Phase Velocities Of Love Waves Research Articles

Study of Love Waves in a Clamped Viscoelastic Medium with Irregular Boundaries

A mathematical model is presented to investigate the effects of sandiness, irregular boundary interfaces, heterogeneity and viscoelasticity on the phase velocity of Love waves. Geometry of the problem is consisting of an initially stressed viscoelastic layer with corrugated irregular boundaries, which is sandwiched between heterogeneous orthotropic semi-infinite half-space with initial stress and pre-stressed dry sandy half-space. Heterogeneity arises in the upper half-space is due to trigonometric variation in elastic parameters of the orthotropic medium. Inclusion of the concept of corrugated irregular viscoelastic layer clamped between two dissimilar half-spaces under different physical circumstances such as initial stress and heterogeneity brings a novelty to the existing literature related to the study of Love wave. Dispersion equation for Love wave is obtained in closed form. The obtained dispersion relation is found to be in well agreement with classical Love wave equation. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, internal friction, wave number and amplitude of corrugations on the phase velocity of Love waves.

An Analytic Study on the Dispersion of Love Wave Propagation in Double Layers Lying Over Inhomogeneous Half-Space

In this work, attempts are made to study the dispersion of Love waves in dry sandy layer sandwiched between fiber reinforced layer and inhomogeneous half space.Inhomogeneity in half space associated with density and rigidity and considered in exponential form. Displacement components for fiber reinforced layer, dry sandy layer and inhomogeneous half-space have been obtained by using method of separable variables. Boundary conditions are defined at the free surface of the fiber reinforced layer and at the interfaces between layers and half space. The dispersion equation has derived in closed form. Numerical calculations for dispersion equation are performed. The study results show the effect of parameters on the velocity of Love waves and presented graphically. Graphs are plotted between wave number and phase velocity to show the effect of reinforced parameter, sandiness parameter and inhomogeneity on the phase velocity of Love waves. From the graphs it can be concluded that phase velocity decreases with respect to wave number.

Love-wave devices with continuous and discrete nanocrystalline diamond coating for biosensing applications

The integration of diamond layers brings biocompatibility and enhanced stability of biomolecules to Love wave devices for promising biosensor applications. Love-Wave Surface Acoustic Wave (LW-SAW) devices consisting of an ST-cut quartz substrate with a silicon oxide layer coated by a thin diamond layer have been fabricated. The effect of nucleation and growth of diamond on the properties of LW-SAW devices was studied. The Love-wave phase velocity was shown to be affected by the diamond coating and dependent on its thickness. Experimental results are in a good agreement with simulations carried out with COMSOL Multiphysics software. Deposition of isolated diamond grains results in a reduction in velocity in the Love waves, which is attributed to a mass loading effect. Conversely, coalesced diamond layers increase the stiffness of the surface, which results in faster propagation of the Love waves. Improved entrapment of the Love waves in the guiding layer was observed in the case of isolated diamond grains, which should ensure higher sensitivity for this type of coating. Diamond coated LW-SAW devices can be used for biosensing applications with appropriated functionalization of the diamond surface.

Generation of Love Wave in a Media with Temperature Dependent Properties Over a Heterogeneous Substratum

The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent. The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for non-dimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.

Crustal Structure Beneath the Wabash Valley Seismic Zone From the Joint Inversion of Receiver Functions and Surface‐Wave Dispersion: Implications for Continental Rifts and Intraplate Seismicity

AbstractSeismicity of several intraplate seismic zones in the North American midcontinent is believed to be related to reactivation of ancient faults in Precambrian continental rifts by the contemporary stress field. Existence of such a rift system beneath the Wabash Valley Seismic Zone (WVSZ) is not clear. Here we obtained a crustal structural image along a 300‐km‐long profile across WVSZ using a dense linear seismic array. We first calculated teleseismic receiver functions of stations and applied the Common‐Conversion‐Point stacking method to image crustal interfaces and the Moho. We then used ambient noise cross correlation to obtain phase and group velocities of Rayleigh and Love waves. Finally, we jointly inverted the receiver function and surface wave dispersion data to determine shear wave velocity structure along the profile. The results show a thick (50‐ to 60‐km) crust with a typical Proterozoic crustal layering: a 1‐ to 2‐km thick Phanerozoic sedimentary layer, an upper crust ∼15 km thick, and a 30‐ to 40‐km‐thick lower crust. The unprecedented high‐resolution image also reveals a 50‐km‐wide high‐velocity body above an uplifted Moho and several velocity anomalies in the upper and middle crust beneath the La Salle Deformation Belt. We interpreted them as features produced by magmatic intrusions in a failed, immature continental rift during the end of Precambrian. Current seismicity in WVSZ is likely due to reactivation of ancient faults of the rift system by a combination of stress fields from the far‐field plate motion and prominent crustal and upper mantle heterogeneities in the region.

