Polarized Shear Waves Research Articles

Shear-wave splitting perspectives from the intense aftershock sequence of Damasi – Tyrnavos

The area of Damasi-Tyrnavos (Thessaloniki, Central Greece), in the vicinity of Larissa, was characterized by low seismic activity during the last decades. Two strong earthquakes of Mw = 6.3 and Mw = 6.0 The area of Damasi – Tyrnavos (Thessaly, Central Greece), in the vicinity of Larissa, was characterized occurred in early March 2021, followed by an intense aftershock sequence, related to WNW-ESE to NW-SE oriented faulting. This sequence was recorded by a dense local seismological network that provided a rich dataset and a unique opportunity to investigate upper crust shear-wave splitting for the first time in the study area. A fully automated technique, employing the eigenvalues method and cluster analysis, was implemented to measure the fast shear-wave polarization direction and the time-delay between the two split-shear-waves. This procedure yielded 655 results of adequate quality grade at 9 stations, after analyzing 1602 events and applying strict selection criteria, including the shear-wave window. The measured directions revealed a complex upper crust anisotropic regime. WNW-ESE to NW-SE, in accordance both with the APE model, being parallel to the local 𝜎 Hmax direction, and the strike of the fault planes. On the other hand, stations at the central part exhibit NNW-SSE and NNE-SSW anisotropy directions. An interesting feature is that the two northern stations are characterized by larger normalized time-delay values, possibly related to the migration of seismicity to the north during the initial stage of the seismic sequence.

Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave

In the poroelasticity theory of de la Cruz and Spanos, fluid shearing within the viscous boundary layer, i.e. fluid vorticity, manifests as an independent process, namely the diffusive slow shear wave. Quantifying its impact on elastic wave propagation remains a research challenge. We analyse the transmissivity of a horizontally polarized shear wave travelling across a stack of porous fluid-saturated layers. The fluid shearing developed at each contact is captured, in a macroscopic sense, through conversion scattering into this diffusive slow shear wave. Generalizing the reflectivity method for elastic waves to the poroelastic case, we develop semi-analytical results for an arbitrary number of layers. We find that the conversion scattering into this diffusion wave reduces the shear wave amplitude, and this reduction accumulates with the number of layers. In the limit when the layer thickness corresponds to the pore diameter, the resulting wave quality factor is close to the predictions of previously reported attempts to capture the fluid vorticity. However, our approach is distinctively different since it is purely based on a wave-theoretic analysis of interacting waves, acknowledging vorticity diffusion as an independent process, thereby avoiding the problems arising when incorporating a pore-scale phenomenon in a macroscopic wave propagation theory.

The Estimation of Fracture Intensity and Pressure Distribution using Analysis of Shear Wave Splitting on “Landak” Geothermal Field

<p><em>Shear wave splitting is a study that utilizes the differences between arrival times of two shear waves (slow and fast) propagating from a source to a receiver to identify the magnitude of the anisotropic medium through which they propagate. Aside from generating a delay time between two shear waves, the anisotropic medium also shifts the polarization of fast shear wave from its initial polarization which is indicated as the main orientation of the related fracture system. The study was conducted on Landak Field, located around Bukit Besar mountain range by analyzing provided data from December 2011 to April 2012. The results of this study show that the polarizations of fast shear waves in several stations are as following; NE-SW orientation at station R09, R17, R25, and R26, N-S orientation at station R08, and NW-SE orientation at station R17. Not only do these orientations of polarization show a good correlation with structural analysis in this area, but also important to be noted that all microseismic stations encounter a wide-spreading polarization phenomenon as an effect of complex anisotropy. The delay time from all stations ranges from 0.03 to 0.07 seconds. The normalization between delay time and length of ray path for all stations results in a fracture intensity parameter ranging from 0.004 to 0.011 seconds/km. This intensity is measured in slowness parameters, which shows increased value towards the Bukit Besar area, which potentially becomes the upflow zone of the geothermal system</em>. The study shows that the distribution of fracture intensity and pressure have correlation and identical trend with temperature distribution.</p>

The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces

The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface.

