Wave Group Velocity Research Articles

Ambient noise tomography of the Aegean region of Türkiye from Rayleigh wave group velocity

We have studied Rayleigh wave group velocities beneath the Aegean region of Türkiye using ambient noise tomography. Noise data were gathered from 43 broadband seismic stations belonging to three permanent broad-band arrays. The cross-correlation method was used to estimate empirical Green’s functions. Group velocities of the fundamental mode Rayleigh waves were determined using multiple filter technique. We measured dispersion for each station pair in a period range of 2–12 s and computed maps of group velocity distribution using the fast marching surface tomography method. The group velocity maps correlate well with the geological and tectonic features of the region, displaying low velocities for the Quaternary alluvial basins, moderate velocities for Cretaceous rocks, and high velocities for the regions where gneiss and granitoid rocks outcrop. Low velocity anomalies may be associated with the grabens and horsts formed by faulting and to deep mantle flow. We detect potential offshore geothermal zones in Izmir and Candarli Bay. The information from broad-band networks improves the resolution of crustal surface wave velocity structures, particularly for shallow depths. This improvement will support the assessment of seismic hazard, as the shallow layers of the crust contribute significantly to seismic activity.

Ocean wave tracing v.1: a numerical solver of the wave ray equations for ocean waves on variable currents at arbitrary depths

Abstract. Lateral changes in the group velocity of waves propagating in oceanic or coastal waters cause a deflection in their propagation path. Such refractive effects can be computed given knowledge of the ambient current field and/or the bathymetry. We present an open-source module for solving the wave ray equations by means of numerical integration in Python v3. The solver is implemented for waves on variable currents and arbitrary depths following the Wentzel–Kramers–Brillouin (WKB) approximation. The ray tracing module is implemented in a class structure, and the output is verified against analytical solutions and tested for numerical convergence. The solver is accompanied by a set of ancillary functions such as retrieval of ambient conditions using OPeNDAP, transformation of geographical coordinates, and structuring of data using community standards. A number of use examples are also provided.

Crustal imbrication and mountain building in the Eastern Iranian Ranges; Insights from receiver function and Rayleigh wave dispersion analysis

The evolution of the Eastern Iranian Ranges (EIR) dates back to the Late Cretaceous, coinciding with the closure of the Neotethys and the accretion of the Lut Block to Eurasia. However, controversy remains regarding its orogenic processes due to limited knowledge of the lithospheric structure. To gain a better understanding of the tectonic processes and mountain formation in eastern Iran, we analyzed seismic data from 29 stations in the northern part of the EIR. We initially perform receiver function (RF) analyses on 2160 high-quality RFs, emphasizing single-station analysis and Common Conversion Point (CCP) stacking to examine structural variations. Subsequently, we jointly invert the RFs with Rayleigh wave group velocity dispersion curves to derive a shear-wave velocity (Vs) model for each station. Our findings reveal a complex structure with west-dipping interfaces, indicating crustal layering and imbrication. We have identified a significant west-dipping layer, approximately 100 km in length, which could potentially indicate an intra-continental decoupling or shear zone. This decoupling may be responsible for the underthrusting of the Eurasian margin beneath the Lut Block, resulting in a deepening of the Moho depth to over 50 km beneath its footwall, compared to the adjacent Moho depth of around 40 km. Additionally, this process has caused an increase in the topography of approximately 1 km. These findings reflect the potential westward underthrusting of the Eurasian margin. In the deeper parts of the model, we observe a low-velocity anomaly below the crust, shedding light on a weakened lithosphere that facilitates crustal deformation in response to the compressional forces of convergence.

