Remarks on Multiple Reflections

One cannot help being impressed by the wonderful arrays of seismograms depicted in Mr. Ellsworth's paper and in the prepared discussions. The regularity of the time intervals of successive impulses and the alternating sequence of the change of phase are readily adapted to a mechanism of multiple reflections. If the latter is accepted, the following questions seem to merit some consideration: (a) the energy concentration, (b) the positions of the reflecting surfaces, (c) the sharpness of the source-impulse, and (d) the velocity contrast of the adjacent media. Even if the absorption of the ground could be entirely neglected, the intensity of energy of a seismic disturbance undergoing multiple reflections would be diminished for at least two reasons. First, the energy may be spread out owing to the divergence of the pencils of rays as shown in Figure rn. This is true when the reflector is a plane. When it is a syncline or a depression as shown in Figure 1b, the spreading may be compensated by the curvature of the reflecting surface. There may even be a focusing effect if the curvature is very favorable, e.g., one optimum focusing is obtained if the surface is a sphere around the source. Secondly, the amplitude of the disturbance is decreased after each reflection as shown in Figure 2a, because a part of the energy must be transmitted. Since there is no perfect reflector of seismic waves in nature, a multiple reflecting layer can never be a conservative system. The loss depends on the transmission coefficient of the interface and cannot be compensated by any converging effect of the reflecting surface. But there might be an accumulation effect in the manner as shown in Figure 2b, if the source is not a sharp pulse, but of finite extent. In the configuration described in Mr. Ellsworth's paper, there are two regions in which multiple reflections might travel: the disturbance may be multiply reflected by the earth's surface and the upper surface of the basalt or, it may be multiply reflected by the upper and lower surfaces of the basalt bed itself, this latter being rather thin. One can, of course, decide which of these alternatives is responsible for the