Velocity Anisotropy Research Articles

Prograde and retrograde stars in nuclear cluster merger. Evolution of the supermassive black hole binary and the host galactic nucleus

Nuclear star cluster (NSC) mergers, involving the fusion of dense stellar clusters near the centres of galaxies, play a pivotal role in shaping galactic structures. The distribution of stellar orbits has significant effects on the formation and characteristics of extreme mass ratio inspirals (EMRIs). In this study, we address the orbital distribution of stars in merging NSCs and the subsequent effects on supermassive black hole binary (SMBHB) evolution. We ran dedicated direct-summation $N$-body simulations with different initial conditions to do a detailed study of the resulting NSC after their progenitors had merged. Our findings reveal that prograde stars form a flattened structure, while retrograde stars have a more spherical distribution. The axial ratios of the prograde component vary based on the presence and mass ratio of the SMBHs. The fraction of prograde and retrograde stars depends on the merger orbital properties and the SMBH mass ratio. The interactions of retrograde stars with the SMBHB affect the eccentricity and separation evolution of the binary. Our analysis reveals a strong correlation between the angular momentum and eccentricity of the SMBH binary. This relationship could serve as a means to infer information about the stellar dynamics surrounding the binary. We find that prograde orbits are particularly close to the binary of SMBHs, a promising fact regarding EMRI production. Moreover, prograde and retrograde stars have different kinematic structures, with the prograde stars typically rotating faster than the retrograde ones. The line-of-sight velocity and velocity dispersion, as well as the velocity anisotropy of each NSC, depend on the initial merger orbital properties and SMBH mass ratios. The prograde and retrograde stars always show different behaviours. The distribution of stellar orbits and the dynamical properties of each kinematic population can potentially be used as a way to tell the properties of the parent nuclei apart, and has an important impact on expected rates of EMRIs, which will be detected by future gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA).

Unveiling the shape: A multi-wavelength analysis of the galaxy clusters Abell 76 and Abell 1307

We analyse the dynamical state of the galaxy clusters Abell 76 and Abell 1307 from the optical point of view, presenting a coherent scenario that responds to the X-ray emissions observed in these structures. Our study is based on 231 and 164 spectroscopic redshifts, for the clusters A76 and A1307, respectively, obtained mostly with the Telescopio Nazionale Galileo, and complemented with others collected from the SDSS DR16 spectroscopic database and the literature. We find that A76 and A1307 are two galaxy clusters at z = 0.0390 and 0.0815, respectively, with a velocity dispersion of 650 ± 56 km s−1 and 863 ± 85 km s−1, and they show velocity distributions following, in practice, Gaussian profiles. From our dynamical analysis, X-ray studies and SZ-Planck emission, we obtain a mean total mass M500 = 1.7 ± 0.6 ⋅ 1014 M⊙ and 3.5 ± 1.3 ⋅ 1014 M⊙ for A76 and A1307, respectively. Using the SDSS DR16 photometric database, we find that the spatial distribution of likely cluster members in the case of A76 is very anisotropic, while A1307 shows a compact distribution of galaxies, but it is double peaked and elongated in the south-north direction. Using XMM-Newton X-ray data, we compared the surface brightness maps with galaxy distributions and noticed that both distributions are correlated. We reconstructed the total mass profile and velocity anisotropy of both clusters by analysing the full projected phase space, through the MG-MAMPOSSt code. Our study reveals a slight indication of radial orbits for A76, while A1307 seems to prefer more isotropic orbits in the whole cluster range. In summary, A76 represents a typical young cluster, in an early stage of formation, with a very low X-ray surface brightness but a high temperature showing a very anisotropic galaxy distribution. A1307 is however more consolidated and massive showing in-homogeneous galaxy distribution and an asymmetric X-ray emission, which suggest a scenario characterised by recent minor mergers.

