Theoretical Dispersion Curves Research Articles

Damage detection by means of broadband local wavenumber estimation in plate-like structures

This short communication evinces the ability of the CFAT methodology [Q. Leclère, JSV, 2015] to detect and characterize thickness-loss defects on homogeneous flat panels. A contactless measurement of the velocity field of an aluminium plate is performed by scanning laser vibrometry, from which the equivalent rigidity (apparent bending stiffness) is locally estimated within a wide frequency band in the ultrasonic domain. The method allows imaging thickness-reduction defects on the hidden face of an aluminium plate up to several hundreds of kilohertz. The first part details the experimental protocol, followed by a second enhancing the identification of the wavenumbers of symmetric S_0 and antisymmetric A_0 modes. The comparison with theoretical Lamb waves dispersion curves reveals the precision of the method. Finally, the methodology validates the possibility to precisely estimate the local material thickness and as a consequence the location, size and depth of a reference defect in the shape of a flat bottom hole (assuming homogeneous material properties of the plate).

Azimuth correction for passive surface wave dispersion based on polarization analysis

SUMMARY Passive surface wave methods have found extensive application in near-surface investigation due to their benefits of low costs, non-invasiveness and high accuracy. Linear arrays are usually adopted in urban environments for their convenience and efficiency. However, the distribution of noise sources in densely populated urban areas varies rapidly in time and space, making it challenging to estimate accurate dispersion spectra using a linear array. To solve this problem, we propose a polarization analysis-based azimuthal correction method. We first obtain the azimuth of each segment by calculating the correlation coefficient of three-component ambient noise data. The normalized correlation coefficient is then applied for quality control to select reliable segments. For selected segments, the overestimated velocity caused by directional sources are corrected to obtain accurate dispersion spectra. A synthetic test is conducted to demonstrate the feasibility of our method. Compared with the dispersion spectra obtained without any correction, the dispersion spectra obtained following the suggested scheme are more consistent with the theoretical dispersion curves. Two real-world examples at crossroads show the superiority of the proposed technique in obtaining higher resolution dispersion energy and more accurate phase velocities. In addition, our approach can attenuate the artefacts and improve the dispersion measurements.

Cold Electron Temperature in the Inner Magnetosphere Estimated Through the Dispersion Relation of ECH Waves From the Arase Satellite Observations

AbstractWe have analyzed Electrostatic Electron Cyclotron Harmonic (ECH) waves observed using interferometry observation mode performed by the Arase satellite to estimate low‐energy electron temperatures. Interferometry can be used to calculate velocities, but the Arase satellite can only perform interferometry observations in a one‐dimensional direction. We proposed a method to estimate the wave vector of the observed ECH waves from the observed electric fields and calculated the phase velocity for each frequency. We determined the particle parameters from the particle detector and the upper hybrid resonance and estimated the unknown low‐energy electron temperature from the agreement between the observed ECH dispersion relation and the theoretical dispersion curves. We performed our analysis for six events and found that the low‐energy electron temperature in the observed region is on the order of 1 eV.

Weak bond evaluation of lap bonding structures by SH guided waves using EMATs

ABSTRACT In this research, simulations and experiments were conducted for the bonding quality evaluation of an aluminum bonding structure, based on the SH guided wave analysis. In order to simulate the propagation of SH waves in the bonded structure, a 3D finite element model was established based on interfacial spring stiffness modeling. The frequency-wavenumber diagram was obtained by doing Fourier transform along the spatial axis in the time frequency domain simulation results. At the same time, the influence of the bonding interface weakening on the propagation characteristics of the guided wave was analyzed. The simulated dispersion curves of SH-guided waves in different bonding states were in good agreement with the theoretically results. In addition, a periodic permanent magnet electromagnetic acoustic transducer (PPM-EMAT) 3D finite element model was established. An optimized transducer was fabricated to excite pure SH0 mode. Then, a series of aluminum lap bonding structures with different bonding states were prepared. The effect of bonding interfaces on the propagation characteristics of SH waves was investigated. The interfacial spring stiffness can be determined when the STFT of the SH waves matches the theoretical dispersion curves. Thus, this method demonstrated an ultrasonic way to distinguish the weakening of the bonding structures.

