ONE-DIMENSIONAL WAVE-PROPAGATION IN A HIGHLY DISCONTINUOUS MEDIUM

A pulse propagates through a one-dimensional medium consisting of a large number N of homogeneous layers. As it propagates the pulse, which consists of multiply scattered energy, is broadened and slightly delayed compared with the first arrival, which travels at the characteristic speed. R. F. O'Doherty and N. A. Anstey first studied this phenomenon in 1971 and gave an incomplete theory predicting the pulse shape and spectrum essentially by summing a diagram. We corroborate their results with a rigorous theory giving the limiting pulse shape as N approaches infinity while the reflection coefficients go to zero like 1/ ROOT N. This work is novel in that: (a) a rigorous theory is given, (b) the development is in the time domain, and (c) probabilistic concepts, such as ensemble averages, are not used; spatial averages suffice.