The effect of boundaries on wave propagation in a liquid-filled porous solid: IX. Love waves in a porous internal stratum

1965 ◽  
Vol 55 (5) ◽  
pp. 919-923
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Porous Layer ◽  
Shear Waves ◽  
Love Waves ◽  
Porous Solid ◽  
Transverse Waves ◽  
Phase Velocities ◽  
Impermeable Layer

abstract The dispersion equation in the second approximation for small porosity is deduced for the problem of transverse waves in a porous layer separating two impermeable elastic half-spaces, and the expression for the dissipation per cycle displayed. It is shown that Love waves can be propagated in a porous layer only with phase velocities smaller than that of body shear waves in either of the half-spaces, whereas in an impermeable layer Love waves may exist having phase velocity equal to that of body shear waves in one of the half-spaces.

The effect of boundaries on wave propagation in a liquid-filled porous solid: II. Love waves in a porous layer

1961 ◽  
Vol 51 (1) ◽  
pp. 51-59
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Viscous Liquid ◽  
Porous Layer ◽  
Unit Volume ◽  
Transcendental Equation ◽  
Love Waves ◽  
Wave Number ◽  
Velocity Of Propagation ◽  
Approximate Scheme

Abstract The transcendental equation is derived relating frequency and phase velocity of propagation of Love waves in a porous layer containing a viscous liquid. This equation, being complex, can be satisfied only if the wave number of the motion is complex, indicating that the disturbance is dissipative. The general expression being intractable analytically, an approximate scheme is employed to determine the phase velocity and measure of dissipation valid for porous materials in which the mass (per unit volume of aggregate) of the interstitial liquid is smaller than that of the solid.

scholarly journals Influence of Poroelasticity of the Surface Layer on the Surface Love Wave Propagation

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Adil El Baroudi
Keyword(s):  
Wave Propagation ◽  
Surface Layer ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Love Wave ◽  
Wave Attenuation ◽  
Love Waves ◽  
Velocity Variation ◽  
Fluid Viscosity ◽  
Benchmark Solutions

This work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure–displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. mathematica software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solutions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theoretical resolution, the results in literature in the case of an homogeneous isotropic surface layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

Finite-Difference Modeling and Characteristics Analysis of Love Waves in Anisotropic-Viscoelastic Media

2021 ◽  
Author(s):  
Shichuan Yuan ◽  
Zhenguo Zhang ◽  
Hengxin Ren ◽  
Wei Zhang ◽  
Xianhai Song ◽  
...  
Keyword(s):  
Finite Difference ◽  
Phase Velocity ◽  
Velocity Dispersion ◽  
Love Waves ◽  
Velocity Anisotropy ◽  
Viscoelastic Media ◽  
Phase Velocities ◽  
Phase Velocity Dispersion ◽  
Anisotropic Elastic ◽  
Attenuation Anisotropy

ABSTRACT In this study, the characteristics of Love waves in viscoelastic vertical transversely isotropic layered media are investigated by finite-difference numerical modeling. The accuracy of the modeling scheme is tested against the theoretical seismograms of isotropic-elastic and isotropic-viscoelastic media. The correctness of the modeling results is verified by the theoretical phase-velocity dispersion curves of Love waves in isotropic or anisotropic elastic or viscoelastic media. In two-layer half-space models, the effects of velocity anisotropy, viscoelasticity, and attenuation anisotropy of media on Love waves are studied in detail by comparing the modeling results obtained for anisotropic-elastic, isotropic-viscoelastic, and anisotropic-viscoelastic media with those obtained for isotropic-elastic media. Then, Love waves in three typical four-layer half-space models are simulated to further analyze the characteristics of Love waves in anisotropic-viscoelastic layered media. The results show that Love waves propagating in anisotropic-viscoelastic media are affected by both the anisotropy and viscoelasticity of media. The velocity anisotropy of media causes substantial changes in the values and distribution range of phase velocities of Love waves. The viscoelasticity of media leads to the amplitude attenuation and phase velocity dispersion of Love waves, and these effects increase with decreasing quality factors. The attenuation anisotropy of media indicates that the viscoelasticity degree of media is direction dependent. Comparisons of phase velocity ratios suggest that the change degree of Love-wave phase velocities due to viscoelasticity is much less than that caused by velocity anisotropy.

