A matrix basis formulation is introduced to represent the 3 x 3 dyadic Greens functions in the frequency domain for the Maxwells equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwells Greens functions into independent TE and TM components, each satisfying a Helmholtz equation, and decompose the elastic wave Greens 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.
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