THE REFLECTION OF ELASTIC WAVES FROM TRANSITION LAYERS OF VARIABLE VELOCITY

Geophysics ◽  
1937 ◽  
Vol 2 (4) ◽  
pp. 357-363 ◽  
Author(s):  
Alfred Wolf
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Wave Length ◽  
Continuous Functions ◽  
Angle Of Incidence ◽  
Variable Velocity ◽  
Transition Layers ◽  
Coefficient Of Reflection ◽  
Continuous Waves ◽  
Explicit Formulae

Elastic waves are reflected not only from discontinuities in the medium in which they are propagated, but also from transition layers in which the elastic constants are continuous functions of position; the coefficient of reflection is then a function of wave length. Section 1 of this paper gives explicit formulae for the coefficient of reflection of continuous waves from such a layer, at vertical incidence. In Section 2 the manner of variation of the coefficient of reflection with the angle of incidence is discussed qualitatively. Finally, in Section 3, the shape of a pulse reflected from a transition layer is determined.

scholarly journals Response of Corrugated Interface on Incident qSV-Wave in Monoclinic Elastic Half-Spaces

2018 ◽  
Vol 23 (3) ◽  
pp. 727-750
Author(s):  
S.S. Singh ◽  
J. Lalvohbika
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Frequency Parameter ◽  
Irregular Waves ◽  
Angle Of Incidence ◽  
Order Of Approximation ◽  
Reflection And Transmission ◽  
First Order ◽  
Transmission Coefficients ◽  
Incident Plane

Abstract This paper is concerned with the problem of reflection and transmission of elastic waves due to an incident plane qSV-wave at a corrugated interface between two dissimilar monoclinic elastic half-spaces. Due to the corrugated nature of the interface, there exist regularly and irregularly reflected and transmitted elastic waves. Using Rayleigh’s method of approximation, the reflection and transmission coefficients of regular and irregular waves are obtained for the first order of approximation. We have found that these coefficients are functions of the angle of incidence, elastic constants, corrugation and the frequency parameter. These coefficients are obtained for a special type of interface, z =dcos py. We have computed these coefficients for a particular model and discussed the effects of corrugation and frequency parameter.

Reflection of plane elastic waves from transition layers with arbitrary varration of velocity and density

1966 ◽  
Vol 56 (3) ◽  
pp. 633-642 ◽  
Author(s):  
Ravindra N. Gupta
Keyword(s):  
Transition Layer ◽  
Elastic Waves ◽  
Numerical Results ◽  
Elastic Parameters ◽  
Transition Layers

abstract The problem of reflection of plane elastic waves is generalized numerically to an arbitrary variation, with depth, of the elastic parameters inside a transition layer between two homogeneous half-spaces. Numerical results are given for some cases of interest.

A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations

1976 ◽  
Vol 66 (6) ◽  
pp. 1881-1885 ◽  
Author(s):  
G. B. Young ◽  
L. W. Braile
Keyword(s):  
Computer Program ◽  
Elastic Waves ◽  
Displacement Amplitude ◽  
Plane Interface ◽  
Angle Of Incidence ◽  
Amplitude Equations ◽  
Elastic Solids ◽  
Displacement Potential ◽  
Energy Equations ◽  
Sample Case

abstract A computer program is presented which calculates Zoeppritz's displacement amplitude coefficients, displacement potential coefficients, and Knott's energy coefficients for plane harmonic elastic waves of P or SV type incident on a plane interface between two isotropic, homogeneous elastic solids. A discussion of these three basic types of coefficients is included. Results of applying the program to a sample case are presented in the form of a graph of the energy coefficients computed for all possible wave types and over a range of angle of incidence of 0° to 90°.

scholarly journals On the total photo-electric emission of electrons from metals as a function of temperature of the exciting radiation

1926 ◽  
Vol 112 (762) ◽  
pp. 599-630 ◽  
Keyword(s):  
Wave Length ◽  
Ultra Violet ◽  
Electric Activity ◽  
Simple Relation ◽  
Exciting Radiation ◽  
Angle Of Incidence ◽  
Positive Elements ◽  
Activity Frequency ◽  
Exciting Frequency ◽  
Electric Effect

