THE SEISMIC WAVE ENERGY REFLECTED FROM VARIOUS TYPES OF STRATIFIED HORIZONS

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 149-155 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Seismic Wave ◽  
Wave Energy ◽  
Incident Energy ◽  
Preceding Paper ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients

Two applications are made of the reflection and transmission coefficients reported in the preceding paper. These concern the effect of the angle of incidence upon the fraction of incident energy returning to the surface, and the effect of velocity stratification upon the energy return.

Dilatational waves at a microstretch solid/fluid interface

2016 ◽  
Vol 23 (20) ◽  
pp. 3448-3467 ◽  
Author(s):  
Dilbag Singh ◽  
Neela Rani ◽  
Sushil Kumar Tomar
Keyword(s):  
Half Space ◽  
Aluminum Matrix ◽  
Elastic Solid ◽  
Specific Model ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Microstretch Fluid

The present work is concerned with the study of reflection and transmission phenomena of dilatational waves at a plane interface between a microstretch elastic solid half-space and a microstretch liquid half-space. Eringen's theory of micro-continuum materials has been employed for addressing the mathematical analysis. Reflection and transmission coefficients, corresponding to various reflected and transmitted waves, have been obtained when a plane dilatational wave strikes obliquely at the interface after propagating through the solid half-space. It is found that the reflection and transmission coefficients are functions of the angle of incidence, the frequency of the incident wave and the elastic properties of the half-spaces. Numerical calculations have been carried out for a specific model by taking an aluminum matrix with randomly distributed epoxy spheres as the microstretch solid medium, while the microstretch fluid is taken arbitrarily with suitably chosen elastic parameters. The computed results obtained have been depicted graphically. The results of earlier studies have been deduced from the present formulation as special cases.

scholarly journals Approximate reflection coefficients for a thin VTI layer

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C1-C11 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Normal Incidence ◽  
Reflection And Transmission Coefficients ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Isotropic Layer ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
P And Sv Waves

We have developed an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer thickness is assumed to be much smaller than the wavelengths of P- and SV-waves inside. The exact reflection and transmission coefficients are derived by the propagator matrix method. In the case of normal incidence, the exact reflection and transmission coefficients are expressed in terms of the impedances of vertically propagating P- and S-waves. For subcritical incidence, the approximate reflection coefficients are expressed in terms of the contrast in the VTI parameters between the layer and the background. Numerical examples are designed to analyze the reflection coefficients at normal and oblique incidence and investigate the influence of transverse isotropy on the reflection coefficients. Despite giving numerical errors, the approximate formulas are sufficiently simple to qualitatively analyze the variation of the reflection coefficients with the angle of incidence.

Propagation of Surface Waves Across an Anisotropic Layer

1994 ◽  
Vol 61 (3) ◽  
pp. 596-604 ◽  
Author(s):  
E. N. Its ◽  
J. S. Lee
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Differential Operators ◽  
Interface Layer ◽  
Reflection And Transmission Coefficients ◽  
Function Technique ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Matrix Differential

Propagation of elastic surface waves across a thin anisotropic interface layer between two vertically inhomogeneous isotropic quarter-spaces is considered. The relationship between the surface wave fields at the opposite sides of the layer is obtained in the form of matrix differential operators. Based on the Green’s function technique, an analytical method is developed to calculate reflection and transmission coefficients of Rayleigh waves at the layer. The reflection and transmission coefficients of Rayleigh waves at the interface layer are calculated as a function of the angle of incidence for various models of layers with hexagonal symmetry and results are discussed in some detail. Several isotropic layers of low or high velocity materials are also considered to examine the trade-off between anisotropy and inhomogeneity of the interface layer.

scholarly journals A numerical study of ultrasonic response of random cortical bone plates

2017 ◽  
Vol 39 (1) ◽  
pp. 79-95
Author(s):  
A. Abdoulatuf ◽  
V-H. Nguyen ◽  
C. Desceliers ◽  
S. Naili
Keyword(s):  
Cortical Bone ◽  
Numerical Study ◽  
Point Of View ◽  
Bone Plates ◽  
Reflection And Transmission Coefficients ◽  
Ultrasound Wave ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids

A probabilistic study on ultrasound wave reflection and transmission from cortical bone plates is proposed. The cortical bone is  modeled by an anisotropic and heterogeneous elastic plate sandwiched between two fluids and has randomly varied elastic properties in the thickness direction. A parametric stochastic model is proposed to describe the elastic heterogeneity in the plate. Reflection and transmission coefficients are computed via the semi-analytical finite element (SAFE) method. The effect of material heterogeneity on reflected and transmitted waves is investigated from a probabilistic point of view. The parametric study highlights effects of the uncertainty of material properties on the reflection and transmission coefficients by varying the frequency, angle of incidence and bone thickness.

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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