The dispersion of Rayleigh waves in orthotropic layered half-space using matrix method

In this paper, the secular equation of Rayleigh surface waves propagating in an orthotropic layered half-space is derived by the matrix method. All the layers and the half-space are assumed to have identical principle axes. The explicit form of the matrizant for each layer is obtained by the Sylvester's theorem. The derived secular equation takes only real values and depends only on the dimensionless variables and dimensionless material parameters. Hence, it is convenient in numerical calculation.

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Fast programs for layered half-space problems

Bulletin of the Seismological Society of America ◽

10.1785/bssa0570061299 ◽

1967 ◽

Vol 57 (6) ◽

pp. 1299-1315

Author(s):

M. J. Randall

Keyword(s):

Half Space ◽

Matrix Method ◽

Transfer Functions ◽

Synthetic Seismograms ◽

Time Function ◽

Source Time Function ◽

Fast Computer ◽

The Matrix ◽

Crustal Reflection ◽

Layered Half Space

Abstract Knopoff's matrix method for the solution of P-SV problems has been somewhat simplified and modified to take account of oceanic structures. Advantage has been taken of a method of separating the frequency-dependent operations from the matrix multiplications to obtain very fast computer programs for calculating Rayleigh dispersion, crustal reflection functions, and crustal transfer functions. Applications include Rayleigh dispersion inversion, QitR, inversion, crustal investigations using pP, crustal transfer corrections to amplitude observations, and the construction of synthetic seismograms for investigation of the source time-function.

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On a technique for deriving explicit transfer matrices of orthotropic layers

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/37/4/6534 ◽

2015 ◽

Vol 37 (4) ◽

pp. 303-315 ◽

Cited By ~ 1

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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The algorithm of dispersion function of Rayleigh waves' in porous layered half-space

Proceedings of the 2014 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications ◽

10.1109/spawda.2014.6998593 ◽

2014 ◽

Author(s):

Shou-guo Yan ◽

Fu-li Xie ◽

Bi-xing Zhang

Keyword(s):

Half Space ◽

Rayleigh Waves ◽

Dispersion Function ◽

Layered Half Space

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Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

Engineering Computations ◽

10.1108/ec-04-2020-0231 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Shishir Gupta ◽

Rishi Dwivedi ◽

Smita Smita ◽

Rachaita Dutta

Keyword(s):

Wave Propagation ◽

Surface Wave ◽

Rayleigh Wave ◽

Penetration Depth ◽

Dispersion Equation ◽

Half Space ◽

Rayleigh Waves ◽

Secular Equation ◽

Rayleigh Surface Wave ◽

Content Type

Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

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