On the dispersion equation of Love waves in a porous layer

1986 ◽  
Vol 58 (3-4) ◽  
pp. 125-136 ◽  
Author(s):  
A. Chattopadhyay ◽  
M. Chakraborty ◽  
V. Kushwaha
Keyword(s):  
Dispersion Equation ◽  
Porous Layer ◽  
Love Waves

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

2014 ◽  
Vol 06 (05) ◽  
pp. 1450050 ◽  
Author(s):  
SANTIMOY KUNDU ◽  
SHISHIR GUPTA ◽  
SANTANU MANNA ◽  
PRALAY DOLAI
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Graphical Representation ◽  
Separation Of Variables ◽  
Classical Equation ◽  
Wave Number ◽  
Fiber Reinforced

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

Wave propagation and subsurface velocity structure at the Virgo gravitational wave detector (Italy)

2020 ◽  
Author(s):  
Gilberto Saccorotti ◽  
Sonja Gaviano ◽  
Carlo Giunchi ◽  
Irene Fiori ◽  
Soumen Koley ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Rayleigh Wave ◽  
Gravitational Wave ◽  
Rayleigh Waves ◽  
Velocity Structure ◽  
Band Frequency ◽  
Frequency Bands ◽  
Phase Velocities ◽  
Wave Phase

<p>The performances and sensitivity of gravitational wave (GW) detectors are significantly affected by the seismic environment. In particular, the seismic displacements and density fluctuations of the ground due to seismic-wave propagation introduce noise in the detector output signal; this noise is referred to as gravity-gradient noise, or Newtonian Noise (NN). The development of effective strategies for mitigating the effects of NN requires, therefore, a thorough assessment of seismic wavefields and medium properties at and around the GW detector. In this work, we investigate wave propagation and the subsurface velocity structure at the Virgo GW detector (Italy), using data from a temporary, 50-element array of vertical seismometers. In particular, we analyze the recordings from the catastrophic Mw=6.2 earthquake which struck Central Italy on August 24, 2016, and six of the following aftershocks.  The general kinematic properties of the earthquake wavefields are retrieved from the application of a broad-band, frequency-domain beam-forming technique. This method allows measuring the propagation direction and horizontal slowness of the incoming signal; it is applied to short time windows sliding along the array seismograms, using different subarrays whose aperture was selected in order to match different frequency bands. For the Rayleigh-wave arrivals, velocities range between 0.5 km/s and 5 km/s, suggesting the interference of different wave types and/or multiple propagation modes. For those same time intervals, the propagation directions are scattered throughout a wide angular range, indicating marked propagation effects associated with geological and topographical complexities. These results suggest that deterministic methods are not appropriate for estimating Rayleigh waves phase velocities. By assuming that the gradient of the displacement is constant throughout the array, we then attempt the estimation of ground rotations around an axis parallel to the surface (tilt), which is in turn linearly related to the phase velocity of Rayleigh waves. We calculate the ground tilt over subsequent, narrow frequency bands. Individual frequency intervals are investigated using sub-arrays with aperture specifically tailored to the frequency (wavelength) under examination. From the scaled average of the velocity-to-rotation ratios, we obtain estimates of the Rayleigh-wave phase velocities, which finally allow computing a dispersion relationship. Due to their diffusive nature, earthquake coda waves are ideally suited for the application of Aki’s autocorrelation method (SPAC). We use SPAC and a non-linear fitting of correlation functions to derive the dispersion properties of Rayleigh wave for all the 1225 independent inter-station paths. The array-averaged SPAC dispersion is consistent with that inferred from ground rotations, and with previous estimates from seismic noise analysis.  Using both a semi-analytical and perturbational approaches, this averaged dispersion is inverted to obtain a shear wave velocity profile down to ~1000m depth. Finally, we also perform an inversion of the frequency-dependent travel times associated with individual station pairs to obtain 2-D, Rayleigh wave phase velocity maps spanning the 0.5-3Hz frequency interval. </p>

