Transmission of Rayleigh waves past a step change in elevation

1965 ◽  
Vol 55 (2) ◽  
pp. 319-334 ◽  
Author(s):  
A. K. Mal ◽  
L. Knopoff
Keyword(s):  
Surface Waves ◽  
Half Space ◽  
Green's Function ◽  
Rayleigh Waves ◽  
Function Method ◽  
Step Change ◽  
Reflection Coefficients ◽  
Homogeneous Half Space ◽  
Transmission And Reflection Coefficients ◽  
Transmission And Reflection

Abstract Using a Green's function method of approximation, transmission and reflection coefficients are computed for the problem of Rayleigh waves incident upon a step change in the elevation of the surface of a homogeneous half-space. Several versions of these approximations are given, differing principally by the method in which the surface waves on the vertical face of the step are taken into account.

scholarly journals scattering of surface waves by a half immersed circular cylinder in fluid of finite depth

1985 ◽  
Vol 8 (1) ◽  
pp. 113-125
Author(s):  
Birendranath Mandel ◽  
Sudip Kumar Goswami
Keyword(s):  
Integral Equation ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Reflection Coefficients ◽  
Infinite Depth ◽  
Transmission And Reflection Coefficients ◽  
Linearized Theory ◽  
Transmission And Reflection

A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers ofa/hstarting with(a/h)2where “a” is the radius of the circular cylinder. It is also shown that the coefficients of(a/h)2in these corrections do not vanish identically.

19.—Propagation of Weak Discontinuities in a Layered Hyperelastic Half-space

1976 ◽  
Vol 75 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Erdogan S. Suhubi ◽  
Alan Jeffrey
Keyword(s):  
Half Space ◽  
Reflection Coefficients ◽  
Initial Condition ◽  
One Dimensional ◽  
Transmission And Reflection Coefficients ◽  
Weak Discontinuities ◽  
Acceleration Waves ◽  
The One ◽  
The Waves ◽  
Transmission And Reflection

SYNOPSISThis paper investigates the one-dimensional propagation of weak discontinuities, that is acceleration waves, in a homogeneous and isotropic half-space composed of an arbitrary number of non-linearly hyperelastic layers. The transmission and reflection coefficients are evaluated in terms of the initial condition at the boundary, and the steepening of the waves to form a shock is discussed. The results are specialised to the case of periodic layering.

On a method to obtain a Green's function for a multi-layered half space

1964 ◽  
Vol 54 (4) ◽  
pp. 1087-1096
Author(s):  
I. Herrera
Keyword(s):  
Surface Wave ◽  
Integral Representation ◽  
Green’S Function ◽  
Surface Waves ◽  
Half Space ◽  
Green's Function ◽  
Rayleigh Waves ◽  
Two Dimensional ◽  
Representation Theorems ◽  
Layered Half Space

Abstract In this paper the surface wave terms of the Green's function for a two-dimensional multilayered half space are obtained. The method used is new and remarkable by its simplicity. It is based on the integral representation theorems for elastodynamics. The orthogonality properties of surface waves are generalized to include not only Love waves but Rayleigh waves as well.

A PHOTOELASTIC STUDY OF STRESS WAVE PROPAGATION IN A QUARTER‐PLANE

Geophysics ◽  
1971 ◽  
Vol 36 (2) ◽  
pp. 296-310 ◽  
Author(s):  
A. N. Henzi ◽  
J. W. Dally
Keyword(s):  
Rayleigh Waves ◽  
Wave Interaction ◽  
P Wave ◽  
Stress Wave Propagation ◽  
Reflection Coefficients ◽  
Stress Distributions ◽  
Full Field ◽  
Transmission And Reflection Coefficients ◽  
Quarter Plane ◽  
Transmission And Reflection

An experimental investigation was conducted on a quarter‐plane loaded with an explosive charge at one point on the boundary. Experimental methods of dynamic photoelasticity and interferometry were used to obtain full‐field data of the dynamic event. Results of the study were obtained for both the P and R‐wave interaction with the corner. Energy reflection coefficients were found for the P‐wave interaction. For the Rayleigh wave, where the response was more significant, transmission and reflection coefficients based on both stress and surface energy were established. Subsurface stress distributions for the transmitted and reflected Rayleigh waves were obtained in the region near the corner.

scholarly journals Transmission, Reflection and Dissipation of Microwaves in Magnetic Composites with Nanocrystalline Finemet-Type Flakes

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3499
Author(s):  
Anatoly B. Rinkevich ◽  
Dmitry V. Perov ◽  
Yuriy I. Ryabkov
Keyword(s):  
Composite Material ◽  
Microwave Absorption ◽  
Nanocrystalline Alloy ◽  
Reflection Coefficients ◽  
Magnetic Composites ◽  
Transmission And Reflection Coefficients ◽  
Wave Interference ◽  
Microwave Losses ◽  
Frequency Dependences ◽  
Transmission And Reflection

The microwave properties of a composite material containing flakes of finemet-type nanocrystalline alloy placed in the epoxy matrix have been investigated. Two compositions have been studied: with 15% and 30% flakes. Frequency dependences of transmission and reflection coefficients are measured in the frequency range from 12 to 38 GHz. The dielectric permittivity and magnetic permeability are obtained, and the microwave losses are calculated. The dependences of transmission and reflection coefficients have been drawn as functions of wave frequency and thickness of the composite material, taking into account the frequency dependences of permittivity and permeability. The regions of maximal and minimal microwave absorption have been defined. The influence of wave interference on the frequency dependence of microwave absorption is studied.

Surface-wave dispersion computations

1970 ◽  
Vol 60 (2) ◽  
pp. 321-344 ◽  
Author(s):  
Fred Schwab ◽  
Leon Knopoff
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Reduction Technique ◽  
Surface Wave Dispersion ◽  
Single Precision ◽  
Homogeneous Half Space ◽  
Full Control ◽  
Significant Figures ◽  
Rayleigh Wave Dispersion

abstract Fundamental-mode Love- and Rayleigh-wave dispersion computations for multilayered, perfectly-elastic media were studied. The speed of these computations was improved, and the accuracy brought under full control. With sixteen decimal digits employed in these computations, fifteen significant-figure accuracy was found possible with Love waves and twelve to thirteen figure accuracy with Rayleigh waves. In order to ensure that the computed dispersion is correct to a specified accuracy, say σ significant figures, (σ + 1)/4 wavelengths of layered structure must be retained above a homogeneous half-space. To this accuracy, the homogeneous half-space is a sufficient model of the true layering it replaces. Using this result, it was possible to refine the usual layer-reduction technique so as to ensure retention of the specified accuracy while employing reduction. With this reduction technique in effect, and with σ specified below single-precision accuracy, the program can be run entirely in single precision; the specified accuracy is maintained without overflow or loss-of-precision problems being encountered during calculations.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

DKP equation with smooth barrier

2021 ◽  
Author(s):  
O. Langueur ◽  
M. Merad ◽  
A. Rassoul
Keyword(s):  
Hypergeometric Function ◽  
Numerical Study ◽  
Confluent Hypergeometric Function ◽  
Reflection Coefficients ◽  
Step Potential ◽  
Dkp Equation ◽  
Transmission And Reflection Coefficients ◽  
Special Cases ◽  
Rectangular Barrier ◽  
Transmission And Reflection

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function [Formula: see text]. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters [Formula: see text] are plotted.

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