Abstract
Finiteamplitude (nonlinear) sound propagation effects in seawater may cause measurement errors in fish and zooplankton abundance estimation and species identification for accessible echo sounder transmit electrical power levels and operating frequencies of about 100 kHz and higher. A sufficiently validated framework to quantify, control, and compensate for such errors in these applications is not available. The conventional power budget equations in fisheries acoustics are valid for smallamplitude signals only. The study aims to fill this “gap”. The conventional theory is generalized to account for finiteamplitude incident sound propagation, arbitrary electrical termination, and the range of electrical and acoustical echo sounder parameters. Equations for use in calibration and oceanic surveying are derived in terms of the backscattering cross section,, and the volume backscattering coefficient,. The “finiteamplitude terms” in these expressions can—for relevant transmit electrical power levels of relevant echo sounders—be measured in controlled tank experiments. Alternatively, they can be calculated using numerical models. The resulting equations enable estimation of finiteamplitude measurement errors in these applications; development of recommended upper limits for echo sounder power levels; controlled reduction of finiteamplitude errors in calibration and surveying; and development of correction factors for survey data already subjected to such measurement errors.
Highlights
Small-amplitude sound propagation has been an underlying assumption from the emergence of fishery research echo sounders in the 1930s until recently
Since dV contains a multitude of objects, this assumption corresponds to assuming a uniform distribution of the scattering objects within Vp
For a sufficiently small amplitude of the transmitted field so that the sound propagation is governed by the Equation (12); Cni linearized (r) defined set by of acoustic field equations, Pni (r, 0, 0) reduces to Pi(r, 0, 0), given by Equation (13) reduces to 1; Bni (r, θ, φ) defined by Equation (8) reduces to Bi(θ, φ), given by Equation (11); and Pni (r, θ, φ) defined by Equation (5) reduces to Pi(r, θ, φ), given by Equation (10)
Summary
Acoustic methods for estimating fish stock abundance have been in regular use for several decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], and constitute a key element in national and international regulations of marine resources, such as fish, zooplankton, and krill. In current scientific echo sounders, sv is calculated from time integration of the squared transmitted and received voltage signals, measured at the transducer’s electrical terminals (“echo integration”) [2,4,6,7,8,9,11,21,22,23,24], using a power budget equation accounting for multiple-target (volume) backscattering [11,20,21,22,23,24,25,26,27,28]. Equations (1)–(3) constitute the generic fundament for abundance estimation, species identification, and target classification in modern fisheries acoustics, serving as the basis for at-sea echo sounder calibration and survey operation [28,29,30]. These inconsistency issues have, been resolved [23,24], and Equations (1)–(3) have been shown to be valid under common assumptions being used in fisheries acoustics (cf. Section 4.2) for specific conditions of electrical termination and electrical impedances at reception [20,22,23,24] (cf. Section 4.1.1)
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