SIMPLIFIED DYNAMIC AND STATIC GREEN-FUNCTIONS IN TRANSVERSELY ISOTROPIC MEDIA

Numerically feasible dynamic Green's function in an unbounded transver sely isotropic (TI) medium is obtained in simple dyadic form by evalua ting in general an inverse Laplacian operator involved in a previous d ynamic Green's function described by Ben-Menahem & Sena (1990). The fi nal dyadic form is close to that of the isotropic dyadic Green's funct ion, therefore, lends itself more easily to analytical and numerical m anipulations. It is expressed through three scalar quantities characte rizing the propagation of SH, P-SV, and P-SV-SH waves in a transversel y isotropic medium. The static Green's function has the same dyadic fo rm as the dynamic Green's function and the three corresponding scalar functions are derived. Using the dynamic Green's function, displacemen ts for three point sources are computed to compare with known numerica l results. The singular property of the Green's functions is addressed through the surface integral of the static function in the case of co inciding receiver and source. The singular contribution is shown to be -1/2 of the applied force when the static-stress Green's function is integrated over a half-elliptical surface. Results of this paper are p articularly suitable to wave-propagation problems involving the bounda ry-element method.