Attenuation Of Love Waves Research Articles

Scattering of Love wave from an interface crack in a viscoelastic waveguide layer bonded to a piezoelectric substrate: an analytical estimate and numerical validation

This study uses an analytical method to examine the scattering of a Love wave from an interfacial crack in a thin lossy media (viscoelastic material) that serves as a waveguide layer attached to an unbounded loss-less media (piezoelectric material). The viscoelastic material is modeled using the Kelvin–Voigt equation. Phase velocity and attenuation have been calculated by equating the real and imaginary parts of the dispersion relation to zero, respectively, due to the complex wave number of viscoelastic material. Using the integral transform approach and the dislocation density function, the scattering field close to the crack tip is determined, resulting in a Cauchy singular integral equation of the first type. It has been transformed into a system of linear algebraic equations using Gauss-Chebyshev numerical integration. It has been investigated how frequency, waveguide layer thickness, and viscoelastic material loss factor affect phase velocity and Love wave attenuation. The mode-III dynamic stress intensity factor at the left and right crack-tip is investigated for various thicknesses of the waveguide layer and loss factor of viscoelastic material. The outcomes were verified using numerical data from the COMSOL Multiphysics 5.6 FEA software. The findings are fundamental and could be used in the design of particular sensors.

Ambient Noise Attenuation Tomography Reveals an Asymmetric Damage Zone Across San Jacinto Fault Near Anza, California

AbstractWe perform seismic attenuation tomography of the shallow structure for the San Jacinto Fault in the Ramona Reservation of southern California. The study uses ambient seismic noise recorded by a linear array of 65 3‐C sensors across the fault. We extract amplitude decay information, with uncertainty, from noise interferometry functions. To account for strong heterogeneities in the complex shallow fault zone structure, we apply a frequency‐dependent amplitude correction for focusing/defocusing effects using inverted phase velocity maps obtained by solving the transport equation. We then estimate the attenuation structure based on the linear station‐triplet method for both Love and Rayleigh waves. The attenuation tomography indicates strong attenuation correlated with known San Jacinto Fault surface traces. The Love wave attenuation tomography reveals an asymmetric damage zone that exists primarily on the fault side with faster seismic velocity, consistent with earthquake ruptures on a fault bimaterial interface with preferred propagation direction to the northwest.

Ambient noise Love wave attenuation tomography for the LASSIE array across the Los Angeles basin.

The Los Angeles basin is located within the North America-Pacific plate boundary and contains multiple earthquake faults that threaten greater Los Angeles. Seismic attenuation tomography has the potential to provide important constraints on wave propagation in the basin and to provide supplementary information on structure in the form of the distribution of anelastic properties. On the basis of the amplitude information from seismic interferometry from the linear LASSIE array in the Los Angeles basin, we apply station-triplet attenuation tomography to obtain a 2D depth profile for the attenuation structure of the uppermost 0.6 km. The array crosses four Quaternary faults, three of which are blind. The attenuation tomography resolves strong attenuation (shear attenuation Qs ~ 20) for the fault zones and is consistent with sharp boundaries across them.

Numerical characterization of Love waves dispersion in viscoelastic guiding-layer under viscous fluid

We present a finite element (FE) based model to accurately investigate the dispersion and attenuation of Love waves in a multilayered structure made of a piezoelectric substrate, a guiding layer, and a viscous fluid. The numerical model solves the general form of the wave equations that includes the materials anisotropy, piezoelectricity, and viscoelasticity. We express the wave equations for elastic waves in a particular formulation in order to solve an eigenvalue problem where the eigenvalue is the complex wavenumber k from which we can derive the phase velocity [ω/Re(k)] and the attenuation rate [Im(k)]. The numerical model enables us to study the effects of the interdigitated electrodes, the materials viscoelasticity and piezoelectricity, and the fluid's viscosity on the wave phase velocity and attenuation. Our FE based model will facilitate optimizing the design of anisotropic piezoelectric platforms for Love waves propagation under viscous fluid loading.

Surface wave in a Maxwell liquid-saturated poroelastic layer

An analytical approach of the propagation and attenuation of Love waves in a viscoelastic liquid-saturated poroelastic layer has been considered in this paper. The equations of motion have been formulated separately for different media under suitable boundary conditions at the interface of viscoelastic liquid, poroelastic layer and elastic substrate. Following Biot’s theory of poroelasticity, a new accurate and simple generalized dispersion equation has been established to design Love wave liquid sensors. The effect of liquid shear viscosity on the Love waves velocity has been studied. The influence of thickness and porosity of the waveguide layer has also been shown on the Love waves velocity and attenuation. The various investigations results can serve as benchmark solutions in design of liquid sensors and nondestructive testing.

