G-Type Seismic Wave in Magnetoelastic Monoclinic Layer

Amares Chattopadhyay, Shishir Gupta, Abhishek K. Singh, Sanjeev A. Sahu

.

DOI: 10.4236/am.2011.22017                

Abstract

This paper deals with the study of propagation of G type waves along the plane surface at the interface of two different types of media. The upper medium is taken as monoclinic magnetoelastic layer whereas the lower half-space is inhomogeneous isotropic. Dispersion equation and condition for maximum energy flow near the surface are obtained in compact form. The dispersion equation is in assertion with the classical Love-type wave equation for the isotropic case. Effect of magnetic field and inhomogeneity on phase velocity and variation of group velocity with scaled wave number has been depicted by means of graphs. It is observed that inhomogenetity decreases phase velocity and the magnetic field has the favouring effect. A comparative study for the case of isotropic layer and monoclinic layer over the same isotropic inhomogeneous half space has been made through graphs.

Keywords

G-Waves, Magnetoelastic, Dispersion Equation, Monoclinic, Transform Technique

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	B. Gutenberg, “Wave Velocities at Depths between 50 and 600 Kilometers,” Bulletin of the Seismological Society of America, Vol. 43, 1953, pp. 223-232.
[2]	B. Gutenberg, “Effects of Low-Velocity Layers,” Pure and Applied Geophysics, Vol. 29, 1954, pp. 1-10. doi:10.1007/BF01988601
[3]	H. Benioff, “Long Waves Observed in the Kamchatka Earthquake of November 4, 1952,” Journal of Geophysical Research, Vol. 63, No. 3, 1958, pp. 589-593. doi:10. 1029/JZ063i003p00589
[4]	H. Benioff and F. Press, “Progress Report on Long Period Seismographs,” Geophysical Journal of the Royal Astronomical Society, Vol. 1, No. 3, 1958, pp. 208-215.
[5]	F. Press, “Some Implications on Mantle and Crustal Structure from G-Waves and Love-Waves,” Journal of Geophysical Research, Vol. 64, No. 5, 1959, pp. 565-568. doi:10.1029/JZ064i005p00565
[6]	M. Bath and A. L. Arroyo, “Attenuation and Dispersion of G-Waves,” Journal of Geophysical Research, Vol. 67, No. 5, 1962, pp. 1933-1942. doi:10.1029/JZ067i005p01 933
[7]	K. Aki, “Generation and Propagation of G-Waves from the Niigata Earthquake of June 16, 1964. Part 2. Estimation of Earthquake Moment, Released Energy, and Stress-Strain Drop from the G-Wave Spectrum,” Bulletin of earthquake Research Institute, Tokyo University, Vol. 44, 1966, pp. 73-88.
[8]	H. Jeffreys, “The Earth," 4th Edition, Cambridge University Press, Cambridge, 1959.
[9]	J. Bhattacharya, “On Short Period Signals Obtained from Explosions within the Earth,” Pure and Applied Geophysics, Vol. 55, 1963, pp. 63-71. doi:10.1007/BF0201 1216
[10]	A. Chattopadhyay, “On the Generation of G Type Seismic Waves,” Acta Geophysical Polonica, Vol. 26, No. 2, 1978, pp. 131-138.
[11]	N. A. Haskell, “Radiation Pattern of Surface Waves from Point Sources in Multi-Layered Medium,” Bulletin of the Seismological Society of America, Vol. 54, No. 1, 1964, pp. 377-393.
[12]	A. K. Mal, “On the Generation of G-Waves,” Gerlands Beitrage zur Geophysik, Vol. 72, No. 2, 1962, pp. 82-88.
[13]	A. Chattopadhyay and A. Keshri, “Generation of G-Type Seismic Waves,” Acta Geophysica Polonica, Vol. 41, No. 1, 1993, pp. 27-35.
[14]	A. Chattopadhyay, S. Gupta, V. K. Sharma and Pato Kumari, “Dispersion of G Type Seismic Waves in Low Velocity Layer,” International Journal of Applied Engineering Research, Vol. 4, No. 3, 2009, pp. 467-479.
[15]	K. G. Valeev, “On Hill’s Method in the Theory of Linear Differential Equations with Periodic Coefficients,” Journal of Applied Mathematics and Mechanics, Vol. 24, 1960, pp. 1493-1505. doi:10.1016/0021-8928(60)90003-4
[16]	H. F. Tiersten, “Linear Piezoelectric Plate Vibrations,” Plenum Press, New York, 1969.
[17]	D. Gubbins, “Seismology and Plate Tectonics,” Cambridge University Press, Cambridge, 1990