Wudalianchi volcanism and mantle dynamics in Northeast China: New insight from Pn and Sn tomography

We determine new tomographic models of Pn anisotropic velocity and Sn isotropic velocity in and around the Wudalianchi volcanic area by inverting high-quality Pn and Sn arrival times manually picked from waveforms recorded at the newly deployed high-dense WAVESArray portable seismic stations. Our high-resolution Pn and Sn velocity models reveal strong lateral heterogeneities in the uppermost mantle under the study region. The average Pn and Sn velocities in the uppermost mantle are 8.2 and 4.5 km/s, respectively. Both Pn and Sn velocity models exhibit obvious low-velocity (low-V) anomalies under the Wudalianchi and Keluo volcanoes, whereas under the Songliao basin distinct high-velocity (high-V) zones are revealed. In particular, our Pn model reveals two separate low-V anomalies under the Nuomihe and Halaha volcanic groups, suggesting that they have different deep origins. A large-scale L-shaped low-V zone exists under the Keluo, Wudalianchi, Erkeshan, and Xunke volcanoes, characterized by Pn-wave fast propagation directions (FPDs) parallel with the low-V zone, suggesting that these volcanoes may have the same deep origin. Furthermore, southeast-opened U-shaped Pn FPDs exist around the Wudalianchi volcano, whereas NE-SW FPDs appear under the Great Xing'an range, which are generally consistent with SKS splitting measurements. This feature may reflect lithosphere-asthenosphere coupling beneath the Wudalianchi volcano associated with horizontal flows in the big mantle wedge and compressional tectonics under the Great Xing'an range. These results shed new lights on the Wudalianchi volcanism and mantle dynamics beneath Northeast China.

A triangular acoustic emission source location method considering its anisotropic propagation behavior on the surface of finger-joint-laminated board

ABSTRACT To understand the anisotropic propagation characteristics of acoustic emission (AE) signals in finger-joint-laminated boards, an improved planar localization method for AE sources is proposed. Initially, the AE source was generated by the pencil-lead break (PLB) at a fixed position on the surface of the glued wood specimen, and two AE sensors were arranged in different directions at a fixed distance of 60 mm, and the AE propagation velocity was calculated according to the time difference of arrival (TDOA). For clarity, the grain parallel direction was defined as 0 degrees, with velocities measured every 10 degrees through a counterclockwise rotation. Using these measurements, two angular anisotropic wave velocity models were developed. Subsequently, three AE sensors arranged linearly on the specimen surface pinpointed the AE source’s location. This source location problem was formulated as a multi-parameter optimization model, constrained by the geometric relationships between the AE source and the sensors. A particle swarm optimization (PSO) algorithm was utilized to estimate the AE source’s angles relative to each sensor. The findings indicate that the located AE sources deviated by 6.0–19.0 mm from the predetermined PLB positions, with inaccuracies largely attributed to the anisotropic AE wave velocity models’ precision.

Fully Kinetic Simulations of Proton-beam-driven Instabilities from Parker Solar Probe Observations

The expanding solar wind plasma ubiquitously exhibits anisotropic nonthermal particle velocity distributions. Typically, proton velocity distribution functions (VDFs) show the presence of a core and a field-aligned beam. Novel observations made by the Parker Solar Probe (PSP) in the innermost heliosphere have revealed new complex features in the proton VDFs, namely anisotropic beams that sometimes experience perpendicular diffusion. In this study, we use a 2.5D fully kinetic simulation to investigate the stability of proton VDFs with anisotropic beams observed by PSP. Our setup consists of a core and an anisotropic beam population that drift with respect to each other. This configuration triggers a proton beam instability from which nearly parallel fast magnetosonic modes develop. Our results demonstrate that before this instability reaches saturation, the waves resonantly interact with the beam protons, causing perpendicular heating at the expense of the parallel temperature.

Surviving the waves: evidence for a dark matter cusp in the tidally disrupting Small Magellanic Cloud

