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Chris Jones, Senior Engineer
Ocean Acoustics Department
Applied Physics Laboratory
University of Washington
Office of Naval Research
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NUMERICAL MODELING A model of scattering from fish combined with range and depth dependent waveguide propagation is a necessary first step for interpreting field data. Towards this objective, a model has been developed and tested to numerically simulate scattering from random schools of fish using waveguide geometries similar to data collected in the field experiments. To simulate scattering from fish only, the waveguide is modeled with a flat sea surface, a homogeneous flat bottom, and linear sound speed profiles. Backscatter from an aggregation of fish is found using a single scatter model and numerically generated PE envelope functions. Time-domain simulations of backscatter are formulated numerically using Fourier synthesis and broadband PE solutions. Monte-Carlo simulations with multiple realizations of random fish populations are used to estimate statistics of the backscattered field. Individual fish are modeled as point scatterers with an isotropic scattering strength. The isotropic scattering amplitude for each fish is modeled using a resonant bubble model [Love:1978, Love:2003]. More complex scattering functions for individual fish can be modeled by representing a single fish as a collection of point scatterers [Huang:1980]. Fish schools are modeled as a cluster of point scatterers with random locations taken from the spatial probability density function defined by Problem F of the Workshop on Shallow Water Reverberation. Total mean backscattered intensity is found as the average of the squared baseband signal magnitude over the finite number of realizations. Several simulation examples are given here to illustrate some of the more important effects the waveguide has on scattering from fish. Figures 7, 8, and 9 show mean backscatter intensity as a function of range along a single radial passing through the center of the fish school. Simulation of multiple radials using directional source and receiver beam patterns would be used to form a two-dimensional waveguide image. Figure 7 shows the mean backscatter intensity for a school as function of range. In this figure the fish are centered at mid water depth (50 m) at ranges 1 km, 5 km and 10 km. The equivalent fish bubble radius of a = 0.008 m is used, which is resonant at 1 kHz and 50 m depth. As a result, the scattering amplitude is a strong function of depth with a maximum at 50 m. Cylindrical spreading loss has been removed from the simulated data by multiplying the backscattered pressure by a factor equal to the horizontal range in meters. Hence, the vertical axis is taken as dB Pa @ 1 m. A simple cylindrical-spreading model would predict that all three echos have the same magnitude in Figure 7, and this is definitely not the case. Thus, use of a heuristic cylindrical spreading loss model for this waveguide would lead to large errors when estimating fish density by echo integration methods. Estimates for the boundaries of the school would also be distorted by multi-path spreading of the incident and scattered pulse. Figure 8 compares the intensity of backscatter from a fish school at different depths and for two different sound speed profiles. Here the fish school is centered at a range of 5 km, but the depth takes on values 10 m, 50 m, and 90 m. The sound speed profile in the upper panel is downward-refracting, referred to as a winter profile. The lower panel shows backscatter from the same fish school with an iso-velocity profile. The bubble radius is a = 0.02 m, which at 1 kHz gives a scattering strength that is approximately constant as a function of depth to avoid confusing depth-dependent scattering strength with propagation effects. Changes in propagation due to the sound speed profile significantly affect the backscatter. In this case, the winter profile shows a strong depth dependence in backscatter, as opposed to the iso-velocity profile, for the same fish schools. |
Figure 9 shows the mean and variance of backscatter intensity for a school centered at 1 km, a center depth of 50 m, and equivalent bubble radius is a = 0.008 m. Scattering from a single realization of a fish school (solid line) is compared to the mean backscattered intensity (dashed line) and variance (dotted line) of 100 realizations. The envelope of the mean intensity is an indicator of the shape of the fish school, with the trailing edge of the signal elongated due to multipath in the waveguide. Since scattering from many fish leads to Gaussian fluctuations in the complex backscattered pressure (Rayleigh envelope statistics), large fluctuations can be expected in a backscatter image without sufficient ensemble averaging. Averaging to reduce statistical fluctuations in field measurements of backscatter, for example, can be achieved by averaging multiple pings over time, assuming the positions of the individual fish have changed between pings and that the overall shape and size of the fish school remains the same. Further insight is gained by illustrating a snapshot in time of a 1kHz pulse that has traveled 1000 meters in a shallow iso-velocity waveguide (Figure 10). The image in Figure 10 is a vertical slice of the waveguide with depth on the ordinate (z-axis) and range on the abscissa (x-axis). A simulated fish school is located at mid-water depth. Strong horizontal and vertical multi-path structure in the waveguide is evident, resulting in the type of depth dependence of scattering as shown in Figure 8. All of these issues (propagation loss, pulse spreading, sound speed profile, variability, etc.) complicate the image interpretation and analysis. Figure 11 illustrates the formation of a fish school backscatter image (looking down from above). Here an image is formed using multiple, steered beams to sample the horizontal extent of a fish school, whereas Figures 7 through 9 are single radials. Backscatter along each radial in azimuth (or steered beam) is plotted as pixels on the horizontal coordinates of the waveguide (x, y). In this image the azimuthal beam width of 2 degrees was used. A single realization of scattering is plotted in Figure 11 with the fish school centered at (x, y, z)=(1000,0,50) in meters. The positions of the fish are drawn as white points. The image on the left is backscatter from a fish school at 50 m depth, and the image on the right is backscatter from the same school at 10 m depth. When the fish are near the surface there is a greater than 10 dB decrease in the backscatter intensity. In addition to the level of scattering, the random fluctuations and elongation of the backscattered signal envelope make it difficult to identify the boundaries of the fish school (shown in the figures as white dots). Notes  Love, R., "Resonant scattering by swimbladder-bearing fish," J. Acoust. Soc. Am., 64, 571-580, 1978. Love, R., C. Thompson, and R. Nero, "Changes in volume reverberation from deep to shallow water in the eastern Gulf of Mexico," J. Acoust. Soc. Am., 114, 2698-2708, 2003. Huang, K., and C.S. Clay, "Backscattering cross sections of live fish: Pdf and aspect," J. Acoust. Soc. Am., 67, 795-802, 1980. |
