Phase Velocity Estimation Research Articles

Distribution of noise sources for seismic interferometry

SUMMARY We demonstrate that the distribution of seismic noise sources affects the accuracy of Green’s function estimates and therefore isotropic and anisotropic tomographic inversions for both velocity and attenuation. We compare three methods for estimating seismic noise source distributions and quantify the potential error in phase velocity, azimuthal anisotropy and attenuation estimates due to inhomogenous source distributions. The methods include: (1) least-squaresinversionofbeamformeroutput,(2)aleast-squaresinversionofyearlongstacked noise correlation functions assuming both a 2-D plane wave source density model and (3) a 3-D plane wave source density model. We use vertical component data from the 190 stations of the Southern California Seismic Network and some US Array stations for 2008. The good agreement between the three models suggests the 2-D plane wave model, with the fewest number of unknown parameters, is generally sufficient to describe the noise density function for tomographic inversions. At higher frequencies, 3-D and beamforming models are required to resolve peaks in energy associated with body waves. We illustrate and assess isotropic and azimuthally anisotropic phase velocity and attenuation uncertainties for the noise source distribution in southern California by inverting isotropic lossless synthetic Fourier transformed noise correlation function predictions from modelled 2-D source distribution. We find that the variation in phase velocity with azimuth from inhomogeneous source distribution yields up to 1 per cent apparent peak-to-peak anisotropy. We predict apparent attenuation coefficients from our lossless synthetics on the same order of magnitude as those previously reported for the region from ambient noise. Since noise source distributions are likely inhomogeneous varying regionally and with time, we recommend that noise correlation studies reporting attenuation and anisotropy incorporate source density information.

Cancellous bone analysis with modified least squares Prony’s method and chirp filter: Phantom experiments and simulation

The presence of two longitudinal waves in porous media is predicted by Biot's theory and has been confirmed experimentally in cancellous bone. When cancellous bone samples are interrogated in through-transmission, these two waves can overlap in time. Previously, the Modified Least-Squares Prony's (MLSP) method was validated for estimation of amplitudes, attenuation coefficients, and phase velocities of fast and slow waves, but tended to overestimate phase velocities by up to about 5%. In the present paper, a pre-processing chirp filter to mitigate the phase velocity bias is derived. The MLSP/chirp filter (MLSPCF) method was tested for decomposition of a 500 kHz-center-frequency signal containing two overlapping components: one passing through a low-density-polyethylene plate (fast wave) and another passing through a cancellous-bone-mimicking phantom material (slow wave). The chirp filter reduced phase velocity bias from 100 m/s (5.1%) to 69 m/s (3.5%) (fast wave) and from 29 m/s (1.9%) to 10 m/s (0.7%) (slow wave). Similar improvements were found for 1) measurements in polycarbonate (fast wave) and a cancellous-bone-mimicking phantom (slow wave), and 2) a simulation based on parameters mimicking bovine cancellous bone. The MLSPCF method did not offer consistent improvement in estimates of attenuation coefficient or amplitude.

Shear wave crustal velocity model of the Western Bohemian Massif from Love wave phase velocity dispersion

We propose a new quantitative determination of shear wave velocities for distinct geological units in the Bohemian Massif, Czech Republic (Central Europe). The phase velocities of fundamental Love wave modes are measured along two long profiles (~200 km) crossing three major geological units and one rift-like structure of the studied region. We have developed a modified version of the classical multiple filtering technique for the frequency-time analysis and we apply it to two-station phase velocity estimation. Tests of both the analysis and inversion are provided. Seismograms of three Aegean Sea earthquakes are analyzed. One of the two profiles is further divided into four shorter sub-profiles. The long profiles yield smooth dispersion curves; while the curves of the sub-profiles have complicated shapes. Dispersion curve undulations are interpreted as period-dependent apparent velocity anomalies caused both by different backazimuths of surface wave propagation and by surface wave mode coupling. An appropriate backazimuth of propagation is found for each period, and the dispersion curves are corrected for this true propagation direction. Both the curves for the long and short profiles are inverted for a 1D shear wave velocity model of the crust. Subsurface shear wave velocities are found to be around 2.9 km/s for all four studied sub-profiles. Two of the profiles crossing the older Moldanubian and Tepla-Barrandian units are characterized by higher velocities of 3.8 km/s in the upper crust while for the Saxothuringian unit we find the velocity slightly lower, around 3.6 km/s at the same depths. We obtain an indication of a shear wave low velocity zone above Moho in the Moldanubian and Tepla-Barrandian units. The area of the Eger Rift (Tepla-Barrandian–Saxothuringian unit contact) is significantly different from all other three units. Low upper crust velocities suggest sedimentary and volcanic filling of the rift as well as fluid activity causing the earthquake swarms. Higher velocities in the lower crust together with weak or even missing Moho implies the upper mantle updoming.

