Body waves in a “real Earth”. Part I

1973 ◽  
Vol 63 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. Cisternas ◽  
O. Betancourt ◽  
A. Leiva
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Power Series ◽  
Arbitrary Number ◽  
Body Waves ◽  
Reflection And Transmission Coefficients ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth

abstract A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

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.

scholarly journals Estimation of S-parameters and dielectric permittivity of quartz ceramics samples in millimeter waveband

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 65-71
Author(s):  
N. A. Pevneva ◽  
D. A. Kondrashov ◽  
A. L. Gurskii ◽  
A. V. Gusinsky
Keyword(s):  
Dielectric Constant ◽  
Dielectric Permittivity ◽  
Ceramic Materials ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Higher Order Modes ◽  
S Parameters ◽  
The Fourier Transform

A modified Nicholson – Ross – Weir method was used to determine complex parameters and dielectric permittivity of ceramic materials in the range 78.33–118.1 GHz. The measuring equipment is a meter of complex reflection and transmission coefficients, a waveguide measuring canal with a special measuring cell, consisting of two irregular waveguides and a waveguide chamber between them, which provides insignificant influence of higher-order modes. The dependences of the amplitude and phase of the reflection and transmission coefficients on frequency were obtained experimentally for fluoroplastic and three ceramic samples in the frequency range 78.33–118.1 GHz. The obtained S-parameters are processed according to an algorithm that includes their averaging based on the Fourier transform in order to obtain the values of the dielectric permittivity. Fluoroplastic was used as a reference material with a known dielectric constant. The dielectric constant of fluoroplastic has a stable value of 2.1 in the above mentioned frequency range. The dielectric constant of sample No. 1 varies from 3.6 to 2.5 at the boundaries of the range, sample No. 2 – from 3.7 to 2.1, sample No. 3 – from 2.9 to 1.5. The experimental data are in satisfactory agreement with the literature data for other frequencies taking into account the limits set by the measurement uncertainty.

Sign in / Sign up

Export Citation Format

Share Document