Pipe wall thickness estimation by frequency–wavenumber analysis of circumferential guided waves

Ultrasonic guided waves in pipes propagating in the circumferential direction carry information about the thickness of the pipe wall. This study proposes a method for estimating the pipe wall thickness based on measurements from circumferentially distributed sensors and a set of pre-computed theoretical dispersion curves. The recorded data are Fourier transformed into a frequency–wavenumber representation. The wall thickness is obtained by identifying the best fitting dispersion curve to the frequency–wavenumber data by determining the maximum stacking power. The thickness estimation method has demonstrated robustness against noise. Given the presence of significant noise (0.0dB signal-to-noise ratio) and simulations where the thickness ranges from 6.0 to 10.0mm, using eight sensors or more attain a mean absolute percentage error of less than 1%. The method is also supported by real laboratory measurements using eight sensor positions, where the error is less than 0.7%. Experimental measurements near the pipe end demonstrate that with appropriate positioning, end-reflections should not have a detrimental effect on the accuracy. The method estimates the mean thickness in cases where the pipe wall has near-uniform thickness but may not be as reliable when there are large shallow defects caused by metal loss, which is typically the case when the inner wall has suffered from erosion. In this case, monitoring of the stacking power curves could detect regional metal loss due to erosion and analysis of the local maxima could uncover information about individual thickness segments around the pipe circumference.

Simultaneous Determination of Young's Modulus and Density of Ultrathin Low‐k Films Using Surface Acoustic Waves

The nondestructive testing (NDT) of mechanical properties in ultrathin low dielectric constant (low‐k) films is a major challenge in integrated circuit manufacturing. Young's modulus and density are closely related parameters for low‐k films. This study presents a method for NDT of Young's modulus and density of porous low‐k black diamond (SiOC:H, BD) films. A linear frequency modulation (LFM) surface acoustic wave (SAW) interdigital transducer (IDT) with a frequency range of 20–250 MHz is designed to generate SAW signals on the samples. The series of SAW waveforms obtained on the samples are processed to obtain experimental SAW dispersion curves across a broad frequency range. By comparing these experimental curves with theoretical dispersion curves, as well as their first‐order derivatives, Young's modulus and density of porous low‐k BD films with thicknesses of 100, 300, 500, and 1000 nm are characterized. To verify Young's modulus measurements from the SAW method, a control experiment using nanoindentation is conducted. The results demonstrate that the SAW method can reduce the impact of the substrate and is independent of the film thickness. This study presents a highly accurate measuring method for simultaneous multiparameter evaluation of ultra‐thin low‐k films.

Cut-off frequency analysis of SH-like guided waves in the three-dimensional component with variable width

ABSTRACT The component with variable width (such as railway turnout) is one of the most critical configurations in infrastructure. Guided waves have already been employed for flat plates, however, the influence of cross-section width change for guided waves can’t be ignored. In this study, the theoretical cut-off frequency of shear-horizontal (SH)-like guided waves in rectangular plate was analysed. The dispersion curves of rectangular plate with different widths were calculated by the periodic finite element (FE) method. Theoretical calculations and dispersion curves both show that the cut-off frequency of SH-like guided waves decreases when the width of rectangular plate increases. A periodic-permanent-magnet (PPM) electromagnetic-acoustic-transducer (EMAT) at the excitation frequency of 200 kHz was constructed and used in the experiments to generate SH-like guided waves on rectangular plates with the widths of 12 mm and 20 mm, respectively. Experimental results show that multiple wave modes of SH-like guided waves appear as the width of the rectangular plate increases. When the SH-like guided waves propagates in a rectangular plate with variable width, the high-order modes will be cut-off and reflected as the width decreases.

Automatic and adaptive picking of surface-wave dispersion curves for near-surface application

Multichannel analysis of surface waves (MASW) is a widely used non-invasive method to reveal the S-velocity structure in near-surface applications. Automatic and adaptive picking of surface wave dispersion curves is crucial for the later surface wave analysis. The traditional way to acquire the dispersion curves is to identify the local extremum energy in phase-velocity images and manually pick the dispersion curve by following peaks at different frequencies. However, the large number of interactive works in extensive surveys could be more efficient, time-consuming, and prone to human error. In this work, we developed an automatic adaptive picking of dispersion curves (AAPDC) strategy, which automatically searches the surface-wave dispersion curve based on the position of the local energy maxima in the dispersion spectrum. This method is straightforward and efficient and requires only a few or no additional parameters to obtain a stable result. The typical synthetic model tests show that the automatic picking agrees with the theoretical dispersion curves. In addition, the proposed AAPDC method is used to land geophone data and DAS data. The final S-velocity tomograms have a good agreement with the geological and other geophysics results, which demonstrate that the AAPDC method could accurately and adaptive extract fundamental dispersion curves from the complex dispersion spectrum.