ABSTRACT We use spectroscopic data for ${\sim }6000$ red giant branch stars in the Small Magellanic Cloud (SMC), together with proper motion data from Gaia Early Data Release 3, to build a mass model of the SMC. We test our Jeans mass modelling method (binulator + gravsphere) on mock data for an SMC-like dwarf undergoing severe tidal disruption, showing that we are able to successfully remove tidally unbound interlopers, recovering the dark matter density and stellar velocity anisotropy profiles within our 95 per cent confidence intervals. We then apply our method to real SMC data, finding that the stars of the cleaned sample are isotropic at all radii (at 95 per cent confidence) and that the inner dark matter density profile is dense, $\rho _{\rm DM}(150\ {\rm pc}) = 1.58_{-0.58}^{+0.80}\times 10^8 \ {\rm M}_{\odot }\, \rm kpc^{-3}$, consistent with a $\Lambda$ cold dark matter cusp. Our model gives a new estimate of the SMC’s total mass within 3 kpc $(M_{\rm tot} \le 3\ {\rm kpc})$ of $2.29\pm 0.46 \times 10^9 \ {\rm M}_{\odot }$. We also derive an astrophysical ‘J-factor’ of $18.99\pm 0.16$ GeV$^2$ cm$^{-5}$ and a ‘D-factor’ of $18.73\pm 0.04$ GeV$^2$ cm$^{-5}$, making the SMC a promising target for dark matter annihilation and decay searches. Finally, we combine our findings with literature measurements to test models in which dark matter is ‘heated up’ by baryonic effects. We find good qualitative agreement with the Di Cintio et al. model but we deviate from the Lazar et al. model at high $M_*/M_{200} > 10^{-2}$. We provide a new, analytical, density profile that reproduces dark matter heating behaviour over the range $10^{-4} < M_*/M_{200} < 10^{-1}$.

First-principles calculations of the elastic anisotropy, thermal conductivity, and optical properties of MAX-phase M2AlC (M = V, Nb, Ta) series carbides

Materials from the MAX phase, such as the M2AlC (M = V, Nb, Ta) series carbides, exhibit superior mechanical, electronic, and thermodynamic properties, making them highly promising for research. Density functional theory (DFT) has been employed to study the elastic anisotropy, thermal conductivity, electronic, and optical properties of these carbides. The results indicate that the formation enthalpies of the M2AlC (M = V, Nb, Ta) series are negative and the phonon spectra do not exhibit imaginary frequencies, confirming the thermodynamic and dynamic stability of these carbides. Additionally, the calculated Poisson's ratios and B/G ratios suggest that these materials are brittle and contain covalent and ionic bonds—a conclusion further corroborated by analyses of electronic structures. The elastic anisotropy is illustrated through anisotropy indices, three-dimensional (3D) surface configurations, and two-dimensional (2D) projections, with the sequence of anisotropy being: Nb2AlC > Ta2AlC > V2AlC. Further investigations into the sound velocities, Debye temperature, anisotropy of sound velocity, thermal conductivity, and optical properties of the M2AlC (M = V, Nb, Ta) series provide substantial theoretical support for the research on MAX phase M2AlC (M = V, Nb, Ta) series carbides.

Understanding the effects of pore pressure–induced crack deformation on the acoustic anisotropy of rocks with aligned cracks

AbstractCracks are extensively existing in rocks and play a significant role in the acoustic anisotropy of cracked rocks. Rocks in nature are affected by pore pressure, whereas the crack deformation with pore pressure and the impacts of the crack deformation on the anisotropic acoustic properties remain little known. Combining the theoretical model with the laboratory measurements of the anisotropic velocities of artificial sandstone samples with and without aligned penny‐shaped cracks, we invert for the crack parameters that characterize the crack deformation as a function of pore pressure and theoretically simulate the impacts of pore pressure–induced variation in the crack parameters on the anisotropic velocities. The results show that with increasing pore pressure, the inverted crack porosity increases exponentially, whereas the inverted crack aspect ratio decreases exponentially and the two crack parameters are linearly correlated. Moreover, model calculation demonstrates that the anisotropic velocities exhibit distinct reductions with the variation in the crack parameters caused by increasing pore pressure. In particular, the reduction in the velocity of the shear wave travelling parallel to the crack plane with polarization perpendicular to the crack plane is the most pronounced. We also demonstrate that the effects of the pore pressure–induced increasing crack porosity on the anisotropic velocities are more pronounced than the impacts of the decreasing crack aspect ratio. The findings not only reveal the variation of the crack geometry with pore pressure and the effects of the crack deformation on the anisotropic velocities of the cracked rocks but also can provide theoretical support for improving the characterization of the cracks through seismic survey.

Collisional Mechanism of Expanding Wavenumbers Range of Weibel-Type Instability in Magnetoactive Plasma

For plasma with anisotropic velocity distribution of particles in the form of two counter-propagating bi-Maxwellian beams, including bi-Maxwellian plasma, in the presence of external magnetic field parallel to the beams, it is shown that in a wide range of parameters, particle collisions lead to the expansion of the wavenumbers range, generally towards the long-wavelength region, and weaken the conditions for the occurrence of the Weibel-type instability. In the specified expanded range, its growth rate, found by means of solving the dispersion equation for the wave vectors orthogonal to the external magnetic field, turns out to be less than or on the order of the frequency of particle collisions. Thus, in this range of parameters, the instability development and formation of large-scale magnetic turbulence in a plasma with weak particle collisions require the long-term injection of particles with anisotropic velocity distribution.

