Regularized Inversion for Towed-Array Shape Estimation
This chapter describes a new approach to the inverse problem of estimating the shape of a ship-towed hydrophone array using near-field acoustic measurements. The data consist of the relative travel times of arrivals along direct and reflected paths from sources deployed by two consort ships maintaining station with the moving tow ship (the “dual-shot method”). Previous inversion algorithms typically apply least-squares methods based on simplifying assumptions, such as straight-line propagation and exact knowledge of the source positions. Here, a regularized inversion is developed based on ray theory, with the source positions included as unknown parameters subject to a priori estimates and uncertainties. In addition, a minimum-structure array shape is determined by minimizing the three-dimensional curvature subject to fitting the data to a statistically meaningful level, thereby reducing spurious fluctuations (roughness) in the solution. Finally, the effect of the survey geometry is investigated by defining a mean sensor-position error measure based on the a posteriori uncertainty of the inversion. The optimal source configuration is determined by minimizing this error with respect to the source positions using an efficient hybrid optimization algorithm. The inversion and optimization procedures are illustrated using realistic synthetic examples.
KeywordsSource Position Inversion Algorithm Linear Inverse Problem Data Misfit Array Shape
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- [B+96]G.H. Brooke, S.J. Kilistoff, and B.J. Sotirin. Array element localization algorithms for vertical line arrays, in J.S. Papadakis (ed.), Proceedings of the Third European Conference on Underwater Acoustics, pp. 537–542, Crete University Press, 1996.Google Scholar
- [Mil83]P.H. Milne. Underwater Acoustic Positioning Systems. Cambridge University Press, Cambridge, 1983Google Scholar
- [OC97]J.C. Osler and D.M.F. Chapman. Seismo-acoustic determination of the shear-wave speed of surficial clay and silt sediments on the Scotian shelf, Canad. Acoust., 24:11–22, 1997.Google Scholar
- [Ste76]B.D. Steinberg. Principles of Aperture and A rray System Design. Wiley, New York, 1976.Google Scholar
- [T+76]W.M. Telford, L.P. Geldart, R.E. Sherif, and D.A. Keys. Applied Geophysics. Cambridge University Press, Cambridge, 1976.Google Scholar