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Artificial boundary conditions, which can be identified as Robin boundary conditions 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 backed by perfectly electric or magnetic conductors. As a first result, we obtain analytical expressions for the differences of Green's functions subject to different boundary conditions.doi:10.2528/pier06030401 fatcat:pdsjhwsr2vgjxbrvmuapuls3y4