Layered Evolution of the Oceanic Lithosphere Beneath the Japan Basin, the Sea of Japan

AbstractThe formation of a new ocean basin provides a unique observational window into the structure and deformation of the oceanic lithosphere. This study offers a detailed 1‐D vertically polarized shear‐wave velocity model of the young Japan Basin by interpreting S receiver functions, seafloor Rayleigh wave ellipticities and phase velocities in a Bayesian trans‐dimensional framework. The models suggest a distinct discontinuity in the mid‐lithosphere. Additional analyses indicate that the upper layer is characterized by strong positive radial anisotropy, while the lower layer is more isotropic. We interpret that the upper layer was formed during the back‐arc opening at 20–15 Ma, where the olivine lattice‐preferred orientation (LPO) fabric induced by passive upwelling contributes to the positive radial anisotropy. The lower, less anisotropic layer may be solidified after the sudden cessation of the opening. Small‐scale convection (SSC) from such a major tectonic event could randomize the LPO enough to weaken radial anisotropy before cooling down the asthenosphere, leaving a radially anisotropic discontinuity in the present‐day mid‐lithosphere. The proposed layered evolution history of the lithosphere beneath the Japan Basin illuminates an important role of the small‐scale convection in modifying the structural fabrics of the asthenosphere in terms of radial anisotropy. Such an SSC‐induced radial anisotropy drop could also occur at the base of the lithosphere in regions with ongoing seafloor spreading and enhance the velocity drop of horizontally polarized shear waves. Thus, the role of SSC is non‐negligible in explaining the sharpness of the Gutenberg discontinuity detected by SS precursors beneath the oceanic lithosphere.

The design of one-dimensional elastic diffusers

The paper presents a stochastic approach to generate randomly rough surfaces with a prescribed mean angular intensity distribution for elastic wave scattering. The analytical and numerical technique is implemented for a linearly elastic medium-vacuum interface, to generate band-limited uniform diffusers which may have applications for wave manipulation and ultrasonic non-destructive evaluation. Longitudinal incidence is assumed, and the theory allows for bulk wave mode conversions, with the surfaces designed to produce prescribed intensity distributions for both reflected compression wave modes, as well as the mode-converted vertically polarized shear wave modes. The angular distribution of these two cases is shown to be significantly different; additional, more exotic intensity distributions are also demonstrated to highlight the versatility of the model.

Crustal Anisotropy in the Martian Lowlands From Surface Waves

AbstractThe largest seismic event ever recorded on Mars, with a moment magnitude of 4.7 ± 0.2, is the first event to produce both Love and Rayleigh wave signals. We measured their group velocity dispersion between about 15 and 40 s period and found that no isotropic depth‐dependent velocity model could explain the two types of waves wave simultaneously, likely indicating the presence of seismic anisotropy. Inversions of Love and Rayleigh waves yielded velocity models with horizontally polarized shear waves traveling faster than vertically polarized shear waves in the top 10–25 km. We discuss the possible origins of this signal, including the preferred orientation of anisotropic crystals due to shear deformation, alignment of cracks, layered intrusions due to an impact, horizontal layering due to the presence of a large‐scale sediment layer on top of the crust, and alternation of sedimentation and basalt layers deposits due to large volcanic eruptions.

Modeling Acoustic Emission due to an Internal Point Source in Circular Cylindrical Structures

In a previous paper [Appl. Sci. 2022, 12, 5272], we developed the first mathematical model for acoustic emission from an internal point source in a transversely isotropic cylinder. The point source, as an internal defect, is the most fundamental source generating AE in homogeneous media; it is represented by a spatiotemporal concentrated force and generates three scalar potentials for compressional, and horizontally and vertically polarized shear waves. The mathematical formulas for the displacements were derived by introducing the concentrated force-incorporated potentials into the Navier–Lamé equation. Since the publication of that paper, we detected some errors. In this paper, we correct the errors and extend the analytical modeling to a cylindrical shell structure. For acoustic emission in general circular cylindrical structures, we derived solutions by applying the boundary conditions at inner and outer surfaces of the structures. Under these conditions, we solve the radial, tangential, and axial displacement fields. Analytical simulations of the acoustic emission were carried out at several point source locations for circular cylindrical geometries. We show that the maximum amplitude of the axial displacement is dependent on the point source position and 2π-aperiodicity of the cylindrical geometry. Our mathematical formulas are very useful for characterizing AE features generated from an internal defect source in cylindrical geometries.

