Asymmetric wave propagation in a transversely isotropic half-space in displacement potentials

Abstract With the aid of a complete representation using two displacement potentials, an efficient and accurate analytical derivation of the fundamental Green’s functions for a transversely isotropic elastic half-space subjected to an arbitrary, time-harmonic, finite, buried source is presented. The formulation includes a complete set of transformed stress-potential and displacement-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. For the numerical evaluation of the inversion integrals, a quadrature scheme which gives the necessary account of the presence of singularities including branch points and pole on the path of integration is implemented. The reliability of the proposed numerical scheme is confirmed by comparisons with existing solutions.

[1]  Horace Lamb,et al.  On the propagation of tremors over the surface of an elastic solid , 1904, Proceedings of the Royal Society of London.

[2]  R. G. Payton,et al.  Elastic Wave Propagation in Transversely Isotropic Media , 1983 .

[3]  R. Ogden,et al.  A Note on Strong Ellipticity for Transversely Isotropic Linearly Elastic Solids , 2003 .

[4]  V. Buchwald.  RAYLEIGH WAVES IN TRANSVERSELY ISOTROPIC MEDIA , 1961 .

[5]  M. Rahimian,et al.  Elastodynamic Potential Method for Transversely Isotropic Solid , 2007 .

[6]  Cristina Padovani,et al.  Strong Ellipticity of Transversely Isotropic Elasticity Tensors , 2002 .

[7]  Tsu-Wei Chou,et al.  Point Force Solution for an Infinite Transversely Isotropic Solid , 1976 .

[8]  R. J. Apsel,et al.  On the Green's functions for a layered half-space. Part II , 1983 .

[9]  D. Haojiang,et al.  The united point force solution for both isotropic and transversely isotropic media , 1997 .

[10]  F. Fedorov.  Theory of Elastic Waves in Crystals , 1968 .

[11]  R. Stoneley,et al.  The Seismological Implications of Aeolotropy in Continental Structure , 1949 .

[12]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[13]  Bojan B. Guzina,et al.  Three-Dimensional Green's Functions for a Multilayered Half-Space in Displacement Potentials , 2002 .

[14]  E. Dill,et al.  Theory of Elasticity of an Anisotropic Elastic Body , 1964 .

[15]  J. W. Brown,et al.  Complex Variables and Applications , 1985 .

[16]  M. Eskandari‐Ghadi,et al.  A Complete Solution of the Wave Equations for Transversely Isotropic Media , 2005 .

[17]  I. N. Sneddon.  The use of integral transforms , 1972 .

[18]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[19]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[20]  R.K.N.D. Rajapakse,et al.  Green's Functions for Transversely Isotropic Elastic Half Space , 1993 .

[21]  J. Synge.  Elastic Waves in Anisotropic Media , 1956 .