  A matrix basis formulation is introduced to represent the 3 x 3 dyadic
Green's functions in the frequency domain for the Maxwell's equations and the
elastic wave equation in layered media. The formulation can be used to
decompose the Maxwell's Green's functions into independent TE and TM
components, each satisfying a Helmholtz equation, and decompose the elastic
wave Green's function into the S-wave and the P-wave components. In addition, a
derived vector basis formulation is applied to the case for acoustic wave
sources from a non-viscous fluid layer.