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.

Properties of Love Waves in Functional Graded Saturated Material.

In the present study, the propagation of Love waves is investigated in a layered structure with two different homogeneity saturated materials based on Biot’s theory. The upper layer is a transversely isotropic functional graded saturated layer, and the substrate is a saturated semi-space. The inhomogeneity of the functional graded layer is taken into account. Furthermore, the gradient coefficient is employed as the representation of the relation with the layer thickness and the material parameters, and the power series method is applied to solve the variable coefficients governing the equations. In this regard, the influence of the gradient coefficients of saturated material on the dispersion relations, and the attenuation of Love waves in this structure are explored, and the results of the present study can provide theoretical guidance for the non-destructive evaluation of functional graded saturated material.

Love Wave Propagation in a Layered Piezoelectric Structure Immersed in a Viscous Fluid

This paper is addressed to the Love wave propagation in a layered piezoelectric structure immersed in a viscous fluid. The layered piezoelectric structure consists of an isotropic layer and a relatively thicker transversely isotropic piezoelectric substrate. The velocity of the Love waves changes due to the presence of the viscous fluid. The exact theory is accurate but not convenient to apply because it is generally difficult to get an explicit relation between the quantities we interest. In this paper, the perturbation approach is applied to obtain the explicit relations for the phase velocity and attenuation of Love waves. The result is useful for the measurement of the viscosity and mass density in Love wave sensors.

Propagation of Love Waves in an Inhomogeneous Fluid Saturated Porous Layered Half-Space with Properties Varying Exponentially

Based on Biot's theory for transversely isotropic fluid saturated porous media, the complex dispersion equation for Love waves in a transversely isotropic fluid-saturated porous layered half-space is derived with the consideration of the inhomogeneity of the layer. The equation is solved by an iterative method. Detailed numerical calculation is presented for an inhomogeneous fluid-saturated porous layer overlying a purely elastic half-space. The dispersion and attenuation of Love waves are discussed. In addition, the upper and lower bounds of Love wave speed are also explored.

On attenuation of Love waves in a two-layered half-space

The problem of attenuation of Love waves propagating in an anelastic layer of uniform thickness overlying an anelastic half-space has been re-examined. Some errors in the attenuation dispersion relation appearing in the literature have been pointed out and the correct form of the attenuation dispersion relation has been given.

Attenuation of Love waves in low-loss media

A theory of Love waves propagating in a viscoelastic surface layer deposited on a perfect elastic substrate was considered. In the case of low losses (ωη44/μB0≪1) an analytical formula relating the attenuation coefficient of the Love wave and the viscoelastic parameters of the waveguide structure was established. This makes it possible to apply the obtained analytical formula in nondestructive testing for determining the rheological parameters of viscoelastic bodies. The established theory of Love waves in viscoelastic media can also be applied in seismology and integrated optics.

Anelasticity of the crust and upper mantle beneath north and central India from the inversion of observed Love and Rayleigh wave attenuation data

The fundamental mode Love and Rayleigh waves generated by earthquakes occurring in Kashmir, Nepal Himalaya, northeast India and Burma and recorded at Hyderabad, New Delhi and Kodaikanal seismic stations are analysed. Love and Rayleigh wave attenuation coefficients are obtained at time periods of 15–100 seconds, using the spectral amplitude of these waves for 23 different paths along northern (across Burma to New Delhi) and central (across Kashmir, Nepal Himalaya and northeast India to Hyderabad and Kodaikanal) India. Love wave attenuation coefficients are found to vary from 0.0003 to 0.0022 km−1 for northern India and 0.00003 km−1 to 0.00016 km−1 for central India. Similarly, Rayleigh wave attenuation coefficients vary from 0.0002 km−1 to 0.0016 km−1 for northern India and 0.00001 km−1 to 0.0009 km−1 for central India. Backus and Gilbert inversion theory is applied to these surface wave attenuation data to obtainQβ−1 models for the crust and uppermost mantle beneath northern and central India. Inversion of Love and Rayleigh wave attenuation data shows a highly attenuating zone centred at a depth of 20–80 km with lowQ for northern India. Similarly, inversion of Love and Rayleigh wave attenuation data shows a high attenuation zone below a depth of 100 km. The inferred lowQ value at mid-crustal depth (high attenuating zone) in the model for northern India can be by underthrusting of the Indian plate beneath the Eurasian plate which has caused a low velocity zone at this shallow depth. The gradual increase ofQβ−1 from shallow to deeper depth shows that the lithosphere-asthenosphere boundary is not sharply defined beneath central India, but rather it represents a gradual transformation, which starts beneath the uppermost mantle. The lithospheric thickness is 100 km beneath central India and below that the asthenosphere shows higher attenuation, a factor of about two greater than that in the lithosphere. The very lowQ can be explained by changes in the chemical constitution taking place in the uppermost mantle.

