Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Czasopismo : Acta Geophysica
Tytuł artykułu : Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Autorzy :
Yamasaki, K.
Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, Japan, yk2000@kobe-u.ac.jp,
Teisseyre, R.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, rt@igf.edu.pl,
Li, C.
School of Computer Engineering and Science, Shanghai University, Shanghai, China, jyyin@staff.shu.edu.cn,
Majdański, M.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, mmajd@igf.edu.pl,
Trojanowski, J.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, jtroj@igf.edu.pl,
Öztürk, S.
Gümüşhane University, Department of Geophysics, Gümüşhane, Turkey, serkanozturk@gumushane.edu.tr,
Chattopadhyay, A.
Department of Applied Mathematics, Indian School of Mines, Dhanbad, India, amares.c@gmail.com,
Abstrakty : The present paper is concerned with the propagation of shear waves in a homogeneous viscoelastic isotropic layer lying over a semi-infinite heterogeneous viscoelastic isotropic half-space due to point source. The inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of shear waves has been obtained using Green's function technique. The dimensionless angular frequency has been plotted against dimensionless wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves. graphical user interface (GUI) software in MATLAB has been developed to show the effect of various inhomogeneity parameters on angular frequency. The topic can be of interest for geophysical applications in propagation of shear waves on the Earth’s crust.

Słowa kluczowe : shear waves, heterogeneity, point source, Green’s function, viscoelastic medium, GUI in Matlab,
Wydawnictwo : Instytut Geofizyki PAN
Rocznik : 2012
Numer : Vol. 60, no. 1
Strony : 119 – 139
Bibliografia : Aki, K., and P.G. Richards (1980), Quantitative Seismology: Theory and Methods 2 Vol., W.H. Freeman, San Francisco.
Awojobi, A.O., and O.A. Sobayo (1977), Ground vibrations due to seismic detonation of a buried source, Earthq. Eng. Struct. Dyn. 5, 2, 131-143.
Borcherdt, R.D. (1973), Rayleigh-type surface wave on a linear viscoelastic halfspace, J. Acoust. Soc. Am. 54, 6, 1651-1653.
Brekhovskikh, L.M., and O.A. Godin (1998), Acoustics of Layered Media, Springer-Verlag, Berlin.
Bullen, K.E. (1940), The problem of the Earth’s density variation, Bull. Seismol. Soc. Am. 30, 3, 235-250.
Caloi, P. (1950), Comportement des ondes de Rayleigh dans un milieu firmoélastique indéfini, Publ. Bur. Centr. Seismol. Int. A 17, 89-108 (in French).
Chattopadhyay, A. (1978), Propagation of SH waves in a visco-elastic medium due to irregularity in the crustal layer, Bull. Calcutta Math. Soc. 70, 303-316.
Chattopadhyay, A., and B.K. Kar (1981), Love waves due to a point source in an isotropic elastic medium under initial stress, Int. J. Non-Lin. Mech. 16, 3-4, 247-258.
Chattopadhyay, A., and A.K. Pal (1984), Dispersion curves of Love waves from a point source in heterogeneous medium, Acta Geophys. Pol. 32, 3, 323-332.
Chattopadhyay, A., M. Chakraborty, and V. Kushwaha (1986), On the dispersion equation of Love waves in a porous layer, Acta Mechanica 58, 3-4, 125-136.
Chattopadhyay, A., S. Gupta, V.K. Sharma, and P. Kumari (2010), Propagation of shear waves in viscoelastic medium at irregular boundaries, Acta Geophys. 58, 2, 195-214.
Cooper, H.F. (1967), Reflection and transmission of oblique plane waves at a plane interface between viscoelastic media, J. Acoust. Soc. Am. 42, 5, 1064-1069.
Covert, E.D. (1958), Approximate calculation of Green’s function for built-up bodies, J. Math. Phys. 37, 58-65.
Červený, V. (2004), Inhomogeneous harmonic plane waves in viscoelastic anisotropic media, Stud. Geophys. Geod. 48, 1, 167-186.