Microseismic event locations and source mechanisms using dominant guided waves recorded in an underground potash mine

Microseismic event locations and moment tensors (MT) in underground mines can provide insights into the subsurface deformation and current state of stress. However, reliable estimation of these source parameters is rather challenging due to high-frequency waveforms and a low signal-to-noise ratio for negative magnitude events. We study microseismicity in an underground potash mine in Saskatchewan, Canada, recorded between 1 March and 30 June 2021, by a network of broadband seismometers. The active mining is carried out in low-velocity evaporites at depths of approximately 1 km below the ground level. The theoretical dispersion curves show that guided waves in the form of leaky P and P-SV/SH normal modes can exist in a 1D velocity model representing mine geology. These guided waves are detected as high-energy dispersive arrivals on the seismograms recorded at the underground receivers. We locate the events using the arrival times of the guided waves and their mean group velocities. Most (approximately 80%) of the detected events cluster around the mine layout between depths of 0.95 to 1.05 km. Next, we compute MT for 92 events using waveforms of guided phases. The MT show nondouble-couple components with only 28 events having double-couple percentages greater than 50%. These events occur near mined-out cavities with source mechanisms corresponding to the layer delamination in the roof and floor or pillar yield related to the closure of cavities. No abnormal microseismicity is detected away from the mine levels in the more competent carbonate rocks above or below the evaporite formations. Thus, guided waves enable the detection of microseismic events up to large distances and can provide high-resolution event locations and MT inversion. These can be interpreted in the context of local geology and mining activities to identify the dominant factors affecting microseismicity.

Six‐Component Earthquake Synchronous Observations Across Taiwan Strait: Phase Velocity and Source Location

AbstractWith the development of rotational seismometers, especially the high‐sensitivity optical seismometers, rotational motions have shown increasing benefits for calculation of dispersion curves, estimation of back azimuth and many other applications. Here we present the six‐component observations of 2019 Hualien mww6.1 earthquake simultaneously on both sides of Taiwan Strait. Seismograms and time‐frequency spectrums show that the attenuations for rotations are more significant than translations. Calculations of the surface wave phase velocity are performed for both stations through single‐station records, indicating a distinct difference owning to the instrument installation conditions and site effect. Comparison of theoretical dispersion curves is consistently in trends with estimations, and reveals the influence of higher‐mode surface waves. For the first time, we locate the source of a earthquake through intersection of two stations' back azimuths estimated through rotational methods. Results of comparing to translational polarization verify that rotational observation can distinctly reduce the deviation of source location.

Water ingress detection in an aluminum honeycomb sandwich structure using laser ultrasonics based on mode conversion behaviors

This paper investigates the method for water ingress detection in an aluminum honeycomb sandwich structure by laser ultrasonics. To clarify the propagation of Scholte waves generated at the solid-liquid interface, the theoretical dispersion curves in the water-aluminum layered structure are calculated by the global matrix method. Using a laser ultrasonic visualizing inspector, the guided wave propagation in the wavefields has been visualized, which shows the mode conversion behaviors occurring in the water ingress area. The clarification of mode conversion is then investigated by the finite element method. The Scholte modes at the solid-fluid interface and the Lamb modes in the face sheet are interconverted because of the change in the waveguide structure. Wavenumber filter reconstruction and the resulting energy maps are applied to illustrate the mode conversion in the wavefields and to detect the water ingress area. Results show that the appearance of the water layer contributes to the mode conversion behaviors during the guided wave propagation in the honeycomb sandwich structure, which offers the potential for water ingress detection based on the mode conversion behaviors.

ПРИМЕНЕНИЕ МЕТОДА С ИСПОЛЬЗОВАНИЕМ ИЗГИБНЫХ ВОЛН ДЛЯ ОБСЛЕДОВАНИЯ ПЛИТНЫХ И СТЕНОВЫХ КОНСТРУКЦИЙ

The paper considers the possibility of estimating the stiffness and strength characteristics of slab and wall structures by thickness based on the results of experimental studies of measurements of bending wave propagation velocities of different frequency ranges. Theoretical dispersion curves of bending wave velocities as a function of their lengths for plate structures of different characteristics at different thicknesses are constructed. Comparison of theoretical and experimental results for estimation of the state of materials by the thickness of slabs has been carried out. Experimental measurements of bending wave propagation velocities on the walls of an existing building in St. Petersburg have been carried out, and the primary assessment of masonry stiffness properties and control of the design wall thickness have been performed. The results of the studies confirmed the possibility of assessing the characteristic of the state of materials in the thickness of slab and wall structures by comparing experimental studies of bending wave propagation velocity measurements at different frequency ranges. The use of bending wave method also allows controlling the design thickness of slab, wall and lining at one-sided access

