scholarly journals THE AMPLITUDES OF WAVES TO BE EXPECTED IN SEISMIC PROSPECTING

Geophysics ◽  
1936 ◽  
Vol 1 (2) ◽  
pp. 252-256 ◽  
Author(s):  
B. Gutenberg
Keyword(s):  
Longitudinal Wave ◽  
Rate Of Change ◽  
Ground Movement ◽  
Angle Of Incidence ◽  
Refraction Angle ◽  
Reflected Waves ◽  
Longitudinal Waves ◽  
Seismic Prospecting ◽  
Shot Point

A method of calculating the amplitudes of bodily waves in earthquakes is applied to a study of the amplitudes of longitudinal waves produced by an artificial explosion. Formulae are given for calculating the energy of the reflected longitudinal wave arriving at the surface. The percentage of energy reflected at a discontinuity increases rapidly after the angle of incidence exceeds the critical refraction angle. However, no corresponding large amplitudes are recorded by the instruments. Instead, the maximum amplitudes of reflected waves are found near the shot point. This is because the ground movement is due both to the arriving wave and to the wave reflected downward from the ground. The amplitude of this movement depends, besides, on the rate of change of the angle of incidence with distance. It is pointed out that the same methods can be applied to a dipping bed, and that the amplitudes of the reflected waves are in general slightly larger in the up‐dip than in the down‐dip direction.

Reflection of Longitudinal Wave in the Micropolar Elasticity with Voids

2020 ◽  
pp. 2050035
Author(s):  
R. Lianngenga ◽  
J. Lalvohbika ◽  
Lalawmpuia Tochhawng ◽  
L. P. Lalduhawma ◽  
Denghmingliani Zadeng
Keyword(s):  
Free Boundary ◽  
Longitudinal Wave ◽  
Volume Fraction ◽  
Micropolar Elasticity ◽  
Elastic Materials ◽  
Reflected Waves ◽  
Longitudinal Waves ◽  
Materials With Voids ◽  
Energy Ratios ◽  
Elastic Materials With Voids

By considering no more interaction between wryness tensor and change in voids volume fraction in the materials, the reflection problem of plane longitudinal waves at a free boundary of micropolar elastic materials with voids has been investigated. We have obtained the amplitude and energy ratios of reflected waves for the incident longitudinal wave by using appropriate boundary conditions. The effect of void parameters in the nondimensional wavenumber, amplitude and energy ratios are computed numerically for the particular material’s model.

Reflection of a longitudinal travelling wave from the notch in a rod

2007 ◽  
Vol 5 ◽  
pp. 212-220 ◽  
Author(s):  
M.A. Ilgamov ◽  
A.G. Khakimov
Keyword(s):  
Inverse Problem ◽  
Longitudinal Wave ◽  
Travelling Wave ◽  
Observation Point ◽  
Reflected Waves ◽  
Reflected Wave ◽  
Using Data

This article investigates the reflection of a longitudinal wave from the transverse notch and its movement along an infinite rod. The dependence is obtained between the reflected wave and parameters of the notch. The statement of the inverse problem allows defining the coordinate of the notch and the parameter that contains its depth and length using data on both the incident and reflected waves at the observation point.

Numerical simulation of internal defect imaging with the longitudinal wave generated by laser induced ultrasonic array

2020 ◽  
pp. 2150103
Author(s):  
Hao Sui ◽  
Kesi Li ◽  
Zhenyu Zhu ◽  
Le Cheng ◽  
Xiaorong Gao ◽  
...  
Keyword(s):  
Longitudinal Wave ◽  
Phased Arrays ◽  
Synthetic Aperture ◽  
Wave Component ◽  
The Finite Element Method ◽  
Internal Defect ◽  
Longitudinal Waves ◽  
Synthetic Aperture Focusing ◽  
Synthetic Aperture Focusing Technique ◽  
Defect Imaging

To verify the performance of longitudinal waves induced by laser phased arrays (LPA) for detection and quantitative evaluation in internal defects, the finite element method (FEM) is utilized to establish the models of LPA scanning processing. The interaction of longitudinal wave and internal defect is analyzed. Besides, the two components of the reflected longitudinal waves (the longitudinal wave component [Formula: see text] and the shear wave component [Formula: see text] are focused on the imaging of defects with the synthetic aperture focusing technique (SAFT) and total focusing method (TFM) algorithms. It shows that the imaging of internal sub-millimeter defect is obtained using the LPA. The defect size and location are simultaneously calculated, with the relative error being 6.7% and 2.9%, respectively. The proposed longitudinal wave-based LPA is a promising method for the imaging and evaluation of internal micro defects.