Experimental Study Of Anisotropic And Dispersion Signature Of Shale Reservoirs: Implications For Synthetic Seismic Well Tie

To investigate velocity anisotropy and dispersion in lacustrine shales, we conducted laboratory measurements of acoustic properties at seismic frequencies (2–100 Hz) and ultrasonic frequencies (1 MHz) under varying effective pressures. Our study reveals significant transverse isotropy, accompanied by notable velocity dispersion and attenuation, with anisotropy coefficients ranging from 0.45 to 0.74 for P-waves and 0.44 to 0.95 for S-waves. Attenuation exhibited weak dependence on frequency and pressure but showed a strong positive correlation with clay content. We interpreted the data by integrating geological and physical analyses. Using rock physics modeling and the propagation matrix method, we found that velocity dispersion primarily caused the mismatch between seismic data and synthetic seismograms, while anisotropy had minimal impact on near-offset seismic data. Our findings suggest that anisotropy and dispersion observed at the core scale persist at the seismic scale. Incorporating these effects into seismic workflows is crucial for improving data processing, inversion, and reservoir characterization. This study provides valuable insights for exploration and production strategies in the study area and similar settings.

Insight into wave propagation in polyimide films and resistive grid sandwich structures towards a hybrid monitoring of hypervelocity impact

Micro-Meteoroid and Orbital Debris pose a significant threat to the safe operation of orbiting spacecraft, potentially leading to mission failure in space exploration. Quantitative characterization of hypervelocity impact (HVI) is crucial to ensure the safety and successful completion of on-orbit missions. Firstly, this study designed a three-layer sandwich structure of polyimide film with orthogonally laid resistive wires, combined with piezoelectric and resistive wire sensors, for the simultaneous acquisition of acoustic emission (AE) signals generated by HVI and measurement of perforation dimensions. Secondly, a semi-analytical finite element (SAFE) analysis of wave dispersion properties in the periodic sandwich structure is conducted with Bloch’s theorem, together with a hybrid model based on three-dimensional smoothed particle hydrodynamics and finite element methods (SPH-FEM) to comprehensively understand the AE waves and damage characteristics induced by HVI. The resulting anisotropic wave propagation characteristics with SAFE and SPH-FEM are closely matched. Thirdly, a time delay-multiplication (TDM) imaging algorithm considering wave velocity anisotropy is proposed for accurate real-time “visualization” of HVI locations. Lastly, correlations are established between projectile and perforation dimensions. The proposed algorithm for HVI multi-parameter quantification and damage detection helps evaluate the space HVI environment and HVI-induced damage to spacecraft.

Guided wave multi-frequency damage localization method in variable-thickness structures by one pair of sensors based on frequency-dependent velocity anisotropy

Variable thickness structures are prevalent in aircraft, ships, and other machines, necessitating numerous sensors for health monitoring to reduce safety hazards. This paper presents a guided wave multi-frequency localization method based on frequency-dependent velocity anisotropy. This method achieves damage localization in variable-thickness structures with a pair of sensors and can effectively reduce the number of sensors used for monitoring. Variations in structural thickness cause a gradient in guided wave velocity that bends the propagation path. Different thickness variations with different directions cause wave velocity anisotropy. As a result, variations in thickness cause possible damage loci determined by echo time to deviate from an elliptical shape. Because the velocity anisotropy is frequency-dependent, damage loci at different frequencies are close but do not overlap and intersect only at the damage location. So, the multi-frequency method can increase the damage information acquired by a single pair of sensors, enabling damage localization. Experimental validation was conducted on a steel plate with linearly varying thicknesses. The feasibility of the multi-frequency localization method was verified by successfully locating the damage at three different locations using a pair of receiver-excitation sensors. In addition, the experiments demonstrated the capability of this multi-frequency method in improving the localization accuracy of sensor networks. The method has potential applications in monitoring systems lightweight, phased arrays, and imaging enhancement.