New formulas derived from seismic interferometry to simulate phase velocity estimates from correlation methods using microtremor

I have developed two theoretical formulas on the basis of the power partition ratios among different modes of Rayleigh waves that are newly derived theoretically from seismic interferometry (SI). These formulas, one for the spatial autocorrelation method (SPAC) and another for the centerless circular array method (CCA), are used to simulate the estimates of the dispersion curves that can be obtained from the correlation methods using microtremor in situations when the higher normal modes are present along with the fundamental mode. The formulas can provide a way to overcome the problem caused by the assumption of the dominance of the fundamental mode, which is not always true. In addition, I have conducted a numerical validation check using the synthetic microtremor waveform data that were produced by the finite-difference method. I have found that the CCA can be an alternative to the SPAC to estimate the dispersion curves. The formula for the CCA can well simulate the dispersion curves estimated by the SPAC and CCA methods, and are better than the formula based on the above-mentioned assumption. Moreover, using the data mentioned above, I have discovered that the dual-mode inversion, which considers the presence of the fundamental and first higher modes on the basis of the formula for the CCA, performs better than the conventional single-mode inversion, which rests on the above-mentioned assumption. These positive results partially support the theoretical consequence of SI, i.e., the power partition ratio, and, further, SI itself on which the theoretically derived formulas fully rely.

Microwave radar probing of a rough water surface: validation of retrieval algorithms using flight experiment data

We studied the microwave backscattering of a rough water surface during a flight above the Gorky water storage basin. A microwave Doppler radar with a knife-like beam (1–16°) was installed on a helicopter and oriented vertically downwards. Analysis of the experimental data confirms that the reflected power and the width of the Doppler spectrum depend on the direction of wave propagation. ‘Antenna’ and ‘angular’ algorithms were used to obtain the variance of the slopes. These algorithms enabled us to determine the slope variance from a moving carrier, without limitations placed on the flight's height. We developed two new algorithms to determine the correlation coefficients of the vertical component of the orbital velocity and water surface slopes as well as the variance of orbital velocities using the width of the Doppler spectrum. We used the results obtained from varying the input parameters of the algorithm to minimize the retrieval error of the correlation coefficient. Comparisons with parameters derived from modelled wave spectra indicate the effectiveness of the retrieval algorithms. We also demonstrate the possibility of extracting estimates of the average phase velocity, the average wavelength and the significant wave height of sea waves.

Decomposition of two-component pulses: Simulation and phantom experiment.

Porous media often support propagation of two compressional waves. When cancellous bone samples are interrogated in through-transmission with broadband sources, these two waves often overlap in time. A method for measuring attenuation and velocity of the two component waves was developed. The method (1) assumes that the transfer function is the sum of two exponentially modulated sinusoids and (2) minimizes the sum of the squared error between a model fit and the data. The method was tested for decomposing a 500-kHz-center-frequency signal containing two overlapping components: one passing through a polycarbonate plate (fast wave) and another passing through a cancellous-bone-mimicking phantom (slow wave). The method yielded estimates of attenuation slopes accurate to within 7% (polycarbonate plate) and 2% (cancellous bone phantom). The method yielded estimates of phase velocities accurate to within 1.5% (both media). The method was tested on simulated data generated using attenuation slopes and phase velocities corresponding to bovine cancellous bone. Throughout broad ranges of signal-to-noise ratio and fast-slow-wave-velocity differential, the method yielded estimates of attenuation slope that were accurate to within 10% and estimates of phase velocity that were accurate to within 5% (fast wave) and 2% (slow wave).

Frequency dependence of phase shifts in human calcaneus in vitro.