A Guided Wave Approach to Defect Detection in Switch Rail

An approach to detect switch rail defect based on ultrasonic guided wave technology is studied. Eight typical cross‐sections are chosen from the switch rail, and each cross‐section's theoretical dispersion curves and wave structures are derived using the semianalytical finite‐element method. The dispersion curve of eight sections has 262 modes at 60 kHz. Based on k‐means clustering analysis algorithm, 25 kinds of classification results are obtained from 262 modes. According to the mean and variance of energy, an optimal set of modes with uniform amplitude over the entire section of the switch rail is selected. The optimal excitation point is determined based on the vibration energy. The defect echo signal is obtained by excitation of these guided wave modes. Field experiment results show that by comparing the sum of the differences between the collected and basic data and setting a certain threshold, the internal defect detection of the switch guide rail can be realized. The research results herein are valuable for analyzing the dispersion characteristics and realizing the nondestructive testing of the variable cross‐section waveguide.

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.

Dispersion characteristics of surface wave in SCCS: theoretical analysis, numerical simulation and MASW-based NDT

To fully validate the feasibility of multichannel analysis of surface waves (MASW)-based interfacial debonding detection for steel–concrete composite structures (SCCS), dispersion characteristics of surface waves in SCCS are systematically investigated using theoretical analysis and elaborate 3D numerical simulations. First, the influences of material strength and thickness of concrete core, steel plate thickness on the dispersion figures are analyzed based on the theoretical dispersion characteristic of Rayleigh wave. Scientific layering strategy, including single steel plate, double-layer, and three-layer medium assumptions, is investigated using the theoretical dispersion analysis of Lamb wave. Besides, the dispersion characteristics of surface wave in circular steel pipes are calculated to determine the appropriate theoretical dispersion curves for MASW measurement. Finally, the stress wave propagation processes in SCCSs with various internal structures, including stiffeners, studs, and diaphragms, as well as the debonding width, are simulated using 3D numerical simulation to validate the research finding of theoretical analysis and detectability of MASW-based non-destructive testing on interfacial debonding defects in rectangular and circular concrete-filled steel tubulars. Finally, the dispersion characteristics corresponding to displacement, velocity, and acceleration of surface waves are comparatively discussed. The research findings of this study are the cornerstone of experimental study and essential theoretical support for identifying interfacial debonding and bond-slip damage of SCCS components utilizing MASW method.

FORWARD MODELING THE GROUP AND PHASE VELOCITIES OF RAYLEIGH AND LOVE SURFACE WAVES BENEATH THE CENTRAL ANATOLIA: FIFTH PARAMETER FOR TRANSVERSE ISOTROPY

The complex dynamic processes such as the magma movements in the crust and uppermost mantle result in the anisotropic wave propagation. In case of the Rayleigh and Love surface waves, this anisotropy is known as the Rayleigh-Love wave discrepancy. The surface wave propagation beneath the Central Anatolia shows this discrepancy for which we utilize the vertical transverse isotropy in the form of forward solutions. We use single-station and two-station methods to attain the observed surface wave dispersion curves in the period range 7-40 s and then apply the two-dimensional (2-D) tomography to convert these curves into the velocity maps defined through a 0.05o x 0.05o – sized grid. The damped least-squares technique is used to invert the individual group and phase velocity curves for the one-dimensional (1-D) structure. The latter 1-D inversion provides the depth profiles for the Voigt isotropic average shear-wave velocity (𝑉𝑆) and the radial anisotropy (𝜉). The 𝑉𝑆 and 𝜉 depth profiles are employed to construct the vertical transverse isotropic (VTI) velocity structure beneath a grid point. Through the forward modeling, the VTI velocity structure is revised to jointly fit the observed Rayleigh and Love group and phase velocities. In the forward modeling, the fifth VTI parameter (𝜂𝐾) measuring the departure from the elliptic condition (𝜂𝐾=1.0) and the anisotropic velocity perturbations (𝑎𝑃2⁄ and 𝑎𝑆2⁄) are primarily adjusted to achieve the fit between the observed and theoretical dispersion curves. In the depth range ~20-30 km, the 𝜂𝐾 is generally found to be 𝜂𝐾<1.0 changing in the range 0.94≤𝜂𝐾≤0.95, which is consistent with the PREM and the expression 𝑎𝑃2⁄=0.5𝑎𝑆2⁄ appears to be valid for the mid-to-lower crust beneath the studied region. In particular, the Rayleigh group velocities require the setting 𝜂𝐾<1.0 in the mid-to-lower crustal depth range.

