This preliminary theoretical study is basically concerned with the estimation of the depth of an explosive source from a knowledge of the radiated Rayleigh wave. Details are given of the dependence of the amplitude spectrum on the explosive yield, depth of burial, horizontal range, and the elastic parameters of the medium. It is assumed that the medium is a homogeneous and isotropic half space which, as far as the Rayleigh wave is concerned, possesses a mechanical quality factor, or Q, which is independent of frequency. Furthermore, it is assumed that the explosive shot has been effectively decoupled from the medium by locating it within a cavity of appropriate size. It is shown that changes in either shot depth or Q can produce an identical change in the Rayleigh wave spectrum. Hence a lack of knowledge of Q limits the accuracy with which source depth may be estimated. An additional inaccuracy may result from the ambient ground motion preventing the recovery of the Rayleigh wave spectrum. For this reason estimates are given of the theoretically anticipated Rayleigh signal-to-noise ratio per kiloton of explosive in a seismically quiet location. It is emphasized that the study is preliminary in nature. To be of significant practical use it is believed that the theory must be extended to take into account the effect of surface layering of the medium.