Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.     

Wave Dispersion and Attenuation in Partially Saturated Sandstones

We investigate the wave dispersion and attenuation in partially water-saturated sandstones based on the improved Biot/squirt (BISQ) model in which the saturation is introduced. Numerical experiments indicate that the phase velocity of the fast P-wave decreases as the saturation increases in the low-frequency range (10^2-10^4 Hz), and reaches the minimum at the full-saturation state. The behaviour of the phase velocity varying with the saturation in the high-frequency range (10^4-10^6 Hz), however, is opposite to that in the low-frequency range. The peak value of P-wave attenuation increases with increasing saturation, and is the maximum at the fully saturated state. Numerical models and experiments show that the improved BISQ model is better than the traditional Gassmann-Biot model.     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

An analysis of seismic attenuation in random porous media

The attenuation of seismic wave in rocks has been one of the interesting research topics, but till now no poroelasticity models can thoroughly explain the strong attenuation of wave in rocks. In this paper, a random porous medium model is designed to study the law of wave propagation in complex rocks based on the theory of Biot poroelasticity and the general theory of stochastic process. This model sets the density of grain, porosity, permeability and modulus of frame as random parameters in space, and only one fluid infiltrates in rocks for the sake of better simulation effect in line with real rocks in earth strata. Numerical simulations are implemented. Two different inverse quality factors of fast P-wave are obtained by different methods to assess attenuation through records of virtual detectors in wave field (One is amplitude decay method in time domain and the other is spectral ratio method in frequency domain). Comparing the attenuation results of random porous medium with those of homogeneous porous medium, we conclude that the attenuation of seismic wave of homogeneous porous medium is far weaker than that of random porous medium. In random porous media, the higher heterogeneous level is, the stronger the attenuation becomes, and when heterogeneity σ = 0.15 in simulation, the attenuation result is consistent with that by actual observation. Since the central frequency (50 Hz) of source in numerical simulation is in earthquake band, the numerical results prove that heterogeneous porous structure is one of the important factors causing strong attenuation in real stratum at intermediate and low frequency.     

Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper,we introduce the complex modulus to express the viscoelasticity of a medium.According to the correspondence principle,the Biot-Squirt(BISQ)equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium.The effective bulk modulus of a multiphase flow is computed by the Voigt formula,and the characteristic squirt-flow length is revised for the gas-included case.We then build a viscoelastic BISQ model containing a multiphase flow.Through using this model,wave dispersion and attenuation are studied in a medium with low porosity and low permeability.Furthermore,this model is applied to observed interwell seismic data.Analysis of these data reveals that the viscoelastic parameter tanδ is not a constant.Thus,we present a linear frequency-dependent function in the interwell seismic frequency range to express tanδ.This improves the fit between the observed data and theoretical results.     

Viscoelastic BISQ Model for Low-Permeability Sandstone with Clay

A modified BISQ （Blot/Squirt） model for wave propagation in low-permeability sandstone is developed by introducing the viscoelastic mechanism of a porous skeleton into Dvorkin＇s model. The linear viscoelasticity of the Kelvin Voigt constitutive law is employed to describe the stress-strain relation of a solid frame with clay while the ultrasonic waves propagate through the fluid-saturated sandstone. The phase velocity and attenuation of two p-waves are given based on the present BISQ model. The comparisons between numerical results and experimental data indicate that our viscoelastic model is more realistic and feasible for wave propagation in the low-permeability sandstone, especially with clay, than traditional BISQ models.     

Study on laser-generated Lamb waves propagation in viscoelastic and anisotropic plate

The propagation characteristics of laser-generated Lamb waves in thin composite plates are theoretically studied. Taking the anisotropic and viscoelastic properties of the composite material into account, the finite element models for simulating laser-generated Lamb waves in the composite material are established in the frequency domain. Numerical results are calculated in purely elastic and viscoelastic transversely isotropic plates, respectively. The effects of the anisotropic and viscoelastic properties on the propagation of Lamb waves are analyzed in detail. The numerical results exhibit that the features of the laser-generated Lamb wave, including attenuation, velocity, frequency, and the dispersive nature, have a close relationship with the anisotropic and viscoelastic properties of the material.     

A Geometry Model for Tortuosity of Flow Path in Porous Media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.     

Metachronal propulsion of non-Newtonian viscoelastic mucus in an axisymmetric tube with ciliated walls

Cilia-induced flow of viscoelastic mucus through an idealized two-dimensional model of the human trachea is presented.The cilia motion is simulated by a metachronal wave pattern which enables the mobilization of highly viscous mucus even at nonzero Reynolds numbers.The viscoelastic mucus is analyzed with the upper convected Maxwell viscoelastic formulation which features a relaxation time and accurately captures normal stress generation in shear flows.The governing equations are transformed from fixed to wave(laboratory)frame with appropriate variables and resulting differential equations are perturbed about wave number.The trachea is treated as an axisymmetric ciliated tube.Radial and axial distributions in axial velocity are calculated via the regular perturbation method and pressure rise is computed with numerical integration using symbolic software MATHEMATICA^‘TM’.The influence of selected parameters which is cilia length,and Maxwell viscoelastic material parameter i.e.relaxation time for prescribed values of wave number are visualized graphically.Pressure rise is observed to increase considerably with elevation in both cilia length and relaxation time whereas the axial velocity is markedly decelerated.The simulations provide some insight into viscous-dominated cilia propulsion of rheological mucus and also serve as a benchmark for more advanced modeling.     

Theoretical and Experimental Study of Time Reversal in Cubic Crystals

The self-adaptive focusing of the time reversal in anisotropic media is studied theoretically and experimentally. It is conducted for the compressional wave field in the cubic crystal silicon. The experimental result is in agreement with our theoretical analysis. The focusing gain and the displacement distributions of the time reversal field are analysed in detail. It is shown that the waves from different elements of the transducer array arrive at the original place of the source simultaneously after the time reversal operation. The waveform distortions caused by the velocity anisotropy can automatically be compensated for after the time reversal processing.