Q-structure beneath the north and central Indian Ocean from the inversion of observed Love and Rayleigh wave attenuation data

The fundamental-mode Love and Rayleigh waves generated by 57 earthquakes which occurred in the north and central Indian Ocean (extending to 40°S) and recorded at Indian seismograph and other WWSSN stations such as HOW, SHL, VIS, MDR, HYB, KOD, CHG, TRD, POO, BOM, GOA, NDI, NIL and QUE are analysed. Love and Rayleigh wave attenuation coefficients are estimated at periods of 15–100 s using the spectral amplitude of these waves for 98 different paths across the Bay of Bengal Fan, the Arabian Fan, and the north and central Indian Ocean. The large standard deviations observed in the surface wave attenuation coefficients may be a result of regional variation of the attenuative properties of the crust and upper mantle beneath these regions. Love wave attenuation coefficients are found to vary from 0.000 03 to 0.000 45 km −1 for the Bay of Bengal Fan; from 0.000 03 to 0.000 85 km −1 for the Arabian Fan; and from 0.000 03 to 0.000 35 km −1 for the north and central Indian Ocean. Similarly, Rayleigh wave attenuation coefficients vary from 0.000 03 to 0.0004 km −1 for the Bay of Bengal Fan; from 0.000 06 to 0.0007 km −1 for the Arabian Fan; and from 0.000 03 to 0.0007 km −1 for the north and central Indian Ocean. Backus and Gilbert inversion theory is applied to these surface wave attenuation data to obtain average Q −1 models for the crust and upper mantle beneath the Bay of Bengal, the Arabian Fan, and the north and central Indian Ocean. Inversion of Love and Rayleigh wave attenuation data shows a high-attenuation zone centred at a depth of > 120 km ( Q β ≈ 125) for the Bay of Bengal Fan. Similarly, a high-attenuation zone ( Q β ≈ 40–70) occurs at a depth of 60–160 km for the Arabian Fan at 100–160 km ( Q β ≈ 115) for the Indian Ocean off Ninetyeast Ridge, and at 80–160 km ( Q β ≈ 80) for the Indian Ocean across the Ninetyeast Ridge. The Q β −1 models show a lithosphere thickness of 120 km beneath the Bay of Bengal Fan. Similarly, lithosphere thickness of 70, 100 and 80 km is estimated beneath the Arabian Fan, and the Indian Ocean off Ninetyeast Ridge and across Ninetyeast Ridge, respectively. The base of the lithosphere is identified as the depth at which there is a significant increase in the Q β −1 value, which attains its maximum value in the asthenosphere. The thinning of Indian lithosphere beneath the Arabian Fan suggests high temperature below Moho depth (60 km from surface) which has caused a high-attenuation zone at this shallow depth.

Q structure of the basin and range from surface waves

Regionalized Rayleigh and Love wave attenuation coefficients have been measured across the Basin and Range province of western United States in the frequency range 0.02–0.2 Hz. The measurements were made by using the methods of Tsai and Aki (1969) and Yacoub and Mitchell (1977) adapted to work on any number of events simultaneously. Rayleigh wave Q values at low frequency approach values near 40, which are significantly lower than previous measurements in the western United States. Love wave Q values, on the other hand, are quite high at low frequencies. We suggest that interference between fundamental and higher modes may explain the Love wave observations. The Rayleigh and Love wave attenuation measurements have been inverted simultaneously for shear‐wave attenuation as a function of depth. A frequency‐independent Q model is consistent with both Rayleigh wave and short‐period Love wave attenuation data. The shear‐wave Q (Qβ) model is characterized by low Qβ in the lower crust (Qβ∼100) and Qβ decreasing in the upper mantle with lowest values (Qβ∼30) beneath 60 km depth. Forward modeling shows that a high‐Q lower crust or upper mantle lid is inconsistent with the data. Our interpretation of these results is that the lithosphere is poorly developed beneath the Basin and Range and that the partially molten asthenosphere may reach very shallow depths, possibly to the base of the crust. This interpretation of the Q model in conjunction with a number of geological and geophysical evidences suggests that attenuation mechanisms involving partial melt predominate in the lower crust and upper mantle of the Basin and Range.

