scholarly journals A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2011
Author(s):  
Mahmoud M. Selim ◽  
Taher A. Nofal
Keyword(s):  
Free Surface ◽  
Reflection Coefficient ◽  
Longitudinal Wave ◽  
Initial Stress ◽  
Half Space ◽  
Seismic Waves ◽  
Initial Stresses ◽  
Reflection Coefficients ◽  
Longitudinal Waves ◽  
Stress Parameter

The aim of this work is to study the behavior of reflection of a longitudinal wave at a free surface of dissipative half-space under the effects of compressive initial stresses. When a longitudinal wave is incident on the free surface of an elastic dissipative half-space, two damped waves (Primarywaves and secondary waves are reflected. Among of these waves, P-waves are affected by compressional initial stresses. The governing equation and corresponding closed-form solutions are derived based on Biot’s incremental deformation theory. The equations of motion are solved analytically and the influence of initial stress parameter on the reflection coefficient of P-wave incidents at the free surface of dissipative half-space is studied in detail. Numerical computations are performed for actual Earth crust and the results analyzing the incident of longitudinal waves are discussed and presented graphically. The analytical solutions and numerical results reveal that the compressive initial stress parameter has notable effects on the reflection coefficient of longitudinal wave incidents on the free surface of dissipative medium. In addition, it has been observed that the presence of compressive initial stresses increases the phase velocity of the longitudinal waves. To the authors’ best knowledge, effects of compressive initial stresses on the reflection coefficients of the incident longitudinal wave on a free surface of dissipative half-space have not been studied before. Since the actual Earth is subject to initial stresses due to different resources, understanding the influences of compressive initial stresses on the reflection coefficient of a longitudinal wave helps seismologists and earthquake engineers to get accurate results of the reflection coefficients of seismic waves propagation in the Earth. Thus, the present study would be useful for seismology and earthquake engineering fields and further study about the nature of seismic waves.

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.

A TWO-DIMENSIONAL STATIC DEFORMATION OF AN IRREGULAR INITIALLY STRESSED MEDIUM

2008 ◽  
Vol 22 (20) ◽  
pp. 3473-3485
Author(s):  
M. M. SELIM
Keyword(s):  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Static Deformation ◽  
Initial Stresses ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Notable Effect ◽  
Approach Method

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

scholarly journals Accounting for Antenna in Half-Space Fresnel Coefficient Estimation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
A. D'Alterio ◽  
R. Solimene
Keyword(s):  
Reflection Coefficient ◽  
Half Space ◽  
Estimation Procedure ◽  
Reflection Coefficients ◽  
Fresnel Reflection ◽  
Reflection Mode ◽  
Coefficient Estimation ◽  
Fresnel Coefficient ◽  
Different Types

The problem of retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration is dealt with. According to our previous results, reflection coefficient estimation is cast as the inversion of linear operator. However, here, we take a step ahead towards more realistic scenarios as the role of antennas (both transmitting and receiving) is embodied in the estimation procedure. Numerical results are presented to show the effectiveness of the method for different types of half-space media.

scholarly journals Effects of a magnetic field and initial stress on reflection of SV-waves at a free surface with voids under gravity

2018 ◽  
Vol 27 (5-6) ◽  
Author(s):  
Augustine Igwebuike Anya ◽  
M.W. Akhtar ◽  
Syed Muhammad Abo-Dahab ◽  
Hajra Kaneez ◽  
Aftab Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Initial Stress ◽  
Half Space ◽  
Significant Role ◽  
Elastic Half Space ◽  
Wave Incident ◽  
P Waves

AbstractThe present study deals with the reflection of SV-waves at a free surface in the presence of magnetic field, initial stress, voids and gravity. When an SV-wave incident on the free surface of an elastic half space, two damped P-waves and an SV-wave are reflected. Among these waves, P-waves are only affected by magnetic fields whereas SV-waves are influenced by both, initial stress and magnetic fields. Effect of gravity is negligible whereas voids played a significant role. These observations can be helpful for seismology and earthquake sciences.

Long-offset AVO inversion of PP reflections from plane interfaces using effective reflection coefficients

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. C65-C79 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Milana Ayzenberg ◽  
Martin Landrø ◽  
Tatyana Nefedkina ◽  
Arkady M. Aizenberg
Keyword(s):  
Reflection Coefficient ◽  
Plane Wave ◽  
Seismic Waves ◽  
Wave Reflection ◽  
Point Sources ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Avo Inversion ◽  
Long Offset ◽  
Head Waves

A conventional amplitude variation with offset (AVO) inversion is based on geometrical seismics which exploit plane-wave reflection coefficients to describe the reflection phenomenon. Widely exploited linearizations of plane-wave coefficients are mostly valid at pre-critical offsets for media with almost flat and weak-contrast interfaces. Existing linearizations do not account for the seismic frequency range by ignoring the frequency content of the wavelet, which is a strong assumption. Plane-wave reflection coefficients do not fully describe the reflection of seismic waves at near-critical and post-critical offsets, because reflected seismic waves are typically generated by point sources. We propose an improved approach to AVO inversion, which is based on effective reflection coefficients (ERCs). ERCs generalize plane-wave coefficients for seismic waves generated by point sources and therefore more accurately describe near-critical and post-critical reflections where head waves are generated. Moreover, they are frequency-dependent and incorporate the local curvatures of the wavefront and the reflecting interface. In our study, we neglect the effect of interface curvature and demonstrate the advantages of our approach on synthetic data for a simple model with a plane interface separating two isotropic half-spaces. A comparison of the inversion results obtained with our approach and the results from an AVO inversion method based on the exact plane-wave reflection coefficient suggests that our method is superior, in particular for long-offset ranges which extend to and beyond the critical angle. We thus propose that long offsets can be successfully exploited in an AVO inversion under the correct assumption about the reflection coefficient. Such long-offset AVO inversion shows the potential of outperforming a conventional moderate-offset AVO inversion in the accuracy of estimated model parameters.

Magneto-elastic SV-wave at the interface of pre-stressed surface with voids under rotation

2016 ◽  
Vol 25 (5-6) ◽  
pp. 153-160
Author(s):  
Rajneesh Kakar ◽  
Shikha Kakar
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Initial Stress ◽  
Seismic Waves ◽  
Elastic Half Space ◽  
Amplitude Ratios ◽  
P Waves ◽  
Stress Rotation ◽  
Acoustic Device ◽  
Stressed Surface

AbstractThe aim of this paper is to study the behaviour of reflection of SV- wave at a free surface under the effects of magnetic field, initial stress, rotation and voids. When a SV- wave is incident on the free surface of an elastic half space, two damped P-waves and a SV-wave is reflected. Among of these waves, P-waves are only affected by magnetic field and rotation whereas SV-wave is influenced by rotation, initial stress and magnetic field. Numerical computations are performed for the developed amplitude ratios of P-, SV- and magneto-elastic waves. This study would be useful for magneto-elastic acoustic device field and further study about nature of seismic waves.

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