De Hoop, A.T. (1995), Handbook of Radiation and Scattering of Waves: Acoustic Waves in Fluids, Elastic Waves in Solids, Electromagnetic Waves, Academic Press, London.
Deresiewich, H. (1962), A note on Love waves in a homogeneous crust overlying an inhomogeneous substratum, Bull. Seismol. Soc. Am. 52, 3, 639-645.
Ewing, W.M., W.S. Jardetzky, and F. Press (1957), Elastic Waves in Layered Media, McGraw-Hill, NewYork.
Ghosh, M.L. (1970), Love waves due to a point source in an inhomogeneous medium, Gerlands Beitr. Geophys.79, 129-141.
Gogna, M.L., and S. Chander (1985), Reflection and transmission of SH-waves at an interface between anisotropic inhomogeneous elastic and viscoelastic halfspaces, Acta Geophys. Pol. 33, 4, 357-375.
Gubbins, D. (1990), Seismology and Plate Tectonics, Cambridge University Press, Cambridge.
Kaushik, V.P., and S.D. Chopra (1983), Reflection and transmission of general plane SH-waves at the plane interface between two heterogeneous and homogeneous viscoelastic media, Geophys. Res. Bull. 20, 1-20.
Manolis, G.D., and A.C. Bagtzoglou (1992), A numerical comparative study of wave propagation in inhomogeneous and random media, Comput. Mech. 10, 6, 397-413.
Manolis, G.D., and R.P. Shaw (1995), Wave motions in stochastic heterogeneous media: a Green’s function approach, Eng. Anal. Bound. Elem. 15, 3, 225-234.
Manolis, G.D. and R.P. Shaw (1996), Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity—II. Applications, Soil Dyn. Earthq. Eng. 15, 2, 129-139.
Park, J., and E. Kausel (2004), Impulse response of elastic half-space in the wave number-time domain, J. Eng. Mech. ASCE, 130, 10, 1211-1222.
Romeo, M. (2003), Interfacial viscoelastic SH waves, Int. J. Solids Struct. 40, 9, 2057-2068.
Sari, C., and M. Salk (2002), Analysis of gravity anomalies with hyperbolic den sity contrast: An application to the gravity data of Western Anatolia, J. Balkan Geophys. Soc. 5, 3, 87-96.
Sato, Y. (1952), Love waves propagated upon heterogeneous medium, Bull. Earthq. Res. Inst. Univ. Tokyo 30, 1-12.
Schoenberg, M. (1971), Transmission and reflection of plane waves at an elasticviscoelastic interface, Geophys. J. Roy. Astron. Soc. 25, 1-3, 35-47.
Sezawa, K. (1935), Love waves generated from a source of a certain depth, Bull. Earthq. Res. Inst. Univ. Tokyo 13, 1-17.
Sezawa, K., and K. Kanai (1938), Damping of periodic visco-elastic waves with increase in focal distance, Bull. Earthq. Res. Inst. Univ. Tokyo 16, 3, 491-503.
Shaw, R.P., and P. Bugl (1969), Transmission of plane waves through layered linear viscoelastic media, J. Acoust. Soc. Am. 46, 3B, 649-654.
Singh, K. (1969), Love waves due to a point source in an axially symmetric heterogeneous layer between two homogeneous halfspaces, Pure Appl. Geophys. 72, 1, 35-44.
Vrettos, C. (1991), Forced anti-plane vibrations at the surface of an inhomogeneous half-space, Soil Dyn. Earthq. Eng. 10, 5, 230-235.
Vrettos, C. (1998), The Boussinesq problem for soils with bounded nonhomogeneity, Int. J. Numer. Anal. Meth. Geomech. 22, 8, 655-669.
Watanabe, K., and R.G. Payton (2002), Green’s function for SH-waves in a cylindrically monoclinic material, J. Mech. Phys. Solids 50, 11, 2425-2439.
DOI :
Cytuj : Yamasaki, K. ,Teisseyre, R. ,Li, C. ,Majdański, M. ,Trojanowski, J. ,Öztürk, S. ,Chattopadhyay, A. , Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space. Acta Geophysica Vol. 60, no. 1/2012
facebook