On the minimum oscillatory character of spherical seismic pulses

Compressional seismic pulses, such as originate from an explosion in a shot hole, can be discussed generally without reference to the non-linear effects, such as heating, fracturing and other departures from Hooke's law, in the neighborhood of the shot. A pulse of finite length from front to back is considered in the present note. It is shown that such a pulse is not as arbitrary as the general solution of the spherical wave equation would indicate, but the dilatation must change algebraic sign at least twice within the pulse. Thus the pulse must generally be, to this minimal extent, oscillatory if the front and rear regions are to be quiet.