If dispersion in a medium is weak and approximately linear with frequency (over an experimental band of frequencies), then it can be shown that the constant term in a polynomial representation of phase shift as a function of frequency can produce errors in measurements of phase velocity differences in through-transmission, substitution experiments. A method for suppressing the effects of the constant phase shift in the context of the single-wave-model was tested on measurements from 30 cancellous human calcaneus samples in vitro. Without adjustment for constant phase shifts, the estimated phase velocity at 500 kHz was 1516 +− 6 m/s (mean +− standard error), and the estimated dispersion was −24 +− 4 m/sMHz (mean +− standard error). With adjustment for constant phase shifts, the estimated mean velocity decreased by 4–9 m/s, and the estimated magnitude of mean dispersion decreased by 50%–100%. The average correlation coefficient between the measured attenuation coefficient and frequency was 0.997 +− 0.0026 (mean +− standard deviation), suggesting that the signal for each sample was dominated by one wave.

Deblurring of frequency-wavenumber images from small-scale seismic arrays

Temporary arrays installed in urban areas for investigating the upper-most geological structure typically comprised of a limited number of stations and are arranged in geometries constrained by environmental boundaries. Therefore, it is expected that the frequency–wavenumber images are significantly blurred by the array transfer function and are corrupted by noise. In this paper, the effect of the Richardson–Lucy regularization method applied to the problem of deblurring frequency–wavenumber images is investigated. The images are computed by analysing data from two small-aperture 2-D arrays, installed with different configurations in a test-site within the town of Potenza (Southern Italy) for near-surface investigations. We show that removing the effects of the array response from the frequency–wavenumber images improve the phase-velocity estimation, reducing the relevant level of uncertainty. Furthermore, the Richardson–Lucy regularization method is effective in reducing the level of noise related to spatial aliasing by eliminating spurious peaks, allowing the maxima related to different seismic sources to be better discriminated.

Decomposition of Two-Component Ultrasound Pulses in Cancellous Bone Using Modified Least Squares Prony Method – Phantom Experiment and Simulation

Porous media such as cancellous bone often support the simultaneous propagation of two compressional waves. When small bone samples are interrogated in through-transmission with broadband sources, these two waves often overlap in time. The modified least-squares Prony's (MLSP) method was tested for decomposing a 500 kHz-center-frequency signal containing two overlapping components: one passing through a polycarbonate plate (to produce the “fast” wave) and another passing through a cancellous-bone-mimicking phantom (to produce the “slow” wave). The MLSP method yielded estimates of attenuation slopes accurate to within 7% (polycarbonate plate) and 2% (cancellous bone phantom). The MLSP method yielded estimates of phase velocities accurate to within 1.5% (both media). The MLSP method was also tested on simulated data generated using attenuation slopes and phase velocities corresponding to bovine cancellous bone. Throughout broad ranges of signal-to-noise ratio (SNR), the MLSP method yielded estimates of attenuation slope that were accurate to within 1.0% and estimates of phase velocity that were accurate to within 4.3% (fast wave) and 1.3% (slow wave). (E-mail: keith.wear@fda.hhs.gov).

全波動場のＧｒｅｅｎ関数を用いた短周期アレー観測記録の解析

We studied the effect of body waves on short period vertical ground motion based on both a numerical simulation and field array observations. The vertical components generated by the vertical point force within a close distance are targeted throughout the study. Firstly, we carried out a numerical simulation and confirmed that the effect of body waves on the full-wave field was generally limited to a close distance from the source with frequency dependence. In a frequency range lower than 5 Hz and at around the 1st predominant frequency (5.8 Hz), the effect appears beyond a far distance; in a range of about 6 to 10 Hz, it still remains up to 10 m or more; in a range higher than 10 Hz, it almost vanishes. Secondly, we analyzed the observed array data excited by a 30-kg sandbag falling 10, 20, and 40 m from the array center. The array configuration was a circle, 1 m in radius, consisting of seven sensors placed in the center and around the circumference at equal intervals. To obtain a better understanding of the results of the array analyses, simulated array data, based on the Green's functions for the full-wave field and for the Rayleigh wave, was produced and analyzed in the same manner as the observed field array data. The phase velocity results were calculated with three different methods, namely, the spatial autocorrelation (SPAC) method, a method based on the spatial 1st Fourier coeffcients in the azimuthal direction with respect to the cross spectral amplitude between the center and one of circumferential stations, and a technique which combined these two methods. In the case of an offset of 10 m (Case 1), the detected phase velocities from the observed data and the simulated data on the full-wave field were much lower than the theoretical phase velocity or that from the Rayleigh wave array data in a frequency range of 5 to 10 Hz, suggesting the strong effect of body waves. In the case of an offset of 20 m (Case 2), the estimated phase velocities from the observed data and the two other simulated array data coincided with the theoretical phase velocity, suggesting the weak effect of body waves. We conclude that in order to properly estimate an underground structure from the array measurement data at a close distance from the source, the analytical technique based on the full-wave Green's function should be applied. Taking a look at the choice of analytical methods for the array data, it can be pointed out that for our interest the two methods which use the spatial 1st Fourier coeffcients produce higher accuracy compared with the SPAC method in a relatively low frequency range. In addition, the phase velocity results were estimated from the CCA (centerless circular array) method by Cho et al. (2004). The CCA method provided similar accuracy compared with the above two methods based on the spatial 1st Fourier coeffcients. The CCA method seems to be applicable to highly directional wave fields located nearby the source.

