The Effect of Viscosity and Heterogeneity on Propagation of G–Type Waves

Abstract Earthquakes yield motions of massive rock layers accompanied by vibrations which travel in waves. This paper analyses the possibility of G-type wave propagation along the plane surface at the interface of two different media which is assumed to be heterogeneous and viscoelastic. The upper layer is considered to be viscoelastic and the lower half space is considered to be an initially stressed heterogeneous half space. The dispersion equation, as well as the phase and group velocities, is obtained in closed form. The dispersion equation agrees with the classical Love type wave. The effects of the nonhomogeneity of the parameters and the initial stress on the phase and group velocities are expressed by means of a graph.

[1]  B. Gutenberg.  Wave velocities at depths between 50 and 600 kilometers , 1953 .

[2]  A. Chattopadhyay,et al.  Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium , 1990 .

[3]  Keiiti Aki,et al.  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. , 1966 .

[4]  S. Vishwakarma,et al.  G-type dispersion equation under suppressed rigid boundary: analytic approach , 2016 .

[5]  Jeng-Tzong Chen,et al.  Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems , 2017 .

[6]  A. Chattopadhyay,et al.  PROPAGATION OF G TYPE SEISMIC WAVES IN VISCOELASTIC MEDIUM , 2010 .

[7]  George A. Hool,et al.  Reinforced Concrete and Masonry Structures , 2015 .

[8]  A. Singh,et al.  Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space , 2017 .

[9]  T. G. Rogers,et al.  Stress in elastic plates reinforced by fibres lying in concentric circles , 1983 .

[10]  On HILL' S method in the theory of linear differential equations with periodic coefficients , 1960 .

[11]  Keiiti Aki,et al.  Generation and Propagation of G Waves from the Niigata Earthquake of June 16, 1964 : Part 1. A statistical analysis. , 1966 .

[12]  B. Gutenberg.  Effects of low-velocity layers , 1954 .

[13]  I. Lehmann.  S and the Structure of the Upper Mantle , 1961 .

[14]  V. Keilis-Borok,et al.  Love Waves and the Structure of the Upper Mantle , 1964 .

[15]  A. K. Singh,et al.  G-type seismic waves in fibre reinforced media , 2012 .

[16]  Santimoy Kundu,et al.  Propagation of G-type seismic waves in heterogeneous layer lying over an initially stressed heterogeneous half-space , 2014, Appl. Math. Comput..