave equation inversion for density

SUMMARY Material density remains poorly constrained in seismic imaging problems, yet knowledge of density would provide important insight into physical material properties for the interpretation of subsurface structures. We test the sensitivity to subsurface density contrasts of spatial and temporal gradients of seismic ambient noise wavefields, using wave equation inversion (WEI), a form of seismic gradiometry. Synthetic results for 3-D acoustic media suggest that it is possible to estimate relative density structure with WEI by using a full acoustic formulation for wave propagation and gradiometry. We show that imposing a constant density assumption on the medium can be detrimental to subsurface seismic velocity images. By contrast, the full acoustic formulation allows us to estimate density as an additional material parameter, as well as to improve phase velocity estimates. In 3-D elastic media, severe approximations in the governing wave physics are necessary in order to invert for density using only an array of receivers on the Earth's free surface. It is then not straightforward to isolate the comparatively weak density signal from the influence of phase velocity using gradiometric WEI. However, by using receivers both at the surface and in the shallow subsurface we show that it is possible to estimate density using fully elastic volumetric WEI.

Signal detrending in elastographic wave data with large motion artifacts through a 2D Whittaker smoother

A variety of advanced shear wave elastography techniques require the measurement of frequency-resolved phase velocity to properly characterize wave signals where factors such as tissue viscosity or guided wave effects are present. However, when applying these techniques in a dynamic environment where extrinsic motion cannot be limited, nonlinear and nonstationary trends can be expected in the motion signal used for phase velocity estimation. Because such extrinsic motion signals can contaminate a broad range of frequencies, they can produce significant errors in the phase velocity estimates. In this study, we propose a spatiotemporal detrending approach for elastography wave motion signals built from a 2D Whittaker smoother. This smoother has its origins in nonparametric regression and is well suited for fitting nonlinear curves of arbitrary shape. The resulting detrending filter was applied to Lamb wave signals from clinical ultrasound bladder vibrometry measurements. We found that the proposed detrending filter allowed for phase velocity estimates to be made in acquisitions that are otherwise be too corrupted by large motion. This works was supported by a grant from the NIH (DK131685)

Evaluation of Robustness of S-Transform Based Phase Velocity Estimation in Viscoelastic Phantoms and Renal Transplants.

Ultrasound shear wave elastography (SWE) methods are being used to differentiate healthy versus diseased tissue on the basis of their viscoelastic mechanical properties. Tissue viscoelasticity is often studied by analyzing shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. Recently, a unique approach using a generalized Stockwell transformation (GST-SFK) was proposed for the calculation of dispersion curves in viscoelastic media over expanded frequency band. In this work, the method's robustness was evaluated on data from five custom-made viscoelastic tissue-mimicking phantoms and sixty in vivo renal transplants. For each phantom, 15 shear wave motion data acquisitions were taken, while 10-13 acquisitions were acquired for renal transplants measured in the renal cortex. For each data-set mean and standard deviation (SD) of estimated phase velocity dispersion curves were studied. In addition, the viscoelastic parameters of the Zener model were examined, which were preceded by a convergence analysis. For viscoelastic phantoms scanned with a research ultrasound scanner, and for the in vivo renal transplants scanned with a clinical scanner, the decisive advantage of the GST-SFK method over the standard two-dimensional Fourier transform (2D-FT) method was shown. The GST-SFK method provided dispersion curve estimates with lower SD over a wider frequency band in comparison to the 2D-FT method. These advantages are relevant to the analysis of the mechanical properties of tissues in clinical practice to discriminate healthy from diseased tissue.

Novel techniques for in situ estimation of shear-wave velocity and damping ratio through MASW testing – I: a beamforming procedure for extracting Rayleigh-wave phase velocity and phase attenuation

SUMMARY A robust, in situ estimate of shear-wave velocity VS and the small-strain damping ratio DS (or equivalently, the quality factor QS) is crucial for the design of buildings and geotechnical systems subjected to vibrations or earthquake ground shaking. A promising technique for simultaneously obtaining both VS and DS relies on the Multichannel Analysis of Surface Waves (MASW) method. MASW can be used to extract the Rayleigh wave phase velocity and phase attenuation data from active-source seismic traces recorded along linear arrays. Then, these data can be inverted to obtain VS and DS profiles. This paper introduces two novel methodologies for extracting the phase velocity and attenuation data. These new approaches are based on an extension of the beamforming technique which can be combined with a modal filter to isolate different Rayleigh propagation modes. Thus, the techniques return reliable phase velocity and attenuation estimates even in the presence of a multimode wavefield, which is typical of complex stratigraphic conditions. The reliability and effectiveness of the proposed approaches are assessed on a suite of synthetic wavefields and on experimental data collected at the Garner Valley Downhole Array and Mirandola sites. The results reveal that, under proper modelling of wavefield conditions, accurate estimates of Rayleigh wave phase velocity and attenuation can be extracted from active-source MASW wavefields over a broad frequency range. Eventually, the estimation of soil mechanical parameters also requires a robust inversion procedure to map the experimental Rayleigh wave parameters into soil models describing VS and DS with depth. The simultaneous inversion of phase velocity and attenuation data is discussed in detail in the companion paper.

