Power-budget and echo-integrator equations for fish abundance estimation

摘要

For abundance estimation and species identification on fisheries acoustic surveys, control with temperature andfinite amplitude effects in the sea demands the calibration factor C of the conventional echo-integrator equationto be fully known in terms of the sonar system’s electrical and acoustical parameters. As no such expression isavailable from earlier literature, the theoretical basis for the power budget and echo-integrator equations isrevisited. The objective is to provide (a) a derivation of these equations for integration in a more completefunctional relationship for abundance measurement, including an expression for the calibration factor C; (b) toaccount for electrical termination; (c) to formulate these expressions in terms of voltage signal echo integrationprocessing; and (d) thereby generalize the Clay-Medwin formulations based on echo integration of “in-water”sound pressure signals, to account for the transducer and electronics components of the echosounder system.Under conditions of small-amplitude (linear) sound propagation, electroacoustic power budget equations arederived for the backscattering cross section in single-target backscattering, used in echosounder calibration; andthe volume backscattering coefficient for multiple-target backscattering, used in oceanic surveys. On this basis amore complete echo-integrator equation is derived for two operational cases, “short-ping-and-long-gate”, and“long-ping-and-short-gate”. The results are consistent with and extend previous work in this area.