EFFECT OF AN IRREGULAR GROUND ON MICROTREMOR H/V SPECTRA AND DISPERSION CURVES

In this paper, wave propagation in an irregular ground due to incident surface waves is formulated by combining the 2.5 dimensional thin layered element method and the 2.5 dimensional finite element method. From this study, the following conclusions are made: 1. From the analysis of the microtremor wave field due to various incident surface (Rayleigh and Love) waves, it has pointed out that H/V spectra and dispersion curves are influenced by both body and surface waves generated from the irregularity (slope in this study) of the ground. 2. It is also confirmed that effect of interference between the incident wave and waves generated from the slope changes depending on the angle of incidence. 3. A comparison with the observation data has shown that the 2.5-D analysis can give good results when compared to the 1-D or 2-D analysis. 4. Estimated phase velocities from observation data show a tendency of accuracy degradation in the vicinity of the H/V spectral peak.

Frequency dependence of average phase shift from human calcaneusin vitro

If dispersion in a medium is weak and approximately linear with frequency (over the experimental band of frequencies), then it can be shown that the constant term in a polynomial representation of phase shift as a function of frequency can produce errors in measurements of phase-velocity differences in through-transmission, substitution experiments. A method for suppressing the effects of the constant phase shift in the context of the single-wave-model was tested on measurements from 30 cancellous human calcaneus samples in vitro. Without adjustment for constant phase shifts, the estimated phase velocity at 500 kHz was 1516+/-6 m/s (mean+/-standard error), and the estimated dispersion was -24+/-4 m/s MHz (mean+/-standard error). With adjustment for constant phase shifts, the estimated mean velocity decreased by 4-9 m/s, and the estimated magnitude of mean dispersion decreased by 50%-100%. The average correlation coefficient between the measured attenuation coefficient and frequency was 0.997+/-0.0026 (mean+/-standard deviation), suggesting that the signal for each sample was dominated by one wave. A single-wave, linearly dispersive model conformed to measured complex transfer functions from the 30 cancellous-bone samples with an average root-mean-square error of 1.9%+/-1.0%.

Fundamental and higher‐mode Rayleigh wave characteristics of ambient seismic noise in New Zealand

In order to use ambient seismic noise for mapping Earth's structure, it is important to understand the spatio‐temporal characteristics of the noise field. This study uses data collected during four austral winter months of 2002 to investigate New Zealand's ambient seismic noise field in the double‐ocean‐wave‐frequency range (0.1–0.3 Hz). It is shown via beamforming analysis that there are two distinct dispersive waves in the data. These waves can be separated. Their estimated phase velocities (2.5–2 and 4–3 km/s in the frequency range 0.14–0.25 Hz) match well with fundamental and higher‐mode Rayleigh dispersion curves. Studies of double‐wave‐frequency microseisms elsewhere generally show the Rayleigh noise fields to be dominated by fundamental mode waves. The reason why higher‐mode signals are observed here may reflect a combination of long ocean wave periods, large waveheights, the direct deep water approach to narrow continental margins, and the proximity of the seismograph array to the source regions.

