Dynamic Green's functions for layered half space by using 3 dimensional Cartesian coordinates / twofold Fourier transform and their verification

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. 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 results of the method of Luco and Apsel, and those of the numerical method using the FEM for a layered elastic half space are shown.