Polarized Shear Waves Research Articles

Влияние геометрических параметров на распространение SH-волн в пьезоэлектрической/пьезомагнитной пластине

The propagation features of horizontally polarized shear waves in a magnetoelectroelastic composite plate in contact with vacuum are investigated within the quasi-static approximation. The plate consists of rigidly coupled piezoelectric and piezomagnetic layers. It is assumed that there are no mechanical stresses on the outer surfaces, and the magnetic potential is zero. Depending on the nature of the specified electrical conditions, problems with electrically open and electrically closed external surfaces are considered. The wave process is initiated by the action of a remote source of harmonic oscillations and is assumed to be steady. The solution of the problems is constructed in Fourier images as an expansion into a set of exponentials. Dispersion equations of the problems, which are presented in a matrix form convenient for numerical implementation, were obtained. Using the example of the PZT-5H/CoFe2O4 plate, the effect of the thickness of each of its layers on the transformation features of phase and group velocities of surface acoustic waves with horizontal polarization (SH-SAW) is established. When changing the geometric parameters, either the plate thickness or the thickness of one of its layers was fixed. Within the framework of the problem with electrically closed external surfaces, significant differences in the behavior of velocities were established depending on the thickness of the piezoelectric and piezomagnetic layers. The conditions for the maximum and minimum effect of the thickness of each layer on the behavior of the 2nd and subsequent SH-SAW modes were determined. It is shown that in the presence of a very thin piezomagnetic layer in the plate, the behavior of the 2nd SAW mode changes significantly: both the mode output frequency and the asymptotic value of the velocity increase. The regularities of the effect of changing the thickness of the piezoelectric and piezomagnetic layers of the plate on the transformation of the electromagnetic-mechanical coupling coefficient in a wide frequency range were revealed. The obtained results are given in dimensionless parameters and can be of interest in the development of new functionally oriented materials, the assessment of their performance characteristics, as well as in the creation of highly efficient devices operating on surface acoustic waves.

Martian seismic anisotropy underneath Elysium Planitia revealed by direct S wave splitting

Seismic anisotropy, arising from the crystallographic/lattice-preferred orientation of anisotropic minerals or the shape-preferred orientation of melts or cracks, can establish a critical link between Mars's past evolution and its current state. So far, seismic anisotropy in Mars has been proposed due to different velocities of vertically and horizontally polarized shear waves in the Martian crust, obtained from crustal converted waves, multiples, and surface waves recorded by the InSight seismometer. However, the shear wave splitting, which stands out as a straightforward indicator of seismic anisotropy, has not been reported using marsquake records. In this study, we employ low-frequency marsquakes detected by the InSight seismometer to reveal shear wave splitting in marsquake recordings. We find that the direct S waves of three marsquake recordings (S0173a, S0235b, and S1133c) with high signal-to-noise ratios exhibit the splitting phenomenon. We rule out the possibility of apparent anisotropy through synthetic tests, affirming the presence of seismic anisotropy in Mars. The delay time measured from the direct S wave splitting is too large to be solely attributed to the seismic anisotropy in the upper crust (0 – 10 km) beneath the InSight. Thus, seismic anisotropy in the deeper region of Mars is required. Combined with other geophysical evidence near the InSight landing site, the seismic anisotropy observed in this study implies the aligned cracks in the crust are greater than 10 km beneath the InSight and/or the existence of mantle flow underneath the Elysium Planitia of Mars.

Factors Influencing Radiation Sound Fields in Logging While Drilling Using an Acoustic Dipole Source

