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An analytic model of Rayleigh waves transference in a fluid containing inhomogeneity as a circular function of depth


The primary purpose of this paper is to examine the role of initial stress, magnetic field, coefficient of heat transfer, rotation, and inhomogeneity parameter on the Rayleigh wave propagation. The present investigation studies the propagation behaviour of Rayleigh surface waves in a liquid medium lying over an orthotropic rotating magneto-thermo-elastic medium under gravity and initial stress. The displacement in the two mediums has been found in the form of Mathieu-even and Mathieu-odd functions. The frequency equation has been achieved analytically with the help of these displacements and intrinsic boundary conditions. Numerical calculations and discussions have been performed with the use of a graphical presentation. It has been observed that the inhomogeneity parameter, initial stress, and the coefficient of heat transfer affect the wave velocity to a great extent, while the magnetic field and rotation produce a slight change in the velocity. The study may help in forecasting geophysical parameters at greater depth through signal processing and seismic data modelling.

Resarch highlights

  • Study of the dynamics of Rayleigh wave dispersion in a liquid medium.

  • Influence of initial stress, magnetic field, and rotation on Rayleigh surface waves.

  • Impact of heat-transfer, gravity, and inhomogeneity on velocity.

  • Initial stress and inhomogeneity affect mostly as compared to the rest.

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Authors extend their sincere thanks to SERB-DST, New Delhi, for providing financial support under the Early Career Research Award with Ref. No. ECR/2017/001185.

Author information




SKV conceived this research and designed the geometry of the problem; TRP and SKV participated in solving the equations and deriving the expression of phase velocity; TRP and RK performed numerical calculation and developing graphical illustrations; SKV and TRP wrote the paper and participated in the revisions of it. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Tapas Ranjan Panigrahi.

Additional information

Communicated by Anand Joshi

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Panigrahi, T.R., Vishwakarma, S.K. & Kaur, R. An analytic model of Rayleigh waves transference in a fluid containing inhomogeneity as a circular function of depth. J Earth Syst Sci 130, 216 (2021).

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  • Initial stress
  • Rayleigh wave
  • gravity field
  • orthotropic
  • magneto-thermo-elastic