In the year 1913 K. T. Compton and O. W. Richardson ('Phil. Mag.,' vol. 26, p. 549 (1913)) published a paper containing an important investigation on the action of homogeneous mono-chromatic radiation on a number of metals. The essential characteristics of the photo-electric activity of various metals are set out in their experimental curves obtained by plotting photo-electric yield of electrons against exciting frequency. These curves contain double maxima in the case of extremely electro-positive elements like Na, and one maxium for a less electro-positive metal Al, while the curves for Pt exhibit no maximum in the range of frequencies covered by their experiments. Later investigations by Souder ('Phys. Rev.,' vol. 8, p. 327 (1916) and O. W. Richardson and A. F. A. Young ('Roy. Soc. Proc.,' A, vol. 107, p. 377 (1925)) have confirmed these general characteristics of photo-electric activity-frequency curves. A photo-electric maximum for the "selective" effect was observed by Pohl and Pringsheim ('Verh. d. Deutsch. Physik. Ges,' vol. 11. p. 1039 (1910)) as early as 1910 in the case of some electro-positive elements. The general shape of the humps in their curves appears to be a function of the angle of incidence of the exciting radiation; nevertheless, the position of the maximum is quite independent and definite. Lately, R. Döpel ('Zeits. für Phys.,' Vol. 33, p. 237 (1925)) has shown that a less electo-positive metal like Sr also shows the photo-electric maximum. It is therefore probable that all metals would exhibit such maximum. It is therefore probable that all metals would exhibit such maximum photo-electric effect if it were possible to extend the range of exciting frequencies far into the ultra-violet. The presence of double maxima in the curves for Na and K probably points to the existence of two photo-electric thresholds in these elements, as suggested by O. W. Richardson ('Proc. Phys. Soc. London,' vol. 36, p. 388 (1924)), and may lead to interesting developments in future. In the following Table I are collected the observed values of the long wavelength limit λ 0 and the wave-length λ m of the maximum photo-electric effect. A comparison of the figures in columns 1 and 3 shows that the frequencies v 0 and v m can be correlated within the range of accuracy and consistency attainable in photo-electric measurements by a simple relation, v m = 3/2 v 0 .

scholarly journals The reflection and diffraction of X-rays

1931 ◽  
Vol 133 (821) ◽  
pp. 274-291 ◽  
Keyword(s):  
Critical Angle ◽  
Close Agreement ◽  
Wave Length ◽  
Length Distribution ◽  
Incident Beam ◽  
Electromagnetic Theory ◽  
Spherical Mirror ◽  
Angle Of Incidence ◽  
X Rays ◽  
Carbon Target

The agreement between the theories of the reflection of X-rays by solids and observations is discussed. Generally the observations so far obtained are not in close agreement with each other or with theory. The writers find that X-rays of wave-lengths 13·3 Å. (Cu Lα) and 44·7 Å. (C Kα) are reflected by glass, quartz and stainless steel at angles considerably greater than the calculated critical angles. The radiation from carbon has been focussed by a spherical mirror for an angle of incidence of 45°. The ratio of the intensity of the reflected to the incident beam, when X-rays from a carbon target are incident on a glass mirror, has been determined approximately by a photographic method and is found to agree with the Fresnel electromagnetic theory provided a higher absorption of the X-rays occurs than has been previously supposed. This evidence of reflection for angles of incidence greater than the critical angle, which is 6° for glass at a wave-length of λ = 44·7 Å., is confirmed by observations with a glass diffraction grating with which the λ = 44·7 Å. line has been observed for angles of incidence on a plane grating up to 19°. A new plane ruled grating spectrometer is described by means of which the C Kα line has been obtained with short exposures in all orders from the 18th negative to the 13th positive. Microphotometer curves of the wave-length distribution of the energy in the grating spectrum of carbon radiation are given, and these indicate that it consists almost entirely of the Kα line, λ = 44·7 Å. Using Rowland’s method of coincidences the wave-length λ C kα is found to be 44·7 5 Å. relative to λ Cu Lα = 13·32 Å.

Determination of elastic constants of a concrete specimen using transient elastic waves

1995 ◽  
Vol 98 (4) ◽  
pp. 2142-2148 ◽  
Author(s):  
T.‐T. Wu ◽  
J.‐S. Fang ◽  
G.‐Y. Liu ◽  
M.‐K. Kuo
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Concrete Specimen

scholarly journals Elastic waves in the Hencky-Murnaghan material

2020 ◽  
pp. 108-120
Author(s):  
Марина Юрьевна Соколова ◽  
Юрий Владимирович Астапов
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Deformable Body ◽  
Polyamide 6 ◽  
Phase Velocities ◽  
Dynamic Methods ◽  
Nonlinear Elastic ◽  
The Given

Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.

The motion excited by an impulsive source in an elastic half-space with a surface obstacle

1971 ◽  
Vol 61 (3) ◽  
pp. 747-763
Author(s):  
Jacob Aboudi
Keyword(s):  
Finite Difference ◽  
Perturbation Method ◽  
Half Space ◽  
Elastic Constants ◽  
Elastic Waves ◽  
Elastic Half Space ◽  
Reflected Waves ◽  
Finite Difference Solution ◽  
Impulsive Source ◽  
Difference Solution

abstract An elastic half-space having a surface obstacle of slightly different elastic constants whose deviation and shape of boundaries are small is considered. By combining a perturbation method and a finite difference solution, the motion of the half-space due to an impulsive source is given. Results show that Rayleigh and reflected waves are highly influenced by the existence of the obstacle and could give some indications for screening purposes of elastic waves.

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