With the increasing number of complex well types in the development stage of oil and gas fields, it is becoming increasingly urgent to use remote detection logging while drilling (LWD) to explore the geological structures in a formation. In this paper, the feasibility and reliability of the dipole remote detection of logging while drilling are demonstrated theoretically. For this purpose, we use an asymptotic solution of elastic wave far-field displacement to derive the calculation formula for the radiation pattern and energy flux of an LWD dipole source. The effects of influencing factors, including the source frequency, formation property, drill collar size, and mud parameter, on the radiation pattern and energy flux are analyzed. The results show that the horizontally polarized shear wave (SH-wave) has a greater advantage in imaging the reflector compared with the cases of the compressive wave (P-wave) and vertically polarized shear wave (SV-wave), which indicates the dominance of the SH-wave in dipole remote detection while drilling. The optimal source excitation frequency of 2.5 kHz and inner and outer radii of the drill collar of 0.02 and 0.1 m, respectively, should be considered in the design of an LWD dipole shear wave reflection tool. However, the heavy drilling mud is not conducive to remote detection during logging while drilling. In addition, the reflection of the SH-wave for the LWD condition is simulated. Under the conditions of optimal source frequency, drill collar size, and mud parameters, the reflection of the SH-wave signal is still detected under the fast formation.

Shear wave velocity in a functionally graded piezoelectric semiconductor plate clamped on a rigid base

Abstract This paper investigates the propagation of horizontally polarized shear waves in a Piezoelectric Semiconductor (PSC)
layered structure. The modal consists of a pre-stressed PSC thin plate atop an elastic dielectric half-space joined
perfectly at the interface. It is postulated that the material parameters and initial stress exhibit an exponential
variation exclusively along the depth. The velocity equation of the considered wave is analytically obtained based
on the traction-free boundary conditions. Numerical examples have been employed to examine the influences of
several parameters, including semiconducting properties, material gradient index, initial stresses, external biasing
electric field, and PSC film thickness, on the characteristics of the wave. Graphs have been generated to visualize
the dependency of wave velocity and attenuation on these factors. The wave’s velocity and damping properties are
significantly influenced by the thickness and steady state carrier density of the PSC plate. Besides yielding critical
results, current findings are instrumental in designing high-frequency SAW devices.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

Defect detection and imaging using electromagnetic acoustic transducer with butterfly coil.

Electromagnetic ultrasonic detection technology utilizes the electromagnetic coupling method to generate and receive ultrasonic waves without a couplant, which is suitable for rapid detection. However, the detection can be affected by the spatial distribution of the acoustic field and the polarization direction of the shear wave, which can result in suboptimal detection performance. The acoustic field directivity of the shear wave generated by the butterfly coil electromagnetic acoustic transducer was measured using the transmission method. The data indicate that the acoustic pressure amplitude of the shear wave is maximized along the axis of the acoustic field, thereby meeting the requirements of synthetic aperture focusing technique imaging. We used the reflection method to detect the through-hole defects and investigated the effect of shear wave polarization direction. By comparing the experimental data and imaging results, it can be concluded that higher echo amplitudes are obtained when the polarization direction of the shear wave is perpendicular to the axis of the through-hole defects. Based on the explosive reflection model, the frequency domain phase shift migration (PSM) method converts the time-domain signal to the frequency domain for processing and uses a phase-shift factor for layer-by-layer imaging. We used the PSM method to process the experimental data, which not only produced high-resolution images but also had a high computational speed.

Depth imaging of multicomponent seismic data through the application of 2D full‐waveform inversion to P‐ and SH‐wave data: SEAM II Barrett model study

AbstractWe examine the value of the nine‐component seismic survey by generating the Kirchhoff depth migration images of compressional wave (P‐wave), converted wave (PS‐wave) and horizontally polarized shear wave (SH shear wave) data simulated from the SEAM II Barrett unconventional model. We first utilize full waveform inversion to obtain a P‐wave velocity model from P‐wave data and an S‐wave velocity model from SH‐wave data. Both P‐wave and SH‐wave data are generated with the maximum frequency of 20 Hz while assuming that the subsurface is isotropic. To implement full waveform inversion, we use a two‐dimensional time‐domain finite‐difference method and the L2 norm to measure the data misfit. We use both refractions and reflections in P‐ and SH‐wave data to reconstruct the P‐ and S‐wave velocity models from the surface to the reservoir. The inverted P‐ and S‐wave velocities contain the main features of the model (e.g., major faults and channels) but have some difficulties in estimating high‐frequency velocity variation within the first 300‐m depth of the model due to the frequency constraint. We then use the inverted P‐ and S‐wave velocities to generate Kirchhoff depth migration gathers and images from the P‐, PS‐ and SH‐wave data. The flat P‐ and SH‐wave common‐image offset gathers suggest that SH‐ and P‐wave full waveform inversion can generate adequate S‐ and P‐wave velocities for migration. Flat PS‐wave gathers and the clear PS‐wave migration image are also obtained using the inverted P‐ and S‐wave velocities simultaneously. This result indicates that obtaining S‐wave velocities from SH‐wave data can aid PS‐wave data processing and imaging. Moreover, the SH‐wave images and S‐wave images of the radial component provide better delineation of fault planes and small‐scale geobodies within the reservoir since the wavelength of the S‐wave is smaller compared to P‐wave when similar frequency ranges are recorded. Therefore, our study shows that S‐wave velocities can be successfully constructed by the two‐dimensional full waveform inversion application of the SH‐wave data. The subsequent imaging of multicomponent seismic data improves the delineation of certain unconventional reservoirs compared to the traditional P‐wave imaging.