Seismic Thermography

ABSTRACT Variations in temperature within the Earth are of great interest because they indicate the thickness and, consequently, mechanical strength of the lithosphere and density variations and convection patterns in the sublithospheric mantle. Seismic tomography maps seismic velocity variations in the mantle, which strongly depend on temperature. Temperatures are, thus, often inferred from tomography. Tomographic models, however, are nonunique solutions of inverse problems, regularized to ensure model smoothness or small model norm, not plausible temperature distributions. For example, lithospheric geotherms computed from seismic velocity models typically display unrealistic oscillations, with improbable temperature decreases with depth within shallow mantle lithosphere. The errors due to the intermediate-model nonuniqueness are avoided if seismic data are inverted directly for temperature. The recently developed thermodynamic inversion methods use computational petrology and thermodynamic databases to jointly invert seismic and other data for temperature and composition. Because seismic velocity sensitivity to composition is much weaker than to temperature, we can invert seismic data primarily for temperature, with reasonable assumptions on composition and other relevant properties and with additional inversion parameters such as anisotropy. Here, we illustrate thus-defined seismic thermography with thermal imaging of the lithosphere and asthenosphere using surface waves. We show that the accuracy of the models depends critically on the accuracy of the extraction of structural information from the seismic data. Random errors have little effect but correlated errors of even a small portion of 1% can affect the models strongly. We invert data with different noise characteristics and test a simple method to estimate phase velocity errors. Seismic thermography builds on the techniques of seismic tomography and relies on computational petrology, but it is emerging as a field with its scope of goals, technical challenges, and methods. It produces increasingly accurate models of the Earth, with important inferences on its dynamics and evolution.

Improved beamforming schemes for estimation of multimode surface wave dispersion curves from seismic noise with reducing effect of the irregular array geometry and/or anisotropic source distribution

SUMMARY Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the earth's structure by applying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been proven to extract the azimuth-averaged multimode surface wave dispersion curves. However, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequency–velocity (f-v) domain. Moreover, the irregular array geometry and uneven source distribution would bias the result of CBF, especially for the estimation of azimuth-dependent velocity. In this paper, two beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier–Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.

Surface-Wave Imaging with Nonrandom Traffic Noise Sources

We analyze the influence of nonrandom traffic noise sources on surface wave imaging. With nonrandom traffic noise sources in time (correlated sources), spurious signals are produced in the crosscorrelation functions. With nonrandom traffic noise sources in space (directional sources), phase velocities are overestimated from the retrieved surface waves. The retrieval of surface waves can be improved by stationary-phase segment selection, cross-coherence and stacking of the results from multiple traffic noise sources. Synthetic results demonstrate that cross-coherence and stacking of multiple traffic noise sources makes the source tend to be random distribution in time and suppresses the spurious signals in the crosscorrelation functions. Enhancing the stationary-phase contribution makes more accurate estimation of surface wave phase velocities.

Estimation of phase velocity using array observation of microtremors with arbitrary shape

To estimate the phase velocity using the array observations of microtremors, some algorithms for the estimation include constraints on the array shape, such as equilateral triangles or the placement of receivers on a circle, in order to reduce the estimation error of the phase velocity. In the present study, a direct estimation technique is introduced for the phase velocity using records obtained through an array with an arbitrary shape based on a complex coherency function (CCF), where CCF is defined as the normalized cross spectrum of the microtremor records observed simultaneously by two receivers. The particle swarm optimization (PSO) method, one of metaheuristic optimization methods, is applied and optimal values are provided for the phase velocity and other unknown parameters. Approximate representations of the stochastic properties for the unknown variables are analytically derived based on the discrete representation of the CCF, for a case where the arrival directions of microtremors are treated as random variables following a uniform distribution. Furthermore, the validity of the proposed method is confirmed using numerical simulations and actual observation records.Graphical