High-resolution seismic velocity structure using induced inter-event interferometry at the geothermal sites, Geysers, Eastern California

The possibility of retrieving Rayleigh wave empirical Green's functions (EGFs) using virtual seismometers provides an opportunity to calculate high-resolution velocity models without a set of dense stations and/or expensive seismic imaging/monitoring. The high-resolution tomographic map can give an overview of the fracturing within the saturated rock. Theoretically, the cross-correlations of earthquakes contain significant information about the EGFs between event-pairs. In this work, we developed an application of virtual seismometers on a very small scale in superficial layers where anthropogenic seismicity occurred. To test this method's capabilities, we applied it to investigate the NW-part of The Geysers (TG) geothermal field. We used 1276 micro-earthquakes, occurred in a cuboid with the horizontal side of ∼1 × ∼2 km and the vertical edge at a depth from 0.9 to 2.2 km, to obtain the high-resolution (100 × 100 m) velocity structure. A group of strict criteria was imposed separately for single event waveform and event pairs to stabilize the tomographic results. After retrieving the inter-event EGF signal and calculating the Rayleigh wave group velocity dispersion curves, we obtained the group velocity maps for each horizontal layer. The tomographic maps as a function of depth indicated a low-velocity anomaly related to existing inactive faults, topography variation of the top of the steam zone, and low-velocity anomalies possibly stimulated by fluid injection. The topography of the top of the steam varies from ∼1.0 km to 1.3 km of maps, and also anomalies connected with fluid migration appear at the depth of injection wells (1.5–1.9 km).

Relativistic kinematic effects in the interaction time of whistler-mode chorus waves and electrons in the outer radiation belt

Abstract. Whistler-mode chorus waves propagate outside the plasmasphere, interacting with energetic electrons in the outer radiation belt. This leads to local changes in the phase space density distribution due to energy or pitch angle diffusion. The wave–particle interaction time (Tr) is crucial in estimating time-dependent processes such as the energy and pitch angle diffusion. Although the wave group and particle velocities are a fraction of the speed of light, the kinematics description of the wave–particle interaction for relativistic electrons usually considers the relativistic Doppler shift in the resonance condition and relativistic motion equation. This relativistic kinematics description is incomplete. In this paper, to the literature we add a complete relativistic description of the problem that relies on the relativistic velocity addition (between the electron and the wave) and the implications of the different reference frames for the estimates of the interaction time. We use quasi-linear test particle equations and the special relativity theory applied to whistler-mode chorus waves parallel propagating in cold-plasma magnetosphere interaction with relativistic electrons. Also, we consider that the resonance occurs in the electron's reference frame. At the same time, the result of such interaction and their parameters are measured in the local inertial reference frame of the satellite. The change pitch angle and the average diffusion coefficient rates are then calculated from the relativistic interaction time. The interaction time equation is consistent with previous works in the limit of non-relativistic interactions (Tnr). For the sake of application, we provide the interaction time and average diffusion coefficient Daa for four case studies observed during the Van Allen Probes era. Our results show that the interaction time is generally longer when applying the complete relativistic approach, considering a non-relativistic calculation. From the four case studies, the ratio Tr/Tnr varies in the range 1.7–3.0 and Daa/Daanr in the range 1.9–5.4. Accurately calculating the interaction time with full consideration of special relativity can enhance the modeling of the electron flux in Earth's outer radiation belt. Additionally, the change in pitch angle depends on the time of interaction, and similar discrepancies can be found when the time is calculated with no special relativity consideration. The results described here have several implications for modeling relativistic outer-radiation-belt electron flux resulting from the wave–particle interaction. Finally, since we considered only one wave cycle interaction, the average result from some interactions can bring more reliable results in the final flux modeling.

Precision Measurement of the Group Velocity of Ultrasound in Samples with Millimeter Thickness

A methodology is proposed for high-precision local measurement of the group velocity of longitudinal waves in solid samples with millimeter thickness. Achievement of the required accuracy involves laser thermo-optical excitation of submicrosecond ultrasonic video pulses and ultrawideband piezoelectric recording of acoustic signals reflected from the test sample. Plane-parallel samples made of duralumin, quartz, and steel with a thickness of 2–6 mm are studied. To achieve the required accuracy in measuring the group velocityof ultrasound, the signal shape is mathematically processed with compensation for diffraction of the ultrasonic beam as it propagates through the sample. The possibility of ensuring the uncertainty in measuring the group velocity of ultrasound in the 1–15 MHz frequency range at a level of 0.1% in samples with millimeterthickness is demonstrated.