Wave Propagation in the Poroviscoelastic VTI Media: Sum-of-exponentials Approximation for the Simulation of Fractional BISQ Equations

In the Earth’s subsurface, there is an extensive presence of porous, viscoelastic, and anisotropic structures, which profoundly influence the propagation of seismic waves. Poroelasticity, based on the Biot-squirt (BISQ) theory, can characterize the impact of fluid flow on seismic waves. However, an improved mechanistic understanding and mathematical representation of seismic wave propagation in porous formations requires the accounting of both velocity and attenuation anisotropy. Here, we derive the wave equations based on an efficient sum-of-exponentials (SOE) approximation, by combining the porous BISQ equations with the Kjartansson’s constant-Q dissipative model to describe seismic wave propagation in poroviscoelastic vertical transversely isotropic (VTI) media. The approximation involves representing the fractional differential equations as a SOE, enabling a reduction in computational costs and storage compared to the traditional L2 scheme. Numerical examples prove that the extended BISQ model can describe the wave propagation characteristics in poroviscoelastic anisotropic media and effectively captures potentially strong, direction-dependent attenuation phenomena.

Modified Layer-based Ultrasound Imaging of Irregularly Cortical Bone

Abstract Cortical bone, known for its multilayered composition with a diverse sound velocity distribution and anisotropy dependent on anatomical position, poses a challenge in conventional medical ultrasound imaging. The limitations arise due to the inability of uniform velocity to appropriately capture the intricate properties of hard tissues, leading to inaccurate reconstruction of the inner cortical layers. To tackle this complexity, a modified layer-based method utilizing a 5-layer model and estimated sound velocity was introduced for irregularly cortical bone imaging. Validated through an ex-vivo study using goat tibia, this method showcased remarkable effectiveness. The experimental outcomes revealed an ultrasound-reconstructed cortical image that closely matched the μCT-measured ground truth model, demonstrating mean cortical thickness errors of 0.31 mm. This method stands as a validated and precise approach for accurately imaging cortical bone using a 5-layer model.

The influence of lamination and fracture on the velocity anisotropy of tectonic coals

The elastic anisotropy of coal formations is important for the prediction of unconventional coalbed methane reservoir performance and hydraulic fracturing. Although essential for a number of geophysical applications, the elastic anisotropy of coals is still poorly understood. Therefore, three sets of cylindrical coal samples are drilled parallel and perpendicular to the bedding plane, and the ultrasonic velocities under different confining pressures are measured in the laboratory. We combine experimental observations and modeling analysis to evaluate the elastic anisotropy of the coals. The results suggest that the velocity of coals parallel to the bedding plane is less sensitive to the confining pressure than that perpendicular to the bedding plane. The fracture densities of coals parallel to the bedding plane are much lower than those perpendicular to the bedding plane, and most of the fractures are closed when the pressure is higher than 15 MPa. The organic matter and clay content and their preferred orientation play dominant roles in the velocity anisotropy, and the fracture effect can significantly enhance it. Velocity anisotropy parameters of coals are positively correlated with the organic matter and clay content, and the preferred orientation of organic matter and clay plays a significant role in coal anisotropy. The results in this study are helpful in the characterization of fractures of coals and can provide an important rock physics basis for microseismic fracture monitoring and reservoir prediction.

The hcp–bcc transition of Be via anisotropy of modulus and sound velocity

Abstract Based on ab initio calculations, we utilize the mean-field potential approach with the quantum modification in conjunction with stress–strain relation to investigate the elastic anisotropies and sound velocities of hcp and bcc Be under high-temperature (0–6000 K) and high-pressure (0–500 GPa) conditions. We propose a general definition of anisotropy for elastic moduli and sound velocities. Results suggest that the elastic anisotropy of Be is more significantly influenced by pressure than by temperature. The pressure-induced increase of c/a ratio makes the anisotropy of hcp Be significantly strengthen. Nevertheless, the hcp Be still exhibits smaller anisotropy than bcc Be in terms of elastic moduli and sound velocities. We suggest that measuring the anisotropy in shear sound velocity may be an approach to distinguishing the hcp–bcc phase transition under extreme conditions.

