A comparative analysis (real-time data and theoretical results) for propagation of SH waves in a viscoelastic model influenced by a point source

Abstract

The propagation of SH waves in a heterogeneous viscoelastic layer lying over a heterogeneous viscoelastic half space from a point source is examined analytically. The significance of the heterogeneity of hyperbolic and exponential variations associated with rigidity, viscosity, and density is investigated mathematically. A dispersion equation and displacement components are computed in a compact form, considering the case that displacement and stress are continuous at the interface and stress vanishes on a free surface. The acquired dispersion equation signifies the relation between phase velocity and dimensionless wavenumber. The dispersion equation is highly influenced by heterogeneous parameters of both the layer and the half space. The dispersion equation is reduced to the classical equation of the Love wave after eliminating all the heterogeneous parameters, in agreement with pre-established results. The analysis uses the technique of Fourier transformation and Green’s function. The wavenumber is supposed to be complex, as the frequency is fixed in the viscoelastic model. Graphs are presented to demonstrate the effect of heterogeneous parameters on phase and damping velocity with respect to wavenumber.

Keywords

Viscoelastic Point source SH wave Green’s function Fourier transformation

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References

Chattopadhyay

Gupta

Singh

et al. Effect of point source, self reinforcement and heterogeneity on the propagation of magnetoelastic shear waves. Appl Math 2011; 2(3): 271–282.

Kundu

Gupta

Vaishnav

PK.

Propagation of Love waves in a heterogeneous medium over an inhomogeneous half-space under the effect of point source. J Vib Control 2016; 22(5): 1380–1391.

Chattopadhyay

Gupta

Kumari

et al. Effect of point source and heterogeneity on the propagation of SH waves in a viscoelastic layer over a viscoelastic half-space. Acta Geophys 2012; 60(1): 119–139.

Robertson

JOA

Blanch

Symes

WW.

Viscoelastic finite difference modeling. Geophysics 1994; 59(9): 1444–1456.

Kumari

Sharma

VK.

Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half-space. Acta Mech 2014; 225(6): 1673–1684.

Kristek

Moczo

Seismic wave propagation in viscoelastic media with material discontinuities: a 3D fourth order staggered grid finite difference modeling. Bull Seismol Soc Am 2003; 93(5): 2273–2280.

Sethi

Sharma

Propagation of SH wave in a double non-homogeneous crustal layers of finite depth lying over an homogeneous half-space. Lat Am J Solids Struct 2016; 13(14): 2628–2642.

Chatterjee

Dhua

Chattopadhyay

Propagation of shear waves in a viscoelastic heterogeneous layer overlying an initially stressed half-space. J Phys Conf Ser 2015; 662: 012001.

Zhu

Guo

Propagation of seismic waves in a viscoelastic medium and the effect of topography. Acta Seismol Sin 1992; 5(3): 493–501.

10.

Dhemaied

Rejiba

Camerlynck

Seismic wave propagation modeling in viscoelastic media using the auxiliary differential equation method. Bull Seismol Soc Am 2011; 10(1): 413–420.

11.

Carcione

Kosloff

Wave propagation simulation in a linear viscoelastic medium. Geophys J Int 1988; 95(3): 597–611.

12.

Brennan

Smylie

DE.

Linear viscoelasticity and dispersion in seismic wave propagation. Rev Geophys 1981; 19(2): 233–246.

13.

Carcione

JM.

Seismic modeling in viscoelastic media. Geophysics 1993; 58(1): 110–120.

14.

Bullen

KE.

An introduction to the theory of seismology. Cambridge: Cambridge University Press, 1963.

15.

Birch

The Earth’s mantle. Eos 1954; 35(1): 79–85.

16.

Kundu

Prasad

Gupta

et al. Propagation of torsional surface wave in an isotropic porous medium over a dry sandy half space. Int J Geomech 2016; 16(2): 04015050.

17.

Gubbins

Seismology and plate tectonics. Cambridge: Cambridge University Press, 1990.

18.

Caloi

Comportement des ondes de Rayleigh dans un milieu firmoélastique indéfini. Publ Bur Centr Seismol Int A 1950; 17: 89–108.

19.

Vavryčuk

Velocity, attenuation and quality factor in anisotropic viscoelastic media: a perturbation approach. Geophysics 2008; 73(5): 63–73.

20.

Pavlović

Veličković

ZS.

Measurement of the seismic waves propagation velocity in the real medium. FU Phys Chem Tech 1998; 1(5): 63–73.