- Sound refraction wind
- Reflection (physics)
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As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a generally polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.
Publication Abstracts Yang et al. AU - Gao, B. AU - Baum, B. AU - Hu, Y. The symmetric tensor of elastic parameters m ij represents the elastic coupling between fluid and solid phases of the porous aggregate. Elastic constant R measures the pressure exerted on fluid to saturate the porous solid frame.londonradiologypartners.com/risat-how-can-i.php
Sound refraction wind
In an initially-stressed medium, the existence of energy density function requires Biot, the elastic tensor c ijkl to satisfy a relation, given by. This system is manipulated algebraically into two sub-systems, which represent the dynamics of wave propagation in a fluid-saturated porous solid under initial stress. One of them relates the two forms of displacements, i.
The other one defines the modified Christoffel equations for the medium as. The Christoffel equation is just the elastic wave equation transformed over space and time.
It specifies the phase velocity and polarization of each plane wave component in frequency domain. The coefficients C j in 23 are complex due to the viscosity of pore-fluid and anelasticity of the solid frame in the porous aggregate. The complex velocities of the four waves, given by will be varying with phase vector N. The vector N with real components implies the same directions for propagation and attenuation vectors of these waves and, hence, make them homogeneous waves.
However, the propagation of inhomogeneous waves can, only, be explained with N as a complex dual vector. The general mathematical model explained in previous sections provides a procedure to specify the complex slowness vectors for the propagation of four inhomogeneous waves in a saturated poroelastic solid under initial stress. The elastic constants for this saturated sandstone are defined in Appendix.
A vertical plane, fixed by , is considered the propagation-attenuation plane for this study. These variations exhibit the anisotropic character of propagation and attenuation of qP 1 wave in the medium considered. It is noted that the phase velocity increases slightly with increase of Q. In other words, it is a kind of critical angle which may represent the forbidden direction for propagation of attenuated wave with chosen value of Q in the model considered.
In Fig. The effect of changes in Q is more clear on the characteristics of qS 1 wave as compared to qP 1 wave in Fig. The same as Fig. Compared to qS 1 wave in Fig. The pocket of discontinuity in the propagation direction of qP 2 wave is noted Fig. To ascertain this, the numerical results were calculated for a numerical example with different physical parameters.
The elastic tensor and permeability tensor for dolomite are given in Appendix. Now, for three faster waves, we have. It can be calculated from 7 that the quality factor Q of attenuation is given by. Similar observation may be found in Carcione for a dissipative medium even in the absence of initial stress. The values of Q chosen for qP 1, qS 1 and qS 2 waves were 80, 30 and 50 respectively.
Their variations with propagation direction are exhibited in Fig. It is noted Fig. The anisotropic symmetry of the poroelastic frame may have some indirect effect on the attenuation due to viscous pore-fluid. Another attribute of the model considered, i. The comparisons of corresponding plots of these two figures provide the contribution of initial stress to the attenuation of three faster waves. Anelasticity of the porous frame is a major factor in the presence of attenuation in the medium considered.
According to correspondence principle, the elastic constants b IJ two-suffixed notations of elastic constants c ijkl are replaced with to represent the anelastic character of the porous solid frame.
The specification of complex slowness vector of a plane harmonic attenuating wave explored in this study can be used directly to calculate the rate of decay of particle motion with propagation. The expression 14 calculates the radial distance r over which the displacements of material particles reduce to half. This implies that dissipation of disturbance increases with the increase of deviation from the propagation direction.
On the other hand, the minimum of r is observed along the direction nearly normal to propagation direction. It is generally believed that the phenomena associated with viscosity of pore fluid is the main cause of intrinsic attenuation of elastic waves in reservoir rocks and other fluidsaturated porous materials.
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In the present work, alongwith pore-fluid viscosity, the effects of pre-stress, anisotropy, frequency, anelasticity of porous frame on intrinsic attenuation are also studied. This study provides a procedure to relate the quality factor of an attenuating wave to its phase velocity and two finite non-dimensional attenuation parameters.
These parameters represents an attenuating wave in a dissipative medium as a general inhomogeneous wave. The homogeneous attenuating wave is then obtained as a special case in this representation. For example, with this specification, it is possible to estimate the rate of radial decay of amplitudes of a wave in different directions in propagation-attenuation plane. Apart from attenuation parameters, this decay rate varies with phase velocity as well as frequency of the attenuating wave. The intrinsic attenuation calculated for the propagation of a homogeneous wave in a dissipative medium is found to be much smaller as compared to the attenuation observed across the seismic range of frequencies.
This implies that a larger intrinsic attenuation of seismic waves in sedimentary rocks may not be along the directions near to their propagation direction. More strictly, it should be in a direction, which is nearly normal to the direction of propagation. In other words, propagation of nearly evanescent waves may be able to explain the larger intrinsic attenuation observed in any anelastic or dissipative material.
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Two recent papers Chapman et al. Hence, the ultimate applications of this study are geophysical, whether for hydrocarbon exploration, earthquake and structural engineering, or to the exploration of the solid earth.
Fresnel Reﬂection, Lenserf Reﬂection and Evanescent Gain | Optics & Photonics News
Albert, D. Biot, M. Low-frequency range, II. Higher frequency range, J. Borcherdt, R. Glassmoyer, and L. Wennerberg, Influence of welded boundaries in anelastic media on energy flow and characteristics P, S-I and S-II waves: Observational evidence for inhomogeneous body waves in low-loss solids, J. Carcione, J. Caviglia, G. Morro, and E. Pagani, Inhomogeneous waves in viscoelastic media, Wave Motion , 12 , —, Cerveny, V.
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Psencik, Plane waves in viscoelastic anisotropic media. Part 1: Theory, Geophys. Part 2: Numerical examples, Geophys. Chapman, M. Liu, and X. Crampin, S. Hosten, B. Deschamps, and B. Tittmann, Inhomogeneous wave generation and propagation in lossy anisotropic solid. Application to the characterisation of viscoelastic composite materials, J. Johnson, D. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J.
Fluid Mech. Liu, E. Chapman, I. As Electromagnetic waves propagate from one homogeneous medium to another, they experience a change of the wave impedance at the interface . The impedance mismatch generally leads to the reflection, absorption, and transmission of Electromagnetic waves . Power reflection and transmission coefficients are found for linearly and circularly polarized plane electromagnetic waves, normally incident on a plasma slab, moving uniformly along a magneto static field, normal to the slab boundaries .
The study of electromagnetic interaction with moving bounded media, in particular plasmas, due to applications in space exploration has received considerable attention in recent literature. Here one requires the knowledge of electrodynamics of moving media and electromagnetic boundary- conditions at a moving boundary.
Review of the electrodynamics of moving media was recently presented by Tai , and a review and kinematic formulation of electromagnetic boundary conditions at a moving boundary were presented by Costen and Adamson . When an Electromagnetic wave is incident on human tissues some of the energy is transmitted and some is reflected back, because of impedance mismatches.
So it is necessary to study the reflection and transmission coefficients of biological tissues. In this unit expressions for and reflection and transmission coefficients are derived from conducting and dielectric media for different incidence cases. As neither E nor H can exist in a perfect conductor, none of the energy is transmitted through it. When an EM wave travelling in one medium is incident upon a second medium, it is partially reflected and partially transmitted. When an EM wave is incident normally on the surface of a dielectric then reflection and transmission take place.