scholarly journals A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2698
Author(s):  
Bo Zhu ◽  
Jaesun Lee
Keyword(s):  
Longitudinal Wave ◽  
Second Harmonic ◽  
Early Stage ◽  
Wave Mixing ◽  
Third Harmonic ◽  
Longitudinal Waves ◽  
Testing Method ◽  
State Evaluation ◽  
Stress Fatigue ◽  
Train Safety

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave nondestructive testing (NDT) method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

Reflection of Plane Waves in a Rotating Temperature-Dependent Thermoelastic Solid with Diffusion

2012 ◽  
Vol 28 (4) ◽  
pp. 599-606
Author(s):  
B. Singh ◽  
L. Singh ◽  
S. Deswal
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Reflected Waves ◽  
Energy Ratios ◽  
Rotation Parameters ◽  
Thermoelastic Solid

ABSTRACTThe governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing equations indicates the existence of four coupled plane waves in x-z plane. The reflection of plane waves from the free surface of a rotating temperature-dependent thermoelastic solid half-space with diffusion is considered. The required boundary conditions are satisfied by the appropriate potentials for incident and reflected waves in the half-space to obtain a system of four non-homogeneous equations in the reflection coefficients. The expressions for energy ratios of the reflected waves are also obtained. The reflection coefficients and energy ratios are found to depend upon the angle of incidence, reference temperature, thermodiffusion and rotation parameters. Aluminum material is modeled as the half-space to compute the absolute values of the reflection coefficients and the energy ratios. Effects of temperature dependence and rotation parameters on the reflection coefficients and energy ratios are shown graphically for a certain range of the angle of incidence of the incident plane wave.

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

scholarly journals Effect of Two Temperatures on Reflection Coefficient in Micropolar Thermoelastic with and without Energy Dissipation Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Rajneesh Kumar ◽  
K. D. Sharma ◽  
S. K. Garg
Keyword(s):  
Energy Dissipation ◽  
Temperature Effects ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflected Waves ◽  
Two Temperatures ◽  
Thermally Conducting ◽  
Without Energy Dissipation ◽  
Two Temperature

The reflection of plane waves at the free surface of thermally conducting micropolar elastic medium with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected waves at different angles of incident wave are obtained. Dissipation of energy and two-temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.

scholarly journals A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

2019 ◽  
Author(s):  
Bo Zhu ◽  
Jaesun Lee
Keyword(s):  
Longitudinal Wave ◽  
Second Harmonic ◽  
Early Stage ◽  
Wave Mixing ◽  
Third Harmonic ◽  
Longitudinal Waves ◽  
Testing Method ◽  
State Evaluation ◽  
Stress Fatigue ◽  
Train Safety

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave NDT method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

scholarly journals About wireless synchronization of a GPR receiver and transmitter when plotting a hodograph.

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
O.A. Gulevich ◽  
◽  
L.B. Volkomirskaya ◽  
A.E. Reznikov ◽  
◽  
...  
Keyword(s):  
Electromagnetic Wave ◽  
Potassium Salt ◽  
Video Signal ◽  
Salt Deposit ◽  
Reflected Waves ◽  
Seismic Prospecting ◽  
Mine Workings ◽  
First Time

The processing of the hodograph data of a monopulse georadar with wireless synchronization is similar to the method of reflected waves in seismic prospecting but has particular differences. The paper describes for the first time the effect of the appearance of steps in the image of the recorded video signal when the receiving and transmitting units of the georadar are moving apart on the example of studies in the mine workings of a potassium salt deposit. Using a kinematic correction in GPR in consideration with the effect of synchronization via electromagnetic wave is especially important for deep research with a large spacing of antenna units.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Devender Sheoran ◽  
Ramesh Kumar ◽  
Sunil Kumar ◽  
Kapil Kumar Kalkal
Keyword(s):  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Conservation Of Energy ◽  
Content Type ◽  
Reflected Waves ◽  
Diffusive Medium ◽  
Energy Ratios ◽  
Two Temperature

Purpose The purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature. Design/methodology/approach A two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB. Findings The problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material. Originality/value The modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

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