Ultrasound shear wave phase velocity imaging using black-box system identification (BSI): a data-driven approach

Objective. Shear wave elasticity imaging (SWEI) is an established approach for diagnosing lesions in human tissue. However, the shear wavelengths used by traditional SWEI are usually not short enough, leading to inferior accuracy in small-target (<10 mm) reconstruction. To exploit short shear wavelengths (high-frequency content), this study introduces a new phase velocity (PV) estimation technique as an alternative to the conventional group velocity (GV) modality. Approach. We propose using a black-box model instead of a fully physics-based model to describe the transition process of two arbitrary shear wave signals. With this representation, local PV can be obtained via black-box system identification (BSI). For validation, two PV estimation scenarios were established: (numerical) dispersion measurements in viscoelastic media, and (real) imaging targets in a CIRS elasticity phantom. BSI was compared with a state-of-the-art PV imaging method that uses local wavenumber estimation (LWE). Main results. BSI showed excellent accuracy in the dispersion estimation for all three viscoelastic media in the simulations. In the phantom study, the two PV methods exhibited good agreement in the frequency dependence of target quantification, and could both generate a higher target reconstruction accuracy than GV. LWE images were strongly affected by noise-induced faulty estimates, whereas BSI showed no notable artifacts. Significance. This study demonstrates the advantage of the PV modality over the GV modality as the former can achieve better target visualization by increasing imaging frequency. It also implies the feasibility of data-driven modeling for soft tissue characterization.

Lithospheric S Wave Velocity Variations Beneath the Mackenzie Mountains and Northern Canadian Cordillera

AbstractThe Mackenzie Mountains (MMs) in the Yukon and Northwest Territories, Canada, are an enigmatic mountain range. They are currently uplifting (Leonard et al., 2008, https//doi.org/10.1029/2007JB005456), yet are about 700 km from the nearest plate boundary. Their arcuate shape is distinct and extends over 100 km eastward from the general trend of the Northern Canadian Cordillera. To better assess the cause and conditions of the current uplift, we processed ambient seismic noise data from a linear array of broadband seismographs crossing the mountains, along with other regional seismic stations, to estimate Rayleigh wave phase velocities between 6 and 40 s periods. From this, we estimated phase velocity dispersion and performed a tomographic inversion to estimate VS. Tomography reveals a low‐velocity structure that extends upward from the base of the ∼50–66 km thick lithosphere to the upper crust, and we hypothesize that inferred low density and low rigidity associated with the VS anomaly localizes the ongoing uplift and thrust‐dominated seismicity of the MMs. Additionally, we find relatively low crustal velocities that extend to the west of the MMs, suggesting that strain transfer from the Gulf of Alaska plate boundary plays a driving role as the crust translates to the northeast and buckles up against the craton consistent with the orogenic float hypothesis of Mazzotti and Hyndman (2002, https//doi.org/10.1130/0091-7613(2002)030〈0495:YCASTA〉2.0.CO;2). Finally, we observe lithospheric azimuthal anisotropy with an NW‐SE fast direction. This is nearly orthogonal to teleseismic shear wave splitting measurements in the central MMs, and suggests that asthenosphere flow and lithospheric strain are not aligned in this region.

Enhancing noise sources in stationary-phase zones for accurate phase-velocity estimation of high-frequency surface waves

Passive surface-wave methods are appealing tools for their ability to noninvasively obtain shear-wave velocity with high accuracy and low costs. A linear array of stations is widely adopted in urban areas for its convenient deployments and efficient utilization of ambient noise energy from stationary-phase zones (SPZs), which contributes the most to surface-wave retrieval. However, noise sources in nonstationary-phase zones may threaten the reliability of velocity estimation when they possess strong energy. To obtain reliable phase-velocity estimation of high-frequency surface waves (&gt;1 Hz), we enhance the contribution of noise sources in SPZs by using the multichannel-coherency-weighted stack (MCWS) method for the stacking of noise crosscorrelation functions and dispersion spectra. We model a nonuniform source distribution with strong offline sources. The seismic interferometry (SI) and passive multichannel analysis of surface waves (PMASW) methods overestimate velocities at lower frequencies (&lt;5 Hz), whereas phase velocities of short wavelengths are relatively accurate. The true velocities of short wavelengths are then set as the velocity scanning range for MCWS, and the waves whose apparent velocities lie within the scanning range would be emphasized by MCWS. Noise sources in SPZs are enhanced because the apparent velocities of waves from other noise sources are higher and not in the scanning range. After using MCWS, the phase-velocity estimations of SI and PMASW are consistent with the theoretical dispersion curve. A field data example at a crossroads demonstrates that uneven source distributions might cause serious artifacts and the feasibility of our method is again confirmed. In addition, the enhancement of noise sources in SPZs is verified through noise source distribution imaging by a matched field processing technique.

