Estimation of Depth and Yield of Underwater Explosions From First and Second Bubble-Oscillation Periods

In this communication, a method is described for estimating the order of magnitude of energy yield and detonation depth for underwater explosions, based on the acoustical signals radiated. The method determines the ratio of the periods of the first two oscillations made by the gas bubble formed by an explosion, with bubble-oscillation periods being extracted from the cepstra of signals recorded on hydrophones. The results of laboratory studies, taken from the literature H. G. Snay and R. V Tipson, “Charts for the parameters of migrating explosion bubbles,” Tech. Rep., NOLTR 62–184 (1963)], are used to convert this ratio into a measure of the maximum bubble radius achieved during the first oscillation, expressed as a fraction of the detonation depth. This fraction, combined with the period of the first oscillation, allows detonation depth and explosion energy yield to be estimated on an order-of-magnitude basis. The method is applied to signals gathered in the Pacific Ocean, at ranges of thousands of kilometers from a series of chemical explosions. Reported values of detonation depths and explosion yields are shown to agree with the order-of-magnitude estimates derived using the method. The method is shown to have a bias towards underestimating explosion energy yield. It is hypothesized that this bias results from the different scales of the at-sea explosions and the laboratory measurements on which the estimation method is based. The uncertainty associated with the method's estimation of charge yield is comparable with those of seismic methods for the estimation of energy yields of underground nuclear tests.