Dynamic Green's functions for layered media by using 3 dimensional Cartesian coordinates and Fourier transform

Abstract

This paper presents the dynamic Green's functions by the use of the stiffness matrix method for layered elastic half space in Cartesian coordinates. From these Green's functions in Cartesian coordinates, the well known Green's functions in cylindrical coordinates are derived. The presented Green's functions in Cartesian coordinates are represented by the two fold Fourier integral, and then the 2 Dimensional Fast Fourier Transform (2DFFT) can be effectively used to calculate the dynamic Green's functions. To verify numerically the validity of the presented Green's functions in Cartesian coordinates, the numerical examples of comparison with the well known dynamic Green's functions of elastic half space in cylindrical coordinates are shown.