Combined analysis of active and passive surface waves for 2D characterization of a landfill

Active and passive surface wave methods have been effective tools for near-surface investigation. For the cases both the near-surface resolution and investigation depth are required, the incorporation of active and passive surface wave methods is necessary to measure the dispersion curve over a broad frequency band. In this work, we carry out the active and passive surface wave methods to characterize a landfill, mainly for delineating its base. Both active and passive surface wave data are collected using a linear array and the roll-along acquisition mode. To analyze the passive data, we use the seismic interferometry technique to generate the virtual source gather. According to the dispersion analysis results, the frequency bands for available phase velocity estimations of active and passive data are different but overlapped. We then employ the multiscale window analysis of surface waves (MWASW) method to extract several dispersion curves from active shot gather and passive virtual source gather. The use of the MWASW method is based on the consideration of heterogeneity in landfills. Once the dispersion curves are extracted, the two kinds of phase velocity data are combined to produce composite dispersion curves. By simultaneously inverting the composite dispersion curves of multisize spatial windows, a 2D shear-wave velocity (Vs) model is generated that shows a clear velocity contrast between the refuse and the underlying stratum at a depth around 5 m consistent with the result of five in-line boreholes. The successful investigation of refuse depth demonstrates that the combination of active and passive surface waves has a good ability to resolve the Vs model of landfills from surface to deep formations.

Observed near-inertial waves and shears east of Luzon during Typhoons Mangkhut and Yutu in 2018

Based on acoustic Doppler current profiler observations from three moorings along the 18° N latitude line east of Luzon (at 122.7° E, 123° E, and 123.3° E), the characteristics, vertical propagation, modes, and shear properties of the near-inertial waves (NIWs) induced by Typhoon Mangkhut and Typhoon Yutu in 2018 were investigated. Energetic NIW events were generated that dominated ocean currents after the passage of the typhoons. The wavenumber–frequency spectra and downward/upward current decomposition demonstrated that the near-inertial currents rotated clockwise and mainly propagated downward energy in the Northern Hemisphere. The estimated phase velocities and vertical wavelengths were 4.9–9.4 m/h and 155–376 m, respectively. The NIWs at the three moorings showed red-shifted frequencies in the upper ocean but blue-shifted frequencies in the deep ocean, which were affected by background vorticity. Vertical mode analysis showed that the near-inertial kinetic energy (NIKE) was dominated by the third, fourth, and fifth higher modes above 400 m and by the first, second, and third lower modes below 400 m. The translation speeds of Typhoons Mangkhut (29 km/h) and Yutu (24 km/h) exceeded the critical value (14.4 km/h). Since the intensity of NIWs decreases with an increase in typhoon translation speed, the maximum NIKE caused by Typhoon Yutu was higher than that caused by Typhoon Mangkhut because of the lower translation speed of Typhoon Yutu. However, the NIKE caused by Typhoon Mangkhut propagated vertically into a deeper layer than that caused by Typhoon Yutu. The strong anticyclonic eddy near the moorings during the period of Typhoon Mangkhut played a more important role in the vertical propagation of NIKE than the weaker anticyclonic eddy during the period of Typhoon Yutu. This study shows the significant contribution of NIWs to shear. NIW-induced near-inertial shear was significantly enhanced after the two typhoons passed, with contributions of more than 50%. Although NIW-induced shear appeared to be stronger during the typhoons, no strong shear instabilities or turbulent mixing were observed.

Extraction of surface-wave phase velocities from ambient noise in the presence of local noise sources based on matched-field processing

Passive surface wave methods have gained much attention from geophysics and civil engineering communities with the advantage of lower costs and deeper penetration depths compared to active seismic methods. The successful extraction of surface waves from ambient noise relies on the assumption of a homogeneous random distribution of noise sources. In urban environments, there are many strong noise sources located in localized areas (i.e., local sources) that violate the ideal noise distribution conditions, which causes errors in surface-wave dispersion extraction. To solve this problem, we propose a new passive surface wave analysis method in the presence of strong local noise sources (local-source passive surface wave analysis, LSPSW). We use the matched field processing (MFP) algorithm to capture noise source distributions and then extract reliable surface wave phase velocities. The MFP algorithm can accurately estimate the distribution of noise sources located either close to or far from the receiver array. Synthetic and field examples demonstrate the feasibility of using LSPSW to estimate phase velocities in complicated noise environments with a pseudo-linear array. Comparisons with other passive surface wave methods (seismic interferometry, the spatial autocorrelation method, pseudo-linear array analysis of passive surface waves based on beamforming) further illustrate the superiority of the MFP-based LSPSW method.

