Transient plane-wave transformation for the point-source seismogram

The point-source seismogram for a horizontally stratified medium needs--contrary to a generally accepted belief--only to be decomposed into a finite continuous spectrum of plane wave seismograms in order to guarantee its exact recovery from the spectrum of plane wave seismograms. In this short note, we present some new and updated forward and inverse transformation formulas with which exact decomposition and composition of a point-source seismogram is achieved in the time domain. The new transformation formulas result from combining certain recently observed fundamental properties of point-source seismograms with well-known formulas of the existing theory of plane wave decomposition (Mueller, 1971; Chapman, 1980; Phinney et al., 1981. The theory of plane-wave decomposition of point-source seismograms is now well established in seismic exploration. It is associated with such concepts as the Fourier-Bessel transform, the Radon transform, backprojection, and slant-stacking.