Separation of fast and slow shear waves and prediction of fracture parameters based on non-orthogonal assumptions

SUMMARY Natural fractures play a significant role in oil and gas reservoirs. Accurate predictions of fracture parameters are vital in reservoir prediction and oil and gas development. The birefringent phenomenon of shear waves in fractured media makes shear wave splitting (SWS) analysis an important tool in formulating fracture predictions. The traditional SWS analysis method is based on an orthogonal assumption of fast and slow shear waves. However, in an orthotropic medium composed of a background vertical transversely isotropic medium and a set of vertical fractures, fast and slow shear waves are not necessarily orthogonal. This causes the traditional SWS analysis method to fail. To solve this problem, we proposed an SWS analysis algorithm with a non-orthogonal assumption of fast and slow shear waves in this study. First, we introduced a parameter (difference angle) to characterize the angle between slow shear waves and the normal polarization directions of the fast shear waves. Subsequently, based on the traditional two-parameter scanning algorithm, a parameter was added to facilitate three-parameter scanning. In addition, we derived an expression for the two-parameter scanning objective function using the non-orthogonal assumption. Two-parameter scanning can accurately extract fast and slow wave time delay data, but it cannot determine an accurate fast shear wave polarization direction. Therefore, we optimized the three-parameter scanning algorithm as follows: first, we used two-parameter scanning to obtain the fast and slow wave time delays and then performed further scanning to determine the polarization direction of the fast shear wave and difference angle. The optimization algorithm significantly improved the computational efficiency. Subsequently, we tested the accuracy of this method using synthetic single-trace and three-component vertical seismic profile data. We demonstrated the implementation process of the three-parameter scanning method using actual data, separated fast and slow shear waves, and predicted fracture parameters. The final fracture parameters were verified.

Anisotropic Characterization of the Chukchi Boardland Based on Ocean-Bottom Seismic Experiment during N11-CHINARE

Abstract The current research focus at Chukchi Boardland (CB) revolves around sediment stratification and crustal structure, but investigations into deep stress fields and mantle dynamics are limited. This article presents a study on the anisotropic characteristics of the CB. Shear-wave splitting measurements were conducted using the transverse energy minimization at six stations recovered from the 11th Chinese National Arctic Research Expedition. The observation period for these six stations ranged from 2 August 2020 to 8 September 2020. The results demonstrate significant anisotropy within the CB, with the fast shear-wave polarization direction ranging from N60°E to N70°E. The time delays between fast and slow shear waves were found to be ∼0.7 s. By comparing the anisotropy observed at the CB with that at land stations in Arctic Alaska, this study suggested that the genesis of anisotropy beneath the CB was related to the formation of the Amerasian basin. The tectonic processes of rifting during basin evolution and midocean ridge spreading led to the development of anisotropy in the lithosphere beneath the CB during expansion.