Love-Wave Phase-Velocity Estimation from Array-Based Rotational Motion Microtremor

2020 ◽  
Author(s):  
Kunikazu Yoshida ◽  
Hirotoshi Uebayashi
Keyword(s):  
Phase Velocity ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Velocity Estimation ◽  
Love Waves ◽  
Phase Velocities ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Spatial Derivatives ◽  
Rotational Motions

ABSTRACT The most popular array-based microtremor survey methods estimate velocity structures from the phase velocities of Rayleigh waves. Using the phase velocity of Love waves improves the resolution of inverted velocity models. In this study, we present a method to estimate the phase velocity of Love waves using rotational array data derived from the horizontal component of microtremors observed using an ordinal nested triangular array. We obtained discretized spatial derivatives from a first-order Taylor series expansion to calculate rotational motions from observed array seismograms. Rotational motions were obtained from a triangular subarray consisting of three receivers using discretized spatial derivatives. Four rotational-motion time histories were calculated from different triangular subarrays in the nested triangular arrays. Phase velocities were estimated from the array of the four rotational motions. We applied the proposed Love-wave phase-velocity estimation technique to observed array microtremor data obtained using a nested triangular array with radii of 25 and 50 m located at the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The phase velocities of rotational and vertical motions were estimated from the observed data, and results showed that the former were smaller than those of the latter. The observed phase velocities obtained from vertical and rotational components agreed well with the theoretical Rayleigh- and Love-wave phase velocities calculated from the velocity structure model derived from nearby PS logs. To show the ability of the rotation to obtain Love wave, we estimated apparent phase velocities from north–south or east–west components. The apparent velocities resulted in between the theoretical velocities of Rayleigh and Love waves. This result indicates that the calculated rotation effectively derived the Love waves from a combination of Love and Rayleigh waves.

scholarly journals TORSIONAL WAVE SCATTERING IN TWO-LAYER PIPE WITH ACCOUNT FOR CONTACT RIGIDITY

2019 ◽  
pp. 91-101
Author(s):  
Konstantin E. Abbakumov ◽  
Nikolay V. Stepanenko
Keyword(s):  
Wave Propagation ◽  
Dispersion Equation ◽  
Torsional Wave ◽  
Problem Solution ◽  
Ultrasonic Methods ◽  
Contact Rigidity ◽  
Phase Velocities ◽  
Torsional Waves ◽  
Scalar Potentials ◽  
Methods Of Control

The purpose of the paper is to study the wave propagation in a two-layer pipe, taking into account the rigidity of the contact between its layers. It is considered by solving the equation of motion for the vector and scalar potentials. A dispersion equation describing the frequency distribution of the phase velocities of waves in the waveguide under investigation is derived. In order to take into account the degree of contact rigidity between layers additional terms are added to the boundary conditions, including the normal (kGN) and tangential (kGT) contact rigidity coefficients. It is shown that torsional waves are separated from other types of waves and can be considered separately. The example of a numerical solution of the dispersion equation shows the possible behavior of dispersion curves without regard to the contact rigidity. The similar problem solution is provided with allowance for contact rigidity at various perforation coefficients. A conclusion is drawn on the effect of contact between layers on torsional wave behavior. The similar method solves the problem for a homogeneous pipe with internal stratification. Recommendations are given for taking into account the revealed regularities in the development of ultrasonic methods of control based on torsional wave propagation.

scholarly journals The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2270
Author(s):  
Olha Hrytsyna ◽  
Jan Sladek ◽  
Vladimir Sladek
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Love Wave ◽  
Short Circuit ◽  
Open Circuit ◽  
Love Waves ◽  
Inertia Effect ◽  
Wave Phase Velocity ◽  
Piezoelectric Structure ◽  
Piezoelectric Structures

The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

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