Applicability of existing CPT-Vs correlations to shallow Holocene Christchurch soils based on direct Push crosshole testing

The applicability of four existing empirical cone penetration test to shear wave velocity (CPT-Vs) correlations to Holocene soils in the Christchurch region of New Zealand was assessed using over 1400 CPT-Vs data pairs. While most existing correlations used seismic CPT (sCPT) or other downhole-based methods in their development, this paper uses a database based on the direct push crosshole (DPCH) method. This database allowed for an assessment of the influence of the Vs measurement method on correlation performance, with sCPT and downhole methods based on vertically propagating, horizontally polarized shear waves, compared to the horizontally propagating, vertically polarized shear waves used for the DPCH. Across the CPT-Vs correlations considered, different ranges of over- or under-predicted Vs were presented. In general, the correlations tend to underestimate the measurements for low cone tip resistance and sleeve friction values, while at higher values, they provide more reasonable estimates or slight overestimates. The correlation developed based on a sCPT database from Christchurch significantly underestimates Vs at depths less than 4 m, likely due to a combination of factors including issues with the assumed wave propagation path used in sCPT processing, variability in soil characteristics within mapped geologic units and extrapolation of the correlation beyond the original database characteristics. Underestimation at greater depths was generally within 10% which likely reflects the influence of soil anisotropy on the measured Vs from each method. The performance of these correlations demonstrates that investigation methods and the characteristics of the databases used in correlation development should be considered when they are applied in practice.

Viscoelastic reduced enhanced isotropic continua as acoustic metamaterials.

We consider a linear enhanced viscoelastic continuum of general nature but of specific type. Namely, we consider a reduced elastic continuum, satisfying Lagrange equations, where the strain energy depends on a certain (special) vectorial generalized coordinate, but does not depend on its gradient, and then add linear dissipation to the existing elastic connections. We may also represent this model as a 'bearing continuum', where all the connections are present (described by one vectorial generalized coordinate), enriched in each point by a 'distributed dynamic absorber' (described by 'special' vectorial generalized coordinate). We look for free harmonic waves in this infinite medium and obtain a reduced spectral problem for the vectorial generalized coordinate of the bearing continuum, for anarbitrary number of degrees of freedom. It was shown earlier that under certain symmetry conditions in the elastic case we obtain a single negative acoustic metamaterial, i.e. a medium that has band gaps. Further, we considerisotropic and gyrotropic reduced media, described by two three-dimensional vectorial generalized coordinates. First, we generalize results of previous studies for more complex elastic coupling, discovering a polarized shear wave, which has both bandgaps and zones of anomalous refraction. Then we introduce linear dissipation of different kinds. We find that viscosity yields in existence of travelling harmonic waves for all frequencies, possibly except for some points. Logarithmic decrement, infinite for the elasticmaterial in bandgaps, becomes finite and decreases as the dissipation increases, at least for small viscosity. An important observation is: an infinitesimal dissipation in most cases transforms bandgaps into zones of travelling evanescent waves that partially are zones of anomalous refraction (decreasing parts of dispersion curves), where the medium is a double negative acoustic metamaterial. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Reverse Time Migration Imaging Using SH Shear Wave Data