Predicting second-harmonic generation in shear wave beams in tissue-mimicking phantoms

Planar nonlinear shear waves in isotropic media are subject to only cubic nonlinear effects and generate only odd harmonics during propagation. However, wavefront curvature in shear wave beams breaks the symmetry and yields quadratic nonlinear effects, and therefore, a second harmonic may be present in shear wave beams depending on the polarization of the wave. Focused radially polarized shear wave beams have been generated in tissue-mimicking phantoms [Cormack et al., IEEE TBME (2024)], and it is postulated that the second harmonic may be used to estimate the quadratic nonlinearity in such a medium as an additional biomarker for diseased tissue. Here, an analytical solution obtained in the paraxial approximation for nonlinear propagation of a shear wave beam in an absorbing medium [Spratt et al., AIP Conf. Proc. 1685, 080007 (2015)] is used to characterize the strength of second-harmonic generation. Feasibility of measuring the second harmonic experimentally in a weakly nonlinear, radially polarized focused shear wave beam propagating in a tissue-like medium is explored. Second-harmonic generation in focused shear wave beams with other polarizations is discussed. [P.G.K. was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Dynamic subsurface changes on El Hierro and La Palma during volcanic unrest revealed by temporal variations in seismic anisotropy patterns

Active hotspot volcanism is the surface expression of ongoing dynamic subsurface changes, such as the generation, transport, and stalling of magmas within the upper mantle and crust. Magmatic influx and migration affects local stress patterns in the crust and lithospheric mantle, which influences seismic anisotropy. A better understanding of those patterns helps improve robustness of models forecasting the likelihood of an eruption and prolonged seismicity, with detailed studies being required to observe the significant variations that can occur on small spatial and temporal scales. Here, we investigate seismic anisotropy before, during and after volcanic eruptions. We use local seismicity around El Hierro and La Palma, the two westernmost islands in the Canaries and sites of the most recent volcanic eruptions in the archipelago. We obtained 215 results in El Hierro during and after the 2011/2012 eruption with five three-component broadband seismic stations and 908 results around the 2021 eruption in La Palma with two three-component broadband stations. On La Palma, the majority of seismicity and splitting results are recorded during the eruption and simultaneous deflation of the island. Seismicity locations do not change significantly and fast shear wave polarisation direction is mostly constant, but some variation can be attributed to changes in the magmatic plumbing system. On El Hierro, the general radial pattern reflects stresses induced by the overall uplift of the island during multiple magma intrusion events. Temporal subsets reveal significant variations in location and depth of the events, as well as significant variations in fast polarisation direction caused by ongoing dynamic changes of under- and overpressurisation. An increase of results starting in 2018 hints towards renewed subsurface activity within deeper parts of the plumbing system, affecting the rate of overall seismicity but not any vertical movement of the island.

Birefringence Technique for Evaluating Thermal Stresses in Railroad Rails

This paper discusses the development of an in situ noncontact electromagnetic acoustic transducer (EMAT) nondestructive evaluation technology to determine rail neutral temperature and estimate rail stress in continuous welded rail (CWR). Stresses develop in CWR due to a lack of expansion joints to accommodate thermal expansion and contraction of the rail when ambient temperatures vary over time. The novelty of the work presented is the usage of ultrasonic birefringence properties using EMATs to estimate thermally induced stresses in rails. EMATs produce polarized shear waves propagating through the rail web in the pulse-echo mode. Experimental tests were performed on machined 136RE and 141RE rail material with applied compressive and tensile stresses to explore the stress-birefringence behavior. Two additional sets of experimental tests were conducted on full-size rail sections with in situ surface conditions to study variations in the in situ birefringence and the acoustic stress constant in different rail materials including 115RE rail, 119RE rail, two different 136RE rails, and 141RE rail. The results show a highly linear relationship between the stresses applied and the measured acoustic birefringence.

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

SKS Polarization Anomalies Due to the Coriolis Force

ABSTRACT The Earth’s Coriolis force has been well-known to impact surface waves and normal modes, which is essential to accurately interpret these waves. However, the Coriolis force on body waves has been assumed to be negligible and mostly ignored. It has been previously shown that the Coriolis force impacts polarizations of shear waves, whereas the wavefronts remain unaffected. We expand on the potential influences of Earth’s Coriolis force on shear-wave polarization measurements by conducting 3D numerical simulations for elastic waves generated by earthquake and explosive sources in a radially symmetric, and 3D mantle and crustal models. The Coriolis force can produce polarization anomalies of mantle shear waves up to 7° and core phases, such as SKS and SKKS, up to 4°. Uncorrected shear-wave polarizations due to the Coriolis force can cause an additional source of error (5°–10° in fast direction, and 0.2–0.3 s delay time depending on the method and seismic phase), inaccurate interpretation of station misalignments, and imprecise estimates of the core–mantle boundary topography. We show how to correct for the Coriolis force on teleseismic shear waves using 1D ray tracing for well-isolated phases. We recommend the use of full waveform simulations to accurately account for earthquake sources parameters, poorly isolated phases that could include interfering phase arrivals within the measurement time window, and the effect of the Coriolis force on the polarizations of shear waves.

