In many types of seismological and engineering problems, it is necessary to perform a surface integral involving a Green's function having either a source or receiver point on the surface. For far-field terms of the Green's function, it is well known that the surface integral can be reduced to a line integral, yielding a considerable computational advantage. In this work we show that a similar transformation to a line integral can be made for the near-field terms when the Green's function is for a uniform whole space. The necessary condition is that the various terms in the Green's function can be transformed into sums of nondispersive pulses. We accomplish this for near-field terms in a whole space by repeatedly time-differentiating the terms.

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