Statistical Properties of ∫p2dt for Pulsed CW Reflected from a Rough Sea Surface

Abstract

Experimental work of M. V. Brown and J. Ricard has shown that, when a succession of “monochromatic” pings of duration T are reflected from a rough ocean surface, the statistical character of the resulting aggregate, ∫0Tp2dt=E, depends on frequency, sea state, and source-receiver range. An approximate theory designed to account for principal features of these experiments has been constructed on the basis of some rather crude assumptions concerning the physics of the reflection process and the statistics of the effective wave height, as sampled by successive pings. Analytical and numerical results are presented, showing the effect of the relevant physical variables on the probability density p(E) and the coefficient of variation (E−E)rmsĒ−1. The validity of the assumptions used in the theoretical derivation is examined in light of the agreement between theory and experiment. [Columbia University, Hudson Laboratories Informal Documentation No. 7. This work was supported by the Office of Naval Research.]