Probing the spatial and velocity anisotropies in stellar halos from the Aquarius simulations

Abstract We analyze the spatial anisotropy and the velocity anisotropy in a set of mock stellar halos from the Aquarius simulations. The spatial anisotropy in each mock stellar halo rises progressively with the increasing distance from the halo centre, eventually reaching a maximum near the periphery. Excluding the bound satellites leads to a significant reduction of the spatial anisotropy in each halo. We compare the measured anisotropy in the mock stellar halos with that from their sphericalized versions where all the shape and substructure induced anisotropies are erased. The growth of spatial anisotropy persists throughout the entire halo when the bound satellites are present but remains limited within the inner halo (<60 h−1 kpc) after their exclusion. This indicates that the spatial anisotropy in the inner halo is induced by the diffuse substructures and the halo shape whereas the outer halo anisotropy is dominated by the bound satellites. We find that the outer parts of the stellar halo are kinematically colder than the inner regions. The stellar orbits are predominantly radial but they become rotationally dominated at certain radii that are marked by the prominent dips in the velocity anisotropy. Most of these dips disappear after the removal of the satellites. A few shallow dips arise occasionally due to the presence of diffuse streams and clouds. Our analysis suggests that a combined study of the spatial and velocity anisotropies can reveal the structure and the assembly history of the stellar halos.

EARA2024: A New Radially Anisotropic Seismic Velocity Model for the Crust and Upper Mantle beneath East Asia and Northwestern Pacific Subduction Zones

EARA2024: A New Radially Anisotropic Seismic Velocity Model for the Crust and Upper Mantle beneath East Asia and Northwestern Pacific Subduction Zones

Effects of background elastic and permeability anisotropy on dynamic seismic signatures of a fluid-saturated porous rock with aligned fractures

Seismic dispersion, attenuation, and frequency-dependent anisotropy due to wave-induced fluid flow (WIFF) in fluid-saturated porous and fractured rocks have been widely studied. However, most of these studies do not consider the effects of background elastic and permeability anisotropy. In this work, we study such effects by considering a fluid-saturated porous rock with penny-shaped fractures embedded in the isotropic plane of a transversely isotropic (TI) background. Starting with P-waves propagating perpendicularly to the fracture plane, we obtain the wavefields in the fluid-saturated porous TI background scattered from a single fracture. This allows for the calculation of effective P-wavenumber through the Foldy approximation and the derivation of a frequency-dependent fracture compliance matrix. The angle-dependent seismic dispersion and attenuation, as well as frequency-dependent anisotropy, can thus be calculated. Using this model, we study a fractured tight sandstone with a TI background. The results show that the background elastic anisotropy primarily affects the seismic frequency-dependent anisotropy, while the background permeability anisotropy not only affects seismic frequency-dependent anisotropy but also influences seismic dispersion and attenuation. In particular, the background permeability anisotropy alters the rate of change in seismic velocities and velocity anisotropy parameters with frequencies and the peaks of seismic attenuation and attenuation anisotropy parameters. By comparing the theoretical predictions of our model to other theories and also to two sets of experimental data, our model is validated. Our model can be applied to characterize the fractured, layered earth.

Shallow Structure and Seismic Amplification Effects in the Weifang Segment of the Tanlu Fault Zone Based on the Spectral Ratio Method

Abstract The Weifang segment of the Tanlu fault zone (TLFZ) is located in the central section of the TLFZ, eastern China, and has been identified as an earthquake gap zone. Previous studies in the region have mainly focused on the crustal velocity structure and anisotropy, with limited attention to the shallow near-surface structures. In this study, we analyzed the distribution of sediment thickness and evaluated the seismic amplification effects in the Weifang segment of the TLFZ using the horizontal-to-vertical spectral ratio (HVSR) method and the standard spectral ratio (SSR) method. The data we used are from a dense array of 302 three-component seismometers deployed in 2017 for three months. The lowest peak frequency of HVSR indicates that the northwestern part of the study area exhibits relatively thicker sedimentary deposits, estimated to be 800–1200 m in thickness, consistent with both tomographic and geological studies. The SSRs are calculated from 43 regional and teleseismic earthquakes with respect to 12 reference stations. The results from SSR show strong amplification in the 0.2–2 Hz frequency range for sites on the northwestern part, and the amplitude can be up to 15 times larger than that of the bedrock site. We also find significant amplification effects as well as thick sedimentary layers at specific stations along the eastern branch of the TLFZ, suggesting a localized low-velocity zone along the fault. Our results also demonstrate that using the single-site seismic method can provide new constraints on the fine structure and site responses of the fault zone, which are important for seismic hazard assessment.