Viscoelastic fluid effect on the surface wave propagation

A novel approach based on the exact theory has been developed to accurately predict the behavior of surface Love wave propagating in elastic waveguide loaded on its surface with a viscoelastic fluid. A detailed study was conducted by varying key parameters such as operating frequency, waveguide and substrate. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. The dispersion curves of attenuation and phase velocity are investigated in function of the above parameters in order to evaluate their sensitivity. The numerical solutions show that the attenuation and phase velocity of surface Love wave are strongly correlated with waveguide thickness and glycerol concentrations. Results also highlighted the substrate thickness effect on the vibration characteristics of the Love wave. Moreover, the Love wave triggers a viscoelastic response in water–glycerol mixtures similar to that of literature. The obtained results are fundamental and can serve as benchmark solution in design of Love wave sensors.

Novel depiction of love wave dispersion and inversion for inversely dispersive medium by full SH-wavefield reflectivity method – part II: field example

In this part we discussed field example of SH wave data recorded using horizontal component of the three-component geophone that might represent characteristic of the inversely dispersive medium. Extraction of the SH wavefield data, both for north- and south-source impact, using tau-pi transform showed increasing phase-velocity dispersion with the frequencies. Such patterns of “effective” dispersion curves illustrated the nature of the inversely dispersive medium. Inversions of the dispersion curves were carried out by utilizing a series of Love wave inversion approaches. These approaches included forward modelling of Love wave dispersion curve by full SH-wavefield method and partial derivatives of the Love wave phase velocity. The inversion procedures utilized a linearized inversion of Occam’s algorithm. Inversions of the Love wave real data, both for north- and south-source impact, confirm the presence of an inversely dispersive medium.

A Study on Propagation of Waves in a Transversely Isotropic Poroelastic Layer Bounded between Two Viscous Liquids

Propagation of Love waves in a transversely isotropic poroelastic layer bounded between two compressible viscous liquids is presented. The equations of motion in a transversely isotropic poroelastic solid are formulated in the framework of Biot’s theory. A closed-form solution for the propagation of Love waves is obtained in a transversely isotropic poroelastic layer. The complex frequency equation for phase velocity and attenuation of Love waves is derived for a transversely isotropic poroelastic layer when it is bounded between two viscous liquids and the results are compared with that of the poroelastic layer. The effect of viscous liquids on the propagation of Love waves is discussed. It is observed that the presence of viscous liquids decreases phase velocity in both transversely isotropic poroelastic layer and poroelastic layer. Results related to the case without viscous liquids have been compared with some of the earlier results and comparison shows good agreement.

Estimation of Love wave phase velocities from horizontal microtremor array records by using frequency – wavenumber (FK) analysis – Comparison of FK analysis and SPAC one –

Estimation of Love wave phase velocities from horizontal microtremor array records by using frequency – wavenumber (FK) analysis – Comparison of FK analysis and SPAC one –

Three-dimensional Green’s function approach for analysis of dispersion and attenuation curve in fibre-reinforced heterogeneous viscoelastic layer due to a point source

The present paper deals with the propagation of Love waves due to the presence of a point source in the fibre-reinforced heterogeneous viscoelastic medium with the aid of Green’s function technique. The physical parameters, i.e. rigidity and density are assumed to be exponentially and linearly varying function of depth for medium and half-space, respectively. Three-dimensional Green’s function representation for stresses and displacements are derived in complex-plane line-integral. The frequency equations of Love-type waves are derived relating the dependence complex wave numbers after developing the mathematical model with the help of Green’s function and Fourier transformation. This representation is useful in various elastodynamic as well as elastostatic problems. The complex expansion of frequency equation is derived to define the phase velocity and attenuation coefficient of Love waves in the proposed model. Dispersion and attenuation curves are plotted by taking different variations in the reinforcement, inhomogeneity and viscoelastic parameters. The results indicate that the effect of these parameters are very pronounced. The final conclusion can be used to understand the nature of propagation of Love waves in the introduced model.

