The complete far–field asymptotic description of a point source acting on a transversely isotropic half–space

2001 ◽  
Vol 457 (2015) ◽  
pp. 2675-2698 ◽  
Author(s):  
Dmitri Gridin ◽  
Larissa Ju. Fradkin
Keyword(s):  
Point Source ◽  
Half Space ◽  
Transversely Isotropic ◽  
Far Field ◽  
Asymptotic Description

Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source

2018 ◽  
Vol 29 (11) ◽  
pp. 2508-2521 ◽  
Author(s):  
Parvez Alam ◽  
Santimoy Kundu ◽  
Shishir Gupta
Keyword(s):  
Point Source ◽  
Half Space ◽  
Hydrostatic Stress ◽  
Finite Thickness ◽  
Transversely Isotropic ◽  
Function Technique ◽  
Isotropic Layer ◽  
Numerical Examples ◽  
Type Wave ◽  
Transversely Isotropic Layer

Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool to calculate the interior deformations of the model; consequently, we obtain a closed-form dispersion relation for the wave. Six numerical examples for the transversely isotropic layer, namely, beryl, magnesium, cadmium, zinc, cobalt, and simply isotropic, have been considered. The role of magneto-elastic coupling parameter, hydrostatic stress, inhomogeneity, the order of the depth variation in inhomogeneity function, and different examples of the layer on the propagation of Love-type wave has been observed by numerical examples and graphical demonstrations.

Exact Rayleigh-Wave Solution from a Point Source in Homogeneous Elastic Half-Space

2020 ◽  
Vol 110 (2) ◽  
pp. 783-792
Author(s):  
Jie Zhou ◽  
Haiming Zhang
Keyword(s):  
Point Source ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Elastic Half Space ◽  
Far Field ◽  
Residue Theorem ◽  
Geometrical Spreading ◽  
Analytical Expressions

ABSTRACT A Rayleigh wave, often the most visible component in the far-field seismograms, is an important type of seismic-wave motion associated with the Earth’s surface. In this study, we explore some of the general properties of the Rayleigh wave in a homogeneous elastic half-space. Starting from the displacement expressed in the form of a wavenumber integral in the frequency domain, we extract the contribution from the pole in the complex wavenumber plane to obtain the excitation formulae of the Rayleigh wave by the residue theorem for complex integrals. Numerical results are compared with the full wavefield solutions to validate our solutions. By examining the analytical expressions obtained, we explore some basic properties of Rayleigh waves such as the particle motion and geometrical spreading. We also demonstrate that these properties of the Rayleigh wave excited by a point source are slightly different from but mostly consistent with the well-known classical properties of plane Rayleigh waves.

Vertical and horizontal vibrations of a rigid disc on a multilayered transversely isotropic half-space

2014 ◽  
Vol 61-62 ◽  
pp. 135-139 ◽  
Author(s):  
Morteza Eskandari-Ghadi ◽  
Seyed Masoud Nabizadeh ◽  
Azizollah Ardeshir-Behrestaghi
Keyword(s):  
Half Space ◽  
Transversely Isotropic ◽  
Rigid Disc
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