Abstract
Echo counting is a standard tool for the estimation of fish density and hence population. Density estimates are readily obtained using an uncalibrated, stable echo sounder with accurate time-varied gain. We extended a standard nonstochastic echo pulse counting model to include the analysis of single fish echo traces as they are obtained from the sounder chart recorder. The trace counting analysis depends strongly on the overlap in the insonified volumes between successive sounder transmissions. An equation for the nonoverlapping volume is given in terms of range, distance between transmissions, and effective beam angles. The near and far range limits of the model are given and the errors associated with the commonly used approximations to the correct model are shown. A generalization of the model considers the analysis of data from a tilted transducer. A sensitivity analysis gives a qualitative indication of the model's performance for echoes from fish with a realistic target strength distribution. Single fish echo returns are analyzed by the echo pulse and trace counting methods to illustrate the model.
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