In this paper, we discussed the reverse time migration imaging of compressional wave (P-wave) and horizontally polarized shear wave (SH shear wave) seismic data, together with P- and SH shear wave constrained velocity model building. In the Sanhu area in Qaidam Basin, there are large areas of gas clouds, which leads to poor P-wave seismic imaging. The P and SH shear wave seismic data of a co-located survey line with the same acquisition geometry were used to access their imaging capability using reverse time migration. We first estimated the change in P-wave and SH shear wave velocity ratio using pre-stack time migration (PSTM) for constraining the overall depth domain velocity model. Additionally, we then used an eighth-order finite difference scheme for P-wave reverse time migration on a variable grid and used the sixth-order combined compact difference (CCD) wave field simulation method for SH shear wave reverse time migration on a regular grid. The results show that the constrained velocity model produces a good match in the overall geological structure shown in the P-wave and SH shear wave reverse time migration results. However, in the gas cloud areas, SH shear wave reverse time migration has obvious imaging advantages, which can clearly image the structure inside the gas clouds.

Elastic wave scattering by flat-bottomed indentations on a plate

• Method for multiple scattering by scatterers with unmatched midplanes is proposed. • The method can analyze coupled flexural and in-plane extensional motions. • Mode conversions between different elastic waves are observed. • Stop bands of shear and flexural waves are captured simultaneously. • Broadband scattering polarization of flexural waves is achieved by multiple scattering. Out-of-plane flexural and in-plane extensional motions are independently analyzed in available studies of multiple scattering due to the assumption of the consistent mid-plane between the scatterer and host medium. When mid-planes of the scatterer and the host medium are inconsistent, such as flat-bottomed indentations, the coupled out-of-plane flexural and in-plane extensional motions should be considered. This paper aims to investigate a general numerical procedure to solve the three-dimensional multiple scattering problem of elastic waves on a plate with cylindrically flat-bottomed indentations. Wave expansion functions derived from the Poisson and Mindlin plate theories are used to express three-dimensional displacements of the host plate and flat-bottomed indentations. A linear matrix representing analytical relationships between wave expansion coefficients of exciting and scattered fields is deduced by the continuity conditions of flat-bottomed indentations. A set of linear algebraic equations is then developed by the fact that the exciting fields around a scatterer are the sum of scattered fields coming from all other scatterers. The numerical collocation method is used to solve the preceding algebraic equations. Simulation results verify mode conversions between compressional, shear, and flexural waves. Details of stop-band formations of shear and flexural waves are captured simultaneously. Furthermore, far-field scattering polarizations of shear and flexural waves are found in the case of multiple scattering.

Surface excitation of focused shear wave beams in soft elastic media: Experiment

Shear waves are employed in medical imaging to reveal variations in the viscoelastic properties of soft tissues, which are useful biomarkers for pathologies such as breast lesions and liver disease. Shear wave excitation methods that employ acoustic radiation force or surface vibration with a small piston have limitations associated with imaging depth and shear wave amplitude. We introduce a new method for surface excitation of shear waves that employs longitudinal motion of a concave-shaped piston source to generate a focused shear wave beam, thereby increasing shear wave amplitude and penetration depth. Focused shear waves are excited in a gel phantom in the frequency range of 200 Hz to 400 Hz using a concave piston with 40 mm radius of curvature and 50 mm diameter. The wave field comprises both transverse and longitudinal displacement components, which are polarized perpendicular and parallel to the propagation direction, respectively. Transversely and longitudinally polarized wave fields are measured using ultrasound speckle tracking. The longitudinally polarized shear wave is of interest because it is measured in elastography applications. Preliminary comparisons exhibit good agreement between measured beam patterns and those predicted by an analytical theory for shear wave beam propagation due to surface excitation with a piston source.

Surface excitation of focused shear wave beams in soft elastic media: Theory

Shear wave propagation is employed in medical ultrasound imaging, because it reveals variation in the viscoelastic properties of tissue. Frequencies below 1 kHz are required for imaging with shear waves in soft tissue due to their high attenuation and low propagation speeds, compared to compressional waves with frequencies above 1 MHz used for ultrasound imaging. Shear waves exhibiting particle motion in the direction of propagation, referred to as longitudinally polarized shear waves, can be generated by applying longitudinal motion of a circular disk to the surface of a soft elastic medium. This approach is used in practice because it permits imaging of the longitudinal shear wave with a conventional ultrasound transducer that is coaxial with the source of the shear wave. Presented here are the theoretical framework and numerical simulations that illustrate effects of focusing on longitudinally polarized shear waves. Longitudinal, transverse, radial, and torsional source polarizations are considered. The present investigation was motivated initially by an experimental study in optics due to Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)]. Our predictions for shear wave beams support their measurements of light beams revealing that the longitudinal electric field component produces a smaller focal spot than the transverse field component.

