Equations describing finite-amplitude effects in acoustic fish abundance estimation

Abstract

Species identification of fish and abundance estimation of zooplankton employ frequencies typically in the range of 20–400 kHz. Estimates are based on measurement of (a) the single-target backscattering cross section, σbs, used in echo sounder calibration and fish target strength measurements; and (b) the volume backscattering coefficient, sv, used in oceanic surveying. The power budget equations used today for σbs and sv pre-assume small-amplitude signals (i.e., linear sound propagation). For operating frequencies about 100 kHz and higher, finite-amplitude (nonlinear) sound propagation effects in seawater may cause measurements errors at accessible echo sounder transmit power levels. In the present work, power budget equations are derived for σbs and sv that account for finite-amplitude sound propagation effects. The expressions derived can be used to establish upper limits for echo sounder transmit power levels, in order to reduce finite-amplitude errors in calibration and surveying. They can alternatively be used to develop correction factors for calibration and/or survey data already subjected to finite-amplitude errors. The expressions derived are fully consistent with the small-signal expressions used in fisheries acoustics today.