Exploring guided wave propagation in composite cylindrical shells with an embedded delamination through refined spectral element method

The elastic wave propagation in a thin-walled composite structure carries information concerning its material properties and structural discontinuities. Towards the damage identification, a refined spectral element method (SEM) is presented to explore the guided wave propagation in composite cylindrical shells with embedded delamination. The governing equations and the natural boundary conditions are derived using the first-order shear deformation theory along with the Hamilton's principle. The spectral shell element is established via the exact strong-form solutions, and the dynamic stiffness matrix is formulated through the force-displacement relations. Transforming the wave differential equations into the frequency domain, the numerical Laplace transform is applied to solve the inverse problems. Following a sub-laminate approach, the delamination is modeled by means of four spectral elements and the interface continuity conditions. In addition, the stiffness reduction method is introduced to approximate the delamination. A comparison with published results in terms of the natural frequencies is made to verify the accuracy of the SEM. The dispersion characteristics of the cylindrical shell are examined including the wave number, phase and group velocities. The interaction of guided waves with the delamination is revealed. The influences of the length, depth, and position of the delamination on the wave responses are demonstrated.

Crustal and uppermost mantle structure near the Gloria Fault, North Atlantic, from ocean bottom seismometer surface wave observations

SUMMARY In this work, we present both 1-D and 3-D shear wave velocity (Vs) models of the oceanic crust and uppermost mantle below the Deep OCean Test ARray area, located ∼ 70 km north of the central section of the Gloria Fault, in the eastern North-Atlantic Ocean. The velocity models are inferred from the dispersion of surface waves recorded on ocean bottom seismometers. Dispersion measurements are obtained from the analysis of ambient seismic noise at short periods (< 14 s) and teleseismic surface waves at long periods (> 14 s) using the two-station method. The 1-D Vs model is inferred from the joint inversion of Rayleigh wave phase velocities and Love wave group and phase velocities. The 3-D tomographic model is obtained by inversion of 2-D Love wave group velocity maps as a function of depth, further constrained by the average of Love wave phase velocities obtained from ambient noise (4–9 s) and the average Rayleigh and Love wave phase velocities calculated from teleseismic data (14–44 s). The 1-D Vs model shows a sediment layer with a low velocity of 1.05 km s−1, similar to previous studies in the region. Below the sediments, we find an oceanic crust with velocities ranging from 3.3 to 4.5 km s−1. The model reaches an unusually high velocity of 4.9 km s−1 in a 20 km thick layer at depths between 16 and 36 km. We interpret this fast velocity layer as indicative of the presence of harzburgite, a residue of enhanced melting that might have been formed by the proximity between the Mid-Atlantic Ridge and the Azores mantle plume. At greater depths the velocity decreases, forming a low-velocity zone that reaches a minimum at ∼ 70 km depth, which we interpret as the maximum depth for the lithosphere–asthenosphere boundary. The 3-D model shows a structure that is mostly horizontally layered, with Vs isocontours at 3.5–4.5 km s−1 highlighting oscillations of the crustal structure with wavelengths of ∼25–30 km. These oscillations may be due to changes in the rate of mantle upwelling and magma supply rate.

Shear-wave velocity models in and around north-east India by modelling Rayleigh wave group velocity dispersion data

Shear-wave velocity models in and around north-east India by modelling Rayleigh wave group velocity dispersion data

THz-range cyclotron super-radiance from photoinjector-formed dense bunch of rotating electrons

We study the possibility of terahertz pulse generation based on cyclotron super-radiance (SR) of an extended (in the scale of the wavelength) bunch of rotating electrons, which moves in a cylindrical waveguide with a translational velocity close to the wave's group velocity. In the rest frame, this group synchronism regime corresponds to radiation of an unmoving bunch of excited cyclotron oscillators at a quasi-cutoff frequency of a waveguide mode. We develop the generalized self-consistent model of cyclotron SR in the group synchronism regime describing both the azimuthal self-bunching of rotating electrons and their longitudinal displacements under the action of Coulomb repulsive forces and recoil effects caused by high-frequency magnetic fields of the generated SR pulse. Within the framework of the developed analytical model and based on direct PIC simulations, we demonstrate the feasibility of generating picosecond SR pulses with a central frequency of 1 THz and a peak power of 90 MW by photoinjector-formed electron bunches guided in a strong magnetic field of 10.5 T. Simulations show that in the group synchronism regime, the SR pulse is less affected by longitudinal forces, as compared to the case of mismatched velocities. In addition, the Lorentz force can provide partial self-compression of the electron bunch with the formation of electron density filaments.

