Artificial boundary conditions (ArBC), defined as Robin boundary conditions (RBC) positioned at a complex space coordinate, are introduced in order to obtain pertinent approximations for the Green's functions in grounded layered media. These artificial boundary conditions include perfectly matched layers (PML) backed by perfectly electric (PEC) or magnetic conductors (PMC). Since weighted sums of Green's functions are again Green's functions, a weighted mixture of ArBC Green's functions of the PML-PEC and PML-PMC type can be utilized to approximate a given Green's function. The advantage of the approach is that it yields a comprehensive eigenexpansion for the Green's function at hand. An example illustrates the goodness of fit between the approximate Green's function and the Green's function for the uniform halfspace.