A Quantitative Evaluation of Seismic Signals at Teleseismic Distances—I Radiation from Point Sources

Summary The aim of the series of papers to be published under the above title is to follow up and improve Carpenter's (1966) attempt to construct realistic pulse shapes for teleseismic body waves from underground explosions. The present work deals with both explosions and shallow earthquakes and with the radiation of surface waves as well as body waves. The extension of Carpenter's theory to take crustal layering more accurately into account involves the matrix theory first introduced by Thomson (1950) and developed by Haskell. We shall use the notation of Haskell's (1964) paper in the following analysis and the initial theoretical work is concerned with some of the groundwork and one or two results which have not been covered by Haskell in his series of papers (1953, 1962, 1964). A point source can be represented either as a system of forces or as a discontinuity in the displacement or stress or their derivatives across an element of surface. We show here that a general source of either type is equivalent in the generation of elastic radiation to a discontinuity across a horizontal plane in the displacement and the stress acting on the plane. This means that any point source can be put into a form suitable for computations based on the Thomson‐Haskell theory. The theory is applied to the construction of theoretical models of earthquake and explosive sources. Some of the more realistic models so far proposed are given in the later section of the paper.