Midcrustal Deformation in the Central Andes Constrained by Radial Anisotropy

AbstractThe Central Andes are characterized by one of the largest orogenic plateaus worldwide. As a result, they are home to some of the thickest continental crust observed today (up to ~75‐km thick). Understanding the response of the crust to such overthickening provides insights into the ductile behavior of the midcrust and lower crust. One of the best tools for examining crustal‐scale features is ambient noise tomography, which takes advantage of the ambient noise wavefield to sample crustal depths in great detail. We extract Love and Rayleigh wave phase velocities from ambient noise data to invert for Vsh, Vsv, and radial anisotropy throughout the Central Andes. We capture detailed crustal structure, including pronounced along‐strike isotropic velocity heterogeneity and substantial (up to 10%) radial anisotropy that varies with depth. This crustal anisotropy may have several origins, but throughout the majority of the Central Andes, particularly beneath the Altiplano, we interpret radial anisotropy as the result of mineral alignment due to ductile crustal deformation. Only in the strongly volcanic Altiplano‐Puna Volcanic Complex is radial anisotropy likely caused by magmatic intrusions.

SH wave structure of the crust and upper mantle in southeastern margin of the Tibetan Plateau from teleseismic Love wave tomography

The deep structure of southeastern Tibet is important for determining lateral plateau expansion mechanisms, such as movement of rigid crustal blocks along large strike-slip faults, continuous deformation or the eastward crustal channel flow. We invert for 3-D isotropic SH wave velocity model of the crust and upper mantle to the depth of 110 km from Love wave phase velocity data using a best fitting average model as the starting model. The 3-D SH velocity model presented here is the first SH wave velocity structure in the study area. In the model, the Tibetan Plateau is characterized by prominent slow SH wave velocity with channel-like geometry along strike-slip faults in the upper crust and as broad zones in the lower crust, indicating block-like and distributed deformation at different depth. Positive radial anisotropy (VSH > VSV) is suggested by a high SH wave and low SV wave anomaly at the depths of 70–110 km beneath the northern Indochina block. This positive radial anisotropy could result from the horizontal alignment of anisotropic minerals caused by lithospheric extensional deformation due to the slab rollback of the Australian plate beneath the Sumatra trench.

Love wave phase velocity estimation by using rotational components obtained from microtremor array records

Love wave phase velocity estimation by using rotational components obtained from microtremor array records

GSpecDisp: A matlab GUI package for phase-velocity dispersion measurements from ambient-noise correlations

We present a graphical user interface (GUI) package to facilitate phase-velocity dispersion measurements of surface waves in noise-correlation traces. The package, called GSpecDisp, provides an interactive environment for the measurements and presentation of the results. The selection of a dispersion curve can be done automatically or manually within the package. The data are time-domain cross-correlations in SAC format, but GSpecDisp measures phase velocity in the spectral domain. Two types of phase-velocity dispersion measurements can be carried out with GSpecDisp; (1) average velocity of a region, and (2) single-pair phase velocity. Both measurements are done by matching the real part of the cross-correlation spectrum with the appropriate Bessel function. Advantages of these two types of measurements are that no prior knowledge about surface-wave dispersion in the region is needed, and that phase velocity can be measured up to that period for which the inter-station distance corresponds to one wavelength. GSpecDisp can measure the phase velocity of Rayleigh and Love waves from all possible components of the noise correlation tensor. First, we briefly present the theory behind the methods that are used, and then describe different modules of the package. Finally, we validate the developed algorithms by applying them to synthetic and real data, and by comparison with other methods. The source code of GSpecDisp can be downloaded from: https://github.com/Hamzeh-Sadeghi/GSpecDisp.

Love wave phase velocity models of the southeastern margin of Tibetan Plateau from a dense seismic array

Love wave dispersion maps across the southeastern margin of the Tibetan Plateau are obtained using earthquake data recorded by the temporary ChinArray and permanent China Digital Seismic Array. Fundamental mode Love wave phase velocity curves are measured by inverting Love wave amplitude and phase with the two-plane-wave method. The phase velocity maps with resolution better than 150km are presented at periods of 20–100s, which is unprecedented in the study area. The maps agree well with each other and show clear correlations with major tectonic structures. The Love wave phase velocity could provide new information about structures in the crust and upper mantle beneath the southeast margin of Tibetan Plateau, like the radial anisotropy.

