The evaluation of noise- and threshold-induced bias in the integration of single-fish echoes

The echo integration of single-fish echoes shows that characteristically the received-signal energy of single targets is small compared with the echo energy of schooled fish. The measuring error is minimized by the application of an integration threshold. The echo energy, however, is often only slightly larger than the noise and reverberation level making the determination of the optimal integration threshold difficult. During the evaluation of data from the echo-integration surveys on redfish in the Irminger Sea it was observed that the integration value of single fish increased steadily with decreasing integration threshold. There is no way to determine the integration threshold by eye as for schooled fish. The approach taken in all past publications for the estimation of the influence of the integration threshold on the integration result has been based on the computation of an equivalent beam angle. The influence of ‘‘environment noise’’ was not considered. Here a model is presented, which considers both influences on the integration result during the integration of single-fish echoes. It is assumed that the targets are distributed evenly in the observed volume and that in each pulse volume of the beam only one target is present. The starting point of the computations is the equation for signal processing implemented in the EK500. The echo signal power received is converted pixel-by-pixel into the appropriate volume-backscattering coefficients, sv and stored as echograms. These echograms are available for post-processing in the Bergen Integrator BI500. To exclude noise and reverberation from the subsequent processing a threshold was introduced. We assume that the fish echoes are always larger than the noise and reverberation. This is a very common situation and the largest part of the energy of noise and reverberation can be eliminated in this way. When a fish echo is received outside the centre of the beam it is attenuated by the beam pattern of the transducer and may therefore lie below the threshold and could be cut off. This leads to the reduction of the measured values and a measuring error. An opposite error arises when the signal crosses the threshold. In practice the signal received always consists of noise and echo signals and has more power than it should have. The measured value is larger and this is another error of the measurement process per se. The object of this paper is to calculate the influence of the threshold level on the result of measurement and to derive a practicable rule for the determination of the threshold level. The noise is modelled as a constant input power. The computations are carried out with model functions of the transducer beam and the received-echo pulse. General statements can be met by defining a signal-to-noise ratio and a signal-to-threshold ratio. The results of the theoretical investigations are applied on acoustic data obtained during redfish survey WH229 in the Irminger Sea and adjacent waters.