Q-structure beneath the Tibetan Plateau from the inversion of Love- and Rayleigh-wave attenuation data

The fundamental mode Love and Rayleigh waves generated by ten earthquakes and recorded across the Tibet Plateau, at QUE, LAH, NDI, NIL, KBL, SHL, CHG, SNG and HKG are analysed. Love- and Rayleigh-wave attenuation coefficients are obtained at time periods of 5–120 s using the spectral amplitudes of these waves for 23 different paths. Love wave attenuation coefficient varies from 0.0021 km −1, at a period of 10 s, to 0.0002 km −1 at a period of 90 s, attaining two maxima at time periods of 10 and 115 s, and two minima at time periods of 25 and 90 s. The Rayleigh-wave attenuation coefficient also shows a similar trend. The very low value for the dissipation factor, Q β , obtained in this study suggests high dissipation across the Tibetan paths. Backus-Gilbert inversion theory is applied to these surface wave attenuation data to obtain average Q β −1 models for the crust and uppermost mantle beneath the Tibetan Plateau. Independent inversion of Love- and Rayleigh-wave attenuation data shows very high attenuation at a depth of ∼50–120 km ( Q β ⋍ 10 ). The simultaneous inversion of the Love and Rayleigh wave data yields a model which includes alternating regions of high and low Q β −1 values. This model also shows a zone of high attenuating material at a depth of ∼40–120 km. The very high inferred attenuation at a depth of ∼40–120 km supports the hypothesis that the Tibetan Plateau was formed by horizontal compression, and that thickening occurred after the collision of the Indian and Eurasian plates.

On propagation and attenuation of Love waves

The period equation for Love waves is derived for a layered medium, which is composed of a compressible, viscous liquid layer sandwiched between homogeneous, isotropic, elastic solid layer and homogeneous, isotropic half space. In general, the period equation will admit complex roots and hence Love waves will be dispersive and attenuated for this type of model. The period equation is discussed in the limiting case when thicknessH 2 and coefficient of viscosity, η2, of the liquid layer tend to zero so as to maintain the ratioP=H 2/η2 constant. Numerical values for phase velocity, group velocity, quality factor (Q) and displacement in the elastic layer and half space have been computed as a function of the frequency for first and second modes for various values of the parameterP. It is shown that Love waves are not attenuated whenP=0 and ∞. The computed values ofQ for first and second modes indicate that whenP≠0 or ∞ the value ofQ attains minimum value as a function of dimensionless angular frequency.

An estimate of the properties of Love-type surface waves in a frictionally bonded layer

abstract An approximate analytical approach is presented for determining the attenuation, dispersion, and intensity of motion at depth associated with Love-type surface waves in an elastic layer bonded by Coulomb friction to an elastic half-space. It is found that the dispersion curves are only slightly affected by a small amount of slip at the interface, but that the level of attenuation in the system increases considerably with the amplitude of motion. The results for the frequency dependence of the attenuation in the system are in basic agreement with experimental data on the attenuation of Love waves in the Earth (Jackson, 1971). The results for the intensity of motion at depth indicate a deterioration of bonding at high frequencies.

Excitation and attenuation of love waves in North America from the November 9, 1968 south central Illinois earthquake.

Excitation and attenuation of love waves in North America from the November 9, 1968 south central Illinois earthquake.

The Attenuation of Love Waves and Toroidal Oscillations of the Earth

An attempt has been made to invert a large set of attenuation data for Love waves and toroidal oscillations in the earth, using a recent method by Backus and Gilbert. The difficulty in finding an acceptable model of internal friction which explains the data, under the assumption that the internal friction is independent of frequency, casts doubt on the validity of this assumption. A frequency-dependent model of internal friction is presented which is in good agreement with the seismic data and with recent experimental measurements of attenuation in rocks.

Universal dispersion tables

Abstract The universal dispersion theory, presented in Part I, is extended to allow computation of group velocity and amplitude partial derivatives. Tables giving the effect of a change in any parameter on phase velocity, group velocity and amplitude are given for two earth models, one oceanic and one continental shield. Tables are given for the fundamental and first three higher Love modes. These tables make it possible to compute dispersion parameters for the first four Love modes for any realistic earth model or to invert observations to an earth model. Attenuation of Love waves for an arbitrary distribution of Q versus depth can also be computed by using techniques previously described.