Rigidity and Irregularity Effect on Surface Wave Propagation in a Fluid Saturated Porous Layer

Document Type : Research Paper


1 Department of Mathematics, Chandigarh University, Gharuan, Mohali-140413, Punjab, India

2 Department of Mathematics, Chaudhary Bansi Lal University, Bhiwani Haryana, India

3 Department of Mathematics, Chaudhary Devi Lal University, Sirsa-Haryana, India



The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen that the phase velocity is strongly influenced by the wave number, the depth of the irregularity, homogeneity parameter and the rigid boundary. The dimensionless phase velocity is plotted against dimensionless wave number graphically for different size of rectangular irregularities and homogeneity parameter with the help of MATLAB graphical routines for both free and rigid boundaries for several cases. The numerical analysis of dispersion equation indicates that the phase velocity of surface waves decreases with the increase in dimensionless wave number.  The obtained results can be useful to the study of geophysical prospecting and understanding the cause and estimating of damage due to earthquakes.


[1] Love A.E.H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York.
[2] Ewing M., Jardetzky W.S., Press F., 1957, Elastic Waves in Layered Media, McGraw-Hill, New York.
[3] Chatopadhyay A.,1975, On the dispersion equation for Love wave due to irregularity in the thickness of non-homogeneous crustal layer, Acta Geophysica 23: 307-317.
[4] Gupta S., Majhi D.K., Kundu S., Vishwakarma S.K., 2013, Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space, Applied Mathematics and Mechanics 34: 249-258.
[5] Kundu S., Gupta S., Majhi D.K., 2013, Love wave propagation in porous rigid layer lying over an initially stressed half space, Applied Physics and Mathematics 3(2): 140-142.
[6] Chattaraj R., Samal S.K., Mahanti N.C., 2013, Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress, International Journal of Geomechanics 13(4): 402-408.
[7] Madan D.K., Kumar R., Sikka J.S., 2014, Love wave propagation in an irregular fluid saturated porous anisotropic layer with rigid boundary, Applied Scientific Research 10: 281-287.
[8] Kumar R., Madan D.K., Sikka J.S., 2014, Shear wave propagation in multilayered medium including an irregular fluid saturated porous stratum with rigid boundary, Advances in Mathematical Physics 2014: 163505.
[9] Kakar R., Gupta M., 2014, Love waves in an intermediate heterogeneous layer lying in between homogeneous and inhomogeneous isotropic elastic half-spaces, EJGE 19: 7165-7185.
[10] Kumari N., 2014, Reflection and transmission of longitudinal wave at micropolar viscoelastic solid/fluid saturated incompressible porous solid interface, Journal of Solid Mechanics 6(3): 240-254.
[11] Kumar R., Madan D.K., Sikka J.S., 2015, Effect of irregularity and inhomogenity on the propagation of Love waves in fluid saturated porous isotropic layer, Journal of Applied Science and Technology 20: 16-21.
[12] Kakar R., 2015, Dispersion of love wave in an isotropic layer sandwiched between orthotropic and prestressed inhomogeneous half-spaces, Latin American Journal of Solids and Structures 12: 1934-1949.
[13] Barak M.S., Kaliraman V., 2018, Propagation of elastic waves at micropolar viscoelastic solid/fluid saturated incompressible porous solid interface, International Journal of Computational Methods 15(1): 1850076(1-19).
[14] Barak M.S., Kaliraman V., 2019, Reflection and transmission of elastic waves from an imperfect boundary between micropolar elastic solid half space and fluid saturated porous solid half space, Mechanics of Advanced Materials and Structures 26: 1226-1233.
[15] Kaliraman V., Poonia R.K., 2018, Elastic wave propagation at imperfect boundary of micropolar elastic solid and fluid saturated porous solid half space, Journal of Solid Mechanics 10(3): 655-671.
[16] Kumar R., Madan D.K., Sikka J.S., 2016, Effect of rigidity and inhomogenity on the propagation of love waves in an irregular fluid saturated porous isotropic layer, International Journal of Mathematics and Computation 27: 55-70.
[17] Gubbins D., 1990, Seismology and Plate Tectonics, Cambridge University Press, Cambridge.