THE REFLECTION OF WAVES IN A GENERALIZED EPSTEIN PROFILE

1965 ◽  
Vol 43 (5) ◽  
pp. 921-934 ◽  
Author(s):  
R. Burman ◽  
R. N. Gould
Keyword(s):  
Refractive Index ◽  
Wave Equation ◽  
Reflection Coefficient ◽  
Approximate Formula ◽  
Reflection And Transmission Coefficients ◽  
Stratified Medium ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Case ◽  
Reflection Of Waves

Epstein (1930) and Rawer (1939) studied the reflection of waves in a stratified medium by transforming the hypergeometric equation into the wave equation. A particular case of the Epstein profile is a symmetrical layer. Considerable attention has been given in the literature to this case as well as to symmetrical layers with certain other profiles of the refractive index. In the present paper a generalized Epstein profile is considered and the reflection and transmission coefficients are obtained. The special case in which the refractive index tends to the same constant value on either side of a layer is then discussed. The symmetrical Epstein profile is a special case of this layer which, in general, is asymmetrical. Particular attention is given to a layer differing only slightly from the symmetrical Epstein layer, a simple approximate formula for the reflection coefficient being derived.

Reflection and transmission coefficients in plane-parallel layers with refractive-index mismatch

1992 ◽  
Vol 31 (1) ◽  
pp. 106 ◽  
Author(s):  
Leonard I. Grossweiner ◽  
James L. Karagiannes ◽  
Linda Ramball Jones ◽  
Porter W. Johnson
Keyword(s):  
Refractive Index ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Plane Parallel

scholarly journals EVALUATION OF HYDRAULIC PERFORMANCE OF WAVE DISSIPATING BLOCK USING POROSITY

2020 ◽  
pp. 29
Author(s):  
Susumu Araki ◽  
Daiki Watanabe ◽  
Shin-ichi Kubota ◽  
Masaya Hashida
Keyword(s):  
Reflection Coefficient ◽  
Transmission Coefficient ◽  
Hydraulic Performance ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients

The reflection and transmission of wave dissipating work mainly depend on the shape and porosity of wave dissipating block. However, the influence of the shape and porosity of wave dissipating block on the reflection and transmission has not been investigated sufficiently. The purpose of this study is to investigate the influence of the porosity of wave dissipating block on the reflection and transmission coefficients through a series of hydraulic experiments where four kinds of wave dissipating blocks were used. Wave dissipating blocks with smaller porosity provided a larger reflection coefficient and a smaller transmission coefficient as a whole. However, a wave dissipating block provided a smaller reflection coefficient and a smaller transmission coefficient in spite of relatively larger porosity. The measured reflection and transmission coefficients were compared with those estimated by existing equations.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/lqyzabMw66U

Reflection and transmission coefficients for seismic waves in ellipsoidally anisotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 27-38 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Wave Propagation ◽  
Anisotropic Medium ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth ◽  
Special Case

The deficiency of an isotropic model of the earth in the explanation of observed traveltime phenomena has led to the mathematical investigation of elastic wave propagation in anisotropic media. A type of anisotropy dealt with in the literature (Potsma, 1955; Cerveny and Psencik, 1972; and Vlaar, 1968) is uniaxial anisotropy or transverse isotropy. A special case of transverse isotropy which assumes the wavefronts to be ellipsoids of revolution has been used by Cholet and Richard (1954) and Richards (1960) in accounting for the observed traveltimes at Berraine in the Sahara and in the foothills of Western Canada. The kinematics of this problem have been treated in a number of papers, the most notable being Gassmann (1964). However, to appreciate fully the effect of anisotropy, the dynamics of the problem must be explored. Assuming a model of the earth consisting of plane transversely isotropic layers with the axes of anisotropy perpendicular to the interfaces, a prime requisite for obtaining amplitude distance curves or synthetic seismograms is the calculation of reflection and transmission coefficients at the interfaces. In this paper the special case of ellipsoidal anisotropy will be considered. That the quasi‐shear SV wavefront is forced to be spherical by this assumption is unfortunate, but it is instructive to investigate this simple anisotropic model as it incorporates many features inherent to wave propagation in a more general anisotropic medium. A brief outline of the theory for wave propagation in an ellipsoidally anisotropic medium is given and the analytic expressions for the reflection and transmission coefficients are listed. A complete derivation of reflection and transmission coefficients in transversely isotropic media can be found in Daley and Hron (1977). Finally, all 24 possible reflection and transmission coefficients and surface conversion coefficients are displayed for varying degrees of anisotropy.

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

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