Interpreting Surface-wave Data for a Site with Shallow Bedrock

The inversion of dispersive Rayleigh-wave data has been shown to be successful in providing reliable estimated shear-wave velocities within unconsolidated materials in the near surface. However, in a case where the multi-channel analysis of surface waves method was applied to a site consisting of clay residuum overlying basalt bedrock, inversion for the fundamental-mode Rayleigh wave resulted in shear-wave velocities within the rock that are less than half of expected values. Forward modeling reveals that the fundamental-mode dispersion curve is hardly sensitive to bedrock velocity perturbations over a practical range of wavelengths, leading to poorly constrained solutions. Standard surface-wave methods can fail because of a shortage of phase-velocity estimates at the low frequencies that are necessary to properly constrain shear-wave velocities at depth. The commonly used guideline that maximum investigation depth is roughly half of the largest recorded wavelength can be misleading. Data at much lower frequencies (i.e., longer wavelengths) than typically acquired might be required to obtain a meaningful shear-wave velocity profile, particularly for a site with a high-velocity half-space beneath a low-velocity layer. For such cases, layer geometry appears to have a large impact on inversion results. Consequently, Rayleigh-wave methods can be effective in determining depth to bedrock in simple, layered geologies (e.g., soft sediment over hard bedrock) when independent information of shear-wave velocity is available. Analysis techniques that address higher modes of Rayleigh-wave propagation may be useful for more accurately resolving depth and velocity of a high-velocity half-space. In the studied case, higher modes can theoretically reach the asymptotic high-velocity limits within the range of recorded frequencies.

Low-frequency sound wave parameter measurement in gravels

Experiments were performed to measure the various sound-wave propagation parameters of two kinds of gravel, a crushed limestone and a stream-formed “pea gravel”, at frequencies between 25 and 200 Hz. The apparatus was a very large standing-wave tube with an array of microphones along its entire length. Measurements were made with the tube in the vertical position, filled to various depths, with a pressure-doubling barrier at the bottom. Values were determined for wavelength and attenuation in the gravel and for input impedance at the boundary between gravel and air. The basic analysis method was to fit the parameters of a presumed Green’s function representing the standing wave in the tube to the measured sound pressure amplitudes measured by the microphones. This worked well for some frequencies and some depths of gravel. In other cases, various modifications of the method gave more consistent results. For crushed limestone, the estimates of phase velocity and attenuation increased monotonically with frequency, ranging between 150 and 250 m/s and 0.1 and 0.8 Np/m, respectively. For pea gravel, the estimates increased monotonically with frequency, with values between 160 and 205 m/s and 0.4 and 1.1 Np/m, respectively.

A Method to Estimate the Phase Velocities of Microtremors Using a Time-Frequency Analysis and Its Applications

The phase velocities of Rayleigh waves provide basic information for estimating the shear-wave velocity structure of the ground. Many methods have been proposed for this purpose; however, it is difficult to estimate phase velocities directly from the data found in microtremor records on the differences in phase angles between two sites. The reason for this difficulty is that the sources of microtremors are not stable in either time or space. In order to counteract this problem, therefore, we consider the nonstationary characteristic of microtremors in short-time range and propose a method that can find the instantaneously corresponding portions of microtremor records at two different sites and that can estimate the apparent phase velocities between the two sites. We use the technique of a time-frequency analysis for which the Hilbert–Huang Transform is adopted. After we confirm the applicability of the proposed method based on some numerical calculations, the method is applied to some actual data on microtremors and reasonable results are obtained.

The Influence of Experimental Condition on the Derivation of Propagation Coefficient in Arterials Systems: Numerical Investigation

Over the last few decades several methods have been used to compute the propagation coefficient, which is a complex number that provides information about the viscoelastic properties of blood vessels. Results from these methods show a considerable disparity between them and when they are compared to theoretical values. Moreover, the attenuation and phase velocity obtained by the three-point method shows more significant discrepancies than those obtained by the other methods. In order to clarify the source of the disparity of results carried out by various methods concerning the estimation of phase velocity and attenuation in the arterial network, we made investigations using numerical tool several methods. We studied, for each method, the effects of distance between measurement sites, the sampling interval and measurement errors on the determination of the propagation coefficient by each of these methods. The values of wave speed and attenuation computed by these methods were compared to the known input values. Our simulation demonstrates that the distance between measurement sites and the sampling interval may introduce significant errors when the noise becomes high. Moreover the error on the values of attenuation and phase velocity obtained by occlusion and three-point methods is significantly higher than the error on the values obtained by RV-I and RV-II methods for all experimental conditions studied within the examined frequency range. This result supports the idea that the discrepancy between studies reported in literature seems to be due to the inaccuracy of experimental measurement techniques and not associated with the methods themselves as concluded by some authors.

