Determining fish number density by a statistical analysis of backscattered sound - Smith, Quinton (Department of Oceanography, 2026)
This thesis involves work done on the statistical analysis of the intensity of high frequancy sound pulses backscattered from fish shoals in order to determine the number density of fish. The abundance of fish species can be estimated from acoustic back-scattering signals without requiring knowledge of the target strength of fish nor calibration of son.ar equipment. To do the statistical analys.is a statistical model of the backscattered intensity is needed. The model is then used to analyse the sampled backscattered intensity in order to determine the fish number density. The model used in this research assumes that fish are identical and independent scatterers of sound and that they are randomly distributed in the water. A generalised model of the statistics of the backscatter from a shoal of fish is developed to answer the question of how the estimates of fish number density vary for different scatterer types and different distributions of fish. An examination is made of all assumptions underlying the statistical model with a view to extending the model still further. The model is applied to various volume distributions including the Poisson distribution and to Ricean,Rayleigh and constant amplitude scattering statistics. The model.is extended to include the non-ideal theoretical beam pattern of both circular and square transducers. An investigation of the number of statistically independent measurements needed in the statistical analysis of data arising from the model is done in order to determine the standard deviation in the resulting estimate of number density obtained from the model. An expression is derived for the standard deviation in the number density in terms of the statistical parameters of the model (such as beamshape, scatterer nature and distribution) and the number of statistical independent measurements used in the analysis of data. A method of dealing with fish shoals which have variations in density within them is developed. A theoretical comparison of this method with the well established method of echo-integration is made. The scope of this study is limited to stationary statistics (which ignores beam divergence) although suggestions are made on extending the model to non-stationary statistics. The model is verified by an analysis of the backscattered sound intensity from which the fish number density is estimated and compared to the estimate obtained by the echo integration method. In the analysis of data a Poisson distribution and Rayleigh amplitude statistics were assumed. It was not within the scope of this thesis to verify these assumptions or to determine the actual fish distribution and scattering statistics in the shoals under investigation. However it is argued that these assumptions are approximately correct. The data was collected at night time on dispersed anchovy and redeye shoals of low density as the method works best on low densities. The statistical estimate was made using a method which applied to shoals containing density variations. An estimate of standard deviation was obtained for the statistical methods' estimate of number density for comparison with echo integration estimates of number densities. Good agreement between the statistical and echo integration method estimates of number density were obtained once standard deviation and scatterer statistics were taken into account. This work suggests a method of estimating fish numberdensity (which does not require target strengths) to be used in fish counting surveys.