A new chevron electromagnetic acoustic transducer design for generating shear horizontal guided wave

Guided wave electromagnetic acoustic transducers (EMATs) have a significant role in non-destructive testing and structural health monitoring. It can generate horizontally polarized shear waves propagating axially or circumferentially to characterize the shape and orientation of pipeline defects. This work proposes a new Chevron pattern-like coil structure design with a periodic permanent magnet (PPM) EMAT configuration. This specific design of the EMAT coil can generate a bi-directional shear horizontal wave (SH-wave) and reduce the side lobes. An optimal Chevron angle of coil wires assists in generating orthogonal propagatingwaveforms. These phenomena lead to the constructive interference of propagating waves and develop a resulting wave along the horizontal direction. A 3D FEM modeling and simulation have been carried out and validated with experimental results. The proposed EMAT results are compared with the conventional racetrack PPM EMAT model, which shows a significant improvement over conventional EMATs. A prototype of this proposed EMAT has been developed. It can be used to inspect surface defects in applications such as fuel transportation pipelines.

Experimental observations of Scholte waves propagating in an incompressible soft solid

Due to the heterogeneous structure of the soft biological tissue, such as the brain, surface waves might be important to elucidate the biomechanics of injury formation from impacts. In this context, surface waves generate a wavelength on the order of the centimeter with a typical penetration length of the same order. Therefore, investigating surface waves at depth is crucial for understanding their relationship with the physics of soft tissue injuries. Planar surface waves produce particle motion along two dimensions, the direction of propagation and the depth direction, making them more challenging to measure when compared to polarized shear waves that only produce motion in one direction. This study presents an experimental setup capable of generating Scholte wave propagating in a soft solid–liquid interface. In particular, we studied a tissue-mimicking phantom material, such as gelatin, under a layer of water. Ultrasound imaging techniques, operating at 8600 frames per second, and a one-dimensional cross-correlation algorithm were used to independently estimate the two components of the wave’s particle displacement. We conducted experiments sweeping frequencies between 50 and 500 Hz for different gelatin stiffness, finding a surface wave speed of 0.86 times the shear wave speed and a penetration distance of 0.35 times the wavelength. These results agree with the theory of Scholte waves propagating in an incompressible semi-infinite elastic medium covered by an incompressible fluid.

Study of the dynamic electro-mechanical and microstructural behaviour on the elastic wave in FGM/FGPM composite structure: WKB asymptotic approach

This paper presents a theoretical investigation of the horizontally polarized shear wave in a composite structure. The assumed composite is composed of Functionally graded piezoelectric material (FGPM) layer constrained between an FGM (Functionally graded material) layer and a couple stress half-space with size-dependent microstructural effect. The variation in rigidities and densities are considered parabolic and linear in the upper and constrained layers, respectively. An analytical WKB (Wentzel–Kramers–Brillouin) asymptotic approach has been adopted for obtaining the dispersion relation. Also, a finite difference scheme (FDS) has been introduced to calculate the phase velocity and group velocity of the SH-wave. If waves travel in the time domain, it is necessary to check the accuracy and stability requirements. So that FDS has been adopted because of its accuracy, reliability, and flexibility. For the purpose of numerical calculation, three sets of FGPMs are considered namely, PZT−4, PZT−5H ceramic, and ceramic. Graphs have been plotted by means of dimensionless phase velocity against dimensionless wave number to show the effect of various parameters on the propagation of SH-wave. Numerical results demonstrated the accuracy and versatility of the phase and group velocity depending on the stability ratio of the FDS.

