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Inverse Approach

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Continuing advances in sonar and computing technologies has increased acoustic data use in the management of harvestable resources and in aquatic ecosystem research. When aquatic organisms are dispersed, echoes from single animals can be counted to tabulate size distributions and to estimate abundance (right side of diagram). When densities of organisms are too high to resolve individuals, a representative acoustic size must be used to transform relative density measures to numeric abundance estimates. Tabulations of in situ target strengths can not be used to choose acoustic size. If single frequency echosounders are available, then echo integration is used to estimate relative density and length-frequencies from catch data are used to translate relative to numeric density (center of diagram). An alternate approach to sizing organisms within aggregations using nets is to analyze multi-frequency acoustic data using the inverse approach (left side of diagram).

Inverse approach flow diagram

The inverse approach (see Holliday 1977; Greenlaw and Johnson 1983; Dalen and Kristensen 1990) combines backscatter model estimates of echo amplitude from individual organisms, with acoustic data collected at discrete frequencies to estimate length-based abundances of insonified targets. Previous use of the inverse approach to estimate length-based abundances of commercial fish species is limited. This can be attributed to the traditional use of nets when sampling commercial fish populations, to the restricted availability of multifrequency echosounders, to the lack of realistic backscatter models of fish, and to logistic constraints of low frequency sound sources. The inverse approach has traditionally been applied in combination with frequencies near the resonance scattering region. Resonance backscatter amplitudes are typically stronger than any other echoes received from a biological target. We were interested in combining the inverse approach with geometric scattering frequencies used by fisheries scientists and the KRM backscatter model.

Simulated population densities and length-frequency distributions were based on size and abundances of Threadfin shad (Dorosoma petenense). Using the KRM model we calculated the total backscatter for our simulated populations and then used the inverse approach to estimate abundances and lengths in specified length-classes.

We found that when using geometric scattering frequencies the ability to predict accuracy of inversion results was not intuitive. Judicious choice of frequency and length classes that maximized the range of scattering amplitudes used in inverse simulations resulted in the most accurate total and within length class abundance estimates. The diagram below highlights optimum three and five frequency reference scattering matrices.

diagram of optimum three frequency reference sacttering matricies diagram of optimum five frequency reference sacttering matricies

Plots are reduced scattering lengths (i.e. echo amplitude standardized by fish length) plotted as a function of fish length over acoustic wavelength. Points on the plots are used as reference points in inverse calculations. Both plots are examples of even-determined problems. The number of length classes is set equal to the number of frequencies. All inverse simulations that resulted in the most accurate abundance estimates encompassed a near-maximal range of backscatter amplitudes, minimized the amount of overlap among reference scattering points, and maximized the number of 'features' defined on the theoretical backscatter curve. Three reference values (local minimum or maximum and two inflection points) are the minimum number of points needed to denote a feature.

Inversion calculations overestimated total abundances by a maximum of 38% and underestimated total abundance by a maximum of 27%. Total abundance deviation index values were consistently low for all frequency and length-class combinations. Within length-class threadfin shad abundance estimates were inconsistent and less accurate than total abundance estimates. Increasing the number of frequencies and length-classes used in an inverse simulation did not guarantee more accurate abundance estimates.


Cited References
Dalen, J. and Kristensen, K.-E. 1990. Comparative studies of theoretical and
empirical target-strength models of euphausiids (krill) in relation to field-experiment data. Rapports et Proces-Verbaux des Réunions du Conseil International pour l'Exploration de la Mer, 189: 336-344.
Greenlaw, C. F. and Johnson, R. K. 1983. Multiple-frequency acoustical
estimation. Biological Oceanography, 2: 227-252.
Holliday, D. V. 1977. Extracting bio-physical information from the acoustic
signatures of marine organisms. In Oceanic sound scattering prediction, pp. 619-624. Ed. by N. R. Andersen and B. J. Zahuranec. Plenum, New York.
Relevant Publications
Horne, J.K. and J.M. Jech. 1999. Multi-frequency estimates of fish abundance:
constraints of rather high frequencies. ICES Journal of marine Science 56: 184-199.

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