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To advance the mathematical and computational treatments of mixed boundary value problems involving multilayered media, a new derivation of the fundamental Green's functions for the elastodynamic problem is presented. By virtue of a method of displacement potentials, it is shown that there is an elegant mathematical structure underlying this class of three-dimensional elastodynamic problems which warrant further attention. Constituted by proper algebraic factorizations, a set of generalizeddoi:10.1061/(asce)0733-9399(2002)128:4(449) fatcat:nhyzxce3ivcc3hcbh2ntskkot4