Investigating the effects of defects and the effect of geometric anisotropy in stainless steel pipes: phased array ultrasonic test, SH-wave

Today, Phased Array Ultrasonic Testing (PAUT) is a suitable method for detecting defects in Non-destructive Testing (NDT). This simulation was done with a new method on a stainless steel pipe with a diameter of 500 mm and a length of 1,000 mm, and cracks were modeled on the external and internal surfaces and corrosion defects on the internal surface. Four probes with a characteristic of 2 MHz were used simultaneously, each probe having 64 elements. By increasing the number of probes and their elements, more accurate information about the defects is obtained, which makes it easier to detect the location and leads to a reduction of scattered signals and noise, which can detect even small size defects. Considering this important advantage, a new use of the method of increasing the number of probes in PAUT is reported in this study to detect defects, especially corrosion defects. The results of geometric anisotropy studies of group velocity and phase of horizontally polarized shear waves (SH-waves) for stainless steel pipe were presented. Due to the isotropic properties of the pipe material, the speed on the outer surface of the pipe in the direction of the cover is 40 m/s higher than the generatrix.

Upper crust anisotropy of the 2020 Jiashi MS 6.4 earthquake

The 2020 Jiashi MS 6.4 earthquake occurred north of the 1997–1998 Jiashi earthquake swarm. Because of its complex tectonic environment and frequent strong earthquake occurrence, scholars have paid extensive attention to this area. To study the upper crustal anisotropy in the source area, we applied microseismic event detection and shear-wave splitting techniques to the seismic data recorded by five stations around the epicenter. First, the earthquake catalog of the Jiashi MS 6.4 earthquake sequence was rebuilt using the “Match & Locate” method. A total of 9,695 earthquake events were obtained, and the number of newly detected earthquakes was approximately 7.3 times the number in the officially released catalog. The newly identified microseismic data greatly increased the number of effective records and improved the reliability of the results. We analyzed shear-wave splitting according to the updated catalog. The results showed that the dominant polarizations of the fast shear waves were in NW or NNW at the stations BPM, XKR, L6505, and L6513, consistent with the stress near the source area. There are also blind faults with an NNW direction in the strike distributing en echelon and parallel to the main stress direction in the Jiashi seismic area. Thus, the fast shear-wave polarization of the four stations may also reflect the strike of multiple buried NNW faults in the study area. The fast shear-wave polarization of station HLJ, located at the Halajun Basin, was E–W, with the overall trend of the Kalpin thrust nappe structure. However, this station didn’t show the same NW or NNW fast-wave direction as the four stations previously mentioned. This finding may indicate that the NW-trending buried faults in the Jiashi seismic area have a limited size in both the length and the depth, only reaching northward near the second row of the Kapingtag nappe structure. The temporal trend of the delay time at station HLJ showed that a stress-release process occurred before the MS 6.4 earthquake and that stress-release occurred again after the mainshock. At station XKR, the delay time rapidly increased and then fell in the early period after the MS 6.4 earthquake, indicating that stress accumulated rapidly after the main earthquake but was released during the aftershock sequence. This study provides novel insights into the complex structural characteristics and seismogenic environment in the Jiashi area.

Free-field wave motion in an inhomogeneous elastic half-plane with surface elasticity effects

Elastic wave propagation in аn inhomogeneous half-plane with surface elasticity effects is studied in this paper. All three types of travelling body waves are considered, namely pressure, vertically polarized shear and horizontally polarized shear waves propagating under time-harmonic conditions. Along the half-plane boundary, a localized constitutive law within the framework of the Gurtin-Murdoch theory is introduced, resulting in non-classical boundary conditions as opposed to the simple traction-free conditions of classical elasticity. The free-field wave motion is analytically derived here by using the wave decomposition technique, in conjunction with appropriate functional transformations for the displacement vector. Next, a series of parametric studies serves to identify the differences in the free field motion between that for the inhomogeneous half-plane with surface elasticity and the reference case of a homogeneous material with a traction-free surface. Finally, the dependence of the free-field wave motion as it develops in the material on the level of inhomogeneity and on the magnitude of the localized surface elasticity parameters, as well as on the type of travelling waves, is quantified in this work.