Love wave propagation in heterogeneous micropolar media

The present paper framed to study the impact of heterogeneity on propagation of Love wave in a heterogeneous micropolar layer over an elastic inhomogeneous stratum, when both rigidity and density are assumed to vary linearly with depth. The equations of motion have been formulated separately for layer and half-space under suitable boundary conditions. Analytical solution for the dispersion equation has been obtained using method of separation of variables by means of the Airy function and Whittaker function. Some particular cases have also been investigated. Further, as a special case the velocity equation for isotropic layer over a homogeneous half-space coincides with the standard result of Love wave. Numerical calculations of frequency relation have been performed and depicted by means of graphs to exhibit the substantial impact of heterogeneity, micropolar parameters and wave number on the phase velocity of Love wave. The wave velocity is strongly influenced by these parameters.

Crustal structure beneath Liaoning province and the Bohai Sea and its adjacent region in China based on ambient noise tomography

The velocity structure of the crust beneath Liaoning province and the Bohai sea in China was imaged using ambient seismic noise recorded by 73 regional broadband stations. All available three-component time series from the 12-month span between January and December 2013 were cross-correlated to yield empirical Green’s functions for Rayleigh and Love waves. Phase-velocity dispersion curves for the Rayleigh waves and the Love waves were measured by applying the frequency-time analysis method. Dispersion measurements of the Rayleigh wave and the Love wave were then utilized to construct 2D phase-velocity maps for the Rayleigh wave at 8–35 s periods and the Love wave at 9–32 s periods, respectively. Both Rayleigh and Love phase-velocity maps show significant lateral variations that are correlated well with known geological features and tectonics units in the study region. Next, phase dispersion curves of the Rayleigh wave and the Love wave extracted from each cell of the 2D Rayleigh wave and Love wave phase-velocity maps, respectively, were inverted simultaneously to determine the 3D shear wave velocity structures. The horizontal shear wave velocity images clearly and intuitively exhibit that the earthquake swarms in the Haicheng region and the Tangshan region are mainly clustered in the transition zone between the low- and high-velocity zones in the upper crust, coinciding with fault zones, and their distribution is very closely associated with these faults. The vertical shear wave velocity image reveals that the lower crust downward to the uppermost mantle is featured by distinctly high velocities, with even a high-velocity thinner layer existing at the bottom of the lower crust near Moho in central and northern the Bohai sea along the Tanlu fault, and these phenomena could be caused by the intrusion of mantle material, indicating the Tanlu fault could be just as the uprising channel of deep materials.

Crustal radial anisotropy in Northeast China and its implications for the regional tectonic extension

We obtain high-resolution Rayleigh and Love wave phase velocity maps from ambient noise tomography using data recorded by NECESSArray in Northeast China. The resulting radial anisotropic model from the joint inversion of Rayleigh and Love wave dispersion curves reveals strong relationship between the crustal radial anisotropy and tectonic provinces, that is, strong positive anisotropy (Vsh > Vsv) beneath the Songliao Basin and weak radial anisotropy beneath the Xinmeng Belt and Changbaishan Region. The Songliao Basin experienced widespread crustal extension during the late Mesozoic. We interpret the lower crustal anisotropy beneath the Songliao Basin as a result of ductile deformation during the rifting stage, which may lead to the alignment of anisotropic minerals and the observed strong radial anisotropy at present. In the northern Songliao Basin, where thick syn-rift and post-rift sediments (≥4 km) are believed to be present, we observe a broader lateral distribution of anisotropy with stronger amplitude compared with the southern basin. We suggest that the broader distribution of crustal radial anisotropy in the northern basin could be the consequence of outward lower crustal flow driven by the sedimentary loading during the post-rift stage, which is also proposed by previous numerical modeling.

Love Wave Propagation in Prestressed Piezoelectric Layered Structure

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.

Propagation of Love waves in an isotropic poroelastic layer bounded between two viscous fluids

The present paper is devoted to the study of Love wave propagation in an infinite isotropic poroelastic layer bounded between two compressible viscous liquids. The equations of motion of an isotropic poroelastic solid are formulated in the framework of Biot’s theory. An analytical solution for the complex frequency equation of Love waves is derived. The analytical expressions for phase velocity of Love waves are obtained and solved numerically for two materials, namely, sandstone saturated with kerosene and sandstone saturated with water. Further, effect of viscosity is observed by considering several particular cases.