Observation of internal tidal currents in the Kaoping Canyon off southwestern Taiwan

Internal tidal currents and associated water-mass displacements were investigated during multiple cruises in the Kaoping Submarine Canyon off southwestern Taiwan. Observations from both moored and shipboard Acoustic Doppler Current Profilers and hydrographic casts were conducted along the canyon. The velocity data showed that in the lower layer the major axis of the tidal currents aligned with the orientation of the canyon, and currents moved up-canyon during flood and down-canyon during ebb. The vertical-phase shift and amplitude of the currents indicated that the semidiurnal internal tide dominated with intensity increasing with depth toward the canyon head. Tidal energy was channeled from the shelf landward with a beamlike internal wave, guided by bottom topography. The estimated phase velocity was 1.4–1.7 m s −1, based on normal mode analysis and the phase lag between sampling stations. Empirical orthogonal function analysis of hydrographic profiles confirmed that the first mode (M 2 internal tide) explained 70% of the total variance. The strong convergence of internal tidal currents near the canyon head during flood may play an important role in the daily migration of cherry shrimps, which burrow along the canyon wall.

S-wave velocity structure beneath the High Lava Plains, Oregon, from Rayleigh-wave dispersion inversion

The High Lava Plains (HLP) “hotspot” track is a prominent volcanic lineament that extends from the southeast corner of Oregon in the northern Great Basin to Newberry volcano in the eastern Cascades. With the age of silicic volcanism decreasing along track to the northwest, the HLP and Newberry volcano are a rough mirror image to the Eastern Snake River Plain and Yellowstone but, in the case of the HLP, at an orientation strongly oblique to North American plate motion. Since this orientation is incompatible with plate motion over a fixed hotspot, other proposed origins for the HLP, such as asthenospheric inflow around a steepening slab, residual effects of a Columbia River/Steens plume, backarc spreading, and Basin and Range extension, relate it to various tectonic features of the Pacific Northwest. To begin distinguishing between these hypotheses, we image upper-mantle structure beneath the HLP and adjacent tectonic provinces with fundamental-mode Rayleigh waves recorded by stations of the USArray Transportable Array, the recently-initiated HLP seismic experiment, the United States National Seismograph Network, and the Berkeley seismic network. We estimate phase velocities along nearly 300 two-station propagation paths that lie within and adjacent to the HLP and cross the region along two azimuths, parallel to and perpendicular to the HLP track. The dispersion curves, which typically give robust results over the period range 16–171 seconds, are grouped by tectonic region, and the composite curves are inverted for S-wave velocity as a function of depth. We also fit a single plane wave to phase delays across the region to identify laterally homogeneous subregions. The resulting variations in upper-mantle structure correlate with variations in surface volcanism and tectonics. The lowest velocities (∼ 4.1 km/s) occur at ∼ 50 km depth in the SE corner of Oregon, where there has been extensive basaltic volcanism in the past 2–5 kyr, and suggest uppermost mantle temperatures sufficient to produce basaltic partial melting. While the seismic velocities of the uppermost mantle beneath the volcanic High Lava Plains are low relative to the standard Tectonic North America (TNA) model, they are only slightly lower than those found for the adjacent northern Great Basin and they appear to be significantly higher than upper-mantle velocities beneath the Eastern Snake River Plain. Our results provide no evidence for a residual plume signature beneath the HLP region, leaving open questions as to the origin of the HLP volcanic track itself.

Determination of dispersive phase velocities by complex seismic trace analysis of surface waves (CASW)

A method for deriving experimental dispersion curves of surface waves from active source recordings is presented. The method is based on the complex seismic trace analysis of surface waves (CASW) and is applicable when only two receivers are available. Reliable phase velocities are obtained when keeping the geophone interval smaller than one λ, allowing both a velocity structure as local as possible to be derived and to avoid long geophone spreads which are difficult to handle in urban areas. A large number of velocity estimates for each frequency can be estimated, even when using only two sensors, allowing statistical validation of the results, and providing a statistically defined uncertainty interval to be used in the dispersion curve inversion. The method is tested using synthetic seismograms and applied to real-world data, showing that it provides reliable estimates of apparent phase velocities. Although a final conclusion cannot yet be drawn, its application to observed data suggests it has the potential to be a useful method for distinguishing different modes.