A look at the blind Kumamoto experiment: combining active and passive seismic observations to avoid Rayleigh-wave mode misidentification

We present our pathway through participation in the blind Kumamoto exercise, particularly the Step 1 of site characterization. The combination of passive and active seismic imaging techniques is used to image the velocity profile beneath the KUMA site. The estimation of the broadband Rayleigh wave dispersion curve is based on cross-correlations of ambient seismic noise and analysis of active seismic shots. We calculate correlations from the entire time series (only vertical components) of each seismic array after classical pre-processing of ambient noise data. Then, a passive seismic section is constructed using all available stations pairs and stacking the cross-correlation traces with similar interstation distances. The obtained passive seismic section is analyzed using a high-resolution Radon transform to obtain the dispersion image of Rayleigh waves traveling through the KUM-LL, KUM-M and KUM-SM arrays. Then, the information is merged and interpolated to obtain the final broadband dispersion curve. In addition, active source seismic data are used with the high-resolution Radon technique to constrain the model at shallow depths (< 30 m). Then, a broadband dispersion image is constructed with significant energy from 0.9 Hz to 45 Hz. The final dispersion curve is inverted using the non-linear neighborhood algorithm. Using just the fundamental mode Rayleigh wave, a first model with normal velocity variation in depth is obtained that corresponds well with the preferred model provided by the organizing committee. The addition of a mHVSR curve in a joint inversion better constrains the deeper part of the model (> 1 km). After comparison of the submitted dispersion curve to the theoretical dispersion curve for the preferred model (Step 4 of the blind test), the authors note that there was a clear misinterpretation in the fundamental mode of their submitted results, especially at frequencies higher than 5 Hz. Using both fundamental (only visible in the passive data set) and first overtones of Rayleigh waves (only visible in the active seismic data set) a refined velocity model could have been inferred, but we decided to keep our first submitted result. This detailed interpretation should be further studied as dispersion images from forward and backward hammer shots are quite different, which may indicate strong variations in the geometry and/or shear-wave velocities of the first meters of the subsurface.Graphical

Multiscale homogenization numerical study on the mechanism of interface debonding detection for steel–concrete composite structures with multichannel surface wave measurements

In order to understand the interface debonding detection mechanism for steel–concrete composite structures (SCCSs) efficiently using multichannel analysis of surface waves (MASW) when the heterogeneity and randomness of the mesoscale structure of concrete are considered, mesoscale homogenization numerical analysis on surface wave propagation in SCCSs is carried out. Firstly, for exploring the theoretical dispersion characteristics of surface waves in SCCSs, dispersion curves of both Lamb wave and Rayleigh wave of three different layering scenarios, including single-layer, two-layer, and three-layer composite models where concrete is treated as homogeneous material, are investigated. Meanwhile, the effect of the steel plate thickness on the dispersion curves is studied. Secondly, to evaluate the effect of mesoscale structure variation of concrete in SCCSs on surface waves, a random aggregate method (RAM) is employed to establish the mesoscale model of concrete composed of randomly distributed aggregates with different shapes. Thirdly, for enhancing numerical simulation efficiency on surface wave propagation, an equivalent homogenization approach and Voigt parallel model are developed to establish the mesoscale homogenization models of SCCSs. Dispersion curves from forwarding analysis on surface wave measurement of the mesoscale models are compared with the corresponding theoretical dispersion curves to reveal surface wave attribution and optimum layering scenarios of SCCSs for MASW method. The influence of mesoscale concrete variation on surface wave fields in SCCSs using equivalent homogenization models is investigated comprehensively and compared with that of the corresponding mesoscale models. Finally, the feasibility of the proposed MASW method for interface debonding length estimation is validated, and wavelength selection criteria of excitation signals considering interface dimension, as well as steel plate thickness, are discussed. The results from the mesoscale homogenization numerical study can provide helpful guidance on the practical application of MASW-based debonding detection for SCCSs where concrete is heterogeneous.

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.

Theoretical dispersion curves for borehole real-valued wave modes in vertically transverse isotropic formations

The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging. The accurate dispersion curves are the precondition of theoretical analysis and inversion process. Generally, these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy (VTI) formations. However, if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other, the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI formations. Few studies have focused on the influence of these real-valued solutions on dispersion curve extraction. To remove these real-valued solutions, we have proposed a modified dispersion equation and its corresponding solving process. When solving the dispersion equation, the Scholte wave velocity of VTI formation at high frequency is used as the initial guess. The two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield, and the new dispersion curve extraction method is suitable for all kinds of VTI formations. Consequently, the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.