Scattering enhancement of partially buried sphere at the water-sand interfaces due to reflected subsonic Rayleigh waves

In view of the development needs of maritime security, the detecting of buried targets over long distances at low frequencies needs to be solved urgently. Through well designed experiments at low frequency (ka = 5–10), this paper presents a study on the scattering echoes from polymethylmethacrylate (PMMA) spheres in partially buried cases (50%, 75% and 100% buried), and the propagation characteristics of subsonic Rayleigh surface waves on the surface of PMMA spheres at the water-sand interface can be clearly observed. It is shown that the fine sand medium with larger impedance brings about smaller circumferential phase and group velocities of subsonic Rayleigh waves on the surface of the PMMA sphere; the resonance peak caused by subsonic Rayleigh waves is shifted toward the low frequency with the deepening of the burial depth, and the offset can be predicted by the circumferential phase velocity of the subsonic Rayleigh wave in different media and burial depth of PMMA sphere, and the experimental and finite element simulation results validate the shift of the Rayleigh resonance peak. The research results of this paper can provide certain reference value for the detection of low frequency buried targets.

Application of linear electron Bernstein current drive models in reactor-relevant spherical tokamaks

Electron Bernstein current drive (EBCD) systems in spherical tokamaks are sensitive to plasma and launch conditions, and therefore require large parametric scans to optimise their design. One particular bottleneck in the simulation workflow is quasilinear modelling of current drive efficiency. Linear adjoint models are an attractive alternative, offering a ∼103 × speed-up compared to quasilinear codes. While linear models are well-tested and commonly used for electron cyclotron current drive (ECCD), they have seen little use in EBCD modelling. In this work, variants of the linear model are applied to EBCD and compared to quasilinear results in a reactor-relevant plasma, i.e. Spherical Tokamak for Energy Production (STEP). This comparison reveals it is important to accurately model the collision operator and finite Larmor radius effects in the linear model. When done properly, good agreement is found with quasilinear calculations, at least for normalised minor radii ρ < 0.7 and at low power densities. The power density threshold for quasilinear effects during EBCD is found to be significantly lower than that of ECCD. This is attributed to the much lower group velocity of the electron Bernstein wave (EBW). Thus, the linear model is only valid for EBCD modelling at low power densities (e.g. ≲ 1 MW launched EBW power in STEP). This may be satisfied in present-day experimental devices, but certainly not in reactors targeting non-inductive operation.

Shear wave crustal velocity structure in the Garhwal-Kumaon Himalaya based on noise cross-correlation of Rayleigh wave

The tectonics of the Garwal-Kumaon Himalaya is characterized by thrusts, tectonic windows, and klippen. We investigate crustal shear wave velocity variations using ambient noise cross-correlation tomography. The studied region encompasses the Kali River valley in the east to Satluj valley in the west, with the adjoining Indo-Gangetic Plain in the south covering the northern part of the Delhi-Haridwar ridge. The fundamental mode group velocities of Rayleigh waves are extracted from cross-correlation data of 33 broadband seismological stations from a regional seismic network. A total of 374 dispersion curves with a period range of 4–29 s show a group velocity variation between ∼2.3 and ∼ 3.4 km/s. The shear wave velocity structure of the uppermost lithosphere down to ∼50 km obtained by non-linear inversion of the Rayleigh wave dispersion data provides new insight into the geometry of the crust. A large variation in Vs in the range of ∼2.8 to ∼4.7 km/s corresponds to a variety of changes in the tectonic deformation, structure, and crustal thickness of the Himalayan wedge. Thick low-velocity sedimentary formations are identified beneath the Indo-Gangetic Plain and the frontal Himalaya. Anomalous low Vs zones are also observed in the mid-crust beneath the higher Himalaya and southern Tibet, indicating partial melting or the presence of aqueous fluid zones. The high-velocity anomalies may be correlated with duplex structures beneath the Lesser Himalaya and with lithospheric flexure.