Seismic surface wave focal spot imaging: numerical resolution experiments

SUMMARY Numerical experiments of seismic wave propagation in a laterally homogeneous layered medium explore subsurface imaging at subwavelength distances for dense seismic arrays. We choose a time-reversal approach to simulate fundamental mode Rayleigh surface wavefields that are equivalent to the cross-correlation results of three-component ambient seismic field records. We demonstrate that the synthesized 2-D spatial autocorrelation fields in the time domain support local or so-called focal spot imaging. Systematic tests involving clean isotropic surface wavefields but also interfering body wave components and anisotropic incidence assess the accuracy of the phase velocity and dispersion estimates obtained from focal spot properties. The results suggest that data collected within half a wavelength around the origin is usually sufficient to constrain the used Bessel functions models. Generally, the cleaner the surface wavefield the smaller the fitting distances that can be used to accurately estimate the local Rayleigh wave speed. Using models based on isotropic surface wave propagation we find that phase velocity estimates from vertical–radial component data are less biased by P-wave energy compared to estimates obtained from vertical–vertical component data, that even strong anisotropic surface wave incidence yields phase velocity estimates with an accuracy of 1 per cent or better, and that dispersion can be studied in the presence of noise. Estimates using a model to resolve potential medium anisotropy are significantly biased by anisotropic surface wave incidence. The overall accurate results obtained from near-field measurements using isotropic medium assumptions imply that dense array seismic Rayleigh wave focal spot imaging can increase the depth sensitivity compared to ambient noise surface wave tomography. The analogy to elastography focal spot medical imaging implies that a high station density and clean surface wavefields support subwavelength resolution of lateral medium variations.

Common-midpoint two-station analysis of estimating phase velocity using high-frequency ambient noise

Two-station analysis is a frequently-used technique in seismology to determine interstation phase velocities of surface waves but it usually suffers from several drawbacks arising from 2π ambiguity and a narrow frequency band. This paper introduces a common-midpoint two-station analysis (CMP-TS) method to suppress the spurious energy due to 2π ambiguity and broaden the frequency band for high-frequency (>1 Hz) passive surface wave imaging. To demonstrate the advantages of the proposed method in estimating phase velocity, the authors compared results obtained by the CMP-TS method and the Multichannel Analysis of Passive Surface waves (MAPS) using synthetic data with homogeneous and inline noise-source distributions. For homogeneous noise-source distribution, phase-velocity dispersion curves obtained by both methods can match with theoretical curves, but the CMP-TS method could enhance the resolution of images of dispersion energy by about 50% compared with the MAPS method. As for inline noise-source distribution, phase velocities generated with the MAPS method can match with theoretical ones while phase velocities measured by the proposed method are underestimated. By modifying the source phase ambiguity term in the proposed method, the authors corrected the systematic measurement bias of phase velocities and concluded that the CMP-TS method is superior to the MAPS method in accuracy and resolution. Results from two field examples further demonstrated the capability of the CMP-TS method in estimating phase velocity with higher image resolution than the MAPS method. Finally, the results showed that it is reasonable for the proposed method to pick phase velocities using the one-wavelength criterion in near-surface applications.

Synchrosqueezed wavelet transform-based method for characterizing the dispersive nature of laser-excited surface acoustic waves propagating through the coated or damaged medium

Dispersion of surface acoustic waves (SAWs) can be used for determination of the mechanical parameters of the film or the damaged layer. The correct evaluation of the experimental dispersion curves is important for backcalculation. In this paper, we present a method to identify experimental dispersion curves from two-station time-varying signals based on time–frequency analysis. Synchrosqueezed wavelet transform (SWT) provides the quantitative description of the propagation of different frequency components of SAWs. Discrete phase velocity estimation is accomplished based on the cross-correlation function. Rényi entropy-based SWT spectrum noise reduction and cosine interpolation are applied for improving the quality of dispersion curves. An example is presented to illustrate the application of the proposed method. Finally, laser ultrasonic experiments are performed on the surface of three typical test samples. The comparison of the resulting dispersion curves shows the effectiveness of the proposed method and the necessity of noise reduction and interpolation.