On the Relationship Between Oceanic Plate Speed, Tectonic Stress, and Seismic Anisotropy.

Seismic radial anisotropy (the squared ratio between the speeds of horizontally and vertically polarized shear waves, ξ=VSH2VSV2) is a powerful tool to probe the direction of mantle flow and accumulated strain. While previous studies have confirmed the dependence of azimuthal anisotropy on plate speed, the first order control on radial anisotropy is unclear. In this study, we develop 2D ridge flow models combined with mantle fabric calculations to report that faster plates generate higher tectonics stresses and strain rates which lower the dislocation creep viscosity and lead to deeper anisotropy than beneath slower plates. We apply the SGLOBE‐rani tomographic filter, resulting in a flat depth‐age trend and stronger anisotropy beneath faster plates, which correlates well with 3D global anisotropic mantle models. Our predictions and observations suggest that as plate speed increases from 2 to 8 cm/yr, radial anisotropy increases by ∼0.01–0.025 in the upper 100–200 km of the mantle between 10 and 60 Ma.

Polarization rotator for shear elastic waves

We designed and characterized a 3D printed acoustic shear wave polarization rotator (PR) based on the specific nature of the fused-deposition-modeling printing process. The principle of the PR is based on rotation of the polarization axis of a shear wave due to the gradual change in orientation of the axis of anisotropy along the direction of wave propagation of a printed layered structure. The component of the shear modulus parallel to the infilled lines within each layer is significantly higher than that in the perpendicular direction. As the PR was printing, a small angle between neighboring layers was introduced, resulting in a 3D helicoidal pattern of distribution of the axes of anisotropy. The polarization of the propagating shear wave follows this pattern leading to the rotation of the polarization axis by a desirable angle. The total rotation angle can be tuned by the number of printed layers. The fabricated 90° rotators demonstrate high performance that can be improved by changing the infill fraction settings.

Anisotropy and fracture analysis for coalbed methane reservoir development in Bokaro coalfield, India

ABSTRACTThe low permeability of coal seams is a constraint in the efficient production of coalbed methane. However, the presence of natural fractures in coal enhances the permeability, and prior knowledge of sub‐surface fractures in coal seams is vital to identify the prospective seam. This paper investigates the anisotropy and identifies fractures by processing the advanced sonic and resistivity image logs to mitigate challenges in the reservoir. Anisotropy is estimated from the difference in the travel time between fast and slow shear waves. The application of Alford's rotation technique determines the fast shear wave polarization angle which is consistent with the fracture orientation along the NE–SW or NW–SE direction in coal seams. Moreover, the crossover of fast and slow shear waves in the slowness versus frequency plot indicates stress‐induced anisotropy that originates from fractures. Besides, drilling‐induced fractures observed along NE–SW in the resistivity image log indicate the maximum horizontal stress direction. Results from this study compare coal seams based on fractures in adopting better operational activities for optimized production and future geomechanical studies in the Bokaro coalfield situated in India.

