[en] The effects of variation in source and medium properties upon near- and far-field spectra for elastic waves are examined theoretically by considering spherical wave propagation in unbounded elastic media. This type of analysis, although idealized, provides insight into the relative effects of the various source and medium parameters on both tamped and decoupled explosions. It also provides a basis for interpreting both field and laboratory experimental data obtained during spherical wave propagation in real media. In this paper I attempt to unify the work that has been done on spherical wave propagation in elastic media. I present the results in nondimensional forms, in hopes that others may find these forms of the solutions useful and some of the conclusions, based upon my parameter studies, enlightening. Also included is a discussion of some of the limitations of the theory and examples of applications of the spherical wave propagation theory in real media