Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source

The focus of this contribution is to develop a transmission and reflection matrices (TRM) method for a layered porous half-space subject to a point force or a fluid point source. Applying the Hankel and the Fourier transformation, the general solutions for the displacements, stresses and pore pressure are derived from the potentials for the solid skeleton and the pore fluid as well as the governing equations of Biot's theory. The transmission and reflection matrices (TRM) for each interface are obtained by using the general solutions as well as the continuity conditions at the interface. The TRM method for the layered porous medium is developed on the basis of the transmission and reflection matrices (TRM) and the boundary conditions as well as the source terms for the point force or the fluid point source. The fundamental solutions of the point force and the point fluid source in both the frequency domain and the time domain are obtained by using the proposed TRM method. Some numerical examples are given in the paper.