Elastic Contrast, Rupture Directivity, and Damage Asymmetry in an Anisotropic Bimaterial Strike‐Slip Fault at Middle Crustal Depths

Mature faults with large cumulative slip often separate rocks with dissimilar elastic properties and show asymmetric damage distribution. Elastic contrast across such bimaterial faults can significantly modify various aspects of earthquake rupture dynamics, including normal stress variations, rupture propagation direction, distribution of ground motions, and evolution of off-fault damage. Thus, analyzing elastic contrasts of bimaterial faults is important for understanding earthquake physics and related hazard potential. The effect of elastic contrast between isotropic materials on rupture dynamics is relatively well studied. However, most fault rocks are elastically anisotropic, and little is known about how the anisotropy affects rupture dynamics. We examine microstructures of the Sandhill Corner shear zone, which separates quartzofeldspathic rock and micaceous schist with wider and narrower damage zones, respectively. This shear zone is part of the Norumbega fault system, a Paleozoic, large-displacement, seismogenic, strike-slip fault system exhumed from middle crustal depths. We calculate elastic properties and seismic wave speeds of elastically anisotropic rocks from each unit having different proportions of mica grains aligned sub-parallel to the fault. Our findings show that the horizontally polarized shear wave propagating parallel to the bimaterial fault (with fault-normal particle motion) is the slowest owing to the fault-normal compliance and therefore may be important in determining the elastic contrast that affects rupture dynamics in anisotropic media. Following results from subshear rupture propagation models in isotropic media, our results are consistent with ruptures preferentially propagated in the slip direction of the schist, which has the slower horizontal shear wave and larger fault-normal compliance.

Revisiting Multiple-Scattering Principles in a Crustal Waveguide: Equipartition, Depolarization and Coda Normalization

Seismic waves radiated by small crustal earthquakes are prone to multiple mode conversions caused by reflection and transmission at interfaces, and scattering by small-scale heterogeneities in the bulk of the medium. The goal of this study is to clarify the complex interplay between volume scattering and interface reflections in crustal waveguides and how it will impact the crustal energy propagation. To carry out this task, we have incorporated a rigorous description of wave polarization in the context of Monte–Carlo simulations of the multiple-scattering process by introducing a five-dimensional Stokes vector. To shed light on the wave content of the regional short-period seismic wavefield, we investigate the asymptotic partitioning of seismic energy onto P, SV and SH polarizations in the coda, as well as the angular distribution of energy flux in the waveguide. In full elastic space, equipartition theory predicts that (1) the energy ratio between P- and S-wave energies tends to $$\beta ^3/(2\alpha ^3)$$ , (2) an equal distribution of energy among SV- and SH-waves and (3) that energy fluxes are isotropic. In the presence of interfaces, we find that the isotropy of the wavefield is systematically broken and that energy ratios are shifted to the detriment of P-waves and in favor of SV-waves in a non-absorbing medium. This implies that a residual polarization is preserved in the waveguide. Through an extensive parametric study, we illustrate in detail how the anisotropy of the wavefield, the partitioning ratios and the shear wave polarization depend on the crustal attenuation parameters. The role of the initial polarization at the source has also been examined. In the case of an explosion and a shear dislocation with equal magnitude, we find that the energy level in the coda can differ by more than one order of magnitude when the effect of crustal scattering becomes very weak compared to reflections or transmissions at interfaces. When comparing different shear dislocation mechanisms, we find that the energy level in the coda can differ by up to 60%. While equipartition, depolarization and coda normalization remain fundamental guides to our understanding of the coda, their application requires a good a priori knowledge of the attenuation properties of the crust.

Evidence for crustal seismic anisotropy at the InSight lander site

We analyzed broadband and low-frequency events recorded on Mars and made the first detection of horizontally polarized shear wave reflections, which help constrain the crustal structure at NASA's InSight lander site. Coherent signals from five well-recorded marsquakes appear to be independent of the focal depth and are consistent with SH-wave reflections off the topmost crustal interface (8 ± 2 km). This phase confirms the existence of the ∼8 km interface in the crust and the large wave speed (or impedance) contrast across it. The range of acceptable parameters determined from the detected SH-wave reflections differs from the majority of the vertically polarized shear wave models resulting from a previous receiver function study, indicating that the velocity of the vertically polarized waves is larger than that of horizontally polarized waves. We propose that this inconsistency results from the presence of seismic anisotropy within the top crustal layer at the lander site. Modeling results show that dry- or liquid-filled cracks/fractures and igneous intrusions can reproduce the observed radial anisotropy.