Dispersion of Love wave in an isotropic layer sandwiched between orthotropic and prestressed inhomogeneous half-spaces

Abstract

An in-depth study has been carried out for the dispersion of Love waves in an isotropic elastic layer sandwiched between orthotropic and prestressed inhomogeneous elastic half-spaces. The inhomogeneities in density and rigidity of the lower half-space are space dependent and an arbitrary function of depth. Simple mathematical techniques are used to obtain dispersion relation for Love wave propagation in an isotropic layer. An extensive analysis is carried out through numerical computation to explore the effect of inhomogeneity and initial stress the lower half on the phase velocity of the Love waves. The numerical analysis of dispersion equation manifests that the phase velocity of the Love wave increases with the increase of stress parameter. The results further indicate that the inhomogeneity of the half space affect the wave velocity significantly. These results can be useful to study geophysical prospecting and understanding the cause and estimation of damage due to earthquakes.

The influence of heterogeneity and initial stress on the propagation of Love-type wave in a transversely isotropic layer subjected to rotation

“…To eliminate the arbitrary constants k 1 , k 2 , k 3 , and k 4 from equation ( 16), we have the following determinant: a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 = 0 (17) Equation ( 17) is the required equation of the Love-type wave in a heterogeneous transversely isotropic elastic layer resting over a heterogeneous a rigid foundation. This dispersion equation being a function of phase velocity, angular velocity, wave number, initial stress, rotation, and heterogeneous parameter associated with the rigidity and density of inhomogeneous layer, reveals the fact that Love-type wave propagation is greatly influenced by above-stated parameters.…”

“…This dispersion equation being a function of phase velocity, angular velocity, wave number, initial stress, rotation, and heterogeneous parameter associated with the rigidity and density of inhomogeneous layer, reveals the fact that Love-type wave propagation is greatly influenced by above-stated parameters. However, under the condition when vanish of inhomogeneity α, rotation Ω, and initial stress S 11 , equation (17) gives the dispersion equation of Love-type wave in homogeneous transversely isotropic layer resting on rigid base obtained by Gubbins 4 and in similar fashion for isotropic materials c ′ 11 = λ + 2μ, c ′ 12 = λ with the vanishing of inhomogeneity α, rotation Ω, and initial stress S 11 , equation (17) gives the dispersion equation of Love-type wave in homogeneous isotropic layer resting on a rigid base obtained by Singh et al 11 The expressions of a ij (i, j = 1, 2, 3, 4) coefficients are given in Appendix.…”

“…Baljeet 14 is to be credited for pointing out how the propagation of plane waves takes place in the case of a “dual-temperature, rotating, and thermoelastic transversely isotropic solid half-space.” In the case of an isotropically layered structure, the dispersion equations for the propagation of various types of seismic surface waves were established by Kundu et al, 15 Zhu et al, 16 and Kakar. 17 Several factors may cause the inside pressure of the Earth to vary such as gravitational pull, atmospheric pressure, overburden and process manufacturing, slow creep process, and so on (Dey and De 18 ). Thus, it has been considered that the Earth is stressed initially.…”

Case-wise analysis of Love-type wave propagation in an irregular fissured porous stratum coated by a sandy layer

“…Ahmed and Abd-Dahab (2010) worked on Love wave propagating in an orthotropic granular layer. Saroj et al (2018) and Kakar (2015) have also involved orthotropic medium in their studies. Ahmed and Abd-Dahab (2010) examined the effect of initial stress on the propagation of Love waves in an orthotropic granular layer lying over a semi-infinite granular medium.…”