Three-Dimensional Green's Function for a Layered Isotropic Half-space

A numerical approach to calculate the Green's function for a layered half space is presented. It is based on the precise integration method (PIM), which is an efficient and accurate numerical method for the solution of one order ordinary differential equations. In the numerical implementation, the layered half space is divided into numerous mini-layers; and the dual vector form of the wave motion equation is introduced to combine two adjacent mini-layers/layers. The advantages of the proposed algorithm are: (a) it overcomes the exponent overflow generally encountered with employing the transfer matrix method; (b) it avoids solving the intractable transcendental functions in the stiffness matrix method and the huge matrix calculation in the thin layer method; (c) it imposes no limit to the thickness of layered strata and ensures convergence at high-frequency range. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)