Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian （LG） beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.

POWER REFLECTION AND TRANSMISSION IN BEAM STRUCTURES CONTAINING A SEMI-INFINITE CRACK

Wave reflection and transmission in a beam containing a semi-infinite crack are studied analytically based on Timoshenko beam theory., Two kinds of crack surface conditions： non-contact （open） and fully contact （closed） cracks, are considered respectively for an isotropic beam. The analytical solution of reflection and transmission coefficients for a semi-infinite crack is obtained. The power reflection and transmission ratios depend on both the frequency and the position of the crack. Numerical results show the conservation of power transport. The transmitted energy among various wave modes is also investigated. A finite element method is used to verify the validity of the analytical results.

Seismic reflection and transmission coeffi-cients at an air-water interface of saturated porous soil

Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences between air-saturated soils and water-saturated soils were theoretically discussed, and the theoretical formulas of reflection and transmission coefficients at an air-water interface were derived. The characteristics of propagation and attenuation of elastic waves in air-saturated soils were given and the relations among the frequency, the angle of incidence and the reflection, transmission coefficients were analyzed by using numerical methods. Numerical results show that the propagation characteristic of the wave in air-saturated soils is great different from that in water-saturated soils. The frequency and the angle of incidence can have great influences on the reflection and transmission coefficients at interface. Some new cognition about the wave propagation is obtained and the study suggests that we may carefully pay attention to the influence of air on the dynamic analysis of seismic wave.

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analytical expressions of the reflected field,internal field as well as transmitted field in each region are obtained.Through numerical simulations,the intensity distributions of the incident beam,reflected beam,internal beam as well as transmitted beam are presented at oblique incidence.Besides,we also compare the intensity distributions of the geometrical-optics beam field,the first order beam mode field and the actual beam field,which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab.Meanwhile,the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated.Finally,the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail.The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.

Reflection and transmission of acoustic waves on multilayered porous media

Based on the Boit theory of acoustic wave propagation in fluid-saturated porous medium we have studied in this paper the acoustic reflection and transmission on multilayered porous media, in which the adequate boundary conditions across the interfaces are taken into account. Numerical calculations of the reflection and transmission coefficients at different incident angles and frequencies of the fast compressional wave incident on porous media with three or four layers are presented. The results indicate that the maximum or minimum reflection and transmission coefficients appear at certain ratios of the wavelength to the thickness. The acoustic incident angle and porous medium properties are shown to affect significantly these coefficients. As an example, the measured transmission coefficients in a water-saturated fused glass bead sample are in good agreement with theoretical prediction.

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.

Reflection and transmission of elastic waves at an interface between two micropolar piezoelectric half-spaces

In the present paper,we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces.The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves.An incident plane wave at an interface between two dissimilar half-spaces generates three reflected and three transmitted waves.The relations between amplitude ratios of reflected and transmitted waves are derived which,in general,depend on material parameters and angle of incidence.The explicit expressions for energy ratios of reflected and transmitted waves are also obtained.For relevant material parameters,the results are illustrated graphically to show the micropolar piezoelectric effects on variations of amplitude ratios and the square root of energy ratios against the angle of incidence.

REFLECTION AND TRANSMISSION OF A PLANAR SOLITARY WAVE

Reflection and transmission of a planar solitary wave by a 2-D cylinder are investigated by matched asymptotic method.Boussinesq equations are the governing equations in the outer field and described by finite difference method.In the near field the governing equation is Laplace equation which is expressed,for a square cylinder,in eigenfunctions in different regions.The outer and inner solu- tions are matched and solved by iteration.As an example,the time history of the change of forces and moment and the evolution of the transmitted and reflected waves are given.

Sign of differential reflection and transmission in pump-probe spectroscopy of graphene on dielectric substrate

Pump-probe differential reflection and transmission spectroscopy is a very effective tool to study the nonequilibrium carrier dynamics of graphene. The reported sign of differential reflection from graphene is not explicitly explained and not consistent. Here, we study the differential reflection and transmission signals of graphene on a dielectric substrate. The results reveal the sign of differential reflection changes with the incident direction of the probe beam with respect to the substrate. The obtained theory can be applied to predict the differential signals of other two-dimensional materials placed on various dielectric substrates.

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

A new numerical technique for simulating the coupled seismic and electromagnetic waves in layered porous media

Chen＇s technique of computing synthetic seismograms, which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen （LAC） generalized reflection and transmission coefficients method, is confirmed to be efficient in dealing with elastic waves in multi-layered media and accurate in any frequency range. In this article, we extend Chen＇s technique to the computation of coupled seismic and electromagnetic （EM） waves in layered porous media. Expanding the involved mechanical and electromagnetic fields by a set of scalar and vector wave-function basis, we obtain the fundamental equations which are subsequently solved by using a recently developed version of the LAC generalized reflection and transmission coefficients method. Our approach and corresponding program is validated by reciprocity tests. We also show a numerical example of a two-layer model with an explosion source. The P-to-EM conversion waves radiated from the interface may have potential application.

A Study of Properties of the Photonic Band Gap of Unmagnetized Plasma Photonic Crystal

In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.

Analysis of the influence of sheath positions,flight parameters and incident wave parameters on the wave propagation in plasma sheath

The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves.Based on the calculation of the flow field of a conical cylindrical,this work studies the propagation of electromagnetic waves in plasma sheath at L-band and Ku-band,and discusses the propagation characteristics in the head,side and tail of the sheath.The dielectric properties of plasma sheath are related to flight speed and altitude.A flight condition corresponds to a unique distribution of dielectric properties.For the conical cylindrical,the results show that flight speed is generally negatively correlated with the transmissivity of the plasma sheath.The reflection characteristics of electromagnetic waves at the L-band and Kuband when obliquely incident to the plasma sheath show a downward trend.When the frequency is increased to Ku-band,the propagation characteristics of electromagnetic waves in the plasma sheath are related to the position of the sheath.

Reflecting and transmitting effect of a planar unidirectionally conducting screen

The reflecting and transmitting effects of a planar unidirectionally conducting screen are analyzed based on the accurate closed-form expression for electric field of an arbitrarily oriented electric dipole.For a dipole oriented along the wire elements of the screen,the screen acts as a perfectly electrically conducting plane.For a dipole perpendicular to the wire elements,the fields reflected by the screen can be interpreted as the contribution of an image dipole and image transmission-line current source,while the transmitted field is arisen from image transmission-line source.The expressions of related surface waves are derived and can be compared with previous results.

Study on Dynamic Response of the “Dualistic” Structure Rock Slope with Seismic Wave Theory

Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.

Scattering of Surface Waves by the Edge of a Small Undulation on a Porous Bed in an Ocean with Ice-cover

Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.

Wave scattering by undulating bed topography in a two-layer ocean

The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.

Scattering of Surface Water Waves Involving Semi-infinite Floating Elastic Plates on Water of Finite Depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Wave Scattering by Porous Bottom Undulation in a Two Layered Channel

The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.