Radiation characteristics of elastodynamic line sources buried in layered media with periodic interfaces. I. SH- wave analysis

1987 ◽  
Vol 77 (6) ◽  
pp. 2181-2191 ◽  
Author(s):  
Vijay K. Varadan ◽  
Akhlesh Lakhtakia ◽  
Vasundara V. Varadan ◽  
Charles A. Langston
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Half Space ◽  
Interesting Case ◽  
Wave Guide ◽  
Sh Wave ◽  
Wave Analysis ◽  
Radiation Characteristics ◽  
Crustal Model ◽  
Scattered Fields

Abstract Using the T matrix method, or the extended boundary condition, the solution for a class of problems involving an SH line source in an elastic wave guide is determined. The boundaries of the wave guide may be periodically corrugated and the wave guide may be embedded between elastic media. Numerical results are given for a seismically interesting case of wave propagation in a one-layer crustal model over a mantle half-space with a corrugated free surface representing the Basin and Range topography in the Western United States. Analysis of the scattered fields at the surface, and of the fields radiated into the half-space, shows complicated field behavior, even with sinusoidal free surface corrugation. These results are directly applicable to regional wave propagation and scattering.

scholarly journals Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

2016 ◽  
Vol 64 (5) ◽  
pp. 1340-1369 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Amrita Das ◽  
Anirban Lakshman ◽  
Amares Chattopadhyay
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Sh Wave

Two-dimensional linear and nonlinear wave propagation in a half-space

1999 ◽  
Vol 89 (4) ◽  
pp. 903-917 ◽  
Author(s):  
Heming Xu ◽  
Steven M. Day ◽  
Jean-Bernard H. Minster
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Phase Velocity ◽  
Rayleigh Wave ◽  
Half Space ◽  
Frequency Band ◽  
Pseudospectral Method ◽  
Two Dimensional ◽  
Wave Phase ◽  
Wave Phase Velocity

Abstract We examine a staggered pseudospectral method to solve a two-dimensional wave propagation problem with arbitrary nonlinear constitutive equations, and evaluate a general image method to simulate the traction-free boundary condition at the surface. This implementation employs a stress-velocity formulation and satisfies the free surface condition by explicitly setting surface shear stress to zero and making the normal stress antisymmetric about the free surface. Satisfactory agreement with analytical solutions to Lamb's problem is achieved for both vertical point force and explosion sources, and with perturbation solutions for nonlinearly elastic wave propagation within the domain of validity of such solutions. The Rayleigh wave, however, suffers much more severe numerical dispersion than do body waves. At four grids per wavelength, the relative error in the Rayleigh-wave phase velocity is 25 times greater than the corresponding error in the body-wave phase velocity. Thus for the Rayleigh wave, the pseudospectral method performs no better than a low-order finite difference method. A substantial merit of the image approach is that it does not assume any particular rheology, the method is readily applicable even when stresses are not analytically related to kinematic variables, as is the case for most nonlinear models. We use this scheme to investigate the response of a nonlinear half-space with endochronic rheology, which has been fit to quasi-static and dynamic observations. We find that harmonics of a monochromatic source are generated and evolve with epicentral range, and energy is transferred from low to higher frequencies for a broadband source. This energy redistribution characteristic of the propagation is strain-amplitude dependent, consistent with laboratory experiments. Compared with the linear response, the nonlinear response of an endochronic layer near the surface shows a deamplification effect in the intermediate-frequency band and an amplification effect in the higher-frequency band. The computational method, with modifications to accommodate realistic nonlinear soil characteristics, could be applied to estimate earthquake strong ground motions and path effects.

Impacts on the Propagation of SH-Waves in a Heterogeneous Viscoelastic Layer Sandwiched between an Anisotropic Porous Layer and an Initially Stressed Isotropic Half Space

2016 ◽  
Vol 33 (1) ◽  
pp. 13-22 ◽  
Author(s):  
S. Kundu ◽  
P. Alam ◽  
S. Gupta ◽  
D. Kr. Pandit
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
Porous Layer ◽  
Separation Of Variables ◽  
Finite Thickness ◽  
Wave Number ◽  
Viscoelastic Layer ◽  
Sh Wave ◽  
Sh Waves

AbstractThe present study deals with the affected behaviour of SH-wave propagation through a viscoelastic layer sandwiched between an anisotropic porous layer of finite thickness and an isotropic half space. The sandwiched viscoelastic layer is considered as heterogeneous medium of finite thickness and isotropic half-space is considered as initially stressed medium. The method of separation of variables has been applied to obtain the dispersion equation of SH-wave in their respective media. The obtained complex dispersion relation has been separated into real and imaginary parts. Moreover, the dispersion relation has been satisfied with the classical condition of Love waves. The effects of heterogeneity, attenuation constant, dissipation factor of viscoelasticity, initial stress (compressive), thickness ratio of two layers and porosity on the propagation of SH-waves have been shown by number of graphs. Graphs have been plotted for the dimensionless phase and damping velocity on the propagation of SH-waves with respect to the dimensionless real wave number. The results may be useful to explore the nature and peculiarity of SH-wave propagation in the viscoelastic structure.

scholarly journals Transient SH Wave Propagation of Elastic Plate

2021 ◽  
Vol 250 ◽  
pp. 02010
Author(s):  
Kotaro Miura ◽  
Makoto Sakamoto ◽  
Yuji Tanabe
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Elastic Plate ◽  
P Wave ◽  
Propagation Problem ◽  
Image Method ◽  
Sh Wave ◽  
Transient Wave ◽  
Wave Propagation Problem ◽  
Transient Wave Propagation

We consider the transient wave propagation problem of linear, isotropic and elastic plate applied SH impact loading on the surface. Analytical solution of half-space obtained by the inverse Fourier-Laplace double transform using Cagniard-De Hoop method. The wave propagation problem of plate was considered by using a half-space exact solution and reflect wave from the boundary of plate are expressed using the image method. Some numerical results of stress and displacement components are presented. The mathematical technique appear in the basic problem can apply to the transient P wave propagation and more advanced problems.

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

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