A modal decomposition approach to topological wave propagation

The design of valley-Hall topological insulators is typically informed by analyzing the primitive unit cell, using the Berry curvature of the Bloch-eigenmodes to predict energy localization on the domain boundary, or the dispersion diagram of the semi-infinite lattice to predict the group velocity of topological waves. However, practical systems are finite in size and the propagating topological wave is composed of a finite bandwidth as guaranteed by the Fourier uncertainty principle. Hence, the propagation predicted by the ideally infinite lattice for a given frequency deviate from practical topological systems driven by finite bandwidth wave packets. In this work, we demonstrate that the propagating topological waves in valley Hall lattices can be interpreted using the linear degenerate modal basis. We show that a small subset of closely spaced modes comprise the topological waves, which enables the construction of analytical reduced-order models that accurately capture the topological wave. This result is related to the sparse density of the modal spectrum inside the topological band gap, which allows for the energy to be carried nearly completely by a narrow band of spectrally isolated eigenmodes that are spatially localized along the domain boundary. This result is then employed to refine group velocity predictions of propagating topological waves with respect to input signal bandwidth and frequency by matching the modal spectrum to the supercell dispersion diagram describing the semi-infinite system. Moreover, we utilize the damped modal spectrum to characterize variations in wave group velocity in damped topological lattices and predict edge-to-bulk transitions. Hence, this work establishes a framework for accurately characterizing undamped and damped topological wave propagation in quantum valley Hall systems using the machinery of classical dynamics.

Determination of Ice Cover Parameters Using Seismoacoustic Noise

A method for estimating ocean ice cover parameters (thickness, Young’s modulus, Poisson ratio, and density) that does not require the use of a source is proposed and tested on experimental data. To realize the approach, two single-channel seismic receivers located on the ice surface are required to record the vertical component of the oscillatory velocity of the seismic noise. The spectral-correlation analysis of the mutual correlation function of the noise registered by the receivers allows us to estimate the dispersion dependence of the group velocity of the bending-gravity wave propagating along the ice plate. The solution of the inverse problem is based on analyzing the variance of not only the group but also the phase velocity, which allows us to increase the amount of primary data. The obtained estimates of ice parameters are consistent with the results of independent observations carried out during the experiment, as well as with the estimates of other authors obtained for ice characteristics in the region of the experiment.

High-resolution shallow crustal shear wave velocity structure of Anyuan mining area and its adjacent region in Jiangxi Province, China

High-resolution seismic image is critically important for mining minerals. In this study, we collected seismic data from a local dense seismic array consisting of 154 stations around the Anyuan mining area and its adjacent region of Pingxiang City, Jiangxi Province in South China, and applied the ambient noise tomography (ANT) method to image the shear wave velocity structure in the study area. Shallow crustal velocities at depths less than 3.3 km were determined by direct inversion of Rayleigh wave group velocity dispersion curves at the period range of 0.5–5.0 s. Overall, the S-wave velocity structure has a tight correlation with surface geological and tectonic features in the study area. The shear wave velocity structure in the shallow crust of the Anyuan Mine and its adjacent areas displayed distinct low-velocity anomalies, which can be attributed to the depression of sedimentary structures and coal mining activities in the Pingxiang-Leping region. The zones surrounding the Anyuan fault (AYF) and Wangkeng fault (WKF) zones exhibited low-velocity anomalies from the ground surface to ~ 3.3 km underground. And the low-velocity anomalies at depths less than 1.2 km could be related to the sedimentary environment of coal mine and the coal mining activities, while the low-velocity anomalies at depths below 1.2 km are caused by the presence of fracture medium, oil and gas in the fault zone. The shear wave velocity changes sharply across the AYF, and the characteristics of the velocity change interface indicate that the AYF is inclined toward the northwest, with its extension reaching depths of approximately 3 km underground.Graphical

Generating 1D depth profile of shear-wave velocity from ambient noise cross-correlation: application to Jakarta array

In the past decade, cross-correlations of ambient seismic noise have been exploited in various applications to model the shallow-to-deep structure of Earth’s interior through tomographic inversions. The stack of cross-correlations between a 2-station pair represents empirical Green’s function and comprises the information of the subsurface structure between those stations. In practice, noise correlation function (NCF) is analyzed to reconstruct surface wave group or phase velocity dispersion; then, the dispersion data is used to model shear-wave velocity (Vs). This study presents a case for temporary seismic networks deployed in the Jakarta Basin; we applied a two-step routine to obtain a representative 1D Vs profile beneath an array. First, we extracted our array’s average phase velocity dispersion based on the relationship between NCF’s spectra and the Bessel function. Then, we invert for the 1D depth profile of Vs using a transdimensional Bayesian inversion to allow for exploring a number of layers in parameterizations. We successfully generate a 1D Vs profile up to 5 km depth reflecting the regional stratigraphy of the Jakarta Basin. In general, a sedimentary basin fill covers the area reaching a depth of 650 m. We suggest that this simple routine can be undertaken for other ambient noise cross-correlation cases; such a 1D depth profile would be beneficial to be used as a reference model.

Ambient Seismic Noise Cross – Correlation of the Tangkuban Parahu Volcano, West Java Indonesia: Preliminary Result

Tangkuban Parahu is an active volcano in Indonesia that is part of the Quaternary Sunda volcanic arc. We used the vertical component of waveform recorded by 55 temporary seismic stations deployed around Tangkuban Parahu volcano from October 2021 to February 2022 to gain a thorough understanding of its seismic structure. To extract empirical Green’s functions, we computed cross-correlations of the vertical component of continuous record data. The empirical Green’s function was extracted from the daily data series, and the cross-correlation data from each day was stacked into a single inter-station cross-correlation data set. The empirical Green’s Function is seen at the band period 1-10 s. In this preliminary result, we obtained the Rayleigh wave group velocity map in period 1 s. The result shows a low-velocity value around the crater surrounded by high velocities. The low velocity is related to the weak zone or fluid presence.

Group velocity and dispersion of Buchwald and Adams shelf waves. A new analytical approach

In this paper, a new analysis of the known topographic models of Rossby waves for piecewise exponential topography profiles is performed. A mathematical method is proposed that allows us to find analytically the group velocity and variance. A numerical comparison is made of the relations presented in the study of Buchwald and Adams and the dependencies obtained within the framework of a new analytical approach. Numerical comparative analysis showed that the discrepancy for the phase velocities lies in the range of five percent. For group speeds, the discrepancy reaches nineteen percent for the first mode and decreases for higher mode numbers. We also consider long-wave asymptotics of eigenfunctions. It is established that the long-wave limit for Rossby shelf waves has specifics: the longitudinal wave number tends to zero, and the transverse wave number reaches a certain finite positive constant, which is the greater the higher the mode number. It is shown that in the long-wave limit, Rossby shelf waves transform into shelf topographic currents, while there is a certain self-similarity for the phase and group velocities of shelf currents depending on the value of the topography gradient.

Ambient Noise Data Processing to Obtain Group Velocity for Subsurface Structure Identification: Preliminary Research in Hululais Geothermal Field, Sumatra, Indonesia

Hululais area lies in the pull-apart basins of the Ketaun Segment and Musi Segment fault as a part of the Sumatra Fault Zone (SFZ). The boundary normal faults of pull-apart basins play an important role as major discharge zones for geothermal fluid because the extensional stress is concentrated in the boundary normal faults. In order to identify the geothermal reservoir structure in Hululais Geothermal Field (HGF), we introduce the local-scale study of the Rayleigh wave group velocity structure using ambient noise tomography (ANT). The ANT studies were collected using 18 seismometers inside 12 km2 area with a spacing of 125 – 500 meters, deployed across the fault structure for 1 month. More than two thousand Rayleigh Green’s Functions are extracted by cross-correlation at available station pairs. Using the estimated green function in this preliminary research, the group velocity as a function of the period can measure the dispersion curve by using multiple filter technique (MFT) and fast marching surface tomography (FMST) scheme to obtain group velocity images. The tomography result as group velocity image shows the subsurface Rayleigh wave structure variation. The NW-SE main structure is reflected by the contrast velocity structure between the central part and the north eastern-south western sides. The central part shows the low periods which are associated with low wave velocity However the margin of the central part shows the high velocity in all periods. The ANT studies have been efficient in time